/*

  Logistic function
  Data from http://data.princeton.edu/eco572/relationalLogit.html

  The logistic formula is defined as:
     1.0/(1.0+exp(-x));

  * Approx 0.1 +,-,*,/,logistic
    [program = (logistic(A + 5.661984475172117) * logistic(6.803754343094191) / (A + 6.803754343094191) + A) / (A / (logistic(B) * B)),res = 0.824515619186605,count = 1]

  * Approx 0.01 +,-,*,/,exp (stopped manually)

    gen = 62548  (time: 11693.860s)
    results_best = [[0.034227830884697,B * B / (B + B) * exp(exp(5.661984475172117 * B + -6.048972614132321))]]

  * Without logistic/1 Approx 0.01 stop_criteria=generations num_gens=1800

    gen = 1338  (time: 84.975s)
    results_best = [[0.364607114474557,exp(lx / (5.36459189623808 - 1.079399115908611 + -3.29554488570222)) * (lx * (5.661984475172117 - 5.36459189623808))]]

    gen = 1451  (time: 93.364s)
    results_best = [[0.359547629962018,(1.079399115908611 + 5.661984475172117) / exp(5.661984475172117 / exp(lx))]]

    gen = 1799  (time: 120.853s)
    results_best = [[0.251078125668164,(lx + exp(-4.444505783936244)) / (lx * -2.112341463618139 - -3.29554488570222)]]


  Cf logit_formula.conf


*/
data(logit_formula,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  Data =  [
[[1,0.9641],0.8499],
[[5,0.9409],0.7691],
[[10,0.9366],0.7502],
[[15,0.9343],0.7362],
[[20,0.9227],0.7130],
[[25,0.9108],0.6826],
[[30,0.8981],0.6525],
[[35,0.8843],0.6223],
[[40,0.8655],0.5898],
[[45,0.8424],0.5534],
[[50,0.8045],0.5106],
[[55,0.7584],0.4590],
[[60,0.6967],0.3965],
[[65,0.6028],0.3221],
[[70,0.4770],0.2380],
[[75,0.3451],0.1521]

  ],
  Unknown = [30,0.8981], 
  Vars = ['age','lx'],
  % Ops = [+,-,*,/,logistic],
  Ops = [+,-,*,/,exp], % can we recover the formula?
  Constants = [frand(-10,10) : _ in 1..10],
  MaxSize = 11,
  Params = new_map([approx=0.01,
                    init_size=1000,
                    show_best=1,
                    stop_criteria=generations,
                    num_gens=1800
                    ]).