/*
  Pi

  Data from https://github.com/celinehocquette/magicpopper/blob/main/magicpopper/examples/magic-pi/exs.pl
  which has the following solution
  """
  f(A,B):- square(A,D),mult(D,3.142,B).
  """
  (MagicPopper recovers both the formula as well as the constant 3.142.)


  * Using math.pi as constant
    [program = X * (X * 3.141592653589793),res = 3.141592653589793,count = 9]
    [program = X * (3.141592653589793 * X),res = 3.141592653589793,count = 9]
  
  * Without math.pi as constant
    [program = (X / -2.112341463618139 + X) * 5.968800669521466 * X,res = 3.143120838715247,count = 1]
   
    Another run
    [program = X - (X * -7.30000000000001 / (2.899999999999983 / X) + X) + X * X / 1.599999999999982,res = 3.142241379310371,count = 1]

    [program = (X / -9.200000000000003 - X * 9.199999999999966) * X * ((3.099999999999983 - 2.899999999999983 + 2.499999999999982) / -8.000000000000007),res = 3.141684782608661,count = 1]

    This simplifies to 
                                   2
                 Out[1]= 3.14168 X


    This solution is a little strange:
    [program = (8.232947158735687 - (X / 8.232947158735687 + X / X + X)) / -4.444505783936244 + (-4.444505783936244 + (5.36459189623808 - (X - X))) + X * X * ((-3.29554488570222 + -3.29554488570222) / -2.112341463618139),res = 2.665297858597132,count = 1]

    This simplifies to
                                                                   2
      Out[2]= 0.920086 - 0.224997 (7.23295 - 1.12146 X) + 3.12028 X

   Using only integer 1..10 + Pi 
   (In general integer seems to be better than than using random floats for these
    kind of problem.)

   [program = (X + (X - X)) * (3.14159 * X),res = 3.14159,count = 7]
   [program = X * (3.14159 * X),res = 3.14159,count = 7]
   [program = X * X * 3.14159,res = 3.14159,count = 6]
   [program = 3.14159 * X * X,res = 3.14159,count = 6]



*/
import util.
data(puzzle2,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  Data = [ [[X], Y] : [X,Y] in  chunks_of([
                    3.974,49.621,
                    6.068,115.69,
                    7.524,177.87,
                    3.633,41.47,
                    6.478,131.852,
                    7.068,156.964,
                    6.98,153.079,
                    7.384,171.313,
                    4.068,51.996,
                    4.093,52.637
  ],2)],
  % Checking the data
  % foreach([[X],Y] in Data)
  %   Z = X*X*math.pi,
  %   Diff = Y-Z,
  %   println([x=X,y=Y,z=Z,diff=Diff])
  % end,
  
  Ops = [+,/,*,-,pow2,pow3,pow4],   
  Constants = [math.pi] ++ [frand(-10,10) : _ in 1..10],
  % Constants = [frand(0,10) : _ in 1..10], % without Pi
  % Constants = 1..10, % ++ [math.pi],  
  Unknown = [1],
  Vars = ['X'],
  MaxSize = 11,
  Params = new_map([
                    total_approx=0.15,
                    remove_dups=true
                    % stop_criteria=generations,
                    % num_gens=1800
                    ]).