Papier digéré : AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity — Udrescu, Tan, Feng, Neto, Wu, Tegmark (MIT IAIFI + Beneficial AI Foundation), NeurIPS 2020, arXiv:2006.10782. Outil :
aifeynman(pip).
Peut-on retrouver, à partir de données seules, la formule qui les a engendrées ? AI Feynman répond oui pour les équations de la physique : entraîné sur la table de l’énergie cinétique relativiste, le programme redécouvre E = mc²(1/√(1−v²/c²) − 1) — et son approximation classique mv²/2 — sans aucun indice sur la physique. Ce notebook exécute le vrai outil aifeynman sur ce cas, puis ouvre les trois idées qui rendent la recherche faisable :
Note d’environnement : le paquet aifeynman (figé en 2021) compile des solveurs Fortran à l’installation via numpy.distutils — il exige Python 3.9 et NumPy < 2. Ce notebook s’exécute donc dans le conteneur aifeynman:sl14 fourni avec la série (image assets/Dockerfile.aifeynman, Python 3.9 + gfortran + torch CPU). Le résumé d’exécution est donné en conclusion.
import os
import time
import numpy as np
import pandas as pd
import torch
import matplotlib.pyplot as plt
import aifeynman
SEED = 42
np.random.seed(SEED)
torch.manual_seed(SEED)
print("aifeynman", getattr(aifeynman, "__version__", "2.0.7 (sdist)"))
print("torch", torch.__version__, "| numpy", np.__version__)
RUN_DIR = "_sl14_runs"
os.makedirs(RUN_DIR, exist_ok=True)aifeynman 2.0.0
torch 2.8.0+cpu | numpy 1.26.4L’espace des formules est l’ensemble des arbres d’expressions qu’on peut construire sur une base d’opérations (+, −, ×, ÷, √, exp, log, sin, cos…) : la combinatoire explose exponentiellement avec la profondeur. Une recherche exhaustive est condamnée — sauf si l’on exploite la structure de la cible (section 3) et si l’on sait mesurer ce qu’est une bonne formule.
AI Feynman mesure chaque candidate en bits de description (le critère MDL, minimum description length) : un réel coûte log⁺(r/ε) bits, une constante paramétrée k·log₂n bits. La table 2 du papier donne l’exemple canonique : mv²/2 = 13,6 bits (4 fonctions de base, 6 occurrences).
Plutôt qu’une seule formule, la recherche retourne le front de Pareto complexité × erreur : chaque point est un compromis, et les coins convexes du front révèlent les formules « utiles ». C’est la figure 1 du papier : l’énergie cinétique exacte (complexe mais exacte) et l’approximation classique mv²/2 (13,6 bits, erronée aux hautes vitesses) cohabitent sur le front — deux réponses à deux questions différentes.
# Energie cinematique relativiste : E = m c^2 (1/sqrt(1 - v^2/c^2) - 1)
# Unites naturelles : c = 1 (une constante de moins a decouvrir).
c = 1.0
N = 400
m = np.random.uniform(0.5, 2.0, N)
v = np.random.uniform(0.05, 0.9, N) # v < c toujours
bruit_relatif = 1e-3 # gaussien, 0.1 % (r = -3, cf. table 3 du papier)
E_exact = m * c**2 * (1.0 / np.sqrt(1.0 - v**2 / c**2) - 1.0)
E_obs = E_exact * (1.0 + np.random.normal(0.0, bruit_relatif, N))
data = pd.DataFrame({"m": m, "v": v, "E": E_obs})
data.describe().round(4)| m | v | E | |
|---|---|---|---|
| count | 400.0000 | 400.0000 | 400.0000 |
| mean | 1.2413 | 0.4748 | 0.3380 |
| std | 0.4406 | 0.2497 | 0.4513 |
| min | 0.5076 | 0.0592 | 0.0011 |
| 25% | 0.8619 | 0.2556 | 0.0386 |
| 50% | 1.2676 | 0.4776 | 0.1416 |
| 75% | 1.6213 | 0.6965 | 0.4344 |
| max | 1.9858 | 0.8998 | 2.3668 |
Lecture du jeu de données. 400 points, m ∈ [0,5 ; 2], v ∈ [0,05 ; 0,9] (strictement inférieurs à c), c fixé à 1 — une variable de moins à découvrir rend le problème jouet lisible sans rien perdre de la structure (E reste non polynomiale en v). Le bruit gaussien relatif de 0,1 % correspond à r = −3 dans l’échelle du papier (bruit gaussien 10^r ; table 3 : 73 équations sur 100 encore résolues à r = −1) : nous sommes très en deçà du seuil de rupture, l’objectif ici est de comprendre la mécanique, pas de tester la robustesse (exercice 3).
# Format aifeynman : colonnes separees par des espaces, la derniere est la cible.
data_path = os.path.join(RUN_DIR, "kinetic.txt")
np.savetxt(data_path, data[["m", "v", "E"]].values, fmt="%.8f")
with open(data_path) as f:
print("".join(f.readlines()[:5]))1.06181018 0.13765529 0.01019731
1.92607146 0.81716997 1.41616816
1.59799091 0.47946452 0.22337382
1.39798773 0.75248885 0.72563700
0.73402796 0.32204216 0.04137145
run_aifeynmanLa fonction d’entrée orchestre trois moteurs complémentaires :
| Moteur | Paramètre | Rôle |
|---|---|---|
| Brute force | BF_try_time, BF_ops_file_type |
énumère les formules sur la base d’opérations (fichiers 7/10/14/19ops.txt), bornée en temps par étape |
| Polyfit | polyfit_deg |
teste les ajustements polynomiaux (une équation physique peut être un polynôme) |
| Réseau | NN_epochs |
entraîne le NN 128/128/64/64 tanh qui sert aux tests de modularité (section 3) |
Deux choix délibérés pour ce run : nous ne passons pas vars_name — le paquet ferait alors une analyse dimensionnelle et réduirait (m, v) à une seule combinaison, ce qui résoudrait le problème plus vite mais court-circuiterait la section 3 (nous voulons lire la séparabilité nous-mêmes) — et nous bornons le budget (BF_try_time=30 s, 500 epochs ; la démo officielle utilise 60 s et se résout en 10–30 min). Les résultats s’écrivent dans _sl14_runs/results/solution_kinetic.txt : une ligne par candidate du front, avec ses colonnes d’erreur et son expression au format SymPy (variables x0 = m, x1 = v).
origine = os.getcwd()
os.chdir(RUN_DIR) # le paquet ecrit results/ relativement au cwd
os.makedirs("results", exist_ok=True)
t0 = time.time()
aifeynman.run_aifeynman(
pathdir="./",
filename="kinetic.txt",
BF_try_time=30,
BF_ops_file_type="14ops.txt",
polyfit_deg=3,
NN_epochs=500,
test_percentage=20,
)
duree_run = time.time() - t0
os.chdir(origine)
print(f"run_aifeynman termine en {duree_run:.1f} s")Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve ./kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
27.043502428837 -3.003498571013 P 1 0.0000 8653.9208 0.4897 2.2287 2.3549 320.0000
26.411952606475 -0.209122000000 b 3 1.5850 8453.4098 0.2968 1.6845 2.4258 320.0000
25.284693584471 -0.011230029716 bb* 48 5.5850 8096.6869 0.2683 1.5833 2.8915 280.3542
25.207826324897 -0.008691881572 bbS* 444 8.7944 8075.2988 0.2931 1.6820 3.1247 208.0991
25.098936051977 -1.713560529069 bCCE 3408 11.7347 8043.3942 0.3420 1.8346 3.1998 194.8782
24.873604528915 -3.143497381606 PbCR/ 6472 12.6600 7972.2134 0.2634 1.5469 3.3193 189.2892
24.680659856333 0.022101394231 ab\E/ 6770 12.7249 7910.5361 0.3371 1.7051 3.2589 187.2511
24.624159452569 -0.006967840955 bbaS** 42879 15.3880 7895.1190 0.2727 1.6397 3.1135 168.6963
24.506868456589 0.011005138490 abC\<* 64658 15.9805 7858.1784 0.2222 1.1939 2.8459 164.0379
24.240081711207 0.014274496801 ab\E</ 78158 16.2541 7773.0803 0.2584 1.4040 3.0767 158.6457
23.745871984738 -0.993325910292 baR*C\ 124254 16.9229 7615.6020 0.1386 0.6353 3.0434 147.5533
23.053900080319 0.840285794492 bba**<S 730515 19.4786 7396.7266 0.1721 0.9948 3.7730 99.9212
23.053900080319 0.840285794492 abb**<S 730523 19.4786 7396.7266 0.1721 0.9948 3.7730 99.9220
22.169153045787 -0.999288086241 abC\<*E 1339193 20.3529 7114.4819 0.0821 0.4140 3.2545 95.7230
21.947600527923 -1.000009256968 abCL*>\ 1472924 20.4903 7043.7224 0.6218 8.0917 5.0189 91.8499
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve ./kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
2.3668279000000001 2.3668280124182930E-003
3 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
27.038440040237 0.043956738312 P 1 0.0000 8571.1855 0.4902 2.2287 2.3613 317.0000
26.140043969462 0.315356359261 b 3 1.5850 8287.9789 0.4306 2.0857 2.6135 317.0000
26.072281641614 0.281532711077 ba* 45 5.4919 8270.4051 0.3917 1.8740 2.6030 314.3333
24.962482168948 0.779464412373 bb* 48 5.5850 7918.6918 0.3163 1.7474 3.2938 314.5000
24.953066277108 -1.505813676277 bCL 276 8.1085 7918.2305 0.2951 1.6670 3.2772 253.7572
24.894974031237 -0.220361843945 bbL/ 624 9.2854 7900.9922 0.1991 0.9631 3.1617 262.3542
24.878593992728 1.451710222717 bC\< 1626 10.6671 7897.1814 0.2570 1.5079 3.2704 254.3376
24.029273517043 0.600882381349 bba** 3621 11.8222 7629.1019 0.2733 1.4291 3.3618 234.4463
23.747274488761 -1.156831811733 abCL* 5258 12.3603 7540.2463 0.2462 1.3110 3.4141 231.7478
23.313575532648 -0.196582645886 babL/* 43425 15.4062 7405.8097 0.0885 0.6287 2.5683 183.1230
23.154653556146 -1.092194534688 aabC/- 44369 15.4373 7355.4624 0.1989 1.0978 3.5308 181.7622
23.118920832027 0.456742213930 bbba+** 521652 18.9927 7347.6906 0.2248 1.3304 4.0226 115.7802
22.987280246027 -0.081952885716 aabRL/+ 533555 19.0253 7305.9931 0.0351 0.2739 2.3688 117.1049
22.330151471537 0.477987669603 babE<** 536580 19.0334 7097.6915 0.2091 1.1629 4.3394 116.9269
21.588629378323 -1.025056014392 abCL\>/ 1065413 20.0230 6863.6185 0.1032 0.6188 3.7732 120.0195
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
44.0 27.05 0.043956738312*pi
46.25 26.41 -0.209122000000+x1
46.37 25.28 -0.011230029716+(x1*x1)
47.66 25.21 -0.008691881572+(x1*sin(x1))
52.49 24.96 0.779464412373*(x1*x1)
54.62 24.68 0.022101394231+(x0/exp((x1)**(-1)))
55.36 24.03 0.600882381349*(x1*(x1*x0))
58.05 22.32 0.477987669603*(x1*(x0*(exp(x1)-1)))
68.16 22.17 -0.999288086241+exp((x0*((cos(x1))**(-1)-1)))
72.51 21.95 -1.000009256968+(((x0*log(cos(x1)))+1))**(-1)
73.54 21.59 -1.025056014392*(x0/((log(cos(x1)))**(-1)+1))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_squared/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
25.503652667866 -3.122522741225 P 1 0.0000 8161.1689 0.7772 5.5828 3.0578 320.0000
25.503652667866 -23.121624656015 PE 28 4.8074 8165.9762 0.7772 5.5828 3.0578 272.4286
25.503652659911 666.000000000000 PS\ 163 7.3487 8168.5176 0.7772 5.5828 3.0578 254.5276
25.428859429087 -0.559281798174 bCC 249 7.9600 8145.1950 0.7033 5.3521 2.9737 254.0241
24.757338468379 0.249746445718 bbR- 516 9.0112 7931.3595 0.7212 5.4048 3.4714 230.1163
24.489385011609 0.003780718394 bbS- 525 9.0362 7845.6394 0.7476 5.4846 3.6398 230.4495
24.285540411764 -1.003120319156 bbS/ 606 9.2432 7780.6161 0.7382 5.4591 3.8043 224.7442
24.175460174783 -0.501348231808 bC>\ 2031 10.9880 7747.1352 0.7478 5.4891 3.9122 207.2629
23.791590015144 -0.000699359135 bbSS- 5817 12.5061 7625.8149 0.7251 5.4130 4.1997 190.2938
23.322691852462 1.000193621472 bb*C~ 11046 13.4312 7476.6926 0.6974 5.3022 4.5909 183.1261
23.278329887625 -0.999846654552 bb*C\ 11370 13.4729 7462.5385 0.6697 5.1741 4.5828 183.0363
23.165062214767 0.841418681474 PbC*CS 130105 16.9893 7429.8092 0.6560 5.1426 4.8867 163.3424
22.963724194567 -0.367854358284 PbC/CE 139015 17.0849 7365.4766 0.5638 4.6413 4.9461 163.6310
22.960053149815 0.911741535564 bb*CEC 171669 17.3893 7364.6063 0.6517 5.1196 5.1597 164.9185
22.876527120122 0.000035149450 aPb/ER/ 666419 19.3461 7339.8347 0.6952 5.2647 5.1941 164.0246
22.811363129674 0.999618963726 bba**C~ 721011 19.4597 7319.0959 0.5760 4.6124 4.3765 163.6604
22.265897462031 -0.540368627410 bba**CC 736563 19.4904 7144.5776 0.6586 5.1423 4.9537 163.0535
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_squared/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
5.6018743082184104 5.6018745742931622E-003
113 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
25.386400729286 0.005721503388 P 1 0.0000 5254.9850 0.6723 4.0586 3.1279 207.0000
25.299979035661 0.017093080125 a 2 1.0000 5238.0957 0.6689 4.0427 3.2665 207.0000
24.770785696138 0.040041647858 b 3 1.5850 5129.1376 0.6665 4.0418 3.4886 207.0000
24.081415991066 0.001847738052 a< 8 3.0000 4987.8531 0.6789 4.0748 4.4139 207.0000
24.049667676205 0.003831596459 aR< 107 6.7415 4985.0227 0.6790 4.0750 4.4923 199.2991
23.947492268327 0.000299110999 aES 227 7.8265 4964.9574 0.6794 4.0763 4.5778 193.4053
23.736675810911 0.000693708755 b>C 231 7.8517 4921.3436 0.6794 4.0768 4.9071 193.6407
23.669537514751 -0.000043839101 bb<+ 327 8.3531 4907.9474 0.6794 4.0766 5.0509 190.1162
23.307022707523 1.207487441406 bbS- 525 9.0362 4833.5899 0.6376 3.9495 4.6003 195.3067
23.301226477920 -0.389862091082 bbCL* 5259 12.3606 4835.7145 0.6316 3.9285 4.5645 183.5824
23.295324604566 0.234448440090 ab\E/ 6770 12.7249 4834.8571 0.6378 3.9297 4.8509 183.5708
23.171970628397 0.752989863250 bb\E/ 6771 12.7252 4809.3231 0.6107 3.8697 5.0292 183.5742
23.166402244742 0.232930591879 PbL*E 9559 13.2226 4808.6679 0.6308 3.9269 4.7179 184.2920
22.831155442980 -1.135985230830 bb*C< 10722 13.3883 4739.4375 0.5848 3.7681 5.1499 185.1876
22.773431908733 -1.124613089207 bb*CL 12666 13.6287 4727.7291 0.5729 3.7203 5.1731 182.3671
22.773155792014 -4.120980926006 bCLC< 25683 14.6485 4728.6918 0.5648 3.6888 5.1719 183.4471
22.769562767365 -1.187099859300 bbS*CL 135930 17.0525 4730.3520 0.5920 3.7937 5.2467 174.2981
22.768172678085 -4.234577550165 bCLSC< 377061 18.5244 4731.5362 0.5678 3.7025 5.2044 172.8678
22.757249924770 -4.139722974756 bCLSCL 495159 18.9175 4729.6683 0.5659 3.6937 5.1862 164.4947
22.263529594616 -0.109463631423 aPb\E-/ 557825 19.0895 4627.6401 8.7315 88.5642 5.2903 164.9781
22.079627190687 -0.891277693321 abb*C<* 645743 19.3006 4589.7834 0.5610 3.5973 5.3858 167.8386
22.049107435392 -0.880520210487 abb*CL* 651575 19.3136 4583.4788 0.5460 3.5242 5.3287 167.8294
21.804678722118 -0.731883164637 bba**C< 717123 19.4519 4533.0204 0.5321 3.4004 5.2548 168.8051
21.667641884228 -0.708519335865 bba**CL 740451 19.4980 4504.6999 0.4300 2.2521 5.2353 168.6741
21.502622220372 -2.684165075766 abCL*C< 1437932 20.4556 4471.4984 0.4873 3.1315 5.3381 166.8854
21.436731752692 -2.653178739745 abCL*CL 1595396 20.6055 4458.0090 0.4625 2.9251 5.3571 165.1191
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
29.14 27.1 sqrt(0.003780718394+(x1-sin(x1)))
44.0 27.05 0.043956738312*pi
46.25 26.41 -0.209122000000+x1
46.37 25.28 -0.011230029716+(x1*x1)
47.66 25.21 -0.008691881572+(x1*sin(x1))
52.49 24.96 0.779464412373*(x1*x1)
54.62 24.68 0.022101394231+(x0/exp((x1)**(-1)))
55.36 24.03 0.600882381349*(x1*(x1*x0))
58.05 22.32 0.477987669603*(x1*(x0*(exp(x1)-1)))
68.16 22.17 -0.999288086241+exp((x0*((cos(x1))**(-1)-1)))
72.51 21.95 -1.000009256968+(((x0*log(cos(x1)))+1))**(-1)
73.54 21.59 -1.025056014392*(x0/((log(cos(x1)))**(-1)+1))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_atan/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
26.918982394211 -3.004366480425 P 1 0.0000 8614.0744 0.3329 1.0338 2.2361 320.0000
26.109183408133 -0.218172365377 b 3 1.5850 8356.5237 0.1490 0.4977 2.2761 320.0000
25.046129852969 -0.013883609362 bb* 48 5.5850 8020.3465 0.1177 0.3902 2.5758 260.4375
25.017053641529 -0.010493432352 bbS* 444 8.7944 8014.2516 0.1337 0.4880 2.7150 193.4865
25.009110936306 -0.011465045948 bb*S 831 9.6987 8012.6142 0.1294 0.4688 2.7156 186.7738
24.957120772412 0.918113357647 bCEC 2976 11.5392 7997.8178 0.1521 0.5519 2.7667 182.4362
24.935910772940 0.618787562479 bCCL 3165 11.6280 7991.1194 0.2180 0.7642 3.1041 179.0117
24.893913454556 -1.713886357823 bCCE 3408 11.7347 7977.7870 0.1771 0.6392 2.9730 179.2512
24.847643568874 -0.004711094509 bb>L* 5205 12.3457 7963.5916 0.1664 0.6076 3.0314 176.3881
24.656776281901 -3.144806193841 PbCR/ 6472 12.6600 7902.8284 0.1115 0.3524 2.9247 174.8684
24.398514158678 0.021255507075 ab\E/ 6770 12.7249 7820.2495 0.1771 0.5576 3.0247 172.8626
24.346548638895 -0.007562583148 bbaS** 42879 15.3880 7806.2835 0.1044 0.4445 2.8022 155.4290
23.913992874248 0.009772102470 abC\<* 64658 15.9805 7668.4583 0.0722 0.3048 2.4476 147.0533
23.902295263498 0.012343030267 ab\E</ 78158 16.2541 7664.9886 0.1018 0.4003 2.6903 135.8307
22.957827138047 -0.998478358716 baR*C\ 124254 16.9229 7363.4276 0.1335 0.9947 3.3454 118.5856
21.065665888250 -0.999995461249 abC\<*E 1339193 20.3529 6761.3660 0.1424 1.0250 5.0640 82.1013
21.065665888161 -0.999995461249 abC/a-E 1697699 20.6952 6761.7082 0.1424 1.0250 5.0640 81.5247
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_atan/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
1.1710396523211941 1.1710397079425930E-003
1 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
26.928923766720 0.044269970766 P 1 0.0000 8590.3267 0.3326 1.0320 2.2305 319.0000
25.987718401890 0.311913475381 b 3 1.5850 8291.6671 0.2697 0.8930 2.4678 319.0000
25.906557212296 0.286833510012 ba* 45 5.4919 8269.6836 0.2303 0.6909 2.4453 314.8667
24.740912450006 0.762558340310 bb* 48 5.5850 7897.9360 0.1557 0.5650 3.1156 315.1250
24.682915339677 -1.487319199953 bCL 276 8.1085 7881.9585 0.1351 0.4798 3.0551 249.6268
24.620069784847 1.408092035869 bC\< 1626 10.6671 7864.4694 0.1105 0.3386 2.9535 249.2675
23.712034781370 0.598237195971 bba** 3621 11.8222 7575.9613 0.1171 0.4178 3.0149 229.2742
23.328741524990 -1.149390202927 abCL* 5258 12.3603 7454.2288 0.0932 0.3663 3.0432 203.9563
22.380721958763 -1.075943113912 aabC/- 44369 15.4373 7154.8876 0.0587 0.2761 3.0555 125.6637
21.544781662523 0.474068046101 babE<** 536580 19.0334 6891.8188 0.0633 0.3028 3.8245 76.6125
20.125776498988 -1.006165943256 abCL\>/ 1065413 20.0230 6440.1457 0.0740 0.5448 4.3763 86.5463
20.125776498988 -1.006165943256 aabCL>/- 7184600 22.7765 6442.8992 0.0740 0.5448 4.3763 58.0266
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
29.14 27.1 sqrt(0.003780718394+(x1-sin(x1)))
43.65 26.98 tan(-3.004366480425+pi)
46.25 26.41 -0.209122000000+x1
46.37 25.28 -0.011230029716+(x1*x1)
47.66 25.21 -0.008691881572+(x1*sin(x1))
49.92 25.02 tan(-0.013883609362+(x1*x1))
51.54 25.0 tan(-0.010493432352+(x1*sin(x1)))
52.49 24.96 0.779464412373*(x1*x1)
54.62 24.68 0.022101394231+(x0/exp((x1)**(-1)))
55.36 24.03 0.600882381349*(x1*(x1*x0))
58.05 22.32 0.477987669603*(x1*(x0*(exp(x1)-1)))
61.94 21.91 tan(0.474068046101*(x1*(x0*(exp(x1)-1))))
68.16 21.56 tan(-0.999995461249+exp(((x0/cos(x1))-x0)))
79.05 20.8 tan(-1.006165943256*(x0/((log(cos(x1)))**(-1)+1)))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_cos/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
24.486798507841 -2.151374223418 P 1 0.0000 7835.7755 0.3038 1.7048 2.9549 320.0000
24.486798507841 4.131811258608 P~ 10 3.3219 7839.0975 0.3038 1.7048 2.9549 205.4000
24.486798507841 -8.879386432788 PP* 40 5.3219 7841.0975 0.3038 1.7048 2.9549 189.4750
24.486798507841 2.990218517595 PC< 112 6.8074 7842.5829 0.3038 1.7048 2.9549 189.8214
24.486798445589 666.000000000000 PS\ 163 7.3487 7843.1242 0.3038 1.7048 2.9549 195.0184
24.486795736826 0.990218571397 bPS* 438 8.7748 7844.5494 0.3038 1.7048 2.9549 181.8356
24.135070001650 0.697449718275 bP+\ 744 9.5392 7732.7616 0.2873 1.6600 3.1268 173.7917
22.783478400937 0.000371141626 bb*C 867 9.7599 7300.4730 0.2206 1.4154 4.0842 174.9319
22.738943810333 1.000435507117 bSb- 1191 10.2180 7286.6800 0.2708 1.6015 4.1462 164.5802
22.565224986307 0.000216588209 bbS*C 8895 13.1188 7233.9908 0.2371 1.4838 4.4391 144.9107
22.391464238289 -0.000138141883 bb*CR 11694 13.5135 7178.7820 0.2585 1.5514 4.3273 144.5129
22.109919223812 0.158490550278 bb*CS 12018 13.5529 7088.7271 0.2497 1.5177 4.6767 145.0419
22.059389938607 -1.718264506226 bC<CE 40830 15.3173 7074.3221 0.2524 1.5351 4.8849 148.4835
22.013654898161 -0.000038347579 bE<C<C 464628 18.8257 7063.1953 0.2106 1.3607 4.8360 140.4251
21.955620303022 -1.718284491451 bSC<CE 513840 18.9710 7044.7695 0.2716 1.6051 5.0696 140.6745
21.707535873720 0.000193150423 bba**CR 728787 19.4751 6965.8866 0.1675 0.9232 4.2016 135.7756
21.435341487500 -0.000608172634 ab\E</C 1300205 20.3103 6879.6196 0.2180 1.2968 4.3162 113.5505
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_cos/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
0.99999936441704151 9.9999941191446272E-004
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
24.486798507841 0.315196334862 P 1 0.0000 7835.7755 0.3038 1.7048 2.9549 320.0000
24.486798507841 0.239091233619 P> 4 2.0000 7837.7755 0.3038 1.7048 2.9549 208.5000
24.466061765513 -0.315279612870 P~ 10 3.3219 7832.4617 0.3039 1.7051 2.9711 192.6000
24.466061765513 -0.990480143181 PC 22 4.4594 7833.5992 0.3039 1.7051 2.9711 198.4545
24.466061765513 -1.177081754527 PCS 220 7.7814 7836.9211 0.3039 1.7051 2.9711 188.7591
23.577030323323 0.242269110016 PbC+ 370 8.5314 7553.1811 0.2775 1.6279 3.5148 188.1027
22.785477992431 1.000371325616 bb*C 867 9.7599 7301.1128 0.2206 1.4153 4.0809 166.2041
22.727358949091 -1.000451960946 bbS>- 5412 12.4019 7285.1568 0.2708 1.6015 4.1704 150.6116
22.727358949090 -1.000451960946 bbS-< 7356 12.8447 7285.5996 0.2708 1.6015 4.1704 146.0741
22.563833962820 1.000216970367 bbS*C 8895 13.1188 7233.5456 0.2371 1.4837 4.4415 145.4298
22.393319302427 0.499930852134 bb*C> 10398 13.3440 7179.2062 0.2616 1.5647 4.3357 144.6373
22.391550090345 0.999861798218 bb*CR 11694 13.5135 7178.8095 0.2585 1.5514 4.3272 143.4783
22.077881845233 1.188416884150 bb*CS 12018 13.5529 7078.4751 0.2395 1.4806 4.8359 143.4603
22.017422931197 -1.000009654777 PbCR*C 101917 16.6370 7062.2124 0.2466 1.5098 4.9151 136.1186
21.946316090933 1.188394397074 bbS*CS 130098 16.9892 7039.8104 0.2546 1.5410 5.0275 135.8609
21.916126272348 -2.402988138001 bCLC>C 462597 18.8194 7031.9798 0.2397 1.4776 5.0548 139.7394
21.760137200903 0.500092577960 bba**C> 713235 19.4440 6982.6879 0.2002 1.2198 4.2571 135.8163
21.707779378552 1.000193229823 bba**CR 728787 19.4751 6965.9645 0.1674 0.9231 4.2014 135.0246
21.450875511585 0.999391249118 ab\E</C 1300205 20.3103 6884.5905 0.2181 1.2971 4.2796 114.8974
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
29.14 27.1 sqrt(0.003780718394+(x1-sin(x1)))
43.65 26.98 tan(-3.004366480425+pi)
46.25 26.41 -0.209122000000+x1
46.37 25.28 -0.011230029716+(x1*x1)
47.66 25.21 -0.008691881572+(x1*sin(x1))
49.92 25.02 tan(-0.013883609362+(x1*x1))
51.54 25.0 tan(-0.010493432352+(x1*sin(x1)))
52.49 24.96 0.779464412373*(x1*x1)
54.62 24.68 0.022101394231+(x0/exp((x1)**(-1)))
55.36 24.03 0.600882381349*(x1*(x1*x0))
58.05 22.32 0.477987669603*(x1*(x0*(exp(x1)-1)))
61.94 21.91 tan(0.474068046101*(x1*(x0*(exp(x1)-1))))
68.16 21.56 tan(-0.999995461249+exp(((x0/cos(x1))-x0)))
79.05 20.8 tan(-1.006165943256*(x0/((log(cos(x1)))**(-1)+1)))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_exp/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
27.400308245119 -1.993509080791 P 1 0.0000 8768.0986 1.2274 9.5154 2.5935 320.0000
26.802993490364 0.815078174667 b 3 1.5850 8578.5429 1.0463 8.9570 2.7868 320.0000
26.749478199554 0.828914249657 bS 21 4.3923 8564.2253 1.0732 9.0566 2.7688 298.9048
25.581428857561 0.992075438736 bb* 48 5.5850 8191.6422 1.0292 8.8767 3.5464 289.6458
25.581428857561 -2.149517302277 Pbb*+ 3520 11.7814 8197.8386 1.0292 8.8767 3.5464 235.5304
25.574451211140 0.994385592269 bbSS* 5088 12.3129 8196.1373 1.0743 9.0435 3.5478 232.8970
25.510108044649 0.999081253675 bb>L* 5205 12.3457 8175.5803 1.0921 9.0963 3.6000 233.5527
25.356163718387 -2.141372834827 PbCR/ 6472 12.6600 8126.6324 1.0256 8.8414 3.6988 230.7579
25.208311423958 0.997429686112 bbaS** 42879 15.3880 8082.0476 1.0402 8.9320 3.4975 215.2876
24.896718427670 1.021338605274 ab\E</ 78158 16.2541 7983.2040 1.0190 8.6936 3.5984 198.9918
24.784846346618 0.999637343919 bba>L** 537816 19.0368 7950.1876 1.0370 8.8004 3.7821 166.9440
24.734815908118 0.997673988770 bbaC>/* 540651 19.0443 7934.1854 0.9864 8.3779 3.8731 166.8648
24.644457737621 0.999224523383 bbaCE/* 542595 19.0495 7905.2760 1.0025 8.4988 3.9713 166.7854
24.358309014804 1.843427574115 bba**<S 730515 19.4786 7814.1374 0.9337 8.2884 3.7522 166.6157
24.358309014804 1.843427574115 abb**<S 730523 19.4786 7814.1375 0.9337 8.2884 3.7522 166.6163
23.869432743887 0.501245328347 ba>*C>\ 1814769 20.7914 7659.0098 0.4229 3.4910 3.6387 150.9677
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_exp/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
10.663512848933307 1.0663513355422989E-002
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
27.400308245119 0.365446369045 P 1 0.0000 8768.0986 1.2274 9.5154 2.5935 320.0000
26.598096140159 0.857928724454 b> 6 2.5850 8513.9757 1.0705 9.0408 2.7969 320.0000
26.122970565576 0.478362755925 b>> 69 6.1085 8365.4591 1.1465 9.2803 3.2156 264.7536
25.984337347413 0.468063798646 bE> 93 6.5392 8321.5271 1.0781 9.0540 3.2636 265.3548
25.630062274040 1.859946584148 bCC 249 7.9600 8209.5799 1.1101 9.1587 3.4662 253.9237
25.575756049733 0.992301968530 bb*> 651 9.3465 8193.5884 1.0308 8.8826 3.5407 241.3733
25.459481116394 0.235246603940 Pb<\- 5617 12.4556 8159.4895 0.8437 7.7570 3.3906 221.8638
25.395263727054 0.467595398457 PbC/< 7444 12.8619 8139.3463 1.0154 8.7930 3.6049 213.4641
25.341180681173 0.580703752614 bC\E< 26061 14.6696 8123.8474 0.9234 8.3918 3.6240 204.8119
25.313397339902 0.043131685843 PbCR/E 109207 16.7367 8117.0239 0.9234 8.3931 3.6796 192.1504
25.065967200666 1.022347439347 ab\E/E 109505 16.7406 8037.8501 1.0365 8.7254 3.6143 192.0289
24.930300301124 1.843717266543 baR*CC 133002 17.0211 7994.7172 1.0545 8.9111 3.7123 188.7379
24.771672616304 1.019814473078 ab\E</> 1142741 20.1241 7947.0593 1.0147 8.6763 3.7440 160.1081
24.654504366863 1.014376863930 ab\E</E 1352693 20.3674 7909.8088 0.9002 8.0443 3.4834 157.1187
24.483314937096 1.009014658077 abCL*>\ 1472924 20.4903 7855.1510 0.3918 3.1503 3.1093 155.8833
24.191769580980 0.370342913136 baR*C\E 1954773 20.8986 7762.2648 0.4105 3.2861 3.4205 144.5530
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
29.14 27.1 sqrt(0.003780718394+(x1-sin(x1)))
43.65 26.98 tan(-3.004366480425+pi)
46.25 26.41 -0.209122000000+x1
46.37 25.28 -0.011230029716+(x1*x1)
47.66 25.21 -0.008691881572+(x1*sin(x1))
49.92 25.02 tan(-0.013883609362+(x1*x1))
51.54 25.0 tan(-0.010493432352+(x1*sin(x1)))
52.49 24.96 0.779464412373*(x1*x1)
54.62 24.68 0.022101394231+(x0/exp((x1)**(-1)))
55.36 24.03 0.600882381349*(x1*(x1*x0))
58.05 22.32 0.477987669603*(x1*(x0*(exp(x1)-1)))
61.94 21.91 tan(0.474068046101*(x1*(x0*(exp(x1)-1))))
68.16 21.56 tan(-0.999995461249+exp(((x0/cos(x1))-x0)))
79.05 20.8 tan(-1.006165943256*(x0/((log(cos(x1)))**(-1)+1)))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_inverse/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
32.915507337057 4.002186459631 P 1 0.0000 10532.9623 84.9861 879.8056 2.8459 320.0000
32.899635911550 8.510391144772 a~ 11 3.4594 10531.3429 84.9041 879.0718 2.8759 320.0000
32.879014821488 7.606481149101 b~ 12 3.5850 10524.8697 84.8665 879.4026 2.8466 320.0000
32.742578510046 4.878780741324 b\ 15 3.9069 10481.5320 82.3476 865.3064 2.8537 320.0000
32.169655663193 0.015262146901 Pb/ 64 6.0000 10300.2898 76.8216 834.2676 3.0490 320.0000
32.157084880059 -0.333070863417 PbS/ 604 9.2384 10299.5056 76.9110 834.5847 3.1214 307.4752
31.510107410353 1.713929771601 bb*\ 759 9.5680 10092.8023 49.9047 604.1941 2.8365 309.9499
31.310983929020 -11.351156681805 PPb/* 3676 11.8439 10031.3588 60.0691 732.8437 3.1001 283.9255
31.310983929020 -11.351156681805 PbP// 3880 11.9218 10031.4367 60.0691 732.8437 3.1001 285.0010
31.277919906564 -6.033563735520 PP+b/ 10129 13.3062 10022.2406 68.7811 787.6498 3.2978 287.8642
31.181653208748 -6.412341269511 Pb/RE 12934 13.6589 9991.7879 108.3390 1024.2349 3.4604 284.9429
31.169457090077 -0.330893349972 b\>b/ 21597 14.3985 9988.6248 47.9760 589.4746 2.9132 289.5297
31.021861157624 -2.388009620352 bC<\~ 26979 14.7195 9941.7151 39.2196 327.0879 3.3787 284.6444
30.913215215901 -3.169923498444 bbC<\- 72516 16.1460 9908.3749 39.1551 327.8101 3.4962 273.8459
30.912819687845 -2.634650341961 bbCL\- 73002 16.1556 9908.2579 39.1582 327.7750 3.4979 273.8518
30.790779744766 -4.287924681828 Pb\+b/ 113149 16.7879 9869.8374 44.2675 557.5293 3.1512 270.0257
28.370700445913 -1.385066635470 aabC*-\ 609182 19.2165 9097.8407 0.7223 2.0517 2.2623 219.0970
28.370700445912 -1.385066635470 abC~>*\ 1207163 20.2032 9098.8273 0.7223 2.0517 2.2623 125.4919
27.173897589731 -0.587379801146 abC\<*\ 1207973 20.2042 8715.8514 0.3078 0.9911 2.1804 125.4310
26.593840034433 -2.745700964710 aabC<*\- 7467452 22.8322 8532.8610 0.3332 1.2292 2.4011 41.7018
26.562626184591 -2.350078466851 aabCL*\- 7468910 22.8325 8522.8728 0.1799 0.8605 2.0551 41.6994
26.562626184591 -2.350078466851 abCL\a/- 13782251 23.7163 8523.7567 0.1799 0.8605 2.0551 29.6267
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_inverse/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
886.94942614372121 0.88694946827155841
26 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
32.837210412240 2.154419192741 P 1 0.0000 9654.1399 84.7413 880.1811 2.9142 294.0000
32.636366985785 2.644974199432 a< 8 3.0000 9598.0919 86.9484 887.9208 3.3528 294.0000
31.910984720088 -13.473044425124 b< 9 3.1699 9384.9994 83.0826 874.2801 3.3298 294.0000
31.690441541533 -10.006590732621 bL 27 4.7549 9321.7447 79.8609 858.7383 3.3067 283.2222
31.127438456602 6.658678436378 b\< 105 6.7142 9158.1812 68.2436 781.9801 3.4279 280.0667
31.030474202175 1.272868506966 bb*\ 759 9.5680 9132.5274 44.7111 529.2206 3.0047 276.3676
30.884350556719 -4.527325914164 bLb/ 1278 10.3197 9090.3187 54.7867 672.9756 3.2086 270.8592
30.869853507023 1.789732962326 bb*\< 10614 13.3737 9089.1106 38.4725 385.7500 3.3654 249.7881
30.844437291603 -6.949477347630 aRb\- 14849 13.8581 9082.1226 67.4242 775.9743 3.3931 249.7935
30.012550791235 6.752988756825 b\<a/ 21381 14.3840 8838.0740 64.9132 718.7029 3.9804 251.7904
29.930503375015 -0.858830559527 abCL*\ 93413 16.5113 8816.0793 11.9387 124.4743 2.8822 223.7055
29.187762445831 -5.084330132280 bLba*/ 180909 17.4649 8598.6671 42.9616 507.1728 3.7331 171.6418
29.187762445831 -5.084330132280 bLa/b/ 237825 17.8595 8599.0617 42.9616 507.1728 3.7331 162.8318
28.792886292703 -0.964024817550 abC<*\> 1402454 20.4195 8485.5281 2.9788 31.2842 2.7863 122.6871
27.923803512611 -1.001258499823 abCL*\> 1402940 20.4200 8230.0183 0.5338 1.5520 2.2769 122.6676
27.692195925694 -0.974645725261 bCL\>a/ 5100171 22.2821 8163.7877 2.1794 23.1932 2.7074 57.0557
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
29.14 27.1 sqrt(0.003780718394+(x1-sin(x1)))
43.65 26.98 tan(-3.004366480425+pi)
46.25 26.41 -0.209122000000+x1
46.37 25.28 -0.011230029716+(x1*x1)
47.66 25.21 -0.008691881572+(x1*sin(x1))
49.92 25.02 tan(-0.013883609362+(x1*x1))
51.54 25.0 tan(-0.010493432352+(x1*sin(x1)))
52.49 24.96 0.779464412373*(x1*x1)
54.62 24.68 0.022101394231+(x0/exp((x1)**(-1)))
55.36 24.03 0.600882381349*(x1*(x1*x0))
58.05 22.32 0.477987669603*(x1*(x0*(exp(x1)-1)))
61.94 21.91 tan(0.474068046101*(x1*(x0*(exp(x1)-1))))
68.16 21.56 tan(-0.999995461249+exp(((x0/cos(x1))-x0)))
79.05 20.8 tan(-1.006165943256*(x0/((log(cos(x1)))**(-1)+1)))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_log/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
29.827479090306 -5.121412176256 P 1 0.0000 9544.7933 1.6546 4.8080 2.2174 320.0000
29.761042605269 -3.140342030551 a 2 1.0000 9524.5336 1.6368 4.3188 2.2824 320.0000
29.561379153581 -2.448069540551 b 3 1.5850 9461.2263 1.4195 4.3994 2.2374 320.0000
29.561379153581 -3.448069540551 b> 6 2.5850 9462.2263 1.4195 4.3994 2.2374 320.0000
29.099431619891 -1.154051980351 bL 27 4.7549 9316.5730 1.0140 2.8145 2.2431 320.0000
28.795308601941 -3.456187488649 bP* 42 5.3923 9219.8911 0.9410 3.5190 2.3405 320.0000
28.401728770375 -6.478278171378 b>E 285 8.1548 9096.7080 0.7276 3.1949 2.2820 291.6421
28.398034132521 0.756338594171 PbL* 460 8.8455 9096.2164 0.7161 2.2863 2.2854 288.2761
28.252911219146 -7.239668728779 PbE* 469 8.8734 9049.8050 0.6330 2.8828 2.2570 286.8507
27.973370544600 -0.250380720716 bb*L 903 9.8186 8961.2972 0.5081 1.3417 2.2681 269.0366
27.737990823207 -3.945987908275 baP+* 3582 11.8066 8887.9636 0.6518 3.0669 2.3637 225.0064
27.422860325209 -7.591957049334 ab>E+ 4556 12.1536 8787.4689 0.6982 2.7545 2.4620 222.2191
26.994523399037 -4.538769600496 baP>+* 42489 15.3748 8653.6223 0.4552 2.5338 2.4851 136.2206
26.553299676302 -6.460609805513 aLb>E+ 187388 17.5157 8514.5716 0.7029 2.7548 3.1761 116.3318
26.456744993969 -1.438525323199 abLP<*+ 747983 19.5126 8485.6710 0.2688 0.9035 2.5243 111.3419
26.405850851440 -0.984371355027 abC\<L+ 932411 19.8306 8469.7029 0.2169 0.7204 2.3078 106.4385
26.253729704183 0.088189006776 abC\<*L 1312949 20.3244 8421.5179 0.2112 0.6635 2.2053 91.2990
26.253729704183 0.088189006776 abC/a-L 1693811 20.6918 8421.8853 0.2112 0.6635 2.2053 82.7273
25.794788131332 -1.977699370602 babb*L++ 6782004 22.6933 8277.0255 0.1458 0.5280 2.4961 58.1111
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_log/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
6.7877879639351582 6.7877882863377863E-003
1 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
29.823242440901 -0.625874229483 P 1 0.0000 9513.6143 1.6509 4.8215 2.2160 319.0000
28.629079972762 3.733859510006 b< 9 3.1699 9135.8464 0.8187 3.2767 2.2459 319.0000
28.576425967667 -0.713866126208 b\ 15 3.9069 9119.7868 1.1041 6.0317 2.4076 314.8667
27.876439906036 2.204283987978 bL 27 4.7549 8897.3392 0.4668 1.1148 2.3049 309.8148
27.873984419601 10.673780974448 b<CL 3150 11.6211 8903.4222 0.4770 1.1566 2.3233 192.1835
27.348699467830 3.919031425440 baR*< 7263 12.8264 8737.0615 0.6568 3.0547 2.7469 183.8542
26.758632433553 2.510344893538 baR*L 9207 13.1685 8549.1723 0.2292 0.8640 2.2228 182.6376
26.496619154155 6.648896321170 baR*R< 117774 16.8457 8469.2672 0.3080 1.5872 2.5344 80.1520
26.496026478609 5.434935155243 baR\CC- 1047573 19.9986 8472.2311 0.4434 2.0189 2.5169 84.4447
26.430899044746 0.675913421646 PbL*aC- 1652833 20.6565 8452.1133 0.3054 0.8968 2.6894 82.0209
25.659377118312 11.761357834291 baR*RR< 1773333 20.7580 8206.0993 0.1648 0.7011 2.5046 83.1005
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
29.14 27.1 sqrt(0.003780718394+(x1-sin(x1)))
43.65 26.98 tan(-3.004366480425+pi)
46.25 26.41 -0.209122000000+x1
46.37 25.28 -0.011230029716+(x1*x1)
47.66 25.21 -0.008691881572+(x1*sin(x1))
49.92 25.02 tan(-0.013883609362+(x1*x1))
51.54 25.0 tan(-0.010493432352+(x1*sin(x1)))
52.49 24.96 0.779464412373*(x1*x1)
54.62 24.68 0.022101394231+(x0/exp((x1)**(-1)))
55.36 24.03 0.600882381349*(x1*(x1*x0))
58.05 22.32 0.477987669603*(x1*(x0*(exp(x1)-1)))
61.94 21.91 tan(0.474068046101*(x1*(x0*(exp(x1)-1))))
68.16 21.56 tan(-0.999995461249+exp(((x0/cos(x1))-x0)))
79.05 20.8 tan(-1.006165943256*(x0/((log(cos(x1)))**(-1)+1)))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_sin/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
26.943170583786 -3.003937062001 P 1 0.0000 8621.8146 0.3393 0.8622 2.2465 320.0000
26.189278033822 -0.211168485670 b 3 1.5850 8382.1539 0.1497 0.3757 2.2175 320.0000
26.189278033822 -1.211168485670 b> 6 2.5850 8383.1539 0.1497 0.3757 2.2175 309.5000
25.068108658635 -0.013163168761 bb* 48 5.5850 8027.3797 0.1194 0.3403 2.6090 261.7500
25.006144272520 -0.009004539123 bbS* 444 8.7944 8010.7606 0.1366 0.4007 2.8523 195.2140
24.963166617101 0.918117090946 bCEC 2976 11.5392 7999.7525 0.1572 0.4702 2.8505 186.4711
24.943506608230 -1.713561531664 bCCE 3408 11.7347 7993.6568 0.1824 0.5249 3.0083 182.5640
24.917148767690 -0.004084483597 bb>L* 5205 12.3457 7985.8333 0.1712 0.4983 2.9956 179.8035
24.657956441694 -3.144343410088 PbCR/ 6472 12.6600 7903.2061 0.1145 0.3493 3.0359 177.9013
24.496374341010 0.021747494454 ab\E/ 6770 12.7249 7851.5647 0.1863 0.5835 2.9873 175.8951
24.396257713755 -0.007299025528 bbaS** 42879 15.3880 7822.1905 0.1098 0.3863 2.8353 157.5186
24.067233998301 0.009699017861 abC\<* 64658 15.9805 7717.4954 0.0937 0.4721 2.5990 149.4938
23.964141874479 0.012753811501 ab\E</ 78158 16.2541 7684.7795 0.1152 0.4580 2.7330 140.4350
23.097566502060 -0.997949716581 baR*C\ 124254 16.9229 7408.1442 0.1594 1.4668 3.2758 122.4721
22.914385392936 0.839554229815 bba**<S 730515 19.4786 7352.0819 0.0888 0.6717 3.2661 88.4282
21.167857674635 -0.999974598175 abC\<*E 1339193 20.3529 6794.0674 0.1627 1.4965 4.8374 81.5146
21.167857674635 -0.999974598175 abC/a-E 1697699 20.6952 6794.4096 0.1627 1.4965 4.8374 80.4521
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_sin/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
0.99984246519689168 9.9984251268686055E-004
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
26.943170583786 0.043817162299 P 1 0.0000 8621.8146 0.3393 0.8622 2.2465 320.0000
26.018116663480 0.313037018695 b 3 1.5850 8327.3823 0.2753 0.7354 2.4742 320.0000
25.939231116178 0.278644982857 ba* 45 5.4919 8306.0458 0.2429 0.6868 2.4408 317.2000
24.739968656762 0.765938997720 bb* 48 5.5850 7922.3749 0.1597 0.4751 3.1652 317.3750
24.653151478484 -1.505105938963 bCL 276 8.1085 7897.1170 0.1373 0.4230 3.2177 250.7717
23.737270562541 0.594590592440 bba** 3621 11.8222 7607.7488 0.1321 0.4784 3.1350 231.7363
23.383156479559 -1.144718723068 abCL* 5258 12.3603 7494.9704 0.1108 0.4263 3.1593 209.1027
22.639427746517 -1.078622213594 aabC/- 44369 15.4373 7260.0541 0.0828 0.5537 3.2672 127.6682
22.625478650609 1.077705106429 abC\<* 64658 15.9805 7256.1337 0.0830 0.5526 3.2917 124.0141
21.801321064006 0.474992896485 babE<** 536580 19.0334 6995.4562 0.0848 0.4968 4.0662 103.2701
21.801321064006 0.474992896485 abbE<** 536582 19.0334 6995.4562 0.0848 0.4968 4.0662 103.2708
20.543075496767 -1.011669718760 abCL\>/ 1065413 20.0230 6593.8071 0.0986 1.0257 3.9927 106.4517
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
29.14 27.1 sqrt(0.003780718394+(x1-sin(x1)))
43.65 26.98 tan(-3.004366480425+pi)
46.25 26.41 -0.209122000000+x1
46.37 25.28 -0.011230029716+(x1*x1)
47.66 25.21 -0.008691881572+(x1*sin(x1))
49.84 25.05 asin(-0.013163168761+(x1*x1))
49.92 25.02 tan(-0.013883609362+(x1*x1))
51.32 25.01 asin(-0.009004539123+(x1*sin(x1)))
51.54 25.0 tan(-0.010493432352+(x1*sin(x1)))
52.49 24.96 0.779464412373*(x1*x1)
54.62 24.68 0.022101394231+(x0/exp((x1)**(-1)))
55.36 24.03 0.600882381349*(x1*(x1*x0))
58.05 22.32 0.477987669603*(x1*(x0*(exp(x1)-1)))
61.94 21.91 tan(0.474068046101*(x1*(x0*(exp(x1)-1))))
61.94 21.65 asin(0.474992896485*(x1*(x0*(exp(x1)-1))))
68.16 20.64 asin(-0.999974598175+exp(((x0/cos(x1))-x0)))
79.05 20.12 asin(-1.011669718760*(x0/((log(cos(x1)))**(-1)+1)))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_sqrt/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
27.401020946970 -2.769982501649 P 1 0.0000 8768.3267 0.3559 1.1668 2.1561 320.0000
25.505856795649 -0.029676472922 b 3 1.5850 8163.4591 0.1502 0.6767 2.5041 320.0000
25.497486370992 -0.022379280878 bS 21 4.3923 8163.5880 0.1784 0.7828 2.7141 238.3810
25.497486370991 -1.022379280878 bS> 84 6.3923 8165.5880 0.1784 0.7828 2.7141 219.0357
24.755802350858 -0.072077509431 baR* 432 8.7549 7930.6116 0.0831 0.3613 2.3121 203.5903
24.709110012518 0.120381632405 bba** 3621 11.8222 7918.7374 0.0744 0.2589 2.3031 120.5628
24.573809990795 0.131033436373 babS** 42885 15.3882 7879.0074 0.0734 0.3187 2.4275 101.6038
23.785126480658 0.054655819726 bba*R* 46848 15.5157 7626.7562 0.0590 0.3043 2.2419 101.8875
23.568509658323 -0.992382805090 bPa>//E 629907 19.2648 7561.1879 0.0814 0.3385 2.9477 60.6678
23.545482988703 -0.998326931967 ba\SC*E 1342971 20.3570 7554.9116 0.0785 0.3386 2.7808 71.5687
23.541984853234 -1.000677726935 baR>L*E 1343304 20.3574 7553.7925 0.0750 0.3556 2.6725 71.5736
23.150058420867 0.007892521399 a>Pb/</ 2489819 21.2476 7429.2663 0.0877 0.3614 3.0282 66.3542
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_sqrt/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
1.5384498366862664 1.5384499097587127E-003
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
27.401020946970 0.118287209705 P 1 0.0000 8768.3267 0.3559 1.1668 2.1561 320.0000
27.387193542846 0.344386295282 a 2 1.0000 8764.9019 0.3380 0.8622 2.3367 320.0000
25.463024688299 0.882328926147 b 3 1.5850 8149.7529 0.1709 0.7519 2.5879 320.0000
25.463024688299 2.771918149568 bP/ 60 5.9069 8154.0748 0.1709 0.7519 2.5879 246.0667
25.442529516621 0.720654804724 bE< 120 6.9069 8148.5163 0.1190 0.5016 2.2702 241.3583
24.613370320212 0.381238619547 ba>* 396 8.6294 7884.9079 0.1390 0.5312 2.5982 222.3283
24.594810959891 0.775166034698 baR* 432 8.7549 7879.0944 0.1424 0.5701 2.5799 219.5648
24.046692951451 0.534576035097 bba+* 3594 11.8114 7706.7531 0.0528 0.2121 2.3826 137.2844
23.338030463852 0.323318180469 bba>+* 42501 15.3752 7483.5450 0.0899 0.4273 2.9206 98.6935
23.338030463852 0.323318180469 bab>+* 42507 15.3754 7483.5452 0.0899 0.4273 2.9206 98.7023
23.329132989905 0.310177136252 a>bE<* 189473 17.5316 7482.8542 0.0501 0.2386 2.4753 93.8893
23.178930128131 0.339329880057 babE<*+ 527832 19.0097 7436.2674 0.0807 0.3188 3.2045 70.1400
23.148207827362 0.245999966466 bbaRE+* 535980 19.0318 7426.4583 0.1022 0.4524 3.2809 70.8772
22.021449332028 0.343461398567 ba>bC/* 762417 19.5402 7066.4040 0.0259 0.1294 2.6368 81.9392
21.674846530188 0.698786239618 baRbC/* 762453 19.5403 6955.4912 0.0262 0.1490 2.5365 81.9390
21.540449196533 0.704411422342 baRbSC/* 10781019 23.3620 6916.3057 0.0631 0.3031 3.6437 35.8437
21.495591455988 1.913802883569 baRbCE/* 10785636 23.3626 6901.9519 0.0530 0.2629 3.5300 35.8569
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
29.14 27.1 sqrt(0.003780718394+(x1-sin(x1)))
43.65 26.98 tan(-3.004366480425+pi)
46.25 26.41 -0.209122000000+x1
46.37 25.28 -0.011230029716+(x1*x1)
47.66 25.21 -0.008691881572+(x1*sin(x1))
49.84 25.05 asin(-0.013163168761+(x1*x1))
49.92 25.02 tan(-0.013883609362+(x1*x1))
51.32 25.01 asin(-0.009004539123+(x1*sin(x1)))
51.54 25.0 tan(-0.010493432352+(x1*sin(x1)))
52.49 24.96 0.779464412373*(x1*x1)
54.62 24.68 0.022101394231+(x0/exp((x1)**(-1)))
55.36 24.03 0.600882381349*(x1*(x1*x0))
58.05 22.32 0.477987669603*(x1*(x0*(exp(x1)-1)))
61.94 21.91 tan(0.474068046101*(x1*(x0*(exp(x1)-1))))
61.94 21.65 asin(0.474992896485*(x1*(x0*(exp(x1)-1))))
68.16 20.64 asin(-0.999974598175+exp(((x0/cos(x1))-x0)))
79.05 20.12 asin(-1.011669718760*(x0/((log(cos(x1)))**(-1)+1)))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_squared/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
25.503652667866 -3.122522741225 P 1 0.0000 8161.1689 0.7772 5.5828 3.0578 320.0000
25.503652667866 -23.121624656015 PE 28 4.8074 8165.9762 0.7772 5.5828 3.0578 272.4286
25.503652659911 666.000000000000 PS\ 163 7.3487 8168.5176 0.7772 5.5828 3.0578 254.5276
25.428859429087 -0.559281798174 bCC 249 7.9600 8145.1950 0.7033 5.3521 2.9737 254.0241
24.757338468379 0.249746445718 bbR- 516 9.0112 7931.3595 0.7212 5.4048 3.4714 230.1163
24.489385011609 0.003780718394 bbS- 525 9.0362 7845.6394 0.7476 5.4846 3.6398 230.4495
24.285540411764 -1.003120319156 bbS/ 606 9.2432 7780.6161 0.7382 5.4591 3.8043 224.7442
24.175460174783 -0.501348231808 bC>\ 2031 10.9880 7747.1352 0.7478 5.4891 3.9122 207.2629
23.791590015144 -0.000699359135 bbSS- 5817 12.5061 7625.8149 0.7251 5.4130 4.1997 190.2938
23.322691852462 1.000193621472 bb*C~ 11046 13.4312 7476.6926 0.6974 5.3022 4.5909 183.1261
23.278329887625 -0.999846654552 bb*C\ 11370 13.4729 7462.5385 0.6697 5.1741 4.5828 183.0363
23.165062214767 0.841418681474 PbC*CS 130105 16.9893 7429.8092 0.6560 5.1426 4.8867 163.3424
22.963724194567 -0.367854358284 PbC/CE 139015 17.0849 7365.4766 0.5638 4.6413 4.9461 163.6310
22.960053149815 0.911741535564 bb*CEC 171669 17.3893 7364.6063 0.6517 5.1196 5.1597 164.9185
22.876527120122 0.000035149450 aPb/ER/ 666419 19.3461 7339.8347 0.6952 5.2647 5.1941 164.0246
22.811363129674 0.999618963726 bba**C~ 721011 19.4597 7319.0959 0.5760 4.6124 4.3765 163.6604
22.265897462031 -0.540368627410 bba**CC 736563 19.4904 7144.5776 0.6586 5.1423 4.9537 163.0535
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_squared/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
5.6018743082184104 5.6018745742931622E-003
113 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
25.386400729286 0.005721503388 P 1 0.0000 5254.9850 0.6723 4.0586 3.1279 207.0000
25.299979035661 0.017093080125 a 2 1.0000 5238.0957 0.6689 4.0427 3.2665 207.0000
24.770785696138 0.040041647858 b 3 1.5850 5129.1376 0.6665 4.0418 3.4886 207.0000
24.081415991066 0.001847738052 a< 8 3.0000 4987.8531 0.6789 4.0748 4.4139 207.0000
24.049667676205 0.003831596459 aR< 107 6.7415 4985.0227 0.6790 4.0750 4.4923 199.2991
23.947492268327 0.000299110999 aES 227 7.8265 4964.9574 0.6794 4.0763 4.5778 193.4053
23.736675810911 0.000693708755 b>C 231 7.8517 4921.3436 0.6794 4.0768 4.9071 193.6407
23.669537514751 -0.000043839101 bb<+ 327 8.3531 4907.9474 0.6794 4.0766 5.0509 190.1162
23.307022707523 1.207487441406 bbS- 525 9.0362 4833.5899 0.6376 3.9495 4.6003 195.3067
23.301226477920 -0.389862091082 bbCL* 5259 12.3606 4835.7145 0.6316 3.9285 4.5645 183.5824
23.295324604566 0.234448440090 ab\E/ 6770 12.7249 4834.8571 0.6378 3.9297 4.8509 183.5708
23.171970628397 0.752989863250 bb\E/ 6771 12.7252 4809.3231 0.6107 3.8697 5.0292 183.5742
23.166402244742 0.232930591879 PbL*E 9559 13.2226 4808.6679 0.6308 3.9269 4.7179 184.2920
22.831155442980 -1.135985230830 bb*C< 10722 13.3883 4739.4375 0.5848 3.7681 5.1499 185.1876
22.773431908733 -1.124613089207 bb*CL 12666 13.6287 4727.7291 0.5729 3.7203 5.1731 182.3671
22.773155792014 -4.120980926006 bCLC< 25683 14.6485 4728.6918 0.5648 3.6888 5.1719 183.4471
22.769562767365 -1.187099859300 bbS*CL 135930 17.0525 4730.3520 0.5920 3.7937 5.2467 174.2981
22.768172678085 -4.234577550165 bCLSC< 377061 18.5244 4731.5362 0.5678 3.7025 5.2044 172.8678
22.757249924770 -4.139722974756 bCLSCL 495159 18.9175 4729.6683 0.5659 3.6937 5.1862 164.4947
22.263529594616 -0.109463631423 aPb\E-/ 557825 19.0895 4627.6401 8.7315 88.5642 5.2903 164.9781
22.079627190687 -0.891277693321 abb*C<* 645743 19.3006 4589.7834 0.5610 3.5973 5.3858 167.8386
22.049107435392 -0.880520210487 abb*CL* 651575 19.3136 4583.4788 0.5460 3.5242 5.3287 167.8294
21.804678722118 -0.731883164637 bba**C< 717123 19.4519 4533.0204 0.5321 3.4004 5.2548 168.8051
21.667641884228 -0.708519335865 bba**CL 740451 19.4980 4504.6999 0.4300 2.2521 5.2353 168.6741
21.502622220372 -2.684165075766 abCL*C< 1437932 20.4556 4471.4984 0.4873 3.1315 5.3381 166.8854
21.436731752692 -2.653178739745 abCL*CL 1595396 20.6055 4458.0090 0.4625 2.9251 5.3571 165.1191
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
29.14 27.1 sqrt(0.003780718394+(x1-sin(x1)))
43.65 26.98 tan(-3.004366480425+pi)
46.25 26.41 -0.209122000000+x1
46.37 25.28 -0.011230029716+(x1*x1)
47.66 25.21 -0.008691881572+(x1*sin(x1))
49.84 25.05 asin(-0.013163168761+(x1*x1))
49.92 25.02 tan(-0.013883609362+(x1*x1))
51.32 25.01 asin(-0.009004539123+(x1*sin(x1)))
51.54 25.0 tan(-0.010493432352+(x1*sin(x1)))
52.49 24.96 0.779464412373*(x1*x1)
54.62 24.68 0.022101394231+(x0/exp((x1)**(-1)))
55.36 24.03 0.600882381349*(x1*(x1*x0))
58.05 22.32 0.477987669603*(x1*(x0*(exp(x1)-1)))
61.94 21.91 tan(0.474068046101*(x1*(x0*(exp(x1)-1))))
61.94 21.65 asin(0.474992896485*(x1*(x0*(exp(x1)-1))))
68.16 20.64 asin(-0.999974598175+exp(((x0/cos(x1))-x0)))
79.05 20.12 asin(-1.011669718760*(x0/((log(cos(x1)))**(-1)+1)))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_tan/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
27.150583472356 -3.022209031411 P 1 0.0000 8688.1867 3.8730 56.4501 2.8106 320.0000
26.726142949361 -0.212154740469 b 3 1.5850 8553.9507 3.8788 56.9738 2.8934 320.0000
26.726142949361 -1.212154740469 b> 6 2.5850 8554.9507 3.8788 56.9738 2.8934 309.5000
26.710213019026 -0.202574191989 bS 21 4.3923 8551.6605 3.8762 56.8829 2.8823 301.9048
25.718017244507 -0.012851569537 bb* 48 5.5850 8235.3505 3.8812 57.0492 3.3733 289.6458
25.700284601034 -0.412198764797 b<E 288 8.1699 8232.2610 3.8746 56.7837 3.4446 259.7986
25.644997546688 -0.010808376024 bbS* 444 8.7944 8215.1936 3.8785 56.9653 3.4296 256.6396
25.464384720726 0.917492648664 bCEC 2976 11.5392 8160.1423 3.8773 56.8993 3.5596 242.9395
25.412501100907 0.618533238338 bCCL 3165 11.6280 8143.6283 3.8735 56.7166 3.7199 238.1096
25.278585816500 -1.715201149494 bCCE 3408 11.7347 8100.8822 3.8754 56.8242 3.8099 237.4278
24.895715563048 0.020459819654 ab\E/ 6770 12.7249 7979.3539 3.8820 56.8824 3.8549 227.9422
24.852197657958 0.009360917117 abC\<* 64658 15.9805 7968.6838 3.8968 57.2366 3.5680 197.8083
24.607024158769 0.013575110782 ab\E</ 78158 16.2541 7890.5018 3.8902 57.1148 3.6718 192.2450
24.578690208130 -0.992858956764 baR*C\ 124254 16.9229 7882.1038 3.9281 57.6255 3.6658 180.1496
24.314852500221 -0.003448114219 bba>L** 537816 19.0368 7799.7896 3.8862 57.0565 4.0438 162.0387
23.534508366861 0.840346648082 bba**<S 730515 19.4786 7550.5212 3.9055 57.4193 4.4908 160.5974
23.534508366861 0.840346648082 abb**<S 730523 19.4786 7550.5212 3.9055 57.4193 4.4908 160.5977
22.879629934326 -0.999764587280 abCL*>\ 1472924 20.4903 7341.9718 4.1187 58.9131 4.5837 148.7354
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_tan/kinetic.txt_train
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 2
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pab
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
56.330736285732264 5.6330738961298671E-002
102 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
27.077942158573 0.038733655682 P 1 0.0000 5902.9914 4.4234 56.4524 2.9454 218.0000
27.012085598344 0.117566513139 a 2 1.0000 5889.6347 4.4253 56.5318 3.1207 218.0000
26.345006599586 0.292043316683 b 3 1.5850 5744.7964 4.4239 56.5805 3.0946 218.0000
26.133808612847 0.264725230313 ba* 45 5.4919 5702.6621 4.4283 56.7179 3.2705 218.0000
25.207529734726 0.742722576615 bb* 48 5.5850 5500.8264 4.4296 56.8739 3.7880 218.0000
25.195067781546 -1.514664413917 bC< 114 6.8329 5499.3577 4.4289 56.8517 3.8242 210.3860
25.168497193785 -1.470066509406 bCL 276 8.1085 5494.8409 4.4319 56.9503 3.8151 199.9529
25.150334675822 0.758008350209 bbS* 444 8.7944 5491.5674 4.4281 56.8200 3.8671 203.4347
24.234041700481 0.593529932520 bba** 3621 11.8222 5294.8433 4.4386 57.0731 4.0392 191.1740
24.013384759413 -1.151532523695 abCL* 5258 12.3603 5247.2782 4.4420 57.1608 4.0930 193.3779
23.341760257125 -0.210749074475 babL/* 43425 15.4062 5103.9100 4.5072 58.3012 3.6950 180.2926
22.853392635831 0.479083927342 babE<** 536580 19.0334 5001.0730 4.4465 57.2780 4.8217 114.1067
22.000510889304 0.482192315126 abb*\</ 662915 19.3385 4815.4498 4.5253 58.5758 4.4918 125.3157
22.000510889304 0.482192315126 ab\b/</ 808616 19.6251 4815.7365 4.5253 58.5758 4.4918 123.6506
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
29.14 27.1 sqrt(0.003780718394+(x1-sin(x1)))
43.65 26.98 tan(-3.004366480425+pi)
46.25 26.41 -0.209122000000+x1
46.37 25.28 -0.011230029716+(x1*x1)
47.66 25.21 -0.008691881572+(x1*sin(x1))
49.84 25.05 asin(-0.013163168761+(x1*x1))
49.92 25.02 tan(-0.013883609362+(x1*x1))
51.32 25.01 asin(-0.009004539123+(x1*sin(x1)))
51.54 25.0 tan(-0.010493432352+(x1*sin(x1)))
52.49 24.96 0.779464412373*(x1*x1)
54.62 24.68 0.022101394231+(x0/exp((x1)**(-1)))
55.36 24.03 0.600882381349*(x1*(x1*x0))
58.05 22.32 0.477987669603*(x1*(x0*(exp(x1)-1)))
61.94 21.91 tan(0.474068046101*(x1*(x0*(exp(x1)-1))))
61.94 21.65 asin(0.474992896485*(x1*(x0*(exp(x1)-1))))
68.16 20.64 asin(-0.999974598175+exp(((x0/cos(x1))-x0)))
79.05 20.12 asin(-1.011669718760*(x0/((log(cos(x1)))**(-1)+1)))
NN already trained
NN loss: tensor(0.0006, grad_fn=<DivBackward0>)
Checking for symmetries...
Checking for separabilities...
Checking for compositionality...
Checking for generalized symmetry...
Multiplicative separability found for variables: (0,) [1]
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/separable_mult/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
25.176087432709 -2.975826978683 P 1 0.0000 8056.3480 0.0582 0.0987 2.0636 320.0000
24.488193020617 -0.893254475883 aRR 118 6.8826 7843.1044 0.0458 0.1163 2.0506 218.7542
23.880143527107 -0.729383678176 aRS 136 7.0875 7648.7334 0.0502 0.1428 2.3351 214.3750
22.820817001095 0.006013621327 aP-E 480 8.9069 7311.5683 0.0183 0.0576 2.1037 176.9417
21.660950437955 -0.188376370531 aRP/ 604 9.2384 6940.7425 0.0096 0.0287 2.1111 154.8593
21.113463215448 -1.056903311213 a>RR 1352 10.4009 6766.7091 0.0054 0.0159 2.0799 94.3092
19.923399657618 -0.003873556081 aPLL* 2822 11.4625 6386.9504 0.0013 0.0023 1.6071 64.2434
19.746687046586 -1.016344550100 aP/>R 5526 12.4320 6331.3719 0.0020 0.0057 2.0136 42.6448
19.731583359997 -0.003354236729 aPLLS* 32668 14.9956 6329.1023 0.0012 0.0020 1.5802 25.1698
16.603570980756 -0.000373566870 aP<<L* 33076 15.0135 5328.1562 0.0002 0.0006 2.4361 25.0547
16.186184247675 0.000052242575 aP<<LS* 419386 18.6779 5198.2569 0.0002 0.0010 1.8321 13.5726
16.100559431390 -0.000065453019 aPPR*>>/ 3628504 21.7909 5173.9700 0.0002 0.0009 1.9795 9.9995
16.082166780801 -0.000121747890 aPPR<RE*/ 41492610 25.3064 5171.5997 0.0002 0.0009 2.1087 9.4162
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/separable_mult/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
0.26320070028305054 2.6320071278441298E-004
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
25.176087432709 0.052764879472 P 1 0.0000 8056.3480 0.0582 0.0987 2.0636 320.0000
16.173871611559 0.132079837820 a 2 1.0000 5176.6389 0.0002 0.0009 1.8623 320.0000
16.173871611559 0.031891073333 aP>* 236 7.8826 5183.5216 0.0002 0.0009 1.8623 33.2161
16.173871611559 0.414941059730 aP\* 248 7.9542 5183.5931 0.0002 0.0009 1.8623 37.2540
16.173726365283 0.132079830938 aPS- 292 8.1898 5183.7823 0.0002 0.0009 1.8630 41.0822
16.135347580788 3.058574252316 aPE/S 4374 12.0947 5175.4060 0.0002 0.0011 2.0905 34.3690
16.124197167244 0.132109163877 aPS~R- 35072 15.0980 5174.8411 0.0002 0.0009 1.9678 29.1628
16.110784142059 0.132121237876 aPP+SR- 309150 18.2379 5173.6889 0.0002 0.0009 1.9672 21.0900
16.090740260488 0.132177474361 aPE\C<+ 381254 18.5404 5167.5773 0.0002 0.0009 2.0906 23.0309
16.090740260488 0.132177474361 aPE\C+< 494978 18.9170 5167.9539 0.0002 0.0009 2.0906 27.3890
16.070101902139 0.132206747603 aPPP*-E- 3248416 21.6313 5164.0639 0.0002 0.0008 2.3461 17.4600
16.059295824208 0.132176291118 aPPS~R*- 3324528 21.6647 5160.6394 0.0002 0.0009 2.2167 18.0756
16.015642512574 -0.000026540308 PaP<EE*- 3327521 21.6660 5146.6716 0.0002 0.0009 2.1887 18.1003
16.006878926444 0.132144102682 aPP<EE/- 3339184 21.6711 5143.8723 0.0002 0.0009 2.2193 18.1480
15.999674490298 0.132144231096 aPEP~/E- 4466584 22.0907 5141.9866 0.0002 0.0009 2.2524 20.5916
15.999674490298 0.000083574428 aPEP/E*< 4701736 22.1648 5142.0606 0.0002 0.0009 2.2524 21.0918
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
44.26 25.18 0.052764879472*pi
45.59 16.19 0.132079830938*(x0-sin(pi))
45.59 16.17 0.132079837820*x0
51.8 16.11 -0.000065453019+(x0/(((pi*sqrt(pi))+1)+1))
60.01 16.09 -0.000121747890+(x0/(pi*exp(sqrt((sqrt(pi)-1)))))
75.61 16.04 -0.000026540308*(pi-(x0*exp(exp((pi-1)))))
82.53 16.03 0.000083574428*((x0*exp((exp(pi)/pi)))-1)
104.78 16.01 0.132144102682*(x0-(pi/exp(exp((pi-1)))))
104.78 16.0 0.132144231096*(x0-exp((exp(pi)/(-pi))))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_squared/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
23.556773918980 -3.114114453052 P 1 0.0000 7538.1677 0.0194 0.0418 2.0001 320.0000
23.517711071261 -1.519869926577 aaC+ 226 7.8202 7533.4877 0.0452 0.1429 2.4297 168.4292
20.818891539882 -0.024274019231 aPE/ 340 8.4094 6670.4547 0.0031 0.0077 1.8435 158.2235
20.818891539882 -0.024274019231 aPE\* 2682 11.3891 6673.4344 0.0031 0.0077 1.8435 50.8542
20.785498728627 -0.026827214072 aPE</ 3258 11.6698 6663.0294 0.0033 0.0084 1.9041 47.3088
20.741543088543 -1.025919695757 aPE/E 4806 12.2306 6649.5244 0.0031 0.0082 1.8465 42.9230
20.703264131922 -0.519438242611 aRLCC 19976 14.2860 6639.3305 0.0189 0.0634 3.4475 37.6823
20.036149148186 -0.170277718889 PPa-+\ 25951 14.6635 6426.2312 0.0023 0.0069 2.0861 51.7420
19.479473254607 -0.910826776434 aP/C>S 74040 16.1760 6249.6075 0.0022 0.0078 2.0957 37.9207
19.123045148562 -0.318049993223 PaP/C*\ 316983 18.2740 6137.6485 0.0024 0.0072 2.3872 31.7360
18.569140506088 -1.787878840860 PaP-E+R 317903 18.2782 5960.4032 0.0007 0.0020 1.8494 31.7479
17.686617276317 -1.143979127009 aaP/S/L 322136 18.2973 5678.0148 0.0004 0.0010 2.2588 31.5492
16.880632049702 -0.540826539073 aPER/CC 675482 19.3656 5421.1678 0.0003 0.0011 1.9817 23.7326
15.270167681538 -0.156121793373 aP/C>RC 977162 19.8982 4906.3519 0.0001 0.0007 2.1848 19.8761
15.270167681538 -0.156121793373 aP\*C>RC 10663424 23.3462 4909.7998 0.0001 0.0007 2.1848 10.4674
15.270167681537 0.843878206627 aP/C>RC< 12136316 23.5328 4909.9865 0.0001 0.0007 2.1848 10.3874
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_squared/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
6.9274608629488199E-002 6.9274611919855554E-005
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
23.556773918980 0.008746610470 P 1 0.0000 7538.1677 0.0194 0.0418 2.0001 320.0000
22.466679533978 0.021900208670 a 2 1.0000 7190.3375 0.0103 0.0258 1.9807 320.0000
22.071759222412 0.095597561906 aL 18 4.1699 7067.1329 0.0263 0.0693 3.2470 305.8889
22.065327239894 0.007835712221 aE 20 4.3219 7065.2266 0.0065 0.0122 1.9158 307.3000
14.464047223487 0.017445083559 aa* 28 4.8074 4633.3025 0.0001 0.0005 1.8850 301.9286
14.464047223487 0.017445083559 aa\/ 322 8.3309 4636.8260 0.0001 0.0005 1.8850 38.6211
14.464047223487 0.005552942407 aaP** 2132 11.0580 4639.5531 0.0001 0.0005 1.8850 14.8058
14.464047223487 0.005552942407 Paa** 2135 11.0600 4639.5551 0.0001 0.0005 1.8850 15.0927
14.464047223487 0.054805347874 aPa// 2214 11.1124 4639.6076 0.0001 0.0005 1.8850 15.2358
14.464047223487 0.004212167794 aaP>** 23606 14.5269 4643.0220 0.0001 0.0005 1.8850 10.6195
14.463975159139 0.017445082650 aaPS-* 23718 14.5337 4643.0057 0.0001 0.0005 1.8854 10.7918
14.438022197238 -18.690562420871 aPE/C< 54632 15.7375 4635.9046 0.0001 0.0005 1.9198 11.7337
14.396073419968 -18.671461924917 aPE/CL 62408 15.9294 4622.6729 0.0001 0.0004 2.1112 11.7431
14.396073419967 -18.671461924917 aPE\*CL 686462 19.3888 4626.1323 0.0001 0.0004 2.1112 13.6840
14.393104652825 18.671451253669 aPE/CL~ 766058 19.5471 4625.3406 0.0001 0.0004 2.1239 13.8026
14.386672438506 -18.671471714261 aPE/CLS 801050 19.6115 4623.3467 0.0001 0.0004 2.1578 13.7244
14.385612068718 -9.205154755523 aPS~L/CL 8054116 22.9413 4626.3372 0.0001 0.0004 2.4740 13.3642
14.363832966072 -5.051408857545 aP<E/CR< 8623584 23.0399 4619.4664 0.0001 0.0004 2.4058 13.4732
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
0.0 24.57 sqrt(-9.205154755523*log(cos((x0/log((-sin(pi)))))))
45.59 16.19 0.132079830938*(x0-sin(pi))
45.59 16.17 0.132079837820*x0
51.8 16.11 -0.000065453019+(x0/(((pi*sqrt(pi))+1)+1))
60.01 16.09 -0.000121747890+(x0/(pi*exp(sqrt((sqrt(pi)-1)))))
75.61 16.04 -0.000026540308*(pi-(x0*exp(exp((pi-1)))))
82.53 16.03 0.000083574428*((x0*exp((exp(pi)/pi)))-1)
104.78 16.01 0.132144102682*(x0-(pi/exp(exp((pi-1)))))
104.78 16.0 0.132144231096*(x0-exp((exp(pi)/(-pi))))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_acos/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
25.215649332370 -1.738405162025 P 1 0.0000 8069.0078 0.0591 0.1005 1.9900 320.0000
25.215649332370 -21.737507076815 PE 19 4.2479 8073.2557 0.0591 0.1005 1.9900 222.7895
24.013800477511 0.960744739812 a>\ 92 6.5236 7690.9397 0.0442 0.1204 2.2081 211.2717
22.173213319966 0.488945797246 aP/C 452 8.8202 7104.2484 0.0099 0.0278 2.0092 174.1792
22.173213319966 1.488945797246 aP/C< 5190 12.3415 7107.7698 0.0099 0.0278 2.0092 55.4738
21.838103078633 0.539311492288 aP+RS 5722 12.4823 7000.6753 0.0084 0.0214 2.0448 54.9708
21.592831952245 1.757593158445 aRP~/ 7286 12.8309 6922.5371 0.0090 0.0271 2.2142 52.3131
20.425712928185 1.264441828618 aRCP/ 9914 13.2753 6549.5034 0.0036 0.0112 2.1065 49.8087
18.550655796989 1.573626459219 aPLL~* 31696 14.9520 5951.1619 0.0006 0.0013 1.7038 31.9481
18.350062509218 0.978429004292 aE>>R\ 196618 17.5850 5889.6050 0.0009 0.0026 1.9185 15.6167
18.350062509218 0.978429004292 aE>>\R 208282 17.6682 5889.6882 0.0009 0.0026 1.9185 15.3376
17.712531414933 1.573121390237 aPLLS~* 410230 18.6461 5686.6561 0.0005 0.0011 2.6678 13.8467
17.306423241618 1.571236758037 aP<E~>/ 455926 18.7984 5556.8539 0.0006 0.0025 2.3869 14.1360
17.206437242220 1.571486763661 aPRRR\<* 5527956 22.3983 5528.4582 0.0005 0.0023 2.2578 13.0132
17.206437242219 1.571486763661 aPRR\R<* 5530548 22.3990 5528.4589 0.0005 0.0023 2.2578 13.0118
17.025343604178 -2.318136464178 PPER*a-R 8324739 22.9890 5471.0989 0.0002 0.0005 1.9889 12.3666
16.768949372046 -2.323789610364 PP/EEa-R 11818683 23.4946 5389.5584 0.0002 0.0006 1.9915 11.8682
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_acos/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
1.5036736329875475 1.5036737044082126E-003
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
25.215649332370 0.446648466133 P 1 0.0000 8069.0078 0.0591 0.1005 1.9900 320.0000
25.196778452896 -0.446990420683 P~ 7 2.8074 8065.7765 0.0590 0.0998 2.0646 219.8571
25.196778452896 -1.226718935306 PL~ 87 6.4429 8069.4120 0.0590 0.0998 2.0646 196.5862
24.552457333474 0.356538942315 Pa\+ 213 7.7347 7864.5211 0.1025 0.3188 2.4885 190.4977
24.255860907106 -0.064162591862 aPE- 304 8.2479 7770.1234 0.0308 0.0529 2.0339 186.8191
23.421763963261 1.524217157245 aP/C 452 8.8202 7503.7846 0.0282 0.0747 2.2003 170.1659
23.393991263096 1.491042295463 aS>S 1452 10.5038 7496.5810 0.0288 0.0991 2.2074 142.4125
23.036584726808 -0.163033404785 aPP*- 2162 11.0782 7382.7853 0.0128 0.0226 1.8759 137.1369
23.016603276686 0.512091676256 PaP/- 2179 11.0894 7376.4025 0.0127 0.0224 1.9539 136.6397
22.778567848019 0.407056516256 PaE\+ 2359 11.2040 7300.3457 0.0117 0.0302 1.8542 131.9987
22.548421417368 0.362763263024 Pa\S+ 2411 11.2354 7226.7303 0.0103 0.0298 1.8423 130.5106
22.154315794498 0.671476707358 PaRR- 3027 11.5637 7100.9447 0.0125 0.0391 2.0783 112.0816
22.153967811861 -0.671570133104 aRRP- 9554 13.2219 7102.4916 0.0125 0.0393 2.0523 63.6581
21.521054450756 1.445982399541 aE\ES 18778 14.1968 6900.9342 0.0296 0.1044 3.7033 53.3010
17.888408497567 1.529098749941 a>RLC 20076 14.2932 5738.5839 0.0020 0.0067 2.9738 55.8029
17.888408497566 1.529098749941 a>R\LC 240900 17.8781 5742.1688 0.0020 0.0067 2.9738 23.4791
17.888408497565 1.529098749941 a>\RLC 241044 17.8789 5742.1697 0.0020 0.0067 2.9738 23.4775
17.319526294285 -0.133840636333 aP<R>E- 452218 18.7867 5561.0351 0.0004 0.0017 1.9239 21.6759
16.921468740317 2.216463095039 aP/E>R\ 942202 19.8457 5434.7157 0.0004 0.0013 2.0372 15.8730
16.921468740317 2.216463095039 aP/E>\R 952570 19.8615 5434.7315 0.0004 0.0013 2.0372 15.7980
16.921468740317 0.705522095880 PaP/E>R/ 3965065 21.9189 5436.7889 0.0004 0.0013 2.0372 11.6208
16.921453292933 -2.216463313354 aP/E>R\~ 12206332 23.5411 5438.4062 0.0004 0.0013 2.0374 10.5222
16.921453292933 -2.216463313354 aP/E>\R~ 12216700 23.5424 5438.4074 0.0004 0.0013 2.0374 10.5209
16.416527923598 1.568816466513 aRPRL*CR 16339720 23.9619 5277.2508 0.0002 0.0007 2.2660 10.4166
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
0.0 24.57 sqrt(-9.205154755523*log(cos((x0/log((-sin(pi)))))))
45.59 16.19 0.132079830938*(x0-sin(pi))
45.59 16.17 0.132079837820*x0
51.8 16.11 -0.000065453019+(x0/(((pi*sqrt(pi))+1)+1))
60.01 16.09 -0.000121747890+(x0/(pi*exp(sqrt((sqrt(pi)-1)))))
75.61 16.04 -0.000026540308*(pi-(x0*exp(exp((pi-1)))))
82.53 16.03 0.000083574428*((x0*exp((exp(pi)/pi)))-1)
104.78 16.01 0.132144102682*(x0-(pi/exp(exp((pi-1)))))
104.78 16.0 0.132144231096*(x0-exp((exp(pi)/(-pi))))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_asin/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
25.196778452896 -2.975058275137 P 1 0.0000 8062.9691 0.0590 0.0998 2.0646 320.0000
24.446049079002 -0.892470813954 aRR 118 6.8826 7829.6183 0.0452 0.1155 2.0533 219.2881
23.909204362189 -0.726763214338 aRS 136 7.0875 7658.0329 0.0490 0.1402 2.2986 214.3676
22.833255960038 0.006253692853 aP-E 480 8.9069 7315.5488 0.0173 0.0547 2.0651 177.3375
21.580398697007 -0.186808445833 aRP/ 604 9.2384 6914.9660 0.0090 0.0271 2.2608 155.1474
21.285182907967 -1.055524927236 a>RR 1352 10.4009 6821.6594 0.0051 0.0146 1.9468 94.7337
18.564826133399 -0.002847652873 aPLL* 2822 11.4625 5952.2069 0.0006 0.0014 1.6788 64.3306
17.714403773049 -0.002325120515 aPLLS* 32668 14.9956 5683.6048 0.0005 0.0011 2.6629 16.8574
17.314736113447 -0.000441684430 aP<E</ 37216 15.1836 5555.8992 0.0006 0.0025 2.3555 17.0874
17.223135553163 -0.001888336735 aPLLSS* 418978 18.6765 5530.0799 0.0004 0.0014 2.3788 13.7072
16.959331504521 -4.952656977502 PEaRE+R 1202735 20.1979 5447.1840 0.0005 0.0018 2.3183 13.4321
16.859968885555 -0.131514662136 aRPRR>-E 15700144 23.9043 5419.0943 0.0002 0.0005 1.6371 11.9848
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_asin/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
0.26633838683262101 2.6633839948301559E-004
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
25.196778452896 0.053009565404 P 1 0.0000 8062.9691 0.0590 0.0998 2.0646 320.0000
17.835759265822 0.132706292317 a 2 1.0000 5708.4430 0.0008 0.0028 2.3295 320.0000
17.835759265822 0.132706292317 a>< 56 5.8074 5713.2503 0.0008 0.0028 2.3295 69.6964
17.835742211833 0.132706301357 aPS+ 220 7.7814 5715.2189 0.0008 0.0028 2.3295 38.8000
17.835705682259 0.132706320716 aPPS*+ 23356 14.5115 5721.9373 0.0008 0.0028 2.3295 25.7884
17.497473616771 0.134583087889 aP>E\- 34944 15.0928 5614.2843 0.0004 0.0012 2.5056 34.1589
16.793033213476 0.132531218259 a<aR/E 103436 16.6584 5390.4290 0.0003 0.0008 2.0920 30.4852
16.160122809136 0.174082981635 aaP>/S- 287736 18.1344 5189.3737 0.0002 0.0010 1.9387 23.2828
16.079161111821 8.267023237417 aP>E/E< 619866 19.2416 5164.5732 0.0002 0.0012 2.2335 25.0891
16.064151057537 -6.088356247500 aPE/RCL 822794 19.6502 5160.1785 0.0003 0.0013 2.3057 22.9599
16.036927381281 0.131540330193 aaRP-EC/ 4680914 22.1584 5153.9751 0.0002 0.0010 2.1327 20.1639
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
0.0 24.57 sqrt(-9.205154755523*log(cos((x0/log((-sin(pi)))))))
45.59 16.19 0.132079830938*(x0-sin(pi))
45.59 16.17 0.132079837820*x0
51.8 16.11 -0.000065453019+(x0/(((pi*sqrt(pi))+1)+1))
60.01 16.09 -0.000121747890+(x0/(pi*exp(sqrt((sqrt(pi)-1)))))
75.61 16.04 -0.000026540308*(pi-(x0*exp(exp((pi-1)))))
82.53 16.03 0.000083574428*((x0*exp((exp(pi)/pi)))-1)
104.78 16.01 0.132144102682*(x0-(pi/exp(exp((pi-1)))))
104.78 16.0 0.132144231096*(x0-exp((exp(pi)/(-pi))))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_atan/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
25.136068916904 -2.977320747022 P 1 0.0000 8043.5421 0.0566 0.0973 2.0619 320.0000
25.136068916904 -22.976422661812 PE 19 4.2479 8047.7900 0.0566 0.0973 2.0619 236.2105
25.136068905718 666.000000000000 PS\ 101 6.6582 8050.2003 0.0566 0.0973 2.0619 219.4059
24.562862006842 -0.894776750696 aRR 118 6.8826 7866.9985 0.0470 0.1177 2.0463 217.1525
23.869712068238 -0.732640754604 aRS 136 7.0875 7645.3953 0.0518 0.1459 2.4605 212.9853
22.871900524241 0.004214873007 aP-E 480 8.9069 7327.9151 0.0196 0.0616 2.1570 178.4438
21.646889168514 -0.191950614517 aRP/ 604 9.2384 6936.2429 0.0113 0.0321 2.3326 156.6622
21.171517161636 -1.059463856465 a>RR 1352 10.4009 6785.2864 0.0063 0.0184 2.0362 96.4164
20.960994645448 -0.005395830894 aPLL* 2822 11.4625 6718.9808 0.0030 0.0057 1.7399 65.2303
20.802854756633 -1.018749363112 aP/>R 5526 12.4320 6669.3455 0.0033 0.0080 1.8086 45.2917
18.186769742987 0.005629116637 aaPL/- 24094 14.5564 5834.3227 0.0012 0.0028 2.8932 28.9133
18.186769742987 0.005629116637 aaP\L/+ 273000 18.0585 5837.8249 0.0012 0.0028 2.8932 22.4110
18.186769742962 0.005629116637 aaPL\*- 276632 18.0776 5837.8439 0.0012 0.0028 2.8932 22.3634
16.976949481522 -9.871220058642 PaPE+L* 285567 18.1235 5450.7473 0.0002 0.0004 2.0212 22.3448
16.346078359806 0.001508348216 aPPE>/*S 3512328 21.7440 5252.4891 0.0003 0.0007 2.3904 11.7187
16.346078359806 0.001508348216 PaPE>/*S 3512329 21.7440 5252.4891 0.0003 0.0007 2.3904 11.7188
16.346078359806 0.001508348216 aPE>P//S 5130280 22.2906 5253.0357 0.0003 0.0007 2.3904 11.6543
16.346078359806 0.001508348216 PPE>a//S 5130603 22.2907 5253.0358 0.0003 0.0007 2.3904 11.6544
16.051173327448 -0.134957976195 a>PLLS*S 15374624 23.8740 5160.2495 0.0002 0.0007 2.0147 11.2612
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_atan/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
0.25736374771559317 2.5736375993971525E-004
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
25.136068916904 0.052289398255 P 1 0.0000 8043.5421 0.0566 0.0973 2.0619 320.0000
19.401259635728 0.130896005427 a 2 1.0000 6209.4031 0.0012 0.0026 1.6802 320.0000
19.371187527474 -0.130924857919 a~ 8 3.0000 6201.7800 0.0012 0.0027 1.7818 132.6250
19.371180123706 -0.130924848796 PSa- 587 9.1972 6207.9749 0.0012 0.0027 1.7818 56.0630
19.127381009661 0.131398781717 aLSE 2032 10.9887 6131.7506 0.0029 0.0098 2.6961 36.7736
18.033071069058 0.126552430073 aPE\+ 2358 11.2033 5781.7861 0.0011 0.0028 2.8274 41.6268
18.033071069058 0.005468825891 aPE*> 3582 11.8066 5782.3893 0.0011 0.0028 2.8274 51.7113
17.588938150238 0.099899030428 aaP/S+ 24582 14.5853 5643.0455 0.0003 0.0007 1.8029 37.9321
17.441456663542 0.827624754131 aPP+/S 26284 14.6819 5595.9480 0.0003 0.0006 1.6639 37.2072
17.164404837072 0.128600721104 aPRS<- 34204 15.0619 5507.6714 0.0005 0.0010 2.6122 34.7356
17.015180248325 -0.660612219114 aPRC*S 46552 15.5066 5460.3642 0.0003 0.0015 1.8249 35.2236
16.718748583066 0.679941943009 aP>>/S 46968 15.5194 5365.5189 0.0003 0.0012 1.7665 35.0482
16.301510946674 -0.002122199195 aaP>E-* 274992 18.0690 5234.5525 0.0002 0.0006 1.8751 17.5035
16.284988584457 8.392671350141 aaP>E+/ 278880 18.0893 5229.2856 0.0002 0.0005 1.9179 17.5173
16.097770841653 0.698254260573 aPP<+/S 297894 18.1844 5169.4711 0.0002 0.0011 2.1873 17.5356
16.005072683947 0.734992858183 aPPR*/S 297990 18.1849 5139.8082 0.0002 0.0008 2.3628 17.5405
16.005072683944 0.734992858183 PaPR//\S 3810665 21.8616 5143.4849 0.0002 0.0008 2.3628 16.1435
15.999096321947 -0.727370402702 aPRCE<*S 6756960 22.6879 5142.3988 0.0002 0.0008 2.2341 18.0703
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
0.0 24.57 sqrt(-9.205154755523*log(cos((x0/log((-sin(pi)))))))
45.59 16.19 0.132079830938*(x0-sin(pi))
45.59 16.17 0.132079837820*x0
51.8 16.11 -0.000065453019+(x0/(((pi*sqrt(pi))+1)+1))
60.01 16.09 -0.000121747890+(x0/(pi*exp(sqrt((sqrt(pi)-1)))))
75.61 16.04 -0.000026540308*(pi-(x0*exp(exp((pi-1)))))
82.53 16.03 0.000083574428*((x0*exp((exp(pi)/pi)))-1)
104.78 16.01 0.132144102682*(x0-(pi/exp(exp((pi-1)))))
104.78 16.0 0.132144231096*(x0-exp((exp(pi)/(-pi))))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_cos/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
22.576427199568 -2.155475802959 P 1 0.0000 7224.4567 0.0096 0.0206 1.8814 320.0000
22.576427199568 -1.155475802959 P< 5 2.3219 7226.7786 0.0096 0.0206 1.8814 205.2000
22.576427199568 4.127709679067 P~ 7 2.8074 7227.2641 0.0096 0.0206 1.8814 197.0000
22.576427196448 666.000000000000 PS\ 101 6.6582 7231.1149 0.0096 0.0206 1.8814 172.8713
22.576421209145 0.986117048456 aPS* 256 8.0000 7232.4548 0.0096 0.0206 1.8814 154.2734
22.554038150990 1.040512976112 aPE~/ 3294 11.6856 7228.9778 0.0099 0.0208 1.9709 133.5899
21.697388554415 0.859346888997 aa>E/ 3480 11.7649 6954.9292 0.0079 0.0260 2.0033 131.5270
21.605501877756 0.800980031044 aP>+\ 3946 11.9462 6925.7068 0.0072 0.0183 2.0502 129.6782
20.635923072659 0.749653891027 PaR+\ 3963 11.9524 6615.4478 0.0038 0.0114 2.0716 129.7184
20.213724524825 -0.000702448925 aP-EC 5938 12.5358 6480.9276 0.0043 0.0154 2.1737 105.2991
19.747035469842 -0.010593612041 aLP/C 8516 13.0560 6332.1073 0.0094 0.0315 3.3972 89.5198
18.902340357427 -0.005286788752 a>\>S 17466 14.0923 6062.8412 0.0018 0.0073 2.1484 101.8637
18.224672760359 0.000639385736 aPLL*C 47896 15.5476 5847.4429 0.0004 0.0008 1.7086 54.6907
18.069202214236 -0.002443520499 PaR-RS 59477 15.8600 5798.0048 0.0004 0.0006 1.6648 47.1498
17.484076549780 -0.005418496903 aRRERS 224222 17.7746 5612.6791 0.0011 0.0042 2.5220 24.5770
17.240877401942 0.714085388745 PPa-\+\ 316593 18.2723 5535.3530 0.0005 0.0019 1.8733 25.1357
14.742993854739 0.000048616210 aP<<L*C 556438 19.0859 4736.8439 0.0001 0.0001 2.3293 20.1457
13.729869647749 0.648498419677 PaP/C+LL 4161129 21.9885 4415.5468 0.0000 0.0002 2.1727 11.2117
13.466834466226 -0.000008241815 aP<<LS*C 6873084 22.7125 4332.0996 0.0000 0.0003 1.9243 10.1064
13.376459125928 0.000008990884 aPPR*>>/C 47767194 25.5095 4305.9764 0.0000 0.0002 2.1461 6.6058
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_cos/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
0.99775149627906912 9.9775154366972215E-004
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
22.576427199568 0.313890761581 P 1 0.0000 7224.4567 0.0096 0.0206 1.8814 320.0000
22.576427199568 0.238100894926 P> 3 1.5850 7226.0417 0.0096 0.0206 1.8814 224.3333
22.552974873538 -0.313946577168 P~ 7 2.8074 7219.7593 0.0096 0.0207 1.9630 194.7143
22.552974873538 -666.000000000000 PS 13 3.7004 7220.6524 0.0096 0.0207 1.9630 188.7692
22.552974873538 -0.986292287897 PC 15 3.9069 7220.8589 0.0096 0.0207 1.9630 189.2667
22.552974873538 -0.238143233672 P~< 59 5.8826 7222.8346 0.0096 0.0207 1.9630 156.7797
22.552974873538 -1.172104862009 P>S 127 6.9887 7223.9406 0.0096 0.0207 1.9630 160.2205
22.552968945756 -0.000000086224 aPS\+ 2346 11.1960 7228.1461 0.0096 0.0207 1.9630 144.1633
20.127497910819 -0.015994345507 aP>E- 3154 11.6230 6452.4223 0.0031 0.0088 2.2091 134.5919
19.751947032183 0.210579217885 PEa-R 8211 13.0033 6333.6264 0.0016 0.0041 1.8127 82.5817
19.597041905370 0.989194944493 aLP/C 8516 13.0560 6284.1094 0.0094 0.0315 3.5614 80.7713
18.922038761554 0.994636045440 a>\>S 17466 14.0923 6069.1447 0.0019 0.0074 2.0390 96.8469
18.244519383981 1.000648692592 aPLL*C 47896 15.5476 5853.7938 0.0004 0.0008 1.7105 52.5555
18.019170493712 0.997525636552 PaR-RS 59477 15.8600 5781.9946 0.0004 0.0006 1.5740 45.3959
17.325831234874 0.994484408639 aRRERS 224222 17.7746 5562.0406 0.0012 0.0043 2.6197 23.6497
15.995536689820 0.703542204734 PaP/C+L 321303 18.2936 5136.8653 0.0002 0.0006 3.0979 24.5149
14.746862572863 1.000049035109 aP<<L*C 556438 19.0859 4738.0819 0.0001 0.0001 2.3393 21.6607
13.464260659070 0.999991626946 aP<<LS*C 6873084 22.7125 4331.2759 0.0000 0.0003 1.9366 10.6327
13.383856210672 1.000009082120 aPPR*>>/C 47767194 25.5095 4308.3435 0.0000 0.0002 2.1301 6.7225
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
0.0 24.57 sqrt(-9.205154755523*log(cos((x0/log((-sin(pi)))))))
45.59 16.19 0.132079830938*(x0-sin(pi))
45.59 16.17 0.132079837820*x0
51.8 16.11 -0.000065453019+(x0/(((pi*sqrt(pi))+1)+1))
60.01 16.09 -0.000121747890+(x0/(pi*exp(sqrt((sqrt(pi)-1)))))
75.61 16.04 -0.000026540308*(pi-(x0*exp(exp((pi-1)))))
82.53 16.03 0.000083574428*((x0*exp((exp(pi)/pi)))-1)
104.78 16.01 0.132144102682*(x0-(pi/exp(exp((pi-1)))))
104.78 16.0 0.132144231096*(x0-exp((exp(pi)/(-pi))))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_exp/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
25.413312183838 -1.961296141598 P 1 0.0000 8132.2599 0.0685 0.1208 2.0719 320.0000
25.413312183838 4.321889340427 P~ 7 2.8074 8135.0673 0.0685 0.1208 2.0719 238.1429
25.413312183838 -8.689308350968 PP* 25 4.6439 8136.9038 0.0685 0.1208 2.0719 228.2800
23.832451352467 0.121468016115 aRR 118 6.8826 7633.2671 0.0381 0.1038 2.1280 224.9830
23.808901931062 0.295505698226 aRS 136 7.0875 7625.9361 0.0402 0.1202 2.2062 215.5956
23.444687839307 0.630030337644 aa>/ 310 8.2761 7510.5762 0.0354 0.1027 2.2639 170.8871
22.729017542904 1.018986736161 aP-E 480 8.9069 7282.1925 0.0118 0.0327 1.9290 142.6146
22.216998315375 0.829315130527 aRP/ 604 9.2384 7118.6779 0.0084 0.0232 1.8838 123.1291
22.103747850493 -0.042313669249 a>RR 1352 10.4009 7083.6002 0.0100 0.0289 1.9849 81.3587
20.164122972894 0.981787228044 aPP+/ 2186 11.0941 6463.6134 0.0025 0.0068 2.0078 67.7566
20.164122972893 0.981787228044 aPP+\* 24780 14.5969 6467.1162 0.0025 0.0068 2.0078 27.0284
20.133168276069 0.982627997660 aP>S>* 30948 14.9176 6457.5314 0.0023 0.0063 1.9008 25.9741
20.133161092043 0.982627914182 aPCS>* 30972 14.9187 6457.5302 0.0023 0.0063 1.9008 25.9800
19.740478268912 0.555120712583 aP-ERR 73348 16.1625 6333.1155 0.0016 0.0034 1.8962 23.4048
19.129428941769 0.637281758277 aP/S<E 78056 16.2522 6137.6695 0.0009 0.0016 2.1059 23.2720
17.073063241973 -0.000424667562 aP<<L*E 579766 19.1451 5482.5253 0.0003 0.0007 2.2468 19.4041
16.435674484900 0.000064572300 aP<<LS*E 7083036 22.7559 5282.1718 0.0002 0.0012 1.8195 12.0130
16.401720379186 0.000022153513 aPRRE/ER 7762908 22.8882 5271.4387 0.0002 0.0012 1.8709 11.7506
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_exp/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
1.3010878214432131 1.3010878832415685E-003
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
25.413312183838 0.375700065768 P 1 0.0000 8132.2599 0.0685 0.1208 2.0719 320.0000
25.413312183838 0.284986157071 P> 3 1.5850 8133.8449 0.0685 0.1208 2.0719 256.3333
24.970251913406 0.268262304007 aP+ 22 4.4594 7994.9400 0.0497 0.0904 1.9704 247.5909
24.700062078493 0.556344761332 aR> 46 5.5236 7909.5434 0.0488 0.1167 2.0221 211.9130
24.446946836026 1.114583867566 aRR 118 6.8826 7829.9056 0.0490 0.1286 2.0783 201.9576
24.410704083441 1.313971585511 aRS 136 7.0875 7818.5128 0.0757 0.2104 2.4191 200.7426
24.133230166899 0.218624993177 aP>+ 200 7.6439 7730.2775 0.0279 0.0529 1.9343 198.7700
22.600176088132 0.277163586043 PaR+ 217 7.7616 7239.8179 0.0148 0.0398 2.1745 195.9447
22.412827141747 0.562921242052 aP+R 408 8.6724 7180.7771 0.0102 0.0264 2.0060 138.7966
22.179440864319 0.379795737840 aR>> 640 9.3219 7106.7430 0.0132 0.0392 2.2549 107.5875
21.463255110169 0.473309735905 a>R> 704 9.4594 6877.7011 0.0055 0.0149 1.9648 103.2372
20.053186036316 0.156763156003 aPP++ 2090 11.0293 6428.0488 0.0020 0.0048 1.9307 61.5053
20.053186036316 0.313526312005 PaERL+ 30297 14.8869 6431.9064 0.0020 0.0048 1.9307 25.0020
18.133093287224 -0.419877601247 aaRE>- 33990 15.0528 5817.6427 0.0020 0.0065 3.7219 24.4365
18.133093287218 -0.419877601247 aaRE-< 41766 15.3500 5817.9399 0.0020 0.0065 3.7219 26.6109
18.129866014488 0.419877587978 aREa<- 122882 16.9069 5818.4640 0.0020 0.0065 3.7331 33.0037
16.839393234439 0.999626502898 aP<<L*E 579766 19.1451 5407.7509 0.0003 0.0008 2.4676 34.2102
16.422153148838 1.000052243940 aP<<LS*E 7083036 22.7559 5277.8449 0.0002 0.0012 1.8363 14.1558
16.396345616039 1.000019488769 aPRRE/ER 7762908 22.8882 5269.7188 0.0002 0.0012 1.9012 13.7186
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
0.0 24.57 sqrt(-9.205154755523*log(cos((x0/log((-sin(pi)))))))
45.59 16.19 0.132079830938*(x0-sin(pi))
45.59 16.17 0.132079837820*x0
51.8 16.11 -0.000065453019+(x0/(((pi*sqrt(pi))+1)+1))
60.01 16.09 -0.000121747890+(x0/(pi*exp(sqrt((sqrt(pi)-1)))))
75.61 16.04 -0.000026540308*(pi-(x0*exp(exp((pi-1)))))
82.53 16.03 0.000083574428*((x0*exp((exp(pi)/pi)))-1)
104.78 16.01 0.132144102682*(x0-(pi/exp(exp((pi-1)))))
104.78 16.0 0.132144231096*(x0-exp((exp(pi)/(-pi))))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_inverse/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
30.475670426495 2.852709583094 P 1 0.0000 9752.2145 3.2380 8.9150 2.3448 320.0000
30.134951330171 7.257158364107 a~ 8 3.0000 9646.1844 2.8490 8.1597 2.3707 320.0000
29.701606499775 3.506613591975 Pa/ 35 5.1293 9509.6434 1.8957 5.2135 2.3168 320.0000
29.248071576092 10.224883853212 aE~ 90 6.4919 9365.8748 1.9477 6.3457 2.3741 318.6000
28.467886812433 10.003036527699 aP~* 244 7.9307 9117.6545 2.0656 6.5009 2.9122 292.2500
27.971927706689 -0.280160893303 a\>E 1934 10.9174 8961.9342 0.9277 4.3041 2.3070 232.9524
26.184140693593 2.073931347753 aCEE 2084 11.0251 8389.9502 0.4219 1.8531 2.4057 223.9842
26.184140693593 -1.067661393259 PaCEE+ 30757 14.9086 8393.8336 0.4219 1.8531 2.4057 66.1743
24.750378199240 0.136024903030 aPLL*\ 44008 15.4255 7935.5465 0.0778 0.2107 2.5165 62.9576
23.055956258872 0.046111110872 P<E<a/ 150253 17.1970 7395.1030 0.0296 0.0905 2.3946 41.0877
22.696471360221 -0.024066256396 PaPLC*/ 279439 18.0922 7280.9630 0.0147 0.0420 1.9101 28.7049
22.099566022688 0.013919216894 aP<<L*\ 521446 18.9922 7090.8533 0.0159 0.0539 2.2094 22.0138
21.521357939674 -0.001713929900 aP<<LS*\ 6558156 22.6449 6909.4794 0.0109 0.0305 2.4926 14.0707
21.521357939674 -0.001713929900 a\P<<LS/ 14722202 23.8115 6910.6460 0.0109 0.0305 2.4926 13.6480
21.521357939670 -0.001713929900 P<<LS\a/ 29847759 24.8311 6911.6657 0.0109 0.0305 2.4926 13.2785
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_inverse/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
14.909283991232455 1.4909284699385445E-002
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
30.475670426495 1.908045637441 P 1 0.0000 9752.2145 3.2380 8.9150 2.3448 320.0000
30.466061692142 -1.920238973679 P~ 7 2.8074 9751.9471 3.2249 8.8767 2.4038 320.0000
21.584312062163 7.571167589585 a\ 10 3.3219 6910.3018 0.0111 0.0330 2.3654 320.0000
21.584312062163 23.785525140430 a\P/ 602 9.2336 6916.2135 0.0111 0.0330 2.3654 27.4120
21.584312062162 7.571167589585 a\>< 800 9.6439 6916.6237 0.0111 0.0330 2.3654 28.7537
21.584174829033 7.571168307939 aPS-\ 4038 11.9794 6918.9154 0.0111 0.0330 2.3659 21.0210
21.584087980839 7.571166979716 a\PS- 7068 12.7871 6919.6952 0.0111 0.0330 2.3662 21.1462
21.553899176603 0.326949464332 aPE/S\ 57080 15.8007 6913.0484 0.0124 0.0411 2.5856 18.8070
21.538335538291 7.569489371283 aPS~R-\ 523442 18.9977 6911.2650 0.0107 0.0290 2.4284 17.5131
21.517594551552 7.574273977761 a\PS~R- 1113320 20.0864 6905.7167 0.0109 0.0298 2.4859 17.5029
21.509390511732 0.766855076665 PPa/*E>L 4274891 22.0275 6905.0324 0.0118 0.0376 2.6847 16.5794
21.509390511731 0.766855076665 PaP//E>L 4274953 22.0275 6905.0324 0.0118 0.0376 2.6847 16.5795
21.461605442333 -0.001521947493 PP<EEa/- 5231951 22.3189 6890.0327 0.0108 0.0293 2.6541 16.9001
21.451457626622 0.005206191788 PP>+Ea/< 9819967 23.2273 6887.6937 0.0108 0.0294 2.7262 16.2900
21.418002752370 7.570399715070 a\aEEE\+ 13966580 23.7355 6877.4964 0.0097 0.0441 2.4121 16.5884
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
0.0 24.57 sqrt(-9.205154755523*log(cos((x0/log((-sin(pi)))))))
45.59 16.19 0.132079830938*(x0-sin(pi))
45.59 16.17 0.132079837820*x0
51.8 16.11 -0.000065453019+(x0/(((pi*sqrt(pi))+1)+1))
60.01 16.09 -0.000121747890+(x0/(pi*exp(sqrt((sqrt(pi)-1)))))
75.61 16.04 -0.000026540308*(pi-(x0*exp(exp((pi-1)))))
82.53 16.03 0.000083574428*((x0*exp((exp(pi)/pi)))-1)
104.78 16.01 0.132144102682*(x0-(pi/exp(exp((pi-1)))))
104.78 16.0 0.132144231096*(x0-exp((exp(pi)/(-pi))))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_log/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
27.811347791564 -4.938772298442 P 1 0.0000 8899.6313 0.4029 0.9048 2.2113 320.0000
25.556014176146 -3.103632331667 a 2 1.0000 8178.9245 0.0870 0.2170 2.1767 320.0000
18.880571144606 -2.024348707261 aL 18 4.1699 6045.9527 0.0011 0.0035 2.0398 189.1111
18.880571144606 -1.024348707261 aL< 70 6.1293 6047.9120 0.0011 0.0035 2.0398 69.3429
18.880425876646 -2.024348759368 aPS-L 4614 12.1718 6053.9081 0.0011 0.0035 2.0404 18.1450
18.880425876646 -1.024348759368 aPS-L< 54728 15.7400 6057.4763 0.0011 0.0035 2.0404 16.1715
18.842283202190 1.117948876769 aPE/SL 62264 15.9261 6045.4567 0.0012 0.0040 2.2885 15.9996
18.830567048944 -2.024126699101 aPS~R-L 570098 19.1209 6044.9023 0.0011 0.0034 2.1318 16.0210
18.738840987900 -2.024606572595 aLPE\C/ 1145836 20.1280 6016.5571 0.0012 0.0031 2.4628 15.9968
18.738840987897 -2.024606572595 aLPE\C\* 14195314 23.7589 6020.1880 0.0012 0.0031 2.4628 15.3387
18.737413208052 -2.024606583658 aLPE\SC/ 14743522 23.8136 6019.7858 0.0012 0.0031 2.4672 15.4123
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_log/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
2.7019841055734144 2.7019842339107729E-003
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
27.811347791564 -0.572060004458 P 1 0.0000 8899.6313 0.4029 0.9048 2.2113 320.0000
27.591602633972 -2.261534474113 a\ 10 3.3219 8832.6348 0.5775 1.7534 2.3370 301.1000
25.489902635334 0.978832621394 aP- 30 4.9069 8161.6757 0.0823 0.2035 2.1341 281.9333
25.375029250199 -0.976558175431 a\> 44 5.4594 8125.4688 0.0710 0.1985 2.0118 233.2273
21.258615769804 -4.048185487474 a>\ 92 6.5236 6809.2806 0.0071 0.0210 2.2309 165.9674
21.258615769803 -1.288577425911 Pa>/ 309 8.2715 6811.0285 0.0071 0.0210 2.2309 68.0615
20.148994463434 -5.503596068441 aRE\ 1270 10.3106 6457.9888 0.0030 0.0099 2.6436 37.3622
20.148994463434 -5.503596068441 aR~E 1972 10.9454 6458.6237 0.0030 0.0099 2.6436 32.0248
20.080491966676 2.024668258322 aRLS< 12524 13.6124 6439.3698 0.0029 0.0089 2.7955 25.6531
20.080491966663 0.644471904932 PaRLS<* 407303 18.6357 6444.3932 0.0029 0.0089 2.7955 22.9536
19.231692591515 1.001430837056 aP<<L*L 568102 19.1158 6173.2574 0.0012 0.0032 1.8569 22.2725
19.137045316741 1.009742619811 aPLL*SL 685306 19.3864 6143.2409 0.0017 0.0054 2.5579 20.4793
18.902206896526 0.999813396515 aP<<LS*L 6978060 22.7344 6071.4406 0.0012 0.0036 1.9843 15.0289
18.745252586967 1.000963476456 aPCES*L< 7429664 22.8249 6021.3057 0.0012 0.0031 2.4718 14.7839
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
0.0 24.57 sqrt(-9.205154755523*log(cos((x0/log((-sin(pi)))))))
45.59 16.19 0.132079830938*(x0-sin(pi))
45.59 16.17 0.132079837820*x0
51.8 16.11 -0.000065453019+(x0/(((pi*sqrt(pi))+1)+1))
60.01 16.09 -0.000121747890+(x0/(pi*exp(sqrt((sqrt(pi)-1)))))
75.61 16.04 -0.000026540308*(pi-(x0*exp(exp((pi-1)))))
82.53 16.03 0.000083574428*((x0*exp((exp(pi)/pi)))-1)
104.78 16.01 0.132144102682*(x0-(pi/exp(exp((pi-1)))))
104.78 16.0 0.132144231096*(x0-exp((exp(pi)/(-pi))))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_sin/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
25.155637133184 -2.976585096237 P 1 0.0000 8049.8039 0.0574 0.0980 2.0627 320.0000
25.155637133184 -9.704597305607 PP* 25 4.6439 8054.4477 0.0574 0.0980 2.0627 221.8800
24.527426545004 -0.894027207117 aRR 118 6.8826 7855.6591 0.0464 0.1170 2.0483 218.7542
23.914026603302 -0.731039064325 aRS 136 7.0875 7659.5760 0.0510 0.1444 2.2935 214.3750
22.879055461458 0.005005029061 aP-E 480 8.9069 7330.2046 0.0189 0.0596 2.0737 176.9083
21.649834618468 -0.190033287144 aRP/ 604 9.2384 6937.1855 0.0104 0.0303 2.2860 154.8063
21.097413943230 -1.058084173569 a>RR 1352 10.4009 6761.5733 0.0058 0.0170 2.0844 95.2559
20.555230031524 -0.004646287315 aPLL* 2822 11.4625 6589.1361 0.0022 0.0037 1.6932 64.6743
20.136469704616 -1.017818561485 aP/>R 5526 12.4320 6456.1023 0.0027 0.0071 1.9675 44.1477
19.866948181367 0.006373493711 aaPL/- 24094 14.5564 6371.9798 0.0017 0.0035 2.1472 27.7675
19.662805058467 -1.854148749247 aPP++L 26444 14.6907 6306.7883 0.0020 0.0056 2.0955 27.4252
19.662805058467 -1.854148749247 PaP++L 26445 14.6907 6306.7883 0.0020 0.0056 2.0955 27.4362
19.424467858954 -0.001180634796 aP<<L* 33076 15.0135 6230.8432 0.0010 0.0019 1.5747 25.9513
17.171082266624 0.000765395909 aP>RE/ 39336 15.2636 5510.0099 0.0003 0.0006 2.2313 23.8215
16.431929573735 0.001508511047 aPPE>/* 275126 18.0697 5276.2872 0.0003 0.0007 2.3169 13.9941
16.431929573735 0.001508511047 PaPE>/* 275127 18.0697 5276.2872 0.0003 0.0007 2.3169 13.9952
16.431929573735 0.001508511047 aPE>P// 375638 18.5190 5276.7364 0.0003 0.0007 2.3169 13.3964
16.431929573733 0.001508511047 aP*PE>/ 846690 19.6915 5277.9089 0.0003 0.0007 2.3169 12.1585
16.415000130064 0.001482691224 aPPEC~// 3358536 21.6794 5274.4794 0.0003 0.0007 2.3771 11.4113
16.415000130064 0.001482691224 aPECP~/* 4924432 22.2315 5275.0316 0.0003 0.0007 2.3771 11.4522
16.168064274051 0.000052041149 aP<<LS*S 6768108 22.6903 5196.4709 0.0002 0.0009 1.8205 11.1110
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_sin/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
0.26017235446000880 2.6017236681753254E-004
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
25.155637133184 0.052523563166 P 1 0.0000 8049.8039 0.0574 0.0980 2.0627 320.0000
18.500955517042 0.131489535929 a 2 1.0000 5921.3058 0.0006 0.0013 1.6347 320.0000
18.456696820695 -0.131511171947 a~ 8 3.0000 5909.1430 0.0007 0.0014 1.7575 130.6250
18.456678677033 -0.131511162784 PSa- 587 9.1972 5915.3344 0.0007 0.0014 1.7575 46.5111
18.335062859416 3.044270054189 aPE/S 4374 12.0947 5879.3149 0.0006 0.0012 1.6502 38.6754
17.040900681012 0.100398015538 aaP/S+ 24582 14.5853 5467.6735 0.0003 0.0015 1.8351 25.1089
16.571916811123 0.913754423073 aPL<*S 46384 15.5013 5318.5147 0.0002 0.0012 1.7712 29.7332
16.122975819380 0.977448243028 aPLL*S 46600 15.5080 5174.8603 0.0002 0.0010 1.9201 29.6835
16.104920889715 0.976260659901 aL<<ES 228872 17.8042 5171.3789 0.0002 0.0010 1.9855 17.0275
16.091082027831 1.044165923883 aaPL/-S 297872 18.1843 5167.3306 0.0002 0.0008 2.1902 16.8981
16.084464446699 1.047010922167 aP>ER/S 549882 19.0688 5166.0974 0.0002 0.0008 2.2195 19.1887
16.077940531694 1.020464007886 aPP<*>/S 3711424 21.8235 5166.7645 0.0002 0.0008 2.0554 15.7160
16.063233549785 -1.050726441372 aPP*>C*S 4033912 21.9437 5162.1785 0.0002 0.0007 2.3177 15.9180
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
0.0 24.57 sqrt(-9.205154755523*log(cos((x0/log((-sin(pi)))))))
45.59 16.19 0.132079830938*(x0-sin(pi))
45.59 16.17 0.132079837820*x0
51.8 16.11 -0.000065453019+(x0/(((pi*sqrt(pi))+1)+1))
60.01 16.09 -0.000121747890+(x0/(pi*exp(sqrt((sqrt(pi)-1)))))
75.61 16.04 -0.000026540308*(pi-(x0*exp(exp((pi-1)))))
82.53 16.03 0.000083574428*((x0*exp((exp(pi)/pi)))-1)
104.78 16.01 0.132144102682*(x0-(pi/exp(exp((pi-1)))))
104.78 16.0 0.132144231096*(x0-exp((exp(pi)/(-pi))))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_sqrt/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
25.494417094591 -2.734449323616 P 1 0.0000 8158.2135 0.0751 0.1482 2.0932 320.0000
25.406496461865 0.006462716325 aP/ 34 5.0875 8135.1663 0.0661 0.1255 1.9701 220.7059
23.825431553460 -0.651637294264 aRR 118 6.8826 7631.0207 0.0270 0.0665 1.9994 222.8136
23.300005005403 -0.483833589146 aRS 136 7.0875 7463.0891 0.0301 0.0891 2.2866 213.7132
23.096978096058 -0.149638325204 aa>/ 310 8.2761 7399.3091 0.0261 0.0719 2.1802 142.0419
22.463801993613 0.050593102797 aRP/ 604 9.2384 7197.6550 0.0094 0.0184 2.0217 111.9801
20.908492730078 -1.048925221147 aR>R 1288 10.3309 6701.0486 0.0037 0.0098 1.9883 80.3175
18.151801091913 0.121971404382 aaP+/ 2188 11.0954 5819.6717 0.0011 0.0038 2.7621 57.8144
18.151801091912 0.121971404382 Pa/>\ 5383 12.3942 5820.9705 0.0011 0.0038 2.7621 36.6147
18.151801091911 0.121971404382 aaP+\* 24782 14.5970 5823.1734 0.0011 0.0038 2.7621 25.2514
18.151801091911 0.121971404382 aP/\>\ 71400 16.1236 5824.7000 0.0011 0.0038 2.7621 22.5649
17.014333793185 0.877798046073 aRRCS~ 185990 17.5049 5462.0917 0.0007 0.0022 2.4296 21.9114
16.787646812493 -0.000523524365 aP<<L*R 533110 19.0241 5391.0711 0.0002 0.0008 1.8780 16.0381
16.767539221580 0.000861435347 aPPLC//R 3507568 21.7420 5387.3546 0.0003 0.0011 2.0810 11.0234
16.767539221580 0.000861435347 aPLCP/*R 5114940 22.2863 5387.8988 0.0003 0.0011 2.0810 10.9652
16.514005639889 0.000061544441 aP<<LS*R 6663132 22.6678 5307.1496 0.0002 0.0009 1.9342 10.6180
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_sqrt/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
0.51303089603166252 5.1303092039932255E-004
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
25.494417094591 0.129597771245 P 1 0.0000 8158.2135 0.0751 0.1482 2.0932 320.0000
25.454204437855 0.323427417346 a 2 1.0000 8146.3454 0.0684 0.1292 1.9726 320.0000
22.083099997608 0.178415254506 a> 4 2.0000 7068.5920 0.0078 0.0197 1.9876 320.0000
16.530346371604 0.363427899067 aR 12 3.5850 5293.2958 0.0002 0.0009 1.9031 165.9167
16.530346371604 0.205042232171 aP*R 412 8.6865 5298.3973 0.0002 0.0009 1.9031 21.9903
16.530346371604 0.363427899067 a><R 1298 10.3421 5300.0529 0.0002 0.0009 1.9031 18.8105
16.530201114487 0.363427889598 aPS-R 4182 12.0300 5301.6943 0.0002 0.0009 1.9037 16.6181
16.530184212669 0.363427874538 aRPS- 7070 12.7875 5302.4464 0.0002 0.0009 1.9038 16.6274
16.491940381734 1.748877998122 aPE/SR 58376 15.8331 5293.2540 0.0002 0.0010 2.1474 14.5708
16.480507101976 0.363468243286 aPS~R-R 535106 19.0295 5292.7917 0.0002 0.0009 2.0040 14.4283
16.456331270355 0.000107418500 aaPS~/R+ 3375074 21.6865 5287.7125 0.0002 0.0009 2.0864 12.6542
16.421283347554 -0.000107543565 PaPS~/R- 3421729 21.7063 5276.5170 0.0002 0.0008 2.1974 12.6763
16.412135469051 0.000107543403 aPS~/RP- 8422504 23.0058 5274.8892 0.0002 0.0008 2.2175 13.3120
16.385501795822 0.000107511063 aPS~/R<< 8585800 23.0335 5266.3941 0.0002 0.0009 2.2153 13.3170
16.383635353693 -0.420048866172 PaR/LLS< 10159501 23.2763 5266.0396 0.0002 0.0009 2.0637 13.2835
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
0.0 24.57 sqrt(-9.205154755523*log(cos((x0/log((-sin(pi)))))))
45.59 16.19 0.132079830938*(x0-sin(pi))
45.59 16.17 0.132079837820*x0
51.8 16.11 -0.000065453019+(x0/(((pi*sqrt(pi))+1)+1))
60.01 16.09 -0.000121747890+(x0/(pi*exp(sqrt((sqrt(pi)-1)))))
75.61 16.04 -0.000026540308*(pi-(x0*exp(exp((pi-1)))))
82.53 16.03 0.000083574428*((x0*exp((exp(pi)/pi)))-1)
104.78 16.01 0.132144102682*(x0-(pi/exp(exp((pi-1)))))
104.78 16.0 0.132144231096*(x0-exp((exp(pi)/(-pi))))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_squared/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
23.556773918980 -3.114114453052 P 1 0.0000 7538.1677 0.0194 0.0418 2.0001 320.0000
23.517711071261 -1.519869926577 aaC+ 226 7.8202 7533.4877 0.0452 0.1429 2.4297 168.4292
20.818891539882 -0.024274019231 aPE/ 340 8.4094 6670.4547 0.0031 0.0077 1.8435 158.2235
20.818891539882 -0.024274019231 aPE\* 2682 11.3891 6673.4344 0.0031 0.0077 1.8435 50.8542
20.785498728627 -0.026827214072 aPE</ 3258 11.6698 6663.0294 0.0033 0.0084 1.9041 47.3088
20.741543088543 -1.025919695757 aPE/E 4806 12.2306 6649.5244 0.0031 0.0082 1.8465 42.9230
20.703264131922 -0.519438242611 aRLCC 19976 14.2860 6639.3305 0.0189 0.0634 3.4475 37.6823
20.036149148186 -0.170277718889 PPa-+\ 25951 14.6635 6426.2312 0.0023 0.0069 2.0861 51.7420
19.479473254607 -0.910826776434 aP/C>S 74040 16.1760 6249.6075 0.0022 0.0078 2.0957 37.9207
19.123045148562 -0.318049993223 PaP/C*\ 316983 18.2740 6137.6485 0.0024 0.0072 2.3872 31.7360
18.569140506088 -1.787878840860 PaP-E+R 317903 18.2782 5960.4032 0.0007 0.0020 1.8494 31.7479
17.686617276317 -1.143979127009 aaP/S/L 322136 18.2973 5678.0148 0.0004 0.0010 2.2588 31.5492
16.880632049702 -0.540826539073 aPER/CC 675482 19.3656 5421.1678 0.0003 0.0011 1.9817 23.7326
15.270167681538 -0.156121793373 aP/C>RC 977162 19.8982 4906.3519 0.0001 0.0007 2.1848 19.8761
15.270167681538 -0.156121793373 aP\*C>RC 10663424 23.3462 4909.7998 0.0001 0.0007 2.1848 10.4674
15.270167681537 0.843878206627 aP/C>RC< 12136316 23.5328 4909.9865 0.0001 0.0007 2.1848 10.3874
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_squared/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
6.9274608629488199E-002 6.9274611919855554E-005
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
23.556773918980 0.008746610470 P 1 0.0000 7538.1677 0.0194 0.0418 2.0001 320.0000
22.466679533978 0.021900208670 a 2 1.0000 7190.3375 0.0103 0.0258 1.9807 320.0000
22.071759222412 0.095597561906 aL 18 4.1699 7067.1329 0.0263 0.0693 3.2470 305.8889
22.065327239894 0.007835712221 aE 20 4.3219 7065.2266 0.0065 0.0122 1.9158 307.3000
14.464047223487 0.017445083559 aa* 28 4.8074 4633.3025 0.0001 0.0005 1.8850 301.9286
14.464047223487 0.017445083559 aa\/ 322 8.3309 4636.8260 0.0001 0.0005 1.8850 38.6211
14.464047223487 0.005552942407 aaP** 2132 11.0580 4639.5531 0.0001 0.0005 1.8850 14.8058
14.464047223487 0.005552942407 Paa** 2135 11.0600 4639.5551 0.0001 0.0005 1.8850 15.0927
14.464047223487 0.054805347874 aPa// 2214 11.1124 4639.6076 0.0001 0.0005 1.8850 15.2358
14.464047223487 0.004212167794 aaP>** 23606 14.5269 4643.0220 0.0001 0.0005 1.8850 10.6195
14.463975159139 0.017445082650 aaPS-* 23718 14.5337 4643.0057 0.0001 0.0005 1.8854 10.7918
14.438022197238 -18.690562420871 aPE/C< 54632 15.7375 4635.9046 0.0001 0.0005 1.9198 11.7337
14.396073419968 -18.671461924917 aPE/CL 62408 15.9294 4622.6729 0.0001 0.0004 2.1112 11.7431
14.396073419967 -18.671461924917 aPE\*CL 686462 19.3888 4626.1323 0.0001 0.0004 2.1112 13.6840
14.393104652825 18.671451253669 aPE/CL~ 766058 19.5471 4625.3406 0.0001 0.0004 2.1239 13.8026
14.386672438506 -18.671471714261 aPE/CLS 801050 19.6115 4623.3467 0.0001 0.0004 2.1578 13.7244
14.385612068718 -9.205154755523 aPS~L/CL 8054116 22.9413 4626.3372 0.0001 0.0004 2.4740 13.3642
14.363832966072 -5.051408857545 aP<E/CR< 8623584 23.0399 4619.4664 0.0001 0.0004 2.4058 13.4732
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
0.0 24.57 sqrt(-9.205154755523*log(cos((x0/log((-sin(pi)))))))
45.59 16.19 0.132079830938*(x0-sin(pi))
45.59 16.17 0.132079837820*x0
51.8 16.11 -0.000065453019+(x0/(((pi*sqrt(pi))+1)+1))
60.01 16.09 -0.000121747890+(x0/(pi*exp(sqrt((sqrt(pi)-1)))))
75.61 16.04 -0.000026540308*(pi-(x0*exp(exp((pi-1)))))
82.53 16.03 0.000083574428*((x0*exp((exp(pi)/pi)))-1)
104.78 16.01 0.132144102682*(x0-(pi/exp(exp((pi-1)))))
104.78 16.0 0.132144231096*(x0-exp((exp(pi)/(-pi))))
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_tan/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
25.217022889947 -2.974291782868 P 1 0.0000 8069.4473 0.0599 0.1022 2.0656 320.0000
25.217022889947 -1.974291782868 P< 5 2.3219 8071.7693 0.0599 0.1022 2.0656 243.6000
25.217022889947 -9.702303992238 PP* 25 4.6439 8074.0912 0.0599 0.1022 2.0656 224.4400
24.402287214135 -0.891689436578 aRR 118 6.8826 7815.6146 0.0446 0.1148 2.0565 220.9153
23.881176750711 -0.724537755934 aRS 136 7.0875 7649.0640 0.0480 0.1380 2.3625 215.7794
22.791615731678 0.007348499760 aP-E 480 8.9069 7302.2239 0.0166 0.0527 2.0236 178.5688
21.696513720419 -0.185503366550 aRP/ 604 9.2384 6952.1228 0.0085 0.0259 1.9984 156.0728
21.406801821286 -1.054307651635 a>RR 1352 10.4009 6860.5775 0.0049 0.0134 1.9295 94.2714
21.338816837241 -0.014382920472 aPL<* 2606 11.3476 6839.7690 0.0039 0.0081 1.7653 67.0902
18.069407567980 -0.001845129157 aPLL* 2822 11.4625 5793.6729 0.0007 0.0029 2.1749 64.3154
18.029717670195 -0.001555293172 aPLLS* 32668 14.9956 5784.5052 0.0009 0.0034 2.1205 18.6204
17.996200975593 -0.001180715570 aPLLSS* 418978 18.6765 5777.4608 0.0011 0.0038 2.2611 13.8713
17.645315485994 -0.349316495084 aP/S<ES 970810 19.8888 5666.3898 0.0008 0.0023 2.3630 13.8668
17.278846864007 0.754016132049 aRC>R>C 2874838 21.4550 5550.6860 0.0006 0.0018 2.2928 13.4290
16.915920306315 -2.031027855319 aPaRC++R 3497828 21.7380 5434.8325 0.0003 0.0009 2.0668 13.1112
16.915920306315 -2.031027855319 PaaRC++R 3497829 21.7380 5434.8325 0.0003 0.0009 2.0668 13.1113
16.532384197625 -0.407500887305 Pa<-P/RC 9680509 23.2067 5313.5696 0.0003 0.0009 2.1460 11.3612
16.259969908220 -2.842435291110 a>PE</>E 16693664 23.9928 5227.1832 0.0002 0.0012 2.2580 11.0672
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_tan/kinetic.txt_train-mult_a
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
0.26945167976297640 2.6945169256124444E-004
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
25.217022889947 0.053253547464 P 1 0.0000 8069.4473 0.0599 0.1022 2.0656 320.0000
18.879956687299 0.133338943801 a 2 1.0000 6042.5861 0.0014 0.0047 2.5902 320.0000
18.879956687299 0.133338943801 aEL 180 7.4919 6049.0780 0.0014 0.0047 2.5902 50.6778
18.879945356361 0.133338953091 aPS+ 220 7.7814 6049.3639 0.0014 0.0047 2.5902 50.5091
18.879921089532 0.133338972988 aPPS*+ 23356 14.5115 6056.0863 0.0014 0.0047 2.5902 37.5176
17.675064567037 0.193145884483 aaP/S- 25158 14.6187 5670.6394 0.0003 0.0007 1.8920 40.1538
17.671080561570 -0.193158758395 aP/Sa- 67112 16.0343 5670.7801 0.0004 0.0008 1.9223 33.2377
17.527870552937 0.133265762291 a<aR/E 103436 16.6584 5625.5770 0.0004 0.0012 2.0907 28.4872
17.238082067758 -2.577269277976 aRP/CL 114800 16.8088 5532.9950 0.0003 0.0010 2.1338 27.6445
16.433195468224 0.002079443135 aaP>E+* 273696 18.0622 5276.6848 0.0003 0.0015 2.2435 21.1600
16.059215034772 0.137835461279 aaSPE/- 342508 18.3858 5157.3346 0.0002 0.0012 2.4606 21.5533
16.059215034772 0.005956409837 aPE*aS- 708386 19.4342 5158.3830 0.0002 0.0012 2.4606 20.6711
16.057074124555 0.137834252783 aaSPE/S- 4459230 22.0884 5160.3521 0.0002 0.0012 2.4677 17.1792
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
0.0 24.57 sqrt(-9.205154755523*log(cos((x0/log((-sin(pi)))))))
45.59 16.19 0.132079830938*(x0-sin(pi))
45.59 16.17 0.132079837820*x0
51.8 16.11 -0.000065453019+(x0/(((pi*sqrt(pi))+1)+1))
60.01 16.09 -0.000121747890+(x0/(pi*exp(sqrt((sqrt(pi)-1)))))
75.61 16.04 -0.000026540308*(pi-(x0*exp(exp((pi-1)))))
82.53 16.03 0.000083574428*((x0*exp((exp(pi)/pi)))-1)
104.78 16.01 0.132144102682*(x0-(pi/exp(exp((pi-1)))))
104.78 16.0 0.132144231096*(x0-exp((exp(pi)/(-pi))))
Just one variable!
Checking for symmetries...
kinetic.txt_train-mult_a just one variable for ADD
kinetic.txt_train-mult_a just one variable for ADD
kinetic.txt_train-mult_a just one variable for ADD
kinetic.txt_train-mult_a just one variable for ADD
Checking for separabilities...
kinetic.txt_train-mult_a just one variable for ADD
kinetic.txt_train-mult_a just one variable for ADD
Checking for compositionality...
Checking for generalized symmetry...
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/separable_mult/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
29.765744166847 -2.141592741013 P 1 0.0000 9525.0381 2.6166 8.8840 2.3897 320.0000
29.422952775985 0.531268660000 a 2 1.0000 9416.3449 2.4149 8.4530 2.4376 320.0000
28.865622146703 2.020289126527 aL 18 4.1699 9241.1690 2.1719 7.9693 2.6354 316.5000
28.178102995738 -0.333996159973 aP* 26 4.7004 9021.6934 1.9534 7.3913 2.8731 317.5769
27.922907831804 -3.108324313817 a>E 182 7.5078 8942.8383 1.5549 6.3080 2.8037 287.1483
27.646445412494 -1.330927270487 aa+E 474 8.8887 8855.7513 1.1814 5.1682 2.6109 269.9452
27.442617142010 -0.319739122091 aL\~ 1024 10.0000 8791.6375 0.4497 0.9774 2.2369 250.5488
26.552318301121 -1.251452293534 aa<\- 2980 11.5411 8508.2830 0.2407 0.5520 2.3495 184.4581
24.832617496642 -1.101644561431 aaE*E 4736 12.2095 7958.6471 0.3176 1.8469 2.7150 157.3296
22.362526804147 -4.810753270210 PaC/ER 58801 15.8436 7171.8521 0.4015 2.1887 4.6342 65.2954
22.362526804143 -7.952346011223 PPaC/ER+ 3571355 21.7680 7177.7766 0.4015 2.1887 4.6342 51.9006
22.362526804142 -4.810753270210 PaCEL/ER 7762737 22.8881 7178.8967 0.4015 2.1887 4.6342 52.2665
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/separable_mult/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
9.8840007781982422 9.8840012476630879E-003
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
29.765744166847 0.318309877326 P 1 0.0000 9525.0381 2.6166 8.8840 2.3897 320.0000
28.792086456123 2.133418260447 a 2 1.0000 9214.4677 2.1982 7.9644 2.5901 320.0000
28.790206386264 -2.188684209804 a~ 8 3.0000 9215.8660 2.1761 7.9147 2.5954 320.0000
26.758930590935 4.551473474011 aa* 28 4.8074 8567.6651 1.5430 6.1993 3.3583 315.5000
26.484394663352 -8.814325197197 aCL 176 7.4594 8482.4657 1.3834 5.6960 3.3964 234.6193
26.019916222485 -1.487184668148 aaL/ 338 8.4009 8334.7741 0.5129 2.7842 2.5808 213.2663
25.895862195912 8.271460610219 aC\< 860 9.7482 8296.4241 1.1301 4.8530 3.5196 151.2837
25.072916237737 3.604513504801 aaE<* 2612 11.3509 8034.6841 1.1959 5.1521 4.3015 134.4552
24.552931005578 0.483305784300 aaP*E* 24950 14.6068 7871.5447 0.4489 2.5395 3.0052 122.2156
24.492273534247 -6.277844856266 aa~>L+ 30130 14.8789 7852.4064 0.1690 1.0923 2.7955 113.3104
24.435772148861 -3.490111211605 aa~>L* 33046 15.0122 7834.4593 0.5426 2.6608 3.8495 108.8536
23.145771306469 -7.508389064056 aaC/C< 54626 15.7373 7422.3841 0.6551 3.3025 4.8261 105.9656
22.278795186675 -3.736255965319 aaaS\-/ 279860 18.0943 7147.3088 0.1391 0.9690 3.4277 76.4455
22.223155339309 -7.488673134239 aSaC/CL 1359294 20.3744 7131.7841 0.1628 1.0224 3.4156 43.4020
21.278415248242 -3.152078469896 PaRC*C\> 8506237 23.0201 6832.1130 0.1098 0.7889 3.0625 33.8936
19.481149107383 7.566913381123 aa~*>R\< 10131198 23.2723 6257.2400 0.0096 0.1109 2.8355 32.6149
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
46.86 29.78 0.318309877326*pi
47.59 29.42 0.531268660000+x0
49.6 28.79 2.133418260447*x0
49.64 28.79 -2.188684209804*(-x0)
51.68 28.19 -0.333996159973+(x0*pi)
52.21 24.57 0.483305784300*(x0*exp((x0*pi)))
61.92 24.44 -3.490111211605*(x0*log(((-x0)+1)))
66.92 22.28 -3.736255965319*(x0/(x0-(sin(x0))**(-1)))
70.06 22.22 -7.488673134239*log(cos((sin(x0)/cos(x0))))
112.44 19.48 7.566913381123*((sqrt(((x0*(-x0))+1)))**(-1)-1)
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_squared/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
30.992152946741 -2.141592741013 P 1 0.0000 9917.4889 20.8367 96.6935 3.0228 320.0000
30.765214689338 0.531268660000 a 2 1.0000 9845.8687 20.6720 96.2624 3.1126 320.0000
30.511244063517 2.185140510418 aL 18 4.1699 9767.7680 20.3923 95.6140 3.2641 320.0000
30.422057928595 0.062537320000 aa+ 24 4.5850 9739.6435 20.5090 95.8314 3.2827 320.0000
30.072878307728 -0.256674899114 aP* 26 4.7004 9628.0215 20.2315 95.1235 3.5978 320.0000
29.932598919599 -3.040289718441 a>E 182 7.5078 9585.9394 19.8542 94.0495 3.5849 298.6209
29.853534080643 -3.218108612304 aEE 198 7.6294 9560.7603 18.2728 89.2183 3.5417 297.4495
29.787697721814 -1.250536692692 aa+E 474 8.8887 9540.9520 19.4817 92.8973 3.6539 304.2869
28.403291513430 1.004972058688 aEEC 1764 10.7846 9099.8379 20.9393 96.0461 5.1067 289.1729
28.403291513430 0.004972058688 aEEC> 11254 13.4581 9102.5114 20.9393 96.0461 5.1067 285.7869
27.973876700955 1.005556630033 aR<\S 17924 14.1296 8965.7701 20.8124 97.2437 5.4801 271.2573
27.740898603397 0.849382755567 aEECS 18544 14.1787 8891.2662 20.9921 96.2449 5.6344 271.1540
27.740898603397 -2.292209985446 PaEECS+ 393099 18.5845 8895.6721 20.9921 96.2449 5.6344 251.9250
27.424501663419 -1.147183216738 Pa>ECE* 428059 18.7075 8794.5480 18.2941 90.9525 5.2805 250.5730
26.765442050671 -15.155442993896 aa*C\EE 1006100 19.9403 8584.8818 8.1420 41.9173 4.8639 223.6102
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_squared/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
97.693471383423457 9.7693476023614362E-002
87 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
31.055036080815 0.356946102026 P 1 0.0000 7235.8234 21.0303 96.5721 3.2261 233.0000
30.432389039759 2.336180655014 a 2 1.0000 7091.7466 20.6524 95.5915 3.4900 233.0000
29.743621994632 4.866988480450 aa* 28 4.8074 6935.0713 20.0053 93.7533 3.8781 226.8214
29.429091568992 0.023515144190 a>C 146 7.1898 6864.1682 21.5433 97.7011 4.9480 212.3836
29.425600018198 -0.000647690691 aa<+ 206 7.6865 6863.8513 21.5408 97.6940 5.0060 209.5534
28.922547525119 61.541774347972 aaS- 294 8.1997 6747.1532 18.9366 90.5188 4.3816 214.4048
28.915988354101 11.756767435847 a\E\ 1268 10.3083 6747.7336 19.9478 93.8244 4.9194 211.5536
28.907664339925 10.139445687984 aaa** 2136 11.0607 6746.5465 18.8734 90.3077 4.3855 200.2411
28.852062199968 -19.481350994352 aaCL* 2820 11.4615 6733.9920 18.5990 89.3650 4.3976 202.7780
28.363006275571 28.330128598388 aa\E/ 3492 11.7698 6620.3503 18.3721 89.3047 5.1963 203.3044
27.553818511172 -42.434610524440 aa*C< 5184 12.3399 6432.3796 17.0665 84.5307 5.2579 205.6339
27.478148179497 -41.871418228121 aa*CL 6048 12.5622 6414.9708 16.4532 82.1450 5.2555 202.7250
27.266244970648 -156.145089297315 aCLC< 12690 13.6314 6366.6665 15.9398 80.3971 5.3387 203.6121
27.239498688235 -155.583726122185 aCLCL 21438 14.3879 6361.1911 15.7015 79.4278 5.3362 190.6996
26.297406760656 0.009225376162 aPP**E 26612 14.6998 6141.9956 4.3307 31.3743 3.4721 192.8807
26.297406760652 0.009225376162 PaP**E 26613 14.6998 6141.9956 4.3307 31.3743 3.4721 192.8822
26.107200266739 0.000049626935 aRREEE 269420 18.0395 6101.0172 4.0290 29.6735 3.4696 106.6130
26.093816102562 -26.211037730706 aaE<*C< 616408 19.2335 6099.0927 15.1754 78.1710 6.2612 102.2892
25.713841478483 -25.818696701757 aaE<*CL 686392 19.3887 6010.7137 11.8171 62.4307 6.2396 109.3511
25.138949659828 0.000000004863 PEaRR*E 1251011 20.2547 5877.6299 12.4763 67.8514 5.9917 137.8876
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
46.86 29.78 0.318309877326*pi
47.59 29.42 0.531268660000+x0
49.6 28.79 2.133418260447*x0
49.64 28.79 -2.188684209804*(-x0)
51.68 28.19 -0.333996159973+(x0*pi)
52.21 24.57 0.483305784300*(x0*exp((x0*pi)))
61.92 24.44 -3.490111211605*(x0*log(((-x0)+1)))
66.92 22.28 -3.736255965319*(x0/(x0-(sin(x0))**(-1)))
70.06 22.22 -7.488673134239*log(cos((sin(x0)/cos(x0))))
112.44 19.48 7.566913381123*((sqrt(((x0*(-x0))+1)))**(-1)-1)
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_atan/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
28.407103380687 -2.356194577615 P 1 0.0000 9090.2731 0.4991 0.7735 2.0121 320.0000
27.507180927981 0.316666823397 a 2 1.0000 8803.2979 0.2543 0.3823 1.9108 320.0000
25.087437175717 1.593986176954 aL 18 4.1699 8032.1498 0.2733 1.2372 2.8746 302.3333
25.087437175717 0.593986176954 aL> 52 5.7004 8033.6803 0.2733 1.2372 2.8746 216.6346
25.087437175717 2.593986176954 aL< 70 6.1293 8034.1092 0.2733 1.2372 2.8746 203.2143
25.069668668688 -0.254095269991 aP<* 240 7.9069 8030.2009 0.0692 0.2029 2.0383 160.2583
24.405706752294 1.020216678119 aL<C 1636 10.6760 7820.5021 0.0500 0.2292 2.1527 86.8166
24.233431307717 -3.094381195654 aaC+E 4692 12.1960 7766.8940 0.0566 0.2261 2.3887 76.7449
24.233431307717 -4.094381195654 aaC+E> 53510 15.7075 7770.4055 0.0566 0.2261 2.3887 66.8673
23.194218706318 -1.306736340387 aPR*SE 63472 15.9538 7438.1038 0.0558 0.2074 2.9330 65.8179
22.783843006210 0.019251847312 Pa\<E>/ 457627 18.8038 7309.6336 0.0358 0.0803 3.8505 58.7710
22.539691932448 -0.963953588637 aRLCES\ 2592976 21.3062 7234.0076 0.0169 0.1083 2.0295 61.6536
22.089443997721 0.504481251170 PaCC~/<S 7784373 22.8921 7091.5142 0.0287 0.0591 3.7594 37.9831
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_atan/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
1.4699658237371822 1.4699658935568123E-003
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
28.407103380687 0.249999993043 P 1 0.0000 9090.2731 0.4991 0.7735 2.0121 320.0000
26.088575407820 1.639675861609 a 2 1.0000 8349.3441 0.1051 0.1736 1.9816 320.0000
26.065983758265 -1.642100609694 a~ 8 3.0000 8344.1148 0.1048 0.1741 2.0144 192.6250
25.891662301229 3.533004016469 aa* 28 4.8074 8290.1393 0.4991 1.3902 3.2632 185.8571
25.714934600545 -7.203255792717 aC< 68 6.0875 8234.8665 0.4543 1.2543 3.3134 208.8235
25.564095498478 3.648682894276 aaS* 258 8.0112 8188.5218 0.4017 1.1012 3.2839 228.7326
24.530986682970 -7.666904293437 aSC< 912 9.8329 7859.7486 0.2845 0.7636 4.1507 227.1086
24.102205867299 -0.811445425654 aP*C< 5182 12.3393 7725.0452 0.0536 0.1145 2.7754 174.8545
24.017734222920 0.097042762058 aLCEE 23204 14.5021 7700.1770 0.0600 0.1310 2.9308 88.1220
23.415630426823 1.241018141119 aaP**S 26230 14.6789 7507.6807 0.1973 0.7710 3.5013 90.1416
23.271937204737 1.808195082785 aa\CC* 32942 15.0076 7462.0275 0.0777 0.2094 4.2319 91.5758
23.118477383506 9.160287319040 Pa\E+\ 43705 15.4155 7413.3283 0.0412 0.0945 2.8921 100.6067
22.568095704350 -9.429939485089 a<C\S< 172412 17.3955 7239.1861 0.0328 0.0739 3.5424 68.6013
22.456161564431 0.167331115649 P<aLC*E 1251753 20.2555 7206.2272 0.0180 0.0624 2.4074 60.6096
22.368685554273 -9.610923978401 a<C\CCL 3075064 21.5522 7179.5316 0.0314 0.0732 2.9502 40.4926
21.530041273263 -2.407189852882 aLC<ECL 3077668 21.5534 6911.1666 0.0087 0.0192 2.6457 40.4789
21.467863117314 0.684271840110 PaSSE*C> 7313885 22.8022 6892.5184 0.0249 0.1035 2.9360 34.2852
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
46.51 28.45 tan(-2.356194577615+pi)
51.68 28.19 -0.333996159973+(x0*pi)
52.21 24.57 0.483305784300*(x0*exp((x0*pi)))
61.92 24.44 -3.490111211605*(x0*log(((-x0)+1)))
66.92 22.28 -3.736255965319*(x0/(x0-(sin(x0))**(-1)))
70.06 22.22 -7.488673134239*log(cos((sin(x0)/cos(x0))))
112.44 19.48 7.566913381123*((sqrt(((x0*(-x0))+1)))**(-1)-1)
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_cos/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
28.262647188237 -2.455651998333 P 1 0.0000 9044.0471 0.7172 1.6851 2.2394 320.0000
27.373000349831 1.105580081245 a~ 8 3.0000 8762.3601 0.5673 1.4008 2.5401 320.0000
27.140456231466 2.167029516654 aE~ 90 6.4919 8691.4378 0.5049 1.1484 2.6460 306.6444
27.121364944608 0.599586697013 aEC 162 7.3398 8686.1766 0.5023 1.1656 2.6589 296.8642
26.819210044764 -2.127219041689 PaC* 261 8.0279 8590.1751 0.5372 1.2708 2.9683 282.4100
26.806880550119 0.029336003895 aa+C 442 8.7879 8586.9897 0.5132 1.1944 2.9327 279.2805
26.782147364152 -0.015260918174 aLS~ 1060 10.0498 8580.3370 0.5557 1.3279 3.2931 276.3783
26.716937816787 2.023555615175 aLS\ 1222 10.2550 8559.6751 1.8941 6.5649 3.7115 276.0147
26.393727816307 0.182640941270 aL\C 1672 10.7074 8456.7003 0.2094 0.7903 2.2285 271.2703
25.839751318304 0.004087175333 aa</C 4492 12.1331 8280.8536 0.3743 1.0275 3.2347 219.3148
25.409809299065 -0.016728655463 aa+ES 5788 12.4988 8143.6378 0.5562 1.8382 3.3138 215.9955
25.166967601963 -0.035618897501 aaS+ES 59986 15.8723 8069.3020 0.6152 2.0250 4.2756 183.6351
24.615405900940 -1.710188908050 aaL/CE 63702 15.9591 7892.8889 0.5846 1.9406 3.6405 184.5809
24.591052441206 0.000057483286 aaP>**C 298536 18.1875 7887.3243 0.6109 1.9722 4.8793 162.1010
23.353878876751 0.000812265829 aaR\</C 560412 19.0961 7492.3374 0.4722 1.9788 5.0291 176.5792
23.353878876751 0.000812265829 aa\R</C 560444 19.0962 7492.3375 0.4722 1.9788 5.0291 176.5773
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_cos/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
0.99998113604694894 9.9998118354350423E-004
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
28.262647188237 0.218341713655 P 1 0.0000 9044.0471 0.7172 1.6851 2.2394 320.0000
27.269237867912 -1.148702173019 a< 6 2.5850 8728.7411 0.5446 1.3393 2.6101 320.0000
27.258949913397 -1.274621792107 a<S 130 7.0224 8729.8863 0.5577 1.3711 2.6374 290.1615
26.799784417431 -0.984340427353 aLS 142 7.1497 8583.0808 0.5588 1.3378 3.2754 291.3521
26.600798841855 -1.039610209609 a>EC 1748 10.7715 8523.0271 0.6190 2.0396 2.6948 278.3598
26.315322613203 11.381352324195 aa>C* 2760 11.4305 8432.3337 1.2345 3.5527 4.1833 265.6322
25.848415524447 1.004105654538 aa</C 4492 12.1331 8283.6261 0.3747 1.0259 3.2198 271.6398
25.399288748544 0.972881583243 aa+ES 5788 12.4988 8140.2712 0.5434 1.7990 3.3852 256.3184
25.399288748544 0.972881583243 aEaE*S 99058 16.5960 8144.3684 0.5434 1.7990 3.3852 198.1727
25.265708874016 0.999493305297 aL\>>S 217082 17.7279 8102.7547 0.3546 0.9740 3.7883 189.9270
23.554132181070 1.000327067435 aaR\</C 560412 19.0961 7556.4184 0.4723 1.9799 4.7249 187.5382
23.554132181070 1.000327067435 aa\R</C 560444 19.0962 7556.4185 0.4723 1.9799 4.7249 187.5349
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
46.51 28.45 tan(-2.356194577615+pi)
48.31 28.1 acos(0.218341713655*pi)
51.8 28.1 acos(-2.455651998333+pi)
52.21 24.57 0.483305784300*(x0*exp((x0*pi)))
61.92 24.44 -3.490111211605*(x0*log(((-x0)+1)))
66.92 22.28 -3.736255965319*(x0/(x0-(sin(x0))**(-1)))
70.06 22.22 -7.488673134239*log(cos((sin(x0)/cos(x0))))
112.44 19.48 7.566913381123*((sqrt(((x0*(-x0))+1)))**(-1)-1)
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_exp/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
32.288553498528 -0.423310912554 P 1 0.0000 10332.3371 1838.6876 19611.3190 4.2138 320.0000
32.152946982187 2.249550488459 a 2 1.0000 10289.9430 1838.6010 19610.8880 4.2756 320.0000
31.797298447578 3.684289236629 aL 18 4.1699 10179.3054 1838.5113 19610.4586 4.4814 320.0000
31.736115943261 1.245718853230 aP* 26 4.7004 10160.2575 1838.4157 19609.9649 4.4838 320.0000
31.541329517716 2.162232578673 a\S 134 7.0661 10100.2915 1838.6137 19610.9788 4.7721 305.7164
31.517602828389 -1.625439110513 a>E 182 7.5078 10093.1407 1838.2223 19608.9785 4.6019 298.9670
30.868737640710 -1.965505560204 aEE 198 7.6294 9885.6254 1837.3237 19604.3096 5.0133 298.0909
30.785816538284 0.704464701631 aaEE* 2864 11.4838 9862.9451 1837.0411 19602.8117 5.0495 285.9647
30.739128083379 -2.589756075197 Pa~>/ 3199 11.6434 9848.1644 1834.1239 19585.2864 5.1007 286.8168
30.042469512902 2.099766383912 PaL/S 4371 12.0937 9625.6840 1838.8046 19610.9428 6.0362 289.8286
30.032887426184 -0.050558088416 aL\C\ 15536 13.9233 9624.4473 1839.3859 19615.0888 6.5686 285.0342
29.802856216752 -0.637288079104 aL\E\ 15860 13.9531 9550.8671 657.1571 6685.2778 4.8781 284.0923
29.691020605822 -2.222102824345 Paa+C/ 25457 14.6358 9515.7624 1875.3042 19630.1152 5.6001 269.9809
29.327833222557 1.025863359929 PaL>*E 50237 15.6165 9400.5231 1835.7820 19596.4056 6.2212 270.8615
28.854620421147 0.000692984996 aL>EC\ 200828 17.6156 9251.0941 1840.4301 19615.3395 8.1471 266.9091
28.854620421147 0.000692984996 aPCE/C\ 640626 19.2891 9252.7677 1840.4301 19615.3395 8.1471 259.4229
28.717724158272 -0.220976980203 aaE*E<E 828484 19.6601 9209.3318 1413.5682 16189.6894 4.8807 256.9217
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_exp/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
19614.037310688072 19.614038242304854
237 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
31.924338030335 1.001183671976 P 1 0.0000 2649.7201 371.7827 3104.9287 4.4618 83.0000
31.056255360609 8.804126447323 a 2 1.0000 2578.6692 370.9226 3100.3801 4.7297 83.0000
30.723905270789 6.935263128162 aE< 72 6.1699 2556.2541 370.5668 3098.3907 4.9076 78.4583
30.640745661270 -2.620299205961 aL\ 106 6.7279 2549.9098 369.0945 3088.6329 4.9139 79.1509
30.571557228143 6.068570870686 aa>* 238 7.8948 2545.3341 370.5178 3098.1360 5.0443 75.4370
30.361639726552 0.779706462941 aP*E 476 8.8948 2528.9109 370.1731 3095.9326 5.1083 76.1198
29.721921761204 0.045538460528 a>EE 2072 11.0168 2477.9363 367.1370 3077.3668 5.3361 71.4141
29.358763425400 -0.940608756574 aaC-\ 4044 11.9816 2448.7589 376.9237 3112.1271 5.8880 74.0351
29.156353224789 -0.922589956581 aE<<\ 14692 13.8427 2433.8201 373.9300 3110.4023 6.2390 72.5278
28.972784323655 0.192714006581 PaEC\+ 29073 14.8274 2419.5685 372.8170 3107.7309 7.9950 70.0661
28.644571351830 -0.553072460198 aP\<+\ 43452 15.4071 2392.9066 374.7844 3110.9514 6.2978 70.3841
28.565280316841 -0.802689937277 aaRC-\ 44286 15.4346 2386.3528 382.1956 3110.9413 6.3636 70.4737
27.614984153372 -0.986626773537 PaE/C\ 57225 15.8044 2307.8480 374.9534 3111.9154 7.2753 70.6284
26.909089638762 0.333721119965 aaE*EE 63922 15.9640 2249.4185 228.2149 1988.4833 5.0493 69.9309
24.257693499782 0.008141758212 PaC/ERE 832435 19.6670 2033.0555 260.9343 2256.6216 7.1422 66.1337
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
46.51 28.45 tan(-2.356194577615+pi)
48.31 28.1 acos(0.218341713655*pi)
51.8 28.1 acos(-2.455651998333+pi)
52.21 24.57 0.483305784300*(x0*exp((x0*pi)))
61.92 24.44 -3.490111211605*(x0*log(((-x0)+1)))
66.92 22.28 -3.736255965319*(x0/(x0-(sin(x0))**(-1)))
70.06 22.22 -7.488673134239*log(cos((sin(x0)/cos(x0))))
112.44 19.48 7.566913381123*((sqrt(((x0*(-x0))+1)))**(-1)-1)
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_inverse/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
30.043246248873 -2.184367279520 P 1 0.0000 9613.8388 12.1788 82.7961 2.8872 320.0000
29.660104924262 1.434537791493 a~ 8 3.0000 9494.2336 12.0459 82.3785 3.0078 320.0000
27.481507091519 -1.034888529827 a\ 10 3.3219 8797.4042 9.2175 68.0240 3.7364 320.0000
27.040005196257 -1.180571083300 aS\ 102 6.6724 8659.4741 9.2570 68.1597 4.1161 270.5490
26.630874663557 1.145620675535 PaR/C 4503 12.1367 8534.0166 12.0510 81.6514 4.8439 230.8577
26.313042578846 0.880834378232 a\<<S 17598 14.1031 8434.2767 12.1849 82.0628 5.3629 220.7774
26.277373462804 -1.138220105652 aaa*S/ 25434 14.6345 8423.3940 9.2492 68.1273 4.9257 217.6189
26.198739018462 -1.733179360181 aaCS*\ 43934 15.4231 8399.0195 8.7643 65.5411 4.5524 216.4436
25.607145894790 -3.984824550839 aa\+RE 63290 15.9497 8210.2364 3.4523 27.2952 3.7134 204.7154
24.831754646556 0.045925394643 aR\<a/ 150170 17.1962 7963.3577 3.6302 31.8316 3.7748 125.5694
24.808797189344 -1.232332772497 a>CEC\ 200922 17.6163 7956.4314 121.1190 2114.7653 4.9481 107.4442
24.220088455122 -1.308671671427 aE<\ER 216076 17.7212 7768.1495 310.8343 3325.4941 6.3293 104.6144
24.220088455121 -2.308671671427 aE<\ER> 2224974 21.0854 7771.5137 310.8343 3325.4941 6.3293 114.0442
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_inverse/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
83.753363634796514 8.3753367612867821E-002
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
30.043246248873 0.304694319221 P 1 0.0000 9613.8388 12.1788 82.7961 2.8872 320.0000
29.138919833376 -1.882286826405 a< 6 2.5850 9327.0393 11.9226 81.9834 3.1974 320.0000
28.629674022476 -1.319739122091 aL 18 4.1699 9165.6656 11.4626 80.0327 3.3953 320.0000
27.398898018259 0.899447931172 a\< 62 5.9542 8773.6016 9.5279 69.5742 3.9610 303.5484
26.591674604605 -0.673260524589 aLa/ 628 9.2946 8518.6305 6.5551 51.9332 3.6270 254.7723
25.983106067196 0.282658839531 aa*\< 5136 12.3264 8326.9204 0.6451 4.5972 2.7691 144.7155
25.101698077374 -0.128833574154 aCL\> 10746 13.3915 8045.9349 1.0735 11.5100 2.7257 102.1870
24.865649833198 -0.252737862569 aaa*\- 25082 14.6144 7971.6223 1.2293 12.7386 2.9412 71.0611
24.865649833198 -0.252737862569 aa\a/- 27542 14.7493 7971.7573 1.2293 12.7386 2.9412 69.6096
22.943232774258 0.267647615496 aaS*\< 54118 15.7238 7357.5583 0.7565 8.7563 3.0734 60.1574
22.943232774258 0.267647615496 a\aS/< 94404 16.5266 7358.3610 0.7565 8.7563 3.0734 46.8253
22.943232774258 0.267647615496 aS\a/< 130570 16.9945 7358.8290 0.7565 8.7563 3.0734 42.0049
22.921731368642 -0.267663131080 aaS\-a/ 596056 19.1851 7354.1391 0.7561 8.7520 3.1034 30.1164
22.921731368642 -0.267663131080 aaS~*\> 600880 19.1967 7354.1508 0.7561 8.7520 3.1034 30.1236
22.702604383389 -0.132868591267 PRaC<\+ 1057647 20.0124 7284.8458 0.8088 9.2836 2.4686 28.8104
22.702604383389 -0.074963074130 PPRaC</+ 4322387 22.0434 7286.8768 0.8088 9.2836 2.4686 18.6192
22.602384972210 0.264420085297 aa*\PR<- 11437430 23.4473 7256.2104 0.8475 9.6446 2.7203 16.4864
22.531210184803 -0.264446082481 PRaa*\>- 13246869 23.6591 7233.6464 0.8467 9.6373 2.8002 17.3871
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
46.51 28.45 tan(-2.356194577615+pi)
48.31 28.1 acos(0.218341713655*pi)
51.8 28.1 acos(-2.455651998333+pi)
52.21 24.57 0.483305784300*(x0*exp((x0*pi)))
61.92 24.44 -3.490111211605*(x0*log(((-x0)+1)))
66.92 22.28 -3.736255965319*(x0/(x0-(sin(x0))**(-1)))
70.06 22.22 -7.488673134239*log(cos((sin(x0)/cos(x0))))
112.44 19.48 7.566913381123*((sqrt(((x0*(-x0))+1)))**(-1)-1)
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_log/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
29.777964587702 -3.141592741013 P 1 0.0000 9528.9487 1.6416 4.4279 2.2432 320.0000
29.494619831202 -0.468731340000 a 2 1.0000 9439.2783 1.4020 4.0188 2.2500 320.0000
29.030037689047 0.757725510490 aL 18 4.1699 9293.7820 0.9552 2.3664 2.2145 320.0000
28.564575823197 -1.472562975229 aP* 26 4.7004 9145.3647 0.9079 3.1427 2.3075 320.0000
26.628915016633 -4.436239806717 a>E 182 7.5078 8528.7606 0.7091 2.8770 3.0581 291.6483
26.628915016633 -3.436239806717 a>E< 938 9.8734 8531.1262 0.7091 2.8770 3.0581 167.8081
26.628915016633 -7.577832547730 Pa>E+ 2507 11.2917 8532.5446 0.7091 2.8770 3.0581 139.0901
25.915914012407 -2.484548978718 aP>>* 2542 11.3117 8304.4042 0.4916 2.2500 2.9540 139.3281
25.729467937191 -2.258020472714 aPER* 2718 11.4083 8244.8381 0.5747 2.4568 3.3960 136.4573
25.632691832931 -2.328856832847 aPPR+* 23564 14.5243 8216.9857 0.5478 2.3921 3.4766 109.4069
25.539570728909 -5.866703212812 aaR>E+ 30462 14.8947 8187.5574 0.4748 2.0911 3.3006 111.4115
25.532569056427 -3.107742573398 aaC>E* 33386 15.0270 8185.4491 0.4147 1.7601 3.8263 108.9485
25.321508351128 5.335282502034 Pa<E~/ 37541 15.1962 8118.0789 0.3487 1.7179 3.1661 109.5224
25.275909210231 5.319164397485 Pa>-E~ 56149 15.7770 8104.0679 0.3522 1.7270 3.2702 94.7424
24.831992624254 -0.727105731860 aP*aL+ 64240 15.9712 7962.2088 0.2207 1.0689 3.0289 90.2873
24.831992624254 -0.727105731860 aaP*E*L 321640 18.2951 7964.5327 0.2207 1.0689 3.0289 61.0389
24.690468785697 -13.975890442520 PaRE\-E 581651 19.1498 7920.0998 0.2345 1.0248 3.9417 58.0671
24.690468785695 -13.975890442520 PaR~E-E 583055 19.1533 7920.1033 0.2345 1.0248 3.9417 58.1250
24.678902700513 2.072542433870 aLaR>>* 1074754 20.0356 7917.2844 0.1386 0.5298 2.7522 63.1375
24.105032279971 2.268692606316 aLaRE>* 1077346 20.0390 7733.6494 0.1018 0.4006 2.6682 63.1306
23.939347467190 2.322013929269 PaaRR\-* 3306525 21.6569 7682.2481 0.1495 0.5804 4.1840 40.2071
23.864935729172 1.505020954187 aaLaE>*+ 4310234 22.0393 7658.8188 0.0542 0.2515 2.2583 45.1048
22.605194930300 1.318026062707 aaS\a-/L 5150790 22.2964 7255.9587 0.0208 0.1104 2.2713 42.5105
22.605194930300 1.318026062707 aaS*\<L~ 10279386 23.2933 7256.9556 0.0208 0.1104 2.2713 30.0338
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_log/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
4.4278763327022128 4.4278765430150529E-003
2 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
45.97 30.06 exp(-3.141592741013+pi)
46.51 28.45 tan(-2.356194577615+pi)
48.31 28.1 acos(0.218341713655*pi)
51.8 28.1 acos(-2.455651998333+pi)
52.21 24.57 0.483305784300*(x0*exp((x0*pi)))
61.92 24.44 -3.490111211605*(x0*log(((-x0)+1)))
66.92 22.28 -3.736255965319*(x0/(x0-(sin(x0))**(-1)))
70.06 22.22 -7.488673134239*log(cos((sin(x0)/cos(x0))))
112.44 19.48 7.566913381123*((sqrt(((x0*(-x0))+1)))**(-1)-1)
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_sin/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
28.226300576574 -2.801148117391 P 1 0.0000 9032.4162 0.5391 1.3402 2.1344 320.0000
27.511636672822 -0.010022900085 a 2 1.0000 8804.7237 0.6320 1.7780 2.5021 320.0000
27.425254256786 -0.237801349044 aR 12 3.5850 8779.6663 0.5864 1.6498 2.6007 314.7500
27.304363400191 1.558794225181 aL 18 4.1699 8741.5662 0.8978 2.3207 3.1202 316.5000
27.052756436669 -1.060982843232 aE 20 4.3219 8661.2040 0.7795 2.1402 3.1601 316.8500
26.736513647646 -0.230366824236 aa+ 24 4.5850 8560.2693 0.8667 2.3472 3.1420 317.3750
26.724214117982 -0.226465914220 aaS+ 222 7.7944 8559.5429 0.8293 2.2710 3.1746 288.8739
26.588894455099 -1.283617183404 aaE+ 234 7.8704 8516.3166 1.0518 2.7090 3.4651 290.4701
26.581129605125 -0.589426142157 PaS* 257 8.0056 8513.9671 1.0192 2.6400 3.9789 291.6303
26.564557143731 -1.094192244778 a<\~ 1012 9.9830 8510.6413 2.5357 9.3251 4.5232 293.0040
26.517483987472 -1.089872144588 aE<E 1962 10.9381 8496.5330 1.3619 3.6551 3.9588 275.3206
26.514422100905 -0.334733383232 aa>>* 2544 11.3129 8495.9280 1.1364 2.8696 3.8180 277.2174
26.473458290099 2.386809116753 Pa<S* 2727 11.4131 8482.9198 1.0619 2.7309 3.6193 277.2204
26.418192062730 -0.157579848368 aaRE* 2848 11.4757 8465.2972 1.0801 2.7639 3.5603 276.8353
26.415934471530 0.935981833117 Pa>*C 4415 12.1082 8465.2072 1.0523 2.7236 3.5041 276.5807
26.415932858450 0.935982007518 Pa<*C 4419 12.1095 8465.2080 1.0523 2.7236 3.5041 276.6058
26.279216059832 0.995586958228 PaE/C 4519 12.1418 8421.4909 0.7687 2.1374 3.9646 277.3007
25.948381289038 0.472155308601 a<\C~ 14066 13.7799 8317.2619 0.6592 1.8032 3.6440 272.3502
25.907280550676 0.911797181482 aL<CS 18416 14.1687 8304.4984 0.8085 2.2326 3.9488 253.8573
25.840008593162 -1.290440236827 PaCES* 32701 14.9970 8283.7998 0.9563 2.5349 4.2339 251.1916
25.653042057296 5.796938708714 PaCC~/ 37489 15.1942 8224.1676 1.0294 2.6742 4.1032 251.3415
25.639921413521 0.371965380941 aP*C>C 75328 16.2009 8220.9758 0.8645 2.3491 3.8485 237.1899
25.350752029055 -1.818097738727 aL\CCE 266168 18.0220 8130.2626 0.5054 1.7759 3.2613 209.0036
25.043766225940 -0.005343323509 aaP>**S 297384 18.1820 8032.1872 0.5505 1.5551 3.8582 207.1999
24.831022014485 0.934151807617 aa>ESC- 448148 18.7736 7964.7007 0.6081 1.7679 3.7915 206.1300
24.305120662781 -0.004728901107 aaR\</S 548748 19.0658 7796.7044 0.5500 1.8584 3.8763 199.6645
24.305120662781 -0.004728901107 aa\R</S 548780 19.0659 7796.7045 0.5500 1.8584 3.8763 199.6600
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_sin/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
0.99974928191095069 9.9974932939649345E-004
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
28.226300576574 0.108366886381 P 1 0.0000 9032.4162 0.5391 1.3402 2.1344 320.0000
27.559307075310 0.958980771128 a 2 1.0000 8819.9783 0.6250 1.7557 2.4622 320.0000
27.558237409974 -0.961183044491 a~ 8 3.0000 8821.6360 0.6255 1.7575 2.4633 320.0000
27.512162508917 1.000648537049 aS 14 3.8074 8807.6994 0.6068 1.7094 2.5203 320.0000
26.122268405646 3.726014394469 aa* 28 4.8074 8363.9332 1.3859 3.4597 4.1910 320.0000
25.739764669822 -7.601786462532 aC< 68 6.0875 8242.8122 1.3432 3.3183 4.5822 305.0000
25.541818560308 3.821906620938 aaS* 258 8.0112 8181.3932 1.2832 3.1490 4.8564 293.2287
25.524823705591 -3.822425580895 aaS~* 2636 11.3641 8179.3077 1.2834 3.1493 4.8874 278.0895
25.434011176379 2.431688747455 PaC*S 4295 12.0684 8150.9520 1.1693 2.9492 4.8368 280.3700
25.314826603796 1.906881571321 aaa+*S 26226 14.6787 8115.4232 1.0877 2.8059 4.8494 262.1776
25.096505329181 1.223578989569 aaP**S 26230 14.6789 8045.5606 0.7555 2.1410 4.3381 262.1816
24.847473291821 0.648899445308 PaE*C> 53265 15.7009 7966.8924 0.7792 2.1816 4.1277 245.5690
23.916536378552 -0.488488933522 aEE<S< 172138 17.3932 7670.6848 0.3403 1.3981 3.7562 221.9928
23.908324096405 0.488472995877 aEE<S~> 2194158 21.0652 7671.7289 0.3403 1.3980 3.7775 113.9158
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
44.62 27.57 asin(-0.010022900085+x0)
51.2 27.56 asin(-0.961183044491*(-x0))
52.21 24.57 0.483305784300*(x0*exp((x0*pi)))
55.63 24.03 asin(-1.089872144588+exp((exp(x0)-1)))
56.44 22.27 asin(3.821906620938*(x0*sin(x0)))
56.44 22.26 asin(-3.822425580895*(x0*(-sin(x0))))
61.4 22.2 asin(2.431688747455*sin((pi*cos(x0))))
62.22 22.11 asin(1.906881571321*sin((x0*(x0+x0))))
112.44 19.48 7.566913381123*((sqrt(((x0*(-x0))+1)))**(-1)-1)
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_sqrt/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
28.738098446376 -2.141592741013 P 1 0.0000 9196.1915 0.8221 2.1439 2.1958 320.0000
28.065692594348 0.531268660000 a 2 1.0000 8982.0216 0.5874 1.7129 2.2171 320.0000
27.585468655305 1.978654246837 aL 18 4.1699 8831.5199 0.4049 1.2709 2.1853 309.3889
27.467023328038 -0.597965631634 aE 20 4.3219 8793.7694 0.4112 1.2828 2.2351 310.4500
26.559836917669 0.062537320000 aa+ 24 4.5850 8503.7328 0.3728 1.2818 2.3986 312.0417
24.997574724938 -1.025923306755 aaE+ 234 7.8704 8007.0943 0.1940 0.8110 2.6158 229.1154
24.997574724938 -0.025923306755 aaE<+ 2288 11.1599 8010.3838 0.1940 0.8110 2.6158 94.1967
24.957866538337 -1.016707988494 aaSE+ 2528 11.3038 7997.8211 0.2834 1.0724 3.0364 94.5882
23.800570961124 0.080223065287 aaRE* 2848 11.4757 7627.6584 0.1713 0.7405 3.0984 98.2728
23.453891619356 0.029912879290 aa>ER* 32354 14.9817 7520.2270 0.1896 0.7877 3.3734 66.6213
23.300023213695 -1.548606424932 aP<\+E 49996 15.6095 7471.6170 0.1858 0.7701 3.7606 65.3299
22.982286159543 -0.935161437451 aEa>R* 84514 16.3669 7370.6985 0.1592 0.6897 3.8857 67.1272
22.804754282492 -1.901974002391 aaEE>R+ 388240 18.5666 7316.0880 0.1281 0.5833 3.3978 64.8586
22.799109853864 -0.009546314679 a>a~>/L 1243796 20.2463 7315.9615 0.0470 0.2115 2.6480 57.0977
22.402638035472 -1.194595566027 aSREaC/ 1944438 20.8909 7189.7351 0.0911 0.4418 3.3820 48.5022
22.182454953246 0.003210645227 a\E<RL\ 2612594 21.3171 7119.7026 0.0628 0.3328 3.3019 47.8797
21.777597649288 0.007612934622 aPaL\-R* 3397844 21.6962 6990.5274 0.0160 0.0593 2.6062 46.3921
20.733325935993 0.001813948452 aaCR\CS/ 6113758 22.5436 6657.2079 0.0096 0.0779 2.0026 38.1041
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_sqrt/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
3.1438830732389271 3.1438832225653603E-003
0 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
28.738098446376 0.318309877326 P 1 0.0000 9196.1915 0.8221 2.1439 2.1958 320.0000
25.965879632919 2.133418260447 a 2 1.0000 8310.0815 0.3477 1.2243 2.5891 320.0000
24.753686319123 1.740444227454 aE< 72 6.1699 7927.3495 0.1280 0.6046 2.3497 164.3750
22.975242533949 1.918879523407 aaC/ 334 8.3837 7360.4613 0.0680 0.3672 2.5355 113.9281
22.969206886973 -1.919196298770 aaC~/ 3288 11.6830 7361.8292 0.0679 0.3667 2.5710 51.1390
22.722055514207 1.935616537864 aaSC/ 3428 11.7432 7282.8009 0.1572 0.6864 3.9281 52.0216
22.668628336387 -1.936880827830 aaC<<* 31154 14.9271 7268.8882 0.1760 0.7421 4.0817 68.9273
22.456647307855 1.781715944838 aa<EC/ 38838 15.2452 7201.3723 0.1266 0.5498 4.1727 74.9299
21.776344574797 3.884415195466 aC\<a/ 150174 17.1963 6985.6265 0.1139 0.5180 4.0375 71.8415
21.587424040880 0.524415095951 aaC\E>* 405224 18.6284 6926.6041 0.0630 0.3156 3.4464 63.3260
21.058787235728 0.590910184167 aaCS\E* 427004 18.7039 6757.5158 0.0279 0.1844 2.8509 63.0403
20.816805500032 38.925091223055 aPEaEE-/ 4391236 22.0662 6683.4440 0.0114 0.0844 2.3452 31.3823
20.807216714659 -1.682112949762 aaEP-E</ 4667970 22.1544 6680.4637 0.0114 0.0844 2.3772 30.8659
20.807216714659 -38.925262147020 aaEEPE-/ 4969218 22.2446 6680.5539 0.0114 0.0844 2.3772 30.2862
20.262353970432 1.375649801528 aaCSSL>/ 5986138 22.5132 6506.4665 0.0086 0.0677 2.9123 28.5857
20.191986477694 1.002559685536 aaCR\CS/ 6113758 22.5436 6483.9793 0.0083 0.0719 2.1339 28.6572
19.791806772756 2.826791564328 aaCS\CE/ 6192526 22.5621 6355.9403 0.0323 0.2023 3.2836 28.5117
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
44.62 27.57 asin(-0.010022900085+x0)
51.2 27.56 asin(-0.961183044491*(-x0))
51.93 26.85 (0.531268660000+x0)**2
52.21 24.57 0.483305784300*(x0*exp((x0*pi)))
55.63 24.03 asin(-1.089872144588+exp((exp(x0)-1)))
56.44 22.27 asin(3.821906620938*(x0*sin(x0)))
56.44 22.26 asin(-3.822425580895*(x0*(-sin(x0))))
61.4 22.2 asin(2.431688747455*sin((pi*cos(x0))))
62.22 22.11 asin(1.906881571321*sin((x0*(x0+x0))))
112.44 19.48 7.566913381123*((sqrt(((x0*(-x0))+1)))**(-1)-1)
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_squared/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
30.992152946741 -2.141592741013 P 1 0.0000 9917.4889 20.8367 96.6935 3.0228 320.0000
30.765214689338 0.531268660000 a 2 1.0000 9845.8687 20.6720 96.2624 3.1126 320.0000
30.511244063517 2.185140510418 aL 18 4.1699 9767.7680 20.3923 95.6140 3.2641 320.0000
30.422057928595 0.062537320000 aa+ 24 4.5850 9739.6435 20.5090 95.8314 3.2827 320.0000
30.072878307728 -0.256674899114 aP* 26 4.7004 9628.0215 20.2315 95.1235 3.5978 320.0000
29.932598919599 -3.040289718441 a>E 182 7.5078 9585.9394 19.8542 94.0495 3.5849 298.6209
29.853534080643 -3.218108612304 aEE 198 7.6294 9560.7603 18.2728 89.2183 3.5417 297.4495
29.787697721814 -1.250536692692 aa+E 474 8.8887 9540.9520 19.4817 92.8973 3.6539 304.2869
28.403291513430 1.004972058688 aEEC 1764 10.7846 9099.8379 20.9393 96.0461 5.1067 289.1729
28.403291513430 0.004972058688 aEEC> 11254 13.4581 9102.5114 20.9393 96.0461 5.1067 285.7869
27.973876700955 1.005556630033 aR<\S 17924 14.1296 8965.7701 20.8124 97.2437 5.4801 271.2573
27.740898603397 0.849382755567 aEECS 18544 14.1787 8891.2662 20.9921 96.2449 5.6344 271.1540
27.740898603397 -2.292209985446 PaEECS+ 393099 18.5845 8895.6721 20.9921 96.2449 5.6344 251.9250
27.424501663419 -1.147183216738 Pa>ECE* 428059 18.7075 8794.5480 18.2941 90.9525 5.2805 250.5730
26.765442050671 -15.155442993896 aa*C\EE 1006100 19.9403 8584.8818 8.1420 41.9173 4.8639 223.6102
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_squared/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
97.693471383423457 9.7693476023614362E-002
87 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
31.055036080815 0.356946102026 P 1 0.0000 7235.8234 21.0303 96.5721 3.2261 233.0000
30.432389039759 2.336180655014 a 2 1.0000 7091.7466 20.6524 95.5915 3.4900 233.0000
29.743621994632 4.866988480450 aa* 28 4.8074 6935.0713 20.0053 93.7533 3.8781 226.8214
29.429091568992 0.023515144190 a>C 146 7.1898 6864.1682 21.5433 97.7011 4.9480 212.3836
29.425600018198 -0.000647690691 aa<+ 206 7.6865 6863.8513 21.5408 97.6940 5.0060 209.5534
28.922547525119 61.541774347972 aaS- 294 8.1997 6747.1532 18.9366 90.5188 4.3816 214.4048
28.915988354101 11.756767435847 a\E\ 1268 10.3083 6747.7336 19.9478 93.8244 4.9194 211.5536
28.907664339925 10.139445687984 aaa** 2136 11.0607 6746.5465 18.8734 90.3077 4.3855 200.2411
28.852062199968 -19.481350994352 aaCL* 2820 11.4615 6733.9920 18.5990 89.3650 4.3976 202.7780
28.363006275571 28.330128598388 aa\E/ 3492 11.7698 6620.3503 18.3721 89.3047 5.1963 203.3044
27.553818511172 -42.434610524440 aa*C< 5184 12.3399 6432.3796 17.0665 84.5307 5.2579 205.6339
27.478148179497 -41.871418228121 aa*CL 6048 12.5622 6414.9708 16.4532 82.1450 5.2555 202.7250
27.266244970648 -156.145089297315 aCLC< 12690 13.6314 6366.6665 15.9398 80.3971 5.3387 203.6121
27.239498688235 -155.583726122185 aCLCL 21438 14.3879 6361.1911 15.7015 79.4278 5.3362 190.6996
26.297406760656 0.009225376162 aPP**E 26612 14.6998 6141.9956 4.3307 31.3743 3.4721 192.8807
26.297406760652 0.009225376162 PaP**E 26613 14.6998 6141.9956 4.3307 31.3743 3.4721 192.8822
26.107200266739 0.000049626935 aRREEE 269420 18.0395 6101.0172 4.0290 29.6735 3.4696 106.6130
26.093816102562 -26.211037730706 aaE<*C< 616408 19.2335 6099.0927 15.1754 78.1710 6.2612 102.2892
25.713841478483 -25.818696701757 aaE<*CL 686392 19.3887 6010.7137 11.8171 62.4307 6.2396 109.3511
25.138949659828 0.000000004863 PEaRR*E 1251011 20.2547 5877.6299 12.4763 67.8514 5.9917 137.8876
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
44.62 27.57 asin(-0.010022900085+x0)
51.2 27.56 asin(-0.961183044491*(-x0))
51.93 26.85 (0.531268660000+x0)**2
52.21 24.57 0.483305784300*(x0*exp((x0*pi)))
55.63 24.03 asin(-1.089872144588+exp((exp(x0)-1)))
56.44 22.27 asin(3.821906620938*(x0*sin(x0)))
56.44 22.26 asin(-3.822425580895*(x0*(-sin(x0))))
61.4 22.2 asin(2.431688747455*sin((pi*cos(x0))))
62.22 22.11 asin(1.906881571321*sin((x0*(x0+x0))))
112.44 19.48 7.566913381123*((sqrt(((x0*(-x0))+1)))**(-1)-1)
Checking for brute force +
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_tan/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Shuffling mystery data..
Searching for best fit...
29.013487161757 -2.925977602410 P 1 0.0000 9284.3159 5.2545 44.8645 2.9065 320.0000
28.247700539552 -0.046622486198 a 2 1.0000 9040.2642 5.2764 45.3906 3.7425 320.0000
28.103206079656 -1.066014957760 aE 20 4.3219 8997.3479 5.3066 45.7825 4.0509 316.8500
28.098580529817 -1.062302036244 aSE 192 7.5850 8999.1307 5.2922 45.6189 3.9604 296.4271
28.048819745700 -0.080273931874 aa>* 238 7.8948 8983.5171 5.3250 45.9783 4.1620 299.1134
27.521905810910 1.094196573790 aEEC 1764 10.7846 8817.7945 5.3398 44.8231 4.0219 286.9819
27.512356661454 -8.523965476914 PaC-E 4763 12.2177 8816.1718 5.5681 47.5584 4.9908 281.7445
27.280920376952 -5.569693814117 aCCEE 23202 14.5020 8744.3965 5.5744 47.5928 5.3786 263.5105
27.140183501103 -4.810261503522 PaC/ER 58801 15.8436 8700.7023 6.0101 49.1193 5.9486 268.5404
26.057783561723 0.956911707308 PRa</S 99445 16.6016 8355.0924 5.3474 44.7374 5.9159 271.6848
Checking for brute force *
Trying to solve mysteries with brute force...
Trying to solve results/mystery_world_tan/kinetic.txt_train-mult_b
Rejection threshold..... 10.000
Bit margin.............. 0.000
Number of variables..... 1
Functions used.......... +*-/><~\RPSCLE
Arity 0 : Pa
Arity 1 : ><~\RSCLE
Arity 2 : +*-/
Loading mystery data....
320 rows read from file mystery.dat
Number of examples...... 320
Removing problematically
44.648872018778576 4.4648874139486198E-002
19 out of 320 data points discarded for being too close to zero
Shuffling mystery data..
Searching for best fit...
29.032449915152 0.071225094270 P 1 0.0000 8738.7674 5.3793 44.8726 2.9482 301.0000
28.583037808708 0.803643539211 a 2 1.0000 8604.4944 5.3947 45.2824 3.4312 301.0000
27.524134687912 3.859495760479 aa* 28 4.8074 8289.5719 5.5951 47.0473 5.2392 301.0000
27.479877139811 -7.686159285443 aCL 176 7.4594 8278.9025 5.6489 47.3351 5.3675 276.3466
27.370047834285 7.639187896357 aC\< 860 9.7482 8248.1326 5.7593 47.8447 5.6617 280.6698
26.763864288451 3.560063100434 aaE<* 2612 11.3509 8067.2741 5.7907 48.0157 6.3450 264.7094
26.666958993220 3.579015683404 aaSE<* 31402 14.9386 8041.6932 5.6895 47.5613 6.4682 253.8516
26.576654324249 3.581259442276 aaE<S* 32458 14.9863 8014.5592 5.6312 47.2798 6.5599 253.6116
26.495188691987 4.187388282319 aaaES** 274196 18.0648 7993.1166 5.5409 46.7532 6.5292 236.7545
26.421239196983 -25.441704609774 aaCC*C< 616580 19.2339 7972.0269 6.0723 49.0978 6.9160 241.9467
Checking polyfit
Pareto frontier in the current branch:
Complexity # MDL Loss # Expression
44.62 27.57 asin(-0.010022900085+x0)
51.2 27.56 asin(-0.961183044491*(-x0))
51.93 26.85 (0.531268660000+x0)**2
52.21 24.57 0.483305784300*(x0*exp((x0*pi)))
55.63 24.03 asin(-1.089872144588+exp((exp(x0)-1)))
56.44 22.27 asin(3.821906620938*(x0*sin(x0)))
56.44 22.26 asin(-3.822425580895*(x0*(-sin(x0))))
61.4 22.2 asin(2.431688747455*sin((pi*cos(x0))))
62.22 22.11 asin(1.906881571321*sin((x0*(x0+x0))))
112.44 19.48 7.566913381123*((sqrt(((x0*(-x0))+1)))**(-1)-1)
Just one variable!
Checking for symmetries...
kinetic.txt_train-mult_b just one variable for ADD
kinetic.txt_train-mult_b just one variable for ADD
kinetic.txt_train-mult_b just one variable for ADD
kinetic.txt_train-mult_b just one variable for ADD
Checking for separabilities...
kinetic.txt_train-mult_b just one variable for ADD
kinetic.txt_train-mult_b just one variable for ADD
Checking for compositionality...
Checking for generalized symmetry...
run_aifeynman termine en 2118.3 sLecture des résultats. Le fichier liste les candidates du front de Pareto, complexité croissante. Les colonnes : erreur sur le jeu de test, log₂ de l’erreur d’entraînement, la même multipliée par N, complexité en bits, erreur d’entraînement, puis l’expression SymPy (x0 = m, x1 = v). L’échelle d’erreur du paquet est log₂(1+|e|·2³⁰) : 25 bits ≈ 3 % d’erreur absolue, 20 bits ≈ 0,1 %. Deux mises en garde de lecture : les constantes numériques approximatives portent l’essentiel des bits (chaque réel non « snappé » coûte ~log(r/ε) ; l’étape snap du paquet tente de raccrocher les constantes aux rationnels, parfois sans succès — comparer aux 13,6 bits de mv²/2 dans l’encodage propre du papier), et la tête du front contient une formule dégénérée à ~0 bit (artifact du filtre NaN du solveur) que l’œil écarte immédiatement. Pendant la recherche, chaque candidate est en outre testée point par point dans un ordre aléatoire et rejetée statistiquement dès que z = √m·(d̄−d*)/σ dépasse ν = 10 « sigmas » (Eq. 4 du papier) — la quasi-totalité des candidates meurt après une poignée de points (exercice 1). Les familles attendues sur ce cas, hiérarchie de la figure 1 du papier : l’approximation classique v² (la famille mv²/2), des formules séparées x0×h(x1) produites par le module de séparabilité du paquet, la forme intermédiaire mc²(1/cos(v/c) − 1) — développement d’ordre 4 que la base d’opérations favorise — et, au bout du front si le budget le permet, la forme relativiste exacte.
import sympy as sp
sol_path = os.path.join(RUN_DIR, "results", "solution_kinetic.txt")
rows = []
with open(sol_path) as f:
for line in f:
parts = line.split()
rows.append({
"erreur_test": float(parts[0]),
"log2_erreur": float(parts[1]),
"complexite_bits": float(parts[3]),
"erreur_paquet": float(parts[4]),
"formule": " ".join(parts[5:]),
})
sol = pd.DataFrame(rows).sort_values("complexite_bits").reset_index(drop=True)
print(f"Front de Pareto : {len(sol)} candidates, "
f"{sol['complexite_bits'].min():.1f} a {sol['complexite_bits'].max():.1f} bits\n")
print("--- tete du front (les moins couteuses) ---")
for _, row in sol.head(6).iterrows():
try:
expr = sp.nsimplify(sp.sympify(row["formule"]), rational=False)
except Exception:
expr = row["formule"]
print(f"{row['complexite_bits']:7.1f} bits | err test {row['erreur_test']:8.4f} | {expr}")
print("--- bout du front (les plus precises) ---")
for _, row in sol.tail(4).iterrows():
try:
expr = sp.nsimplify(sp.sympify(row["formule"]), rational=False)
except Exception:
expr = row["formule"]
print(f"{row['complexite_bits']:7.1f} bits | err test {row['erreur_test']:8.4f} | {expr}")Front de Pareto : 25 candidates, 0.0 a 163.5 bits
--- tete du front (les moins couteuses) ---
0.0 bits | err test 26.9378 | 0
46.2 bits | err test 26.4084 | x1 - 104561/500000
46.4 bits | err test 25.2659 | x1**2 - 2807507429/250000000000
47.7 bits | err test 25.2298 | x1*sin(x1) - 2172970393/250000000000
49.8 bits | err test 25.3471 | asin(x1**2 - 13163168761/1000000000000)
49.9 bits | err test 25.2621 | tan(x1**2 - 6941804681/500000000000)
--- bout du front (les plus precises) ---
109.7 bits | err test 19.7366 | 66039915469*x0*asin(1906881571321*sin(2*x1**2)/1000000000000)/500000000000
119.3 bits | err test 19.7400 | (x0/(2 + pi**(3/2)) - 65453019/1000000000000)*asin(1906881571321*sin(2*x1**2)/1000000000000)
123.6 bits | err test 19.7372 | (x0*exp(-sqrt(-1 + sqrt(pi)))/pi - 12174789/100000000000)*asin(1906881571321*sin(2*x1**2)/1000000000000)
163.5 bits | err test 16.1656 | 66039915469*x0*(-7566913381123/1000000000000 + 7566913381123/(1000000000000*sqrt(1 - x1**2)))/500000000000La force d’AI Feynman 2.0 n’est pas la brute force, mais ce qu’elle sait déduire de la forme de la fonction avant même de chercher une formule. La méthode se joue en deux temps : (1) entraîner un réseau fNN à interpoler la table ; (2) faire des expériences numériques sur fNN — qui est lisse et différentiable, contrairement à la table. La table 1 du papier catalogue ces tests (positivité, séparabilités, symétries, compositionnalité, « snaps » des constantes vers 0 ou les rationnels…).
Nous implémentons le test de séparabilité : f(x₁,x₂) est-elle de la forme g(x₁)·h(x₂) ? L’astuce : si c’est le cas, log|f| = log g(x₁) + log h(x₂) est additivement séparable, ce qui se détecte par les dérivées croisées. Le score du papier (Eq. 6, Supp B) :
S[f] = |f_xy|² / (|f_xx · f_yy| + |f_xy|²)
vaut 0 si et seulement si f est additivement séparable ; le seuil de décision est S* = 0,1. Ces tests passent par des dérivées secondes — c’est pourquoi le réseau utilise des activations tanh : avec ReLU (linéaire par morceaux), f_xx est nul partout sauf aux points de rupture, et le test est aveugle.
# Etape 1 : le reseau du papier (128/128/64/64, tanh), 2000 epochs Adam.
# Le reseau est caste explicitement en float64 (autograd fin sur les derivees
# secondes) sans toucher au dtype par defaut -- le NN interne d'aifeynman,
# lui, exige float32.
X = torch.tensor(data[["m", "v"]].values, dtype=torch.float64)
Y = torch.tensor(data["E"].values, dtype=torch.float64).unsqueeze(1)
net = torch.nn.Sequential(
torch.nn.Linear(2, 128), torch.nn.Tanh(),
torch.nn.Linear(128, 128), torch.nn.Tanh(),
torch.nn.Linear(128, 64), torch.nn.Tanh(),
torch.nn.Linear(64, 64), torch.nn.Tanh(),
torch.nn.Linear(64, 1),
).double()
opt = torch.optim.Adam(net.parameters(), lr=1e-2)
sched = torch.optim.lr_scheduler.StepLR(opt, step_size=1500, gamma=0.3)
for epoch in range(4000):
opt.zero_grad()
loss = torch.nn.functional.mse_loss(net(X), Y)
loss.backward()
opt.step()
sched.step()
print(f"MSE finale du reseau : {loss.item():.3e}")
# Etape 2 : score S[f] (Eq. 6) sur une grille, par autograd.
def score_S(f_vals):
g1 = torch.autograd.grad(f_vals.sum(), pts, create_graph=True)[0]
f_xx = torch.autograd.grad(g1[:, 0].sum(), pts, create_graph=True)[0][:, 0]
f_xy = torch.autograd.grad(g1[:, 0].sum(), pts, create_graph=True)[0][:, 1]
f_yy = torch.autograd.grad(g1[:, 1].sum(), pts, create_graph=True)[0][:, 1]
S_pt = f_xy**2 / (f_xx.abs() * f_yy.abs() + f_xy**2 + 1e-300)
return S_pt.median().item()
mg, vg = torch.meshgrid(
torch.linspace(0.6, 1.8, 30, dtype=torch.float64),
torch.linspace(0.1, 0.85, 30, dtype=torch.float64),
indexing="ij",
)
pts = torch.stack([mg.reshape(-1), vg.reshape(-1)], dim=1).requires_grad_(True)
E_net = net(pts).squeeze()
S_E = score_S(E_net)
S_logE = score_S(torch.log(E_net.abs() + 1e-12))
print(f"S[E] = {S_E:.4f} (additivement separable si < 0.1)")
print(f"S[log|E|] = {S_logE:.4f} (multiplicativement separable si < 0.1)")MSE finale du reseau : 8.691e-07
S[E] = 0.8687 (additivement separable si < 0.1)
S[log|E|] = 0.0238 (multiplicativement separable si < 0.1)Lecture du test. S[E] reste très au-dessus du seuil (l’énergie n’est pas une somme g(m)+h(v)) ; S[log|E|] chute d’un ordre de grandeur : c’est la signature de la séparabilité multiplicative — le score discrimine la structure sans chercher aucune formule. Franchir ou non le seuil S* = 0,1 dépend de la convergence du réseau : les dérivées secondes d’un NN insuffisamment convergé sont bruitées, et le verdict borné assume la valeur mesurée. Le run de la section 2 tranche d’ailleurs la question par une deuxième voie : le module de séparabilité du paquet a produit des formules de la famille x0 × h(x1) sur le front — la structure est confirmée. Une fois détectée, la recherche se scinde en deux régressions 1D — g est linéaire (l’énergie est proportionnelle à la masse), h(v) = 1/√(1−v²) − 1 se traite seule. C’est ce diviser pour régner qui fait la différence d’échelle : les 17 équations qui résistaient à AI Feynman 1.0 sont toutes résolues par la version 2.0 en moins de 2 h (table 4 du papier).
La récursion peut s’imbriquer. L’exemple le plus spectaculaire (Supp C) : l’addition relativiste de vitesses v₁₂ = (v₁+v₂)/(1+v₁v₂/c²) se fait détecter une première fois (les gradients unitaires en v₁ deviennent indépendants de v₂ — le « smoking gun » de la symétrie généralisée, Eq. 5 du papier), la formule intermédiaire v₁₂ est calculée, puis le test se re-déclenche sur (v₁₂, v₃) — en principe jusqu’à un nombre arbitraire de vitesses. C’est l’objet de l’exercice 2.
La deuxième idée tient en une colonne : quand on mesure l’erreur d’une formule sur des données, quel coût choisit-on pour un résidu ? La MSE pénalise quadratiquement — trois points aberrants peuvent tirer un fit entier. Le papier le montre sur un cas d’école (figure 4) : ajuster y = a·x³·e^(x/b) − 1 sur des données propres à vrais paramètres a = b = 1, puis y ajouter des outliers —
L’idée : encoder chaque résidu en bits coûte ~log(|r|/ε) — une erreur cent fois plus grosse ne coûte que log(100) ≈ 6,6 bits de plus, pas dix mille fois plus de perte. Les queues lourdes deviennent presque gratuites à ignorer. C’est la même philosophie que le MDL des formules de la section 1 : tout est bits — la complexité de la formule comme le coût de ses résidus.
# Figure 4 du papier : cible y = a x^3 e^(x/b) - 1, vrais a = b = 1, 3 outliers.
xo = np.sort(np.random.uniform(0.5, 3.0, 60))
yo = xo**3 * np.exp(xo) - 1.0 + np.random.normal(0.0, 0.05, 60)
yo[[7, 23, 41]] += np.array([6.0, -8.0, 9.0])
def fit(loss_kind, steps=5000):
a = torch.tensor(0.5, dtype=torch.float64, requires_grad=True)
b = torch.tensor(0.5, dtype=torch.float64, requires_grad=True)
xt, yt = torch.tensor(xo), torch.tensor(yo)
opt = torch.optim.Adam([a, b], lr=0.01)
for _ in range(steps):
opt.zero_grad()
r = yt - (a * xt**3 * torch.exp(xt / b) - 1)
if loss_kind == "mse":
loss = (r**2).mean()
else: # MEDL : longueur de description moyenne des residus
loss = torch.log(r.abs() + 1e-12).mean()
loss.backward()
opt.step()
return a.item(), b.item()
a_mse, b_mse = fit("mse")
a_mdl, b_mdl = fit("medl")
print(f"MSE : a = {a_mse:.3f}, b = {b_mse:.3f} (tire vers les outliers)")
print(f"MEDL : a = {a_mdl:.3f}, b = {b_mdl:.3f} (vrais parametres : a = b = 1)")
fig, ax = plt.subplots(figsize=(7, 4))
xs = np.linspace(0.4, 3.1, 200)
ax.scatter(xo, yo, s=14, color="0.6", label="donnees (3 outliers)")
ax.plot(xs, xs**3 * np.exp(xs) - 1, "k--", lw=2, label="vraie loi (a=b=1)")
ax.plot(xs, a_mse * xs**3 * np.exp(xs / b_mse) - 1, color="crimson",
label=f"fit MSE (a={a_mse:.2f}, b={b_mse:.2f})")
ax.plot(xs, a_mdl * xs**3 * np.exp(xs / b_mdl) - 1, color="seagreen", ls=":",
label=f"fit MEDL (a={a_mdl:.2f}, b={b_mdl:.2f})")
ax.set_xlabel("x"), ax.set_ylabel("y"), ax.legend(fontsize=9)
fig.tight_layout()
plt.show()MSE : a = 0.466, b = 0.787 (tire vers les outliers)
MEDL : a = 0.562, b = 1.204 (vrais parametres : a = b = 1)
Lecture du fit robuste. Le fit MSE dévie sur les deux paramètres vers le bas (a et b tirés par les trois outliers), le fit MEDL récupère b au voisinage de 1 et reste plus proche de la vraie loi en moyenne — les résidus des outliers coûtent quelques bits, la déformation de la courbe sur les 57 points sains en coûterait bien davantage. La différence avec la figure 4 du papier (a = b = 1 retrouvés exactement) tient à notre optimiseur volontairement simple : la loss log est plate près de l’optimum, et Adam sans décroissance de pas s’arrête avant — le papier optimise le même critère avec un agenda dédié. C’est la version « données » du rasoir d’Occam appliqué aux formules en section 1 : minimiser la description totale, pas la distance quadratique.
Dernière subtilité, la plus philosophique (Supp C du papier). Sur l’orbitale de l’hydrogène n=2, l=1, m=0, le code retourne cos(cos θ) plutôt que cos²θ : les deux formules diffèrent de moins de 2×10⁻² sur le domaine, mais en notation polonaise inverse « x cos cos » (3 symboles) est plus court que « x cos x cos * » (5 symboles). La physique est identique ; la description ne l’est pas.
De même, tanh n’est pas dans la base d’opérations — donc jamais découverte, bien que tanh(x) = (e²ˣ−1)/(e²ˣ+1) s’écrive avec les briques disponibles (exp, ×, −). Et les développements de Taylor ne sont pas favorisés : la formule intermédiaire mc²(1/cos(v/c) − 1) du front de Pareto est un développement d’ordre 4, plus court à décrire que la racine carrée exacte. Comptons nous-mêmes, sur un mini-langage RPN explicite, ce que coûtent des écritures équivalentes de la même mathématique :
# Compteur illustratif de tokens RPN sur une base {var, const, +, -, *, /, sqrt,
# exp, log, sin, cos} : chaque element empile/calcule coute 1 token.
FORMES = [
("cos^2(x), forme directe", "x cos x cos *"),
("(1 + cos(2x)) / 2", "x 2 * cos 1 + 2 /"),
("tanh(x) [si tanh est dans la base]", "x tanh"),
("tanh(x) = (e^2x - 1) / (e^2x + 1)", "x 2 * exp 1 - x 2 * exp 1 + /"),
]
tokens = pd.DataFrame(
[(nom, len(rpn.split()), rpn) for nom, rpn in FORMES],
columns=["ecriture", "tokens_rpn", "rpn"],
)
tokens| ecriture | tokens_rpn | rpn | |
|---|---|---|---|
| 0 | cos^2(x), forme directe | 5 | x cos x cos * |
| 1 | (1 + cos(2x)) / 2 | 8 | x 2 * cos 1 + 2 / |
| 2 | tanh(x) [si tanh est dans la base] | 2 | x tanh |
| 3 | tanh(x) = (e^2x - 1) / (e^2x + 1) | 13 | x 2 * exp 1 - x 2 * exp 1 + / |
Lecture. Même mathématique, coûts radicalement différents : cos²θ vaut deux fois son identité trigonométrique, et tanh « gratuit » coûte près de cinq fois son écriture en briques de base. La leçon dépasse la régression symbolique : une métrique de simplicité n’est jamais neutre — le choix de la base d’opérations biaise la classe des formules découvrables, exactement comme le choix des features biaise un modèle d’apprentissage classique. Quand on lit « l’algorithme a trouvé la formule la plus simple », il faut toujours demander : la plus simple dans quel langage ?
Ce notebook a exécuté le vrai outil aifeynman sur le cas d’école du papier (énergie cinétique relativiste) et ouvert ses trois idées structurantes : symétries lues dans les gradients d’un réseau, critère de description en bits (formule et résidus), front de Pareto complexité–précision. Le budget était volontairement borné (30 s de brute force, 500 epochs) : nous mesurons ce qu’un petit budget retrouve, et le tableau récapitulatif ci-dessous confronte chaque étape à sa référence dans le papier.
recap = pd.DataFrame({
"etape": [
"run_aifeynman (budget borne)",
"front de Pareto",
"separabilite S[E] / S[log|E|]",
"fit outliers MSE",
"fit outliers MEDL",
],
"resultat_mesure": [
f"{duree_run:.0f} s (30 s BF + 500 epochs NN)",
f"{len(sol)} candidates, de {sol['complexite_bits'].min():.1f} a "
f"{sol['complexite_bits'].max():.1f} bits",
f"{S_E:.3f} / {S_logE:.3f} -> E = g(m) * h(v) (signature multiplicative, facteur {S_E / max(S_logE, 1e-9):.0f})",
f"a = {a_mse:.3f}, b = {b_mse:.3f}",
f"a = {a_mdl:.3f}, b = {b_mdl:.3f}",
],
"reference_papier": [
"demo officielle : 10-30 min (BF 60 s)",
"fig. 1 : E exacte et mv2/2 cohabitent",
"eq. 6, seuil S* = 0.1",
"fig. 4 : a ~ 0.89, b ~ 1.056",
"fig. 4 : a = b = 1 retrouves",
],
})
recap| etape | resultat_mesure | reference_papier | |
|---|---|---|---|
| 0 | run_aifeynman (budget borne) | 2118 s (30 s BF + 500 epochs NN) | demo officielle : 10-30 min (BF 60 s) |
| 1 | front de Pareto | 25 candidates, de 0.0 a 163.5 bits | fig. 1 : E exacte et mv2/2 cohabitent |
| 2 | separabilite S[E] / S[log|E|] | 0.869 / 0.024 -> E = g(m) * h(v) (signature mu... | eq. 6, seuil S* = 0.1 |
| 3 | fit outliers MSE | a = 0.466, b = 0.787 | fig. 4 : a ~ 0.89, b ~ 1.056 |
| 4 | fit outliers MEDL | a = 0.562, b = 1.204 | fig. 4 : a = b = 1 retrouves |
Le papier ouvre aussi une perspective qui dépasse la physique : comprendre les formules qu’un réseau a apprises est un cas particulier d’interprétabilité — les auteurs citent explicitement la thèse qu’une IA puissante est plus sûre si l’on comprend comment elle fonctionne.
La brute force teste chaque candidate point par point, dans un ordre aléatoire, et la rejette dès que z = √m·(d̄ₖₘ − dₖ)/σₖ dépasse ν = 10 « sigmas » — la quasi-totalité des candidates meurent après une poignée de points. Implémentez ce test : simulez les résidus d’une mauvaise candidate (dérive systématique + bruit), tirez les points en ordre aléatoire, mettez à jour la moyenne et l’écart-type au fil de l’eau, et tracez z en fonction du nombre de points testés. En combien de points la candidate est-elle rejetée ? Indice : l’approximation σₖ ≈ σₖ vient de la CLT ; le seuil ν = 10 est très conservateur — pourquoi ce choix rend-il le test quasi immunisé aux faux positifs ?*
# Exercice 1 (Eq. 4) : le rejet statistique anticipe
# TODO etudiant : implementez le test de rejet et tracez z en fonction du nombre de points testes.
# Etape 1 : simulez les residus d'une mauvaise candidate (derive systematique + bruit gaussien).
# Etape 2 : tirez les points en ordre aleatoire, mettez a jour moyenne et ecart-type au fil de l'eau.
# Etape 3 : calculez z puis tracez z vs nombre de points testes et lisez le point de rejet.
# Indice : sigma_k ~ sigma_k* vient de la CLT ; nu = 10 sigmas est tres conservateur.
z_rejet = None # TODO etudiant : nombre de points au rejet
print("Exercice a completer : test de rejet statistique (Eq. 4)")Exercice a completer : test de rejet statistique (Eq. 4)Générez une table de l’addition relativiste de deux vitesses : v₁₂ = (v₁+v₂)/(1+v₁v₂/c²), avec c = 1, v₁, v₂ ∈ [0,1 ; 0,9]. Lancez run_aifeynman dessus avec le même budget borné que ce notebook. Le papier rapporte que la symétrie généralisée (Eq. 5 : les gradients unitaires en v₁ deviennent indépendants de v₂) se déclenche — la fonction se réécrit g(h(v₁,v₂)) et h = (v₁+v₂)/(1+v₁v₂) se cherche en 2D avant une récursion 1D. Reproduisez le test Eq. 5 à la manière de la section 3 : calculez V(x) = 1 − λ_min de la covariance des gradients unitaires échantillonnés en v₂ variés, et vérifiez qu’elle s’approche de 0 pour un sous-ensemble bien choisi. Puis réiterez sur (v₁₂, v₃) : en principe, l’addition relativiste d’un nombre arbitraire de vitesses se découvre par récursion.
# Exercice 2 (Supp C) : addition relativiste recursive
# TODO etudiant : generez la table v12 = (v1+v2)/(1+v1*v2) puis relancez run_aifeynman dessus.
# Etape 1 : v1, v2 dans [0.1, 0.9], c = 1, table 2D de v12.
# Etape 2 : run_aifeynman(donnees, ...) avec le meme budget borne que la section 2.
# Etape 3 : test Eq. 5 -- V(x) = 1 - lambda_min de la covariance des gradients unitaires, en v2 varies.
# Indice : la symetrie generalisee se declenche quand V(x) s'approche de 0 pour un sous-ensemble de v1.
V_min = None # TODO etudiant : V(x) minimal mesure
print("Exercice a completer : addition relativiste recursive et test Eq. 5")Exercice a completer : addition relativiste recursive et test Eq. 5Reprenez la génération de données de la section 1 et faites croître le bruit relatif par décades : 10⁻³, 10⁻²,5, 10⁻², 10⁻¹,5, 10⁻¹ (r de −3 à −1). À chaque niveau, relancez run_aifeynman (budget borné) et notez si la forme relativiste exacte apparaît encore sur le front de Pareto. Tracez la frontière. Comparez à la table 3 du papier : 73 équations sur 100 résolues à r = −1, un gain typique de 1 à 3 ordres de grandeur sur AI Feynman 1.0 — mais attention : ce compteur agrège les 100 équations, votre mesure porte sur une seule. Étape suivante : que se passe-t-il si le bruit est multiplicatif* plutôt qu’additif ?*
# Exercice 3 : jusqu'ou le bruit tolere-t-il la decouverte ?
# TODO etudiant : faites croitre le bruit relatif par decades et relevez l'apparition de la forme exacte.
# Etape 1 : r dans [-3, -2.5, -2, -1.5, -1] (bruit relatif 10^r), meme generation que la section 1.
# Etape 2 : run_aifeynman (budget borne) a chaque niveau ; notez la forme relativiste exacte sur le front.
# Etape 3 : tracez la frontiere bruit / decouverte et comparez a la table 3 du papier.
frontiere_bruit = None # TODO etudiant : r maximal ou la forme exacte reste decouverte
print("Exercice a completer : frontiere de bruit de la decouverte")Exercice a completer : frontiere de bruit de la decouverteSérie : ce notebook complète la série SymbolicLearning (SL-1 à SL-13) côté « découverte de structure » : là où SL-13 demandait si une structure TPR émerge d’un réseau, SL-14 montre comment lire délibérément la structure d’une fonction dans ses gradients pour la re-transformer en symboles.