/*
  Binomial

  Here is implementation that might be found:
    binomial_fac(N,K) = factorial(N) // factorial(K) // factorial(N-K).
  
  With the binomial/2 function it's easy.

  AllGood:
  [program = binomial(I,J),res = 462,count = 10]

  resultMap = [462 = 1]


  Without binomial/2:
  Best so far:
  gen = 2467  (time: 20.289s)
  results_best = [[29,1 + J * (I - J),check = 11]]



*/
import util.
data(sorted,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  Data = [
[[0,0],1],
[[1,0],1],
[[1,1],1],
[[2,0],1],
[[2,1],2],
[[2,2],1],
[[3,0],1],
[[3,1],3],
[[3,2],3],
[[3,3],1],
[[4,0],1],
[[4,1],4],
[[4,2],6],
[[4,3],4],
[[4,4],1],
[[5,0],1],
[[5,1],5],
[[5,2],10],
[[5,3],10],
[[5,4],5],
[[5,5],1],
[[6,0],1],
[[6,1],6],
[[6,2],15],
[[6,3],20],
[[6,4],15],
[[6,5],6],
[[6,6],1],
[[7,0],1],
[[7,1],7],
[[7,2],21],
[[7,3],35],
[[7,4],35],
[[7,5],21],
[[7,6],7],
[[7,7],1],
[[8,0],1],
[[8,1],8],
[[8,2],28],
[[8,3],56],
[[8,4],70],
[[8,5],56],
[[8,6],28],
[[8,7],8],
[[8,8],1],
[[9,0],1],
[[9,1],9],
[[9,2],36],
[[9,3],84],
[[9,4],126],
[[9,5],126],
[[9,6],84],
[[9,7],36],
[[9,8],9],
[[9,9],1],
[[10,0],1],
[[10,1],10],
[[10,2],45],
[[10,3],120],
[[10,4],210],
[[10,5],252],
[[10,6],210],
[[10,7],120],
[[10,8],45],
[[10,9],10],
[[10,10],1]
  ],
  Vars = ['I','J'],
  Unknown = [11,5],
  Constants = [], % 1..10,
  % Ops = [+,-,*,div,binomial,factorial_restricted],
  Ops = [+,-,*,div,factorial_restricted],  
  MaxSize = 11,
  Params = new_map([
                    init_size=1000,
                    num_gens=1000
                   ]).