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[(,3,4,6,),-,6,8]
[2,*,1,7,3,-,6,8]
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[3,4,6,*,1,-,6,8]
[1,7,3,*,2,-,6,8]
[9,+,3,3,7,-,6,8]
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[3,4,7,-,1,-,6,8]
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[3,5,2,-,6,-,6,8]
[3,5,3,-,7,-,6,8]
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[(,3,4,7,),-,6,9]
[1,*,3,4,7,-,6,9]
[3,4,7,*,1,-,6,9]
[9,+,3,3,8,-,6,9]
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[3,5,3,-,6,-,6,9]
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[3,5,6,-,9,-,6,9]
[(,3,4,8,),-,7,0]
[3,*,1,1,6,-,7,0]
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[1,*,3,4,8,-,7,0]
[2,9,*,1,2,-,7,0]
[1,2,*,2,9,-,7,0]
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[1,1,6,*,3,-,7,0]
[9,+,3,3,9,-,7,0]
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[3,5,5,-,7,-,7,0]
[3,5,6,-,8,-,7,0]
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[(,3,4,9,),-,7,1]
[1,*,3,4,9,-,7,1]
[3,4,9,*,1,-,7,1]
[9,+,3,4,0,-,7,1]
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[6,+,3,4,3,-,7,1]
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[3,5,5,-,6,-,7,1]
[3,5,6,-,7,-,7,1]
[3,5,7,-,8,-,7,1]
[3,5,8,-,9,-,7,1]
[(,3,5,0,),-,7,2]
[2,*,1,7,5,-,7,2]
[1,*,3,5,0,-,7,2]
[3,5,*,1,0,-,7,2]
[2,5,*,1,4,-,7,2]
[1,4,*,2,5,-,7,2]
[1,0,*,3,5,-,7,2]
[3,5,0,*,1,-,7,2]
[1,7,5,*,2,-,7,2]
[9,+,3,4,1,-,7,2]
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[6,+,3,4,4,-,7,2]
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[2,+,3,4,8,-,7,2]
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[3,5,1,-,1,-,7,2]
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[3,5,5,-,5,-,7,2]
[3,5,6,-,6,-,7,2]
[3,5,7,-,7,-,7,2]
[3,5,8,-,8,-,7,2]
[3,5,9,-,9,-,7,2]
[(,3,5,1,),-,7,3]
[3,*,1,1,7,-,7,3]
[1,*,3,5,1,-,7,3]
[2,7,*,1,3,-,7,3]
[1,3,*,2,7,-,7,3]
[3,5,1,*,1,-,7,3]
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[3,6,0,-,9,-,7,3]
[(,3,5,2,),-,7,4]
[2,*,1,7,6,-,7,4]
[1,*,3,5,2,-,7,4]
[3,2,*,1,1,-,7,4]
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[1,6,*,2,2,-,7,4]
[1,1,*,3,2,-,7,4]
[3,5,2,*,1,-,7,4]
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[9,+,3,4,3,-,7,4]
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[6,+,3,4,6,-,7,4]
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[(,3,5,3,),-,7,5]
[1,*,3,5,3,-,7,5]
[3,5,3,*,1,-,7,5]
[9,+,3,4,4,-,7,5]
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[3,6,0,-,7,-,7,5]
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[(,3,5,4,),-,7,6]
[3,*,1,1,8,-,7,6]
[2,*,1,7,7,-,7,6]
[1,*,3,5,4,-,7,6]
[3,5,4,*,1,-,7,6]
[1,7,7,*,2,-,7,6]
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[3,5,5,-,1,-,7,6]
[3,5,6,-,2,-,7,6]
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[3,5,9,-,5,-,7,6]
[3,6,0,-,6,-,7,6]
[3,6,1,-,7,-,7,6]
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[3,6,3,-,9,-,7,6]
[(,3,5,5,),-,7,7]
[1,*,3,5,5,-,7,7]
[3,5,5,*,1,-,7,7]
[9,+,3,4,6,-,7,7]
[8,+,3,4,7,-,7,7]
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[6,+,3,4,9,-,7,7]
[5,+,3,5,0,-,7,7]
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[3,5,6,-,1,-,7,7]
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[3,6,0,-,5,-,7,7]
[3,6,1,-,6,-,7,7]
[3,6,2,-,7,-,7,7]
[3,6,3,-,8,-,7,7]
[3,6,4,-,9,-,7,7]
[(,3,5,6,),-,7,8]
[2,*,1,7,8,-,7,8]
[1,*,3,5,6,-,7,8]
[3,5,6,*,1,-,7,8]
[1,7,8,*,2,-,7,8]
[9,+,3,4,7,-,7,8]
[8,+,3,4,8,-,7,8]
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[6,+,3,5,0,-,7,8]
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[3,4,7,+,9,-,7,8]
[3,5,7,-,1,-,7,8]
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[3,6,0,-,4,-,7,8]
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[3,6,2,-,6,-,7,8]
[3,6,3,-,7,-,7,8]
[3,6,4,-,8,-,7,8]
[3,6,5,-,9,-,7,8]
[(,3,5,7,),-,7,9]
[3,*,1,1,9,-,7,9]
[1,*,3,5,7,-,7,9]
[2,1,*,1,7,-,7,9]
[1,7,*,2,1,-,7,9]
[3,5,7,*,1,-,7,9]
[1,1,9,*,3,-,7,9]
[9,+,3,4,8,-,7,9]
[8,+,3,4,9,-,7,9]
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[3,5,8,-,1,-,7,9]
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[3,6,0,-,3,-,7,9]
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[3,6,2,-,5,-,7,9]
[3,6,3,-,6,-,7,9]
[3,6,4,-,7,-,7,9]
[3,6,5,-,8,-,7,9]
[3,6,6,-,9,-,7,9]
[(,3,5,8,),-,8,0]
[2,*,1,7,9,-,8,0]
[1,*,3,5,8,-,8,0]
[3,5,8,*,1,-,8,0]
[1,7,9,*,2,-,8,0]
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[3,6,4,-,6,-,8,0]
[3,6,5,-,7,-,8,0]
[3,6,6,-,8,-,8,0]
[3,6,7,-,9,-,8,0]
[(,3,5,9,),-,8,1]
[1,*,3,5,9,-,8,1]
[3,5,9,*,1,-,8,1]
[9,+,3,5,0,-,8,1]
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[6,+,3,5,3,-,8,1]
[5,+,3,5,4,-,8,1]
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[3,5,3,+,6,-,8,1]
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[3,6,4,-,5,-,8,1]
[3,6,5,-,6,-,8,1]
[3,6,6,-,7,-,8,1]
[3,6,7,-,8,-,8,1]
[3,6,8,-,9,-,8,1]
[(,3,6,0,),-,8,2]
[3,*,1,2,0,-,8,2]
[2,*,1,8,0,-,8,2]
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[2,0,*,1,8,-,8,2]
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[8,*,9,*,5,-,8,2]
[9,*,5,*,8,-,8,2]
[5,*,9,*,8,-,8,2]
[8,*,5,*,9,-,8,2]
[5,*,8,*,9,-,8,2]
[9,+,3,5,1,-,8,2]
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[3,6,1,-,1,-,8,2]
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[3,6,7,-,7,-,8,2]
[3,6,8,-,8,-,8,2]
[3,6,9,-,9,-,8,2]
[(,3,6,1,),-,8,3]
[1,*,3,6,1,-,8,3]
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[(,3,6,2,),-,8,4]
[2,*,1,8,1,-,8,4]
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[9,+,3,5,3,-,8,4]
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[3,6,9,-,7,-,8,4]
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[(,3,6,3,),-,8,5]
[3,*,1,2,1,-,8,5]
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[3,6,3,*,1,-,8,5]
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[9,+,3,5,4,-,8,5]
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[(,3,6,4,),-,8,6]
[2,*,1,8,2,-,8,6]
[1,*,3,6,4,-,8,6]
[2,8,*,1,3,-,8,6]
[2,6,*,1,4,-,8,6]
[1,4,*,2,6,-,8,6]
[1,3,*,2,8,-,8,6]
[3,6,4,*,1,-,8,6]
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[9,+,3,5,5,-,8,6]
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[(,3,6,5,),-,8,7]
[1,*,3,6,5,-,8,7]
[3,6,5,*,1,-,8,7]
[9,+,3,5,6,-,8,7]
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[(,3,6,6,),-,8,8]
[3,*,1,2,2,-,8,8]
[2,*,1,8,3,-,8,8]
[1,*,3,6,6,-,8,8]
[3,6,6,*,1,-,8,8]
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[1,2,2,*,3,-,8,8]
[9,+,3,5,7,-,8,8]
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[(,3,6,7,),-,8,9]
[1,*,3,6,7,-,8,9]
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[(,3,6,8,),-,9,0]
[2,*,1,8,4,-,9,0]
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[2,3,*,1,6,-,9,0]
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[(,3,6,9,),-,9,1]
[3,*,1,2,3,-,9,1]
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[3,6,9,*,1,-,9,1]
[1,2,3,*,3,-,9,1]
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[3,7,6,-,7,-,9,1]
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[3,7,8,-,9,-,9,1]
[(,3,7,0,),-,9,2]
[2,*,1,8,5,-,9,2]
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[3,7,*,1,0,-,9,2]
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[3,7,0,*,1,-,9,2]
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[3,7,5,-,5,-,9,2]
[3,7,6,-,6,-,9,2]
[3,7,7,-,7,-,9,2]
[3,7,8,-,8,-,9,2]
[3,7,9,-,9,-,9,2]
[(,3,7,1,),-,9,3]
[1,*,3,7,1,-,9,3]
[3,7,1,*,1,-,9,3]
[9,+,3,6,2,-,9,3]
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[3,7,7,-,6,-,9,3]
[3,7,8,-,7,-,9,3]
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[3,8,0,-,9,-,9,3]
[(,3,7,2,),-,9,4]
[3,*,1,2,4,-,9,4]
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[(,3,7,3,),-,9,5]
[1,*,3,7,3,-,9,5]
[3,7,3,*,1,-,9,5]
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[3,7,8,-,5,-,9,5]
[3,7,9,-,6,-,9,5]
[3,8,0,-,7,-,9,5]
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[3,8,2,-,9,-,9,5]
[(,3,7,4,),-,9,6]
[2,*,1,8,7,-,9,6]
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[3,4,*,1,1,-,9,6]
[2,2,*,1,7,-,9,6]
[1,7,*,2,2,-,9,6]
[1,1,*,3,4,-,9,6]
[3,7,4,*,1,-,9,6]
[1,8,7,*,2,-,9,6]
[9,+,3,6,5,-,9,6]
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[size=23138,time=56]
23138= removing duplicate symbol...
2479= removing ()...
2024= removing ops...
18= searching...
17-[1,0,2,3,-,7,4,5]=8.57536-max(none,-1)+sec(38)
16-[1,0,2,6,-,7,4,8]=8.55347-max([1,0,2,3,-,7,4,5],8.57536)+sec(38)
15-[1,0,3,2,-,7,5,4]=8.78166-max([1,0,2,3,-,7,4,5],8.57536)+sec(39)
14-[1,0,3,4,-,7,5,6]=8.7416-max([1,0,3,2,-,7,5,4],8.78166)+sec(39)
13-[1,0,3,6,-,7,5,8]=8.67432-max([1,0,3,2,-,7,5,4],8.78166)+sec(37)
12-[1,0,4,3,-,7,6,5]=8.61899-max([1,0,3,2,-,7,5,4],8.78166)+sec(38)
11-[1,0,6,2,-,7,8,4]=8.74749-max([1,0,3,2,-,7,5,4],8.78166)+sec(38)
10-[1,0,6,3,-,7,8,5]=8.6548-max([1,0,3,2,-,7,5,4],8.78166)+sec(38)
9-[1,2,3,4,-,9,5,6]=8.61198-max([1,0,3,2,-,7,5,4],8.78166)+sec(38)
8-[1,2,3,6,-,9,5,8]=8.60251-max([1,0,3,2,-,7,5,4],8.78166)+sec(38)
7-[1,2,3,8,-,9,6,0]=8.62362-max([1,0,3,2,-,7,5,4],8.78166)+sec(37)
6-[1,2,4,3,-,9,6,5]=8.49033-max([1,0,3,2,-,7,5,4],8.78166)+sec(38)
5-[1,2,4,5,-,9,6,7]=8.61173-max([1,0,3,2,-,7,5,4],8.78166)+sec(38)
4-[1,2,4,8,-,9,7,0]=8.55415-max([1,0,3,2,-,7,5,4],8.78166)+sec(37)
3-[1,2,5,4,-,9,7,6]=8.64207-max([1,0,3,2,-,7,5,4],8.78166)+sec(38)
2-[1,2,5,6,-,9,7,8]=8.58979-max([1,0,3,2,-,7,5,4],8.78166)+sec(38)
1-[1,2,6,3,-,9,8,5]=8.5993-max([1,0,3,2,-,7,5,4],8.78166)+sec(38)
0-[1,2,6,5,-,9,8,7]=8.6642-max([1,0,3,2,-,7,5,4],8.78166)+sec(37)
Play: 1032-754
Answ: --+--!--
reduced=10
9-[8,9,+,9,*,7,*,3]=2.92193-max(none,-1)+sec(0)
8-[8,9,+,3,*,7,*,9]=2.92193-max([8,9,+,9,*,7,*,3],2.92193)+sec(1)
7-[9,+,8,+,8,7,*,3]=3.12193-max([8,9,+,9,*,7,*,3],2.92193)+sec(1)
6-[8,+,9,+,8,7,*,3]=3.12193-max([9,+,8,+,8,7,*,3],3.12193)+sec(1)
5-[8,*,7,+,3,7,*,6]=3.12193-max([9,+,8,+,8,7,*,3],3.12193)+sec(1)
4-[7,*,8,+,3,7,*,6]=2.92193-max([8,*,7,+,3,7,*,6],3.12193)+sec(0)
3-[3,7,*,6,+,7,*,8]=2.32193-max([8,*,7,+,3,7,*,6],3.12193)+sec(1)
2-[3,*,8,8,+,7,+,7]=2.84644-max([8,*,7,+,3,7,*,6],3.12193)+sec(1)
1-[8,8,*,3,+,7,+,7]=2.64644-max([8,*,7,+,3,7,*,6],3.12193)+sec(1)
0-[3,3,*,8,+,7,+,7]=1.77095-max([8,*,7,+,3,7,*,6],3.12193)+sec(1)
Play: 8*7+37*6
Answ: !!!!!!!!
____________________
% mathler tool by S.Devulder

:- use_module(lists).
:- use_module(date).
:- use_module(random).
%:- use_module(aggregate).

writeln(X) :- write(X),nl.

%rat(P/Q) :- integer(P),integer(Q).
rat(P/_) :- integer(P).

calc(U, V, P/Q) :- % normalize
    X is U,
    (   X=0 ->
        P=0,
        Q=1
    ;   Y is V,
        Z is gcd(X,Y),
        P is X div Z,
        Q is Y div Z
    ), P>=0, Q>=1.
/*
calc(0/1, +, _, _) :- !, fail.
calc(_, +, 0/1, _) :- !, fail.
calc(_, -, 0/1, _) :- !, fail.
calc(0/1, *, _, _) :- !, fail.
calc(_, *, 0/1, _) :- !, fail.
calc(1/1, *, _, _) :- !, fail.
calc(_, *, 1/1, _) :- !, fail.
calc(0/1, /, _, _) :- !, fail.
calc(_, /, 1/1, _) :- !, fail.
*/

%calc(A ,O,B,C) :- member(O,[*,-]),write([A,O,B,=,C] ),nl,fail.

calc(A/1, +, B/1, C/1) :- !, C is A+B.
calc(A/B, +, C/D, R) :- calc(A*D+B*C, B*D, R).

calc(A/1, -, B/1, C/1) :- !, C is A-B.
calc(A/B, -, C/D, R) :- calc(A*D-B*C, B*D, R).

calc(A/1, *, B/1, C/1) :- !, C is A*B.
calc(A/B, *, C/D, R) :- calc(A*C, B*D, R).

calc(_, /, 0/_, _) :- !, fail. % can’t divide by 0
calc(A/1, /, B/1, R) :- !, calc(A,B,R).
calc(A/B, /, C/D, R) :- calc(A*D, B*C, R).

iszero(0/_,true).
iszero(N/_,false) :- N\=0.

% given a basic equation W = U op V,
% - if W is known, find U such that the equation holds. Then apply the goal with a known U value (faster).
% - if not, try all poossible U that satisfy the goal and return each possible W value.

solve(Expr, Goal) :- solve2(Expr, Goal).
%solve(Expr, Goal) :- solve2(Expr, Goal), \+ reject_op(Expr). % heuristic to accept only a subset of operations

%solve2(E, _) :- write(E),nl, fail.

solve2(W=U+V, Goal) :-
    (   rat(W) ->
        calc(W, -, V, U),
        call(Goal)
    ;   call(Goal),
        calc(U, +, V, W)
    ).
solve2(W=U-V, Goal) :-
    (   rat(W) ->
        calc(W, +, V, U),
        call(Goal)
    ;   call(Goal),
        calc(U, -, V, W)
    ).
solve2(W=U/V, Goal) :-
    iszero(V, false),
    (   rat(W) ->
        calc(W, *, V, U),
        call(Goal)
    ;   call(Goal),
        calc(U, /, V, W)
    ).
solve2(W=U*V, Goal) :-
    (   rat(W) ->
        (   iszero(W, true) ->
            (   U = 0/1
            ;   V = 0/1
            )
        ;   iszero(V, false) ->
            calc(W,/,V,U)
        ;   !,
            false
        ),
        call(Goal)
    ;   call(Goal),
        calc(U,*,V,W)
    ).


/*
Find Equations evaluating to Num using the following BNF rules:

  expression  ::= term    | expression + term | expression - term
  term        ::= factor  | term * factor     | term / factor
  factor      ::= integer | ( expression )

expression(-Num, +Equation).
*/
%main :- expression(54/1, [2,4,/,4,*,9]), write(true), nl.

split(X,Y,Z,T) :- append(X,[Y|Z],T),X=[_|_],Z=[_|_].

expression(_,[]) :- !,fail.
expression(W,R) :- term(W, R).
expression(W,R) :- split(E,+,T,R), term(V,T), solve(W=U+V,expression(U,E)).
expression(W,R) :- split(E,-,T,R), term(V,T), solve(W=U-V,expression(U,E)).

term(_, []) :-!,fail.
term(W,R) :- factor(W, R).
term(W,R) :- split(T,*,F,R), factor(V,F), solve(W=U*V,term(U,T)).
/*
numdigit(N,1):- 0=<N,N=<9.
numdigit(N,R) :- N>=0, M is N/10, numdigit(M,T),R is T+1.
*/
term(P/Q, R) :-integer(P),P>0,!,
    split(T,/,F, R),
    length(T,Lt),
    length(F,Lf),
    Max is floor(min(10**Lt/P,10**Lf/Q))+1,%ceil doesn’t exists here
%    A is 1+floor((log(10)*Lt-log(abs(P+0.001)))/log(10)),
%    B is 1+floor((log(10)*Lf-log(abs(Q+0.001)))/log(10)),
%    Max is round(10**min(A,B)-1),
%    writeln(P+Q-Lt+Lf=A-B- Max),
    between(2,Max,I),
    V is Q*I,
    factor(V/I, F),
    U is P*I,
    term(U/I, T).

term(W,R) :- split(T,/,F,R), factor(V,F), solve(W=U/V,term(U,T)).

factor(_, []) :-!,fail.
factor(N,L) :- reverse(L,R), num(N,R).
factor(V,['('|L]) :- parentheses(true), append(E,[')'],L), expression(V,E). % parentheses can be disabled

/*
num(?Num,+List)
Generates or accepts numbers that exactly fit the list.
*/
num(0/1,[0]) :- accept_zero(true).  % we can disable zero in the expression.
num(N/1, R) :-
    num_bounds(R, Lo, Hi),
    (   var(N) ->
        num1(N, R)
    ;   Lo=<N,
        N=<Hi,
        num2(N, R)
    ).

%digit(D) :- between(0,9,D).
%digit(D) :- member(D,[0,1,2,3,4,5,6,7,8,9]).
digit(0). digit(D) :- digit1(D).
digit1(1). digit1(2). digit1(3).
digit1(4). digit1(5). digit1(6).
digit1(7). digit1(8). digit1(9).

num1(N,[N]) :- !,digit1(N).
num1(N,[P|Q]) :-num1(M,Q), digit(P), N is M*10+P.

num2(0,[]):-!.
num2(N,[R|S]) :- R is mod(N,10), Q is div(N,10), num2(Q,S).

% defines number size
num_bounds([_],1,9).
num_bounds([_,_],10,99).
num_bounds([_,_,_],100,999).
num_bounds([_,_,_,_],1000,9999).
num_bounds([_,_,_,_,_],10000,99999).
%num_bounds([_,_,_,_,_,_],100000,999999).
%num_bounds([_,_,_,_,_,_,_],1000000,9999999).
%num_bounds([_|T], Lo, Hi) :- num_bounds(T, Lo2, Hi2), Lo is Lo2*10, Hi is Hi2*10+9.

% heuristics to accept certain operations
reject_op(_=0*_). % reject absorbing element
reject_op(_=0/_).
reject_op(_=_*0).

reject_op(_=0+_). % reject additive neutral element
reject_op(_=0-_).
reject_op(_=_+0).
reject_op(_=_-0).

reject_op(_=1*_). % reject multiplicative neutral element
reject_op(_=1/_).
reject_op(_=_*1).
reject_op(_=_/1).

reject_op(W=_) :- W =< 0. % accept only strictly positive results

% update possibilities from result.
update(Eq,Code,StateIn,StateOut) :-
    update1(Eq,Code,StateIn,Tmp),  % absent symbols
    update2(Eq,Code,Tmp,StateOut). % present symbols

update1([Symb|T1],[-|T2],state(Mand,AllIn),StateOut) :- !,  % gray
    del_symb(Symb,AllIn,Tmp),  % excude gray from all possibilities.
    update1(T1,T2,state(Mand,Tmp),StateOut).
update1([_|T1],[_|T2],StateIn,StateOut) :-
    update1(T1,T2,StateIn,StateOut).
update1([],[],State,State).

del_symb(Symb,[P1|T1],[P2|T2]) :-
    delete(P1,Symb,P2),
    del_symb(Symb,T1,T2).
del_symb(_,[],[]).

update2([Symb|T1],[!|T2],state(MandIn,[H3|T3]),state(Mand,[[Symb]|T4])) :- !, % green
    member(Symb,H3),
    update2(T1,T2,state(MandIn,T3),state(Mand,T4)).
update2([Symb|T1],[+|T2],state(MandIn,[P1|T3]),state(Mand,[P2|T4])) :- !,  % yellow
    delete(P1,Symb,P2),
    (member(Symb,MandIn)->Tmp=MandIn;Tmp=[Symb|MandIn]),
    update2(T1,T2,state(Tmp,T3),state(Mand,T4)).
update2([_|T1],[-|T2],state(MandIn,[H|T3]),state(Mand,[H|T4])) :-  % gray -> update1
    update2(T1,T2,state(MandIn,T3),state(Mand,T4)).
update2([],[],state(Mand,[]),state(Mand,[])).

% check compatibility
is_compatible(Eq,state(Mand,Possibilities)) :-
    subset(Mand,Eq),
    is_compatible(Eq, Possibilities).
is_compatible([S|T1],[P|T2]) :- member(S,P), !, is_compatible(T1,T2).
is_compatible([],[]).

% compute entropy
entropy(Eq, Codes, Data, Entropy) :-
    entropy(Eq, Codes, Data, 0, Entropy).

entropy(_, [], _, Acc, Acc):-!.
entropy(Eq, [Code|Codes], Data, Acc1, Acc) :-
    (Data=data(State,Sols,NumSols),
    update(Eq, Code, State, NewState) ->
    count_compat(Sols, NewState, 0, NumCompat),
%    write(entrop-Eq+Code=NumCompat), nl,
    (   NumCompat>0 ->
        P is NumCompat/NumSols,
        Acc2 is Acc1-P*log(P)/log(2)
    ;   Acc2=Acc1
    );Acc2=Acc1),
    entropy(Eq, Codes, Data, Acc2, Acc).

%count_compat(L,S,_,N) :- !, findall(Eq,(member(Eq,L),is_compatible(Eq,S)),T), length(T,N).
%count_compat(L,S,_,N) :- !,aggregate_all(count, (member(Eq,L),is_compatible(Eq,S)),N).
count_compat([], _, Acc, Acc):-!.
count_compat([Eq|Eqs], State, Acc1, Acc) :-
    (   is_compatible(Eq, State) ->
%        write(Eq),nl,
        succ(Acc1, Acc2),
        count_compat(Eqs, State, Acc2, Acc)
    ;   count_compat(Eqs, State, Acc1, Acc)
    ).


% find the eq which maximizes the entropy
best_eq(Eqs, Data, Eq) :-
    best_eq(Eqs, Data, max(none,-1), max(Eq, _)).
best_eq([],_, Max,Max).
best_eq([Eq|Eqs], Data, Max1, Max) :-
    Data=data(Codes,State,Sols),
    length(Sols, NumSols),
    now(T1),
    entropy(Eq, Codes, data(State,Sols,NumSols), Entropy),
    now(T2),
    T3 is T2-T1,
    length(Eqs,Togo),
    writeln(Togo-Eq=Entropy-Max1+sec(T3)),
    update_max(Max1, max(Eq,Entropy), Max2),
    best_eq(Eqs, Data, Max2, Max).

update_max(max(X,Y), max(_, Z), max(X,Y)) :- Z=<Y, !.
update_max(_, Max, Max).

% generates codes
is_code([]).
is_code([H|T]) :- member(H,[+,-,!]),is_code(T).

% init state
init_state(N, state([],P), Codes) :-
    init_state2(N, P),
    findall(Code, (length(Code,N),is_code(Code)), Codes).
init_state2(0, []) :- !.
init_state2(N, [[1,2,3,4,5,6,7,8,9,0,+,-,*,/,'(',')']|L]) :-
    succ(P,N),
    init_state2(P, L).

% options
parentheses(true).
accept_zero(truex).
/*
main :-
    Size=5,
    Goal=26,
    init_state(Size, State),
    findall(Code, (length(Code,Size),is_code(Code)), Codes),
    now(T1),
    findall(L, (length(L,Size),expression(Goal,L),write(L),nl), S),
    now(T2),
    T3 is T2-T1,
    length(S, N),
    writeln([size=N,time=T3]),
    best_eq(S, data(Codes,State,S), Eq),
    writeln(best=Eq),
    length(S,NumSols),
    entropy(Eq, Codes, data(State,S,NumSols), Entropy),
    writeln(Eq=Entropy),
    true.

*/

string2code([H1|T1], [H2|T2]) :-
    string2code2(H1, H2),
    string2code(T1, T2).
string2code([], []).

string2code2(0'+,+). string2code2(0'-,-). string2code2(0'!,!).

play(Eq, Sols, Codes, State) :-
    write('Play: '),
    forall(member(X,Eq), write(X)), nl,
    write('Answ: '),
    flush_output,
    findall(X, (member(_,Eq),get(X)), String),
    string2code(String, Code),
    update(Eq, Code, State, State2),
    findall(Eq2, (member(Eq2,Sols),is_compatible(Eq2,State2)), Sols2),
    (Sols2=[]->writeln('ERROR'),play(Eq,Sols,Codes,State);true),
    length(Sols2, N),
    writeln(reduced=N),
    play2(Sols2, Codes, State2).
play2([Eq], _, _) :-
    write('Solved: '),
    forall(member(X,Eq), write(X)),
    nl, !,
    true.
play2(Sols, Codes, State) :-
    best_eq(Sols, data(Codes,State,Sols), Eq), !,
    play(Eq, Sols, Codes, State).

nonduplicate(L) :- sort(L,M), same_length(L,M).

maxop([],_).
maxop(_, -1) :- !,fail.
maxop([H|T],N) :- member(H,[+,-,*,/]), !, N1 is N-1, maxop(T,N1).
maxop([_|T],N) :- maxop(T,N).

first(State, Codes, Eqns, Eq) :-
    Data = data(Codes,State,Eqns),
    (   length(Eqns, N),
        N>100 ->
        writeln(N='removing duplicate symbol...'),
        findall(Eq, (member(Eq,Eqns),nonduplicate(Eq)), Nodup),
        first1(Nodup, data(Codes,State,Nodup), Eq)
    ;   first1(Eqns, Data, Eq)
    ).
first1(Eqns, Data, Eq) :-
    (   length(Eqns, N),
        N>100 ->
        writeln(N='removing ()...'),
        findall(Eq, (member(Eq,Eqns),\+ member('(',Eq)), Eqn2),
        first2(Eqn2, Data, Eq)
    ;   first2(Eqns, Data, Eq)
    ).
first2(Eqns, Data, Eq) :-
    (   length(Eqns, N),
        N>100 ->
        writeln(N='removing ops...'),
        findall(Eq, (member(Eq,Eqns),maxop(Eq,1)), Eqn2),
        first3(Eqn2, Data, Eq)
    ;   first3(Eqns, Data, Eq)
    ).
first3(Eqns, Data, Eq) :-
    (   length(Eqns, N),
        N>100 ->
        writeln(N='removing 0'),
        findall(Eq, (member(Eq,Eqns),\+member(0,Eq)), Eqn2),
        first4(Eqn2, Data, Eq)
    ;   first4(Eqns, Data,Eq)
    ).
first4(Eqns, Data, Eq) :-
    (   length(Eqns, N),
        N>100 ->
        writeln(N='removing 5'),
        findall(Eq, (member(Eq,Eqns),\+member(5,Eq)), Eqn2),
        first5(Eqn2, Data, Eq)
    ;   first5(Eqns, Data, Eq)
    ).
first5(Eqns, Data, Eq) :-
    length(Eqns, N),
    writeln(N='searching...'),
    best_eq(Eqns, Data, Eq).

main :-
    Size=8,
    Goal=278,

    now(T1),
    findall(L, (length(L,Size),expression(Goal/1,L),writeln(L)), Eqns),
    now(T2),
    T3 is T2-T1,
    length(Eqns,N),
    writeln([size=N,time=T3]),
    !,
    init_state(Size, State, Codes),
    first(State,Codes,Eqns,Eq),
    play(Eq,Eqns,Codes,State).

/*

%    random_permutation(S,Sols1),
    findall(Eq, (member(Eq,S),noduplicate(Eq)),Nodup),
    Sols1=S,
%    findall(L, (length(L,Size),expression(Goal,L),write(L),nl), Sols1),
%    member([5,7,6,/,1,2],Sols1),
%    best_eq(Nodup, data(Codes,State1,Nodup), Eq1),
Eq1=[3,0,9,4,/,1,8,2],
%Eq1=[5,7,6,/,1,2],
%Eq1=[7,9,+,6,-,2],
    write(best=Eq1),nl,!,
    play(Eq1, "+---++-+", State1, State2),!,
    findall(Eq, (member(Eq,Sols1),is_compatible(Eq,State2)), Sols2),
    best_eq(Sols2, data(Codes,State2,Sols2), Eq2),
    write(best=Eq2),nl,
    play(Eq2, "!+++-+--", State2, State3),!,
    findall(Eq, (member(Eq,Sols2),is_compatible(Eq,State3)), Sols3),
    best_eq(Sols3, data(Codes,State3,Sols3), Eq3),
    write(best=Eq3),nl,
    true.

*/