/* 
   http://answers.yahoo.com/question/index?qid=20090822191824AArEhO6
   1/1 3/2 7/5 17/12 41/29,?
   1., 1.500000000, 1.400000000, 1.416666667, 1.413793103,?

   It's related to continued fractions of sqrt(2).
   See  OEIS sequence https://oeis.org/A000129
   """
   Also denominators of continued fraction convergents to sqrt(2): 1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, 577/408, 1393/985, 3363/2378, 8119/5741, 19601/13860, 47321/33461, 114243/80782,
   """
  
   The next value should be 99/70 = 1.41428571428571428571

   * With approx 0.1 if finds a couple of constants, including 99/70:
     [program = 59 / 40,res = 1.475,count = 9]
     [program = 10 / 7,res = 1.428571428571429,count = 9]
     [program = 73 / 47 - A / 16,res = 1.464829420396185,count = 8]
     [program = 40 / 27,res = 1.481481481481481,count = 7]
     [program = 99 / 70,res = 1.414285714285714,count = 6]
     [program = 71 / 48,res = 1.479166666666667,count = 6]
     [program = 78 / (54 + A),res = 1.407591785936528,count = 5]
     [program = 49 / 33,res = 1.484848484848485,count = 5]
     [program = 76 / (99 * 14 / 26),res = 1.425685425685426,count = 3]
     [program = 64 / (45 - A),res = 1.468354430379747,count = 3]
     [program = 98 / 68,res = 1.441176470588235,count = 2]
     [program = 96 / 65,res = 1.476923076923077,count = 2]
     [program = (A + 80) / (54 + A),res = 1.469197261978842,count = 1]
     [program = 94 / (65 + A),res = 1.415368639667705,count = 1]
     [program = 80 / 56,res = 1.428571428571429,count = 1]

     resultMap = [1.428571428571429 = 2,1.484848484848485 = 1,1.481481481481481 = 1,1.479166666666667 = 1,1.476923076923077 = 1,1.475 = 1,1.469197261978842 = 1,1.468354430379747 = 1,1.464829420396185 = 1,1.441176470588235 = 1,1.425685425685426 = 1,1.415368639667705 = 1,1.414285714285714 = 1,1.407591785936528 = 1]


   * Approx 0.01
   [program = (2 + A) / (A / A + A),res = 1.414285714285714,count = 1]
   [program = (A + 2) / (1 + A),res = 1.414285714285714,count = 8]

   However, if we add sqrt as an allowed function, it's easier (but probably 
   considered cheating):
   [program = sqrt(82) / (A + 5),res = 1.411861123688092,count = 1]
   [program = (sqrt(A) + sqrt(35)) / (sqrt(13) + A),res = 1.415545451236626,count = 1]
   [program = sqrt(5 - A) * (A * 41 / (55 * A)),res = 1.411688373486107,count = 1]
   [program = (A + A + sqrt(A)) / (A + A),res = 1.420510723160162,count = 1]

   But it has hard time finding sqrt(2)=1.414213562373095, and that because the error
   is larger than 0.01, it's 0.1!

   If we add sqrt(2) as a constant:

   % Found the solution sqrt(2) immediate, but too large difference
   gen = 1  (time: 0.104s)
   results_best = [[0.1,sqrt(2),check = 1.414213562373095]]
   ...

   AllGood:
   [program = (sqrt(A) + (A + A)) / (A + A), res = 1.42051072316016236, count = 3]

   resultMap = [1.42051072316016236 = 1]

   * With approx 0.1 with sqrt/1 and sqrt(2) as constant:
  
     AllGood:
     [program = sqrt(2), res = 1.41421356237309515, count = 10]
     [program = 1.41421 - (A - 6) / 64, res = 1.48587304513171592, count = 9]
     [program = sqrt(3 - A / A), res = 1.41421356237309515, count = 9]
     [program = sqrt(85 / 41), res = 1.43985094079467735, count = 8]
     [program = 56 / (30 + 8), res = 1.47368421052631571, count = 6]
     [program = 26 / (A - (17 - 33)), res = 1.49306930693069284, count = 5]
     [program = A * 54 / A / (35 + A), res = 1.48295454545454541, count = 4]
     [program = 60 / 41, res = 1.46341463414634143, count = 4]
     [program = 59 / 42, res = 1.40476190476190466, count = 4]
     [program = 12 / sqrt(71), res = 1.42413798983262385, count = 3]
     [program = sqrt(61 / 31), res = 1.40276225194573545, count = 3]
     [program = 68 / 48, res = 1.41666666666666674, count = 2]
     [program = 60 / 42, res = 1.42857142857142860, count = 2]
     [program = 82 / 56, res = 1.46428571428571419, count = 1]
     [program = 78 / 53, res = 1.47169811320754707, count = 1]
     [program = 77 / (A * 54 / A), res = 1.42592592592592582, count = 1]
     [program = 96 / 66 - A / 75, res = 1.43569487983281086, count = 1]
     [program = (1.41421 / A + (A - A)) * A, res = 1.41421356237309537, count = 1]
     [program = sqrt(7) * (50 / 90), res = 1.46986183948032822, count = 1]

     resultMap = [1.41421356237309515 = 2,1.49306930693069284 = 1,1.48587304513171592 = 1,1.48295454545454541 = 1,1.47368421052631571 = 1,1.47169811320754707 = 1,1.46986183948032822 = 1,1.46428571428571419 = 1,1.46341463414634143 = 1,1.43985094079467735 = 1,1.43569487983281086 = 1,1.42857142857142860 = 1,1.42592592592592582 = 1,1.42413798983262385 = 1,1.41666666666666674 = 1,1.41421356237309537 = 1,1.40476190476190466 = 1,1.40276225194573545 = 1]


 
   * And just for fun, using force_constants to force a solution with Pi and E (approx 0.1):

     AllGood:
     [program = 3.14159 - sqrt(2.71828), res = 1.49287138288966492, count = 1]

     resultMap = [1.49287138288966492 = 1]

     AllGood:
     [program = 3.14159 / 2.71828 * sqrt(sqrt(2.71828)), res = 1.48398329189270739, count = 1]

     resultMap = [1.48398329189270739 = 1]


*/
data(sequence_5,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  make_seq([1/1, 3/2, 7/5, 17/12, 41/29],1,Data,Unknown,Vars),  
  Ops = [+,-,*,/],
  % Ops = [+,-,*,/,sqrt], 
  % Ops = [sqrt],
  Constants = 1..100,  
  % Constants = [sqrt(2), math.pi,math.e]++1..100,
  MaxSize = 5,
  Params = new_map([init_size=1000,
                    approx=0.01
                    % approx=0.1
                    % , force_constants=[math.pi,math.e]
                     ]).