/*
  Test of exp 

  Can we recover 2*exp(x) without exp?
     
  * Let's start with no noise: 2*exp(A) approx 0.1

    Compare with the noise-free:
    Picat> X=2*exp(1)
    X = 5.43656365691809


  * A little harder problem: 2*exp(A)+frand()/10 - 0.5
    approx = 0.1

    [program = exp(x) - 1 + exp(x) + 1.069799168533553 / 2,res = 4.971463241184867,count = 1]
    [program = exp(x) * 2 - 8 / 17.973083014587445,res = 4.991453600201222,count = 1]


    Compare with the noise-free 
    Picat> X=2*exp(1) - 0.5
    X = 4.93656365691809

  * without exp: approx=0.1 stop_criteria=generations num_gens=1800
    gen = 1786  (time: 102.540s)
    results_best = [[5601176.18397971894592,(16.761058958601694 + x) * x * (x * ((x - -5.901666109404371) * x))]]

    gen = 1306  (time: 68.462s)
results_best = [[5137271.251957050524652,(x * (x / (9 / x)) - x) * (x * (x - 9 / cos(-3.990855116392883)) * x + x)]]

    adding pow_mod2 and sum_i
    gen = 1097  (time: 58.426s)
    results_best = [[2442900.649097330868244,pow_mod2(4,sum_i(5,x)) * sqrt(sum_i(10.79655345100749,x))]]

    gen = 1081  (time: 69.869s)
    results_best = [[254374.002386659121839,x / 1.069799168533553 * (sum_i(9,sum_i(10.79655345100749,x) * x) + x)]]


  Cf exp_formula_no_exp.conf

*/
import util.
data(eureqa_test,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  Data = [ [[A],B] : _ in 1..20, A = frand(-15,15), B=2*exp(A)+frand()/10],
  % Data = [ [[A],B] : _ in 1..20, A = frand(-15,15), B=2*exp(A)+frand()/10 - 0.5],  
  Ops = [+,/,-,*,sin,cos,sqrt,log,pow_mod2,sum_i],
  Constants = 0..10 ++ [frand(-20,20) : _ in 1..10],
  Vars = ['x'],
  Unknown = [1],
  MaxSize = 51,
  Params = new_map([
                    approx=0.1,
                    show_best=1,
                    stop_criteria=generations,
                    num_gens=1800
                   ]).