/*
  http://irclog.perlgeek.de/perl6/2013-01-03#i_6294536


  gen = 32698  (time: 3594.566s)
results_best = [[0.182101959989253,sqrt(5.968800669521466 - 5.661984475172117 + n) + (n * sqrt(1.079399115908611) - n)],[0.182101959989253,n * sqrt(1.079399115908611) - n + sqrt(5.968800669521466 - 5.661984475172117 + n)],[0.218272786988548,sqrt(n * sqrt(1.079399115908611)) + (n * sqrt(1.079399115908611) - n)],[0.218272786988548,n * sqrt(1.079399115908611) - n + sqrt(n * sqrt(1.079399115908611))],[0.371115726550596,sqrt(sqrt(n + pow2(n))) + (n * sqrt(1.079399115908611) - n)],[0.371115726550596,n * sqrt(1.079399115908611) - n + sqrt(sqrt(n + pow2(n)))],[0.621946714940211,sqrt(n * sqrt(1.079399115908611)) + n * pow4(5.36459189623808 - 8.232947158735687 - -3.29554488570222)],[0.621946714940211,n * pow4(5.36459189623808 - 8.232947158735687 - -3.29554488570222) + sqrt(n * sqrt(1.079399115908611))],[0.634055942207529,n * sqrt(1.079399115908611) - n + sqrt(n)],[7.290155435714471,1.079399115908611 * sqrt(n)]]
good = []

gen = 32699  (time: 3594.624s)
% error: OUT OF MEMORY
*** error(resource_error(out_of_memory),stack_heap)

picat symbolic_regression.pi symbolic_regression_carls_problem.pi  3594,80s user 163,16s system 99% cpu 1:02:38,01 total


  Cf carls_problem.conf
*/
import util.
data(carls_problem,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  Data = [ [[X],Y] : [X,Y] in chunks_of([
1,1.00000000000000000000,
2,1.50000000000000000000,
3,1.88888888888888883955,
4,2.21875000000000000000,
5,2.51040000000000018687,
6,2.77469135802469146768,
7,3.01813870071143819374,
8,3.24501800537109375000,
9,3.45831574488565562930,
10,3.66021567999999986043,
11,3.85237205073735911043,
12,4.03607367509895098578,
13,4.21234791295252009036,
14,4.38202942438351872312,
15,4.54580728514722842704,
16,4.70425824707267814517,
17,4.85787082080162679887,
18,5.00706309899289259135,
19,5.15219620095744801347,
20,5.29358458600090031609,
21,5.43150408335278367389,
22,5.56619822786014317728,
23,5.69788331894651811638,
24,5.82675250392258714527,
25,5.95297910624526060985 % ,
% 26,6.07671936268610313192,
% 27,6.19811469287891725344,
% 28,6.31729359534338552606,
% 29,6.43437324248885378353,
% 30,6.54946083103302445494,
% 31,6.66265473217578296783,
% 32,6.77404547666974110598,
% 33,6.88371660286463793454,
% 34,6.99174539032805153482,
% 35,7.09820349736623157355,
% 36,7.20315751739854803759,
% 37,7.30666946646435278012,
% 38,7.40879721200369889544,
% 39,7.50959485133421367209,
% 40,7.60911304685489486843,
% 41,7.70739932387502069133,
% 42,7.80449833603898834866,
% 43,7.90045210255500318652,
% 44,7.99530022080455893274,
% 45,8.08908005738541646679,
% 46,8.18182692020321411519,
% 47,8.27357421386018287990,
% 48,8.36435358028073494552,
% 49,8.45419502625294860820,
% 50,8.54312703934394868099,
% 51,8.63117669345875171416,
% 52,8.71836974515170837208,
% 53,8.80473072166183534648,
% 54,8.89028300152501849141,
% 55,8.97504888851411486428,
% 56,9.05904967956976570065,
% 57,9.14230572730834012418,
% 58,9.22483649762680713025,
% 59,9.30666062286680073612,
% 60,9.38779595094904806274,
% 61,9.46825959084544699351,
% 62,9.54806795471703040334,
% 63,9.62723679701174539503,
% 64,9.70578125078599995845,
% 65,9.78371586148722016674,
% 66,9.86105461841088448693,
% 67,9.93781098402495643995,
% 68,10.01399792133569022212,
% 69,10.08962791945232950752,
% 70,10.16471301749371569656,
% 71,10.23926482696606754530,
% 72,10.31329455273006878713,
% 73,10.38681301266425549557,
% 74,10.45983065612253071208,
% 75,10.53235758127492438518,
% 76,10.60440355141316537413,
% 77,10.67597801029550375063,
% 78,10.74709009659918201862,
% 79,10.81774865754314340904,
% 80,10.88796226173842462970,
% 81,10.95773921131913830607,
% 82,11.02708755340267643419,
% 83,11.09601509092385995814,
% 84,11.16452939288436319032,
% 85,11.23263780405560829934,
% 86,11.30034745417018271496,
% 87,11.36766526663443244161,
% 88,11.43459796679244355744,
% 89,11.50115208976917458017,
% 90,11.56733398791872780009,
% 91,11.63314983790185763723,
% 92,11.69860564741484232343,
% 93,11.76370726159063018201,
% 94,11.82846036909159259665,
% 95,11.89287050791163835584,
% 96,11.95694307090472818800,
% 97,12.02068331105520293534,
% 98,12.08409634650456432325,
% 99,12.14718716534838982568,
% 100,12.20996063021597421994
  ],2)],
  Unknown = [50],
  Vars = ['n'],
  Ops = [+,-,*,sqrt,pow2,pow3,pow4,pow_mod2],  
  Constants = [frand(-10,10) : _ in 1..10],
  MaxSize = 31,
  Params = new_map([init_size=1000,approx=0.1,mutation_rate=0.2,pick_from_pct=1]).