/*

  Duelling cowboys. 

  See http://hakank.org/webppl/duelling_cowboys.wppl

  Here I try to recover the probability that A survives when A and B starts 
  with equal probability.

  The test of [0.3, 0.7] should return 0.24683544303797486


  * Here's a (not exactly correct) solution in generation 29:
    [program = A / (A + B) * ((2 / 2 - (B - 1 - A)) / 2),res = 0.24,count = 9]
    -->
               A (2 + A - B)
     Out[1]= -------------
               2 (A + B)


  * With approx = 0.05:
    [program = A / (B * (-1 / -9 + (B - A)) + A + B),res = 0.220949263502455,count = 1]

  * With stop_criteria=generations  num_gens=1800
    gen = 1098  (time: 81.569s)
    results_best = [[0.535431442166878,A * 7.999999999999988 / (3.700000000000002 * B * (A + 3.600000000000002))],[0.550399873633033,A * (2.800000000000001 / (0.0 + B)) / (4.799999999999999 + A)]

    gen = 559  (time: 40.918s)
    results_best = [[0.546472016516566,A / (1.8 * (B - A * A / (B - 8.399999999999986)))]]



  My JGAP SymbolicRegression program give a nice solution: http://hakank.org/jgap/duelling_cowboys.conf

    A / (A + (((B - A) * (B - (B - (B / (2.0 - B))))) + B)) [1]
    0.3 0.7    Result: 0.2468354430379747

    In[2]:= A / (A + (((B - A) * (B - (B - (B / (2.0 - B))))) + B)) // FullSimplify                  #          

             0.5 A (-2. + B)
    Out[2]= ------------------
            A (-1. + B) - 1. B


*/
import util.
data(duelling_cowboys,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-  
  Data = [ [[X,Y], Z] : [X,Y,Z] in  chunks_of([
                                  % a   b   prob(A survives)
                                  0.1,0.1,0.5,
                                  0.1,0.2,0.32142857142857095,
                                  0.1,0.3,0.22972972972972974,
                                  0.1,0.4,0.17391304347826053,
                                  0.1,0.5,0.13636363636363646,
                                  0.1,0.6,0.10937499999999976,
                                  0.1,0.7,0.08904109589041062,
                                  0.1,0.8,0.07317073170731696,
                                  0.1,0.9,0.0604395604395603,
                                  0.2,0.2,0.5,
                                  0.2,0.3,0.38636363636363663,
                                  0.2,0.4,0.3076923076923075,
                                  0.2,0.5,0.24999999999999978,
                                  0.2,0.6,0.20588235294117652,
                                  0.2,0.7,0.17105263157894735,
                                  0.2,0.8,0.1428571428571429,
                                  0.2,0.9,0.11956521739130402,
                                  0.3,0.3,0.5,
                                  0.3,0.4,0.4137931034482764,
                                  0.3,0.5,0.34615384615384626,
                                  0.3,0.6,0.29166666666666646,
                                  0.3,0.7,0.24683544303797486,
                                  0.3,0.8,0.20930232558139525,
                                  0.3,0.9,0.17741935483870974,
                                  0.4,0.4,0.5,
                                  0.4,0.5,0.4285714285714287,
                                  0.4,0.6,0.3684210526315791,
                                  0.4,0.7,0.3170731707317074,
                                  0.4,0.8,0.27272727272727276,
                                  0.4,0.9,0.2340425531914893,
                                  0.5,0.5,0.5,
                                  0.5,0.6,0.4374999999999997,
                                  0.5,0.7,0.38235294117647045,
                                  0.5,0.8,0.33333333333333326,
                                  0.5,0.9,0.2894736842105264,
                                  0.6,0.6,0.5,
                                  0.6,0.7,0.4431818181818181,
                                  0.6,0.8,0.39130434782608736,
                                  0.6,0.9,0.34375000000000006,
                                  0.7,0.7,0.5,
                                  0.7,0.8,0.4468085106382979,
                                  0.7,0.9,0.3969072164948454,
                                  0.8,0.8,0.5,
                                  0.8,0.9,0.44897959183673464,
                                  0.9,0.9,0.5
  ],3)],
  Vars = ['A','B'],
  Unknown = [0.3,0.7],  % expected answer: 0.3,0.7,0.24683544303797486,
  Ops = [+,*,/,-],
  % RandomFloats = [frand(0,10) : I in 1..10],
  RandomInts = [random(-10,10) : I in 1..10],  
  Constants = 0.0..0.1..10.0, % [0.5,1,2,3,4,5,6,7,8,9,10],
  Params = new_map([approx = 0.01,
                    % total_approx=1,
                    num_gens=1800,
                    init_size=500,
                    % show_only_improvements=false,
                    % mutate_rate=0.3,
                    % crossover_rate=0.8,
                    debug=false,
                    stop_criteria=generations,
                    % , stop_criteria=loops                    
                    % pick_from_pct=0.2,
                    show_best=10,
                    remove_dups=true
                    % , random_seed=1
                    % keep_programs_pct=0.1
                    ]),
  MaxSize = 31.