/*
  Regression problem
#
  From John Koza's Lisp implementation
  ftp://cs.ucl.ac.uk/genetic/ftp.io.com/code/koza-book-gp-implementation.lisp

  The solutions should be:
     (* 0.5 x x)

  OK, that's an easy one.
  [program = X * X / 2,res = 0.5,count = 10]
  [program = X * X / (5 - 3),res = 0.5,count = 8]
  [program = X / 2 * X,res = 0.5,count = 8]
  [program = X / 2 * (X - 0),res = 0.5,count = 5]
  [program = X * 5 * (X / 10),res = 0.5,count = 3]

  Using ** tends to blow up. Here is a solution:
  [found_function = X ** 2 / (6 - 4),check = 0.5]

  Using the restricted pow2/1 (X**2), etc, does not blow up:
  AllGood:
  [program = X / 2 * X,res = 0.5,count = 7]
  [program = pow2(X) / 2,res = 0.5,count = 6]
  [program = pow2(X) / (4 - 2),res = 0.5,count = 4]
  [program = X * (X / 2),res = 0.5,count = 4]
  [program = X * X / (4 - 2),res = 0.5,count = 3]


  Cf http://hakank.org/jgap/regression_koza.conf
 
*/
data(regression_koza,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  Data = [
          [[0.0],0.0],
          [[0.1],0.0050000004],
          [[0.2],0.020000001],
          [[0.3],0.045],
          [[0.4],0.080000006],
          [[0.5],0.125],
          [[0.6],0.18],
          [[0.7],0.24499999],
          [[0.8],0.32000002],
          [[0.9],0.40499997]
          ],
  Vars = ['X'],
  Unknown = [1.0],
  println(data=Data),
  % Ops = [+,-,*,/],
  Ops = [+,-,*,/,pow2,pow3,pow4,pow5], % ** will probably blow up
  Constants = 0..10,
  MaxSize = 3,
  Params = new_map([approx=0.01]).