use strict;
use Math::Symbolic qw(:all);
use Math::Symbolic::Custom::Collect;
use Test::Simple 'no_plan';
# constant expressions
my %const_expr = (
        '-0/1' => 0,
        '0/1' => 0,
        '(0+(8/13))+(5/13)' => 1,
        '-10/5' => -2,
        '10/5' => 2,
        '-1+(1/2)' => -0.5,
        '-1-(1/2)' => -1.5,
        '1+(1/2)' => 1.5,
        '1-(1/2)' => 0.5,
        '11/2' => 5.5,
        '(11/2)*2' => 11,
        '-11/-22' => 0.5,
        '-11/5' => -2.2,
        '11/5' => 2.2,
        '(1/2)-1' => -0.5,
        '-(1/2)-1' => -1.5,
        '(1/2)+(1/2)' => 1,
        '(1/2)-(1/2)' => 0,
        '-(1/2)+(-1/2)' => -1,
        '-(1/2)-(1/-2)' => 0,
        '(1/2)+(1/4)+(1/4)' => 1,
        '(1/2)-(3/4)' => -0.25,
        '-(1/2)-(3/-4)' => 0.25,
        '-1*2*3*4*5*6*7*8*9' => -362880,
        '-1+2*3+4*5+6*7+8*9' => 139,
        '-1+2+3+4-5+6+7+8+9' => 33,
        '-1+2-3+4-5+6-7+8-9' => -5,
        '-1-2-3-4-5-6-7-8-9' => -45,
        '-1/2/-3/4/-5/6/-7/-8/9' => -2.75573192239859e-06,
        '1*2*3*4*5*6*7*8*9' => 362880,
        '1+2*3+4*5+6*7+8*9' => 141,
        '1+2+3+4+5+6+7+8+9' => 45,
        '1+2-3+4-5+6-7+8-9' => -3,
        '1-2-3-4-5-6-7-8-9' => -43,
        '1/2/3/4/5/6/7/8/9' => 2.75573192239859e-06,
        '(1/4)/(1/2)' => 0.5,
        '-(1/4)/(1/-2)' => 0.5,
        '(1/4)*(1*2*3)' => 1.5,
        '-(1/4)*(1*2*3)' => -1.5,
        '-(1/4)*(1*-2*3)' => 1.5,
        '(1/4)*(1/3)*(1/2)*5' => 0.208333333333333,
        '-(1/4)*(1/3)*(1/2)*5' => -0.208333333333333,
        '-1/-7' => 0.142857142857143,
        '-1/7' => -0.142857142857143,
        '1/-7' => -0.142857142857143,
        '1/7' => 0.142857142857143,
        '2001/3000' => 0.667,
        '2/1' => 2,
        '2*(10/2)' => 10,
        '-2*(1/-4)' => 0.5,
        '2*(1/4)' => 0.5,
        '(-2/-3)-(1/6)' => 0.5,
        '(-2/3)-(1/6)' => -0.833333333333333,
        '(2/-3)-(1/6)' => -0.833333333333333,
        '(2/3)-(-1/-6)' => 0.5,
        '(2/3)-(-1/6)' => 0.833333333333333,
        '(2/3)-(1/-6)' => 0.833333333333333,
        '(2/3)-(1/6)' => 0.5,
        '(2/4)+(1/4)' => 0.75,
        '(2/4)-(2/8)' => 0.25,
        '(2*4+3^3)-(9+8+7+6+5+4+3+2+1)' => -10,
        '24/36' => 0.666666666666667,
        '(2*4)-(6*3)' => -10,
        '(2*4)-(6-3)' => 5,
        '(2*4)-(9+8+7+6+5+4+3+2+1)' => -37,
        '2740/8220' => 0.333333333333333,
        '3*((10+12)/6)' => 11,
        '(3/10)/(18/25)' => 0.416666666666667,
        '-3*(1/4)' => -0.75,
        '3*(1/4)' => 0.75,
        '(3*3)/(3-1)' => 4.5,
        '36/30' => 1.2,
        '(4/5)*(2/3)' => 0.533333333333333,
        '45/75' => 0.6,
        '-5/1' => -5,
        '5/1' => 5,
        '-5/10' => -0.5,
        '5/-10' => -0.5,
        '-7/4' => -1.75,
        '7/4' => 1.75,
        '(8+3^3)-(9+8+7+6+5+4+3+2+1)' => -10,
        '8-(6*3)' => -10,
        '8-(6-3)' => 5,
        '8-(9+8+7+6+5+4+3+2+1)' => -37,
        '-cos(10/5)' => 0.416146836547142,
        'cos(10/5)' => -0.416146836547142,
        '-cos(11/5)' => 0.588501117255346,
        'cos(11/5)' => -0.588501117255346,
        '-cos(-1/-7)' => -0.989813260446615,
        '-cos(-1/7)' => -0.989813260446615,
        '-cos(1/-7)' => -0.989813260446615,
        'cos(-1/-7)' => 0.989813260446615,
        'cos(-1/7)' => 0.989813260446615,
        'cos(1/-7)' => 0.989813260446615,
        '-cos(5/1)' => -0.283662185463226,
        'cos(5/1)' => 0.283662185463226,
        '-cos(7/4)' => 0.178246055649492,
        'cos(7/4)' => -0.178246055649492,
    'sqrt(4)*sqrt(9)' => 6,
    'sqrt(-4)*sqrt(-9)' => -6,
    '10^100 + 1 - 10^100' => 1,
    '(5 ^ 104) / (5 ^ 102)' => 25,
    '(10 ^ 199) - (10 ^ 199)' => 0,
    '((10 ^ (-199)) + 1) - (10 ^ (-199))' => 1,
    '(10 ^ 199) / (10 ^ 198)' => 10,
    '5 ^ 4' => 625,
    '((6 ^ 199) + 1) - (6 ^ 199)' => 1,
    '1 * 10^-300 * 10^300' =>  1,
    '(10^100 + 1) - 10^100 + 1' => 2,
);
TEST_CONSTANTS: while ( my ($test, $ans) = each %const_expr ) {
    my $f1 = parse_from_string($test);
    # can the parser parse the test string?
    ok( defined($f1), "parsing test string [$test]" );
    if (!defined $f1) {
        next TEST_CONSTANTS;
    }  
    my $f2 = $f1->to_collected();
    ok( defined($f2), "to_collected() returns defined [$f2] ($test)" );
    if (!defined $f2) {
        next TEST_CONSTANTS;
    }   
    my $val = $f2->value();
    ok( sprintf("%.11f", $val) == sprintf("%.11f", $ans), "Evaluation matches pre-calculated answer to 11 dp ($test)" );    
}
# variable expressions
my %var_expr = (
        '((((1/5)*(x+(z*y)))/2)*(((1/5)*(x+(z*y)))/3))/4' => [1,2,3,4,5,6,7,8,9],
        '(((x+y)/2)*((x+y)/3))/(x+y)' => [1,2,3,4,5,6,7,8,9],
        '(((x+y)/2)*((x+y)/3))/4' => [1,2,3,4,5,6,7,8,9],
        '((1/(3*p))-(1/(3*q)))/((p/q)-(q/p))' => [1,2,3,4,5,6,7,8,9],
        '((1/2)*x^2 + 2*x + (1/4))*(x+z+y)' => [1,2,3,4,5,6,7,8,9],
        '((1/2)*x^2 + 2*x + (1/4))*2' => [1,2,3,4,5,6,7,8,9],
        '((1/2)*x^2 + 2*x + (1/4))*x^2' => [1,2,3,4,5,6,7,8,9],
        '((1/4)+(1/2))*3*x' => [1,2,3,4,5,6,7,8,9],
        '((x*(2/14))+(x*y))*y' => [1,2,3,4,5,6,7,8,9],
        '((x+y)^2)/7' => [1,2,3,4,5,6,7,8,9],
        '((x+y)^p) * ((x+y)^q)' => [1,2,3,7,8,9],
        '((x+y+z)*x^2)/5' => [1,2,3,4,5,6,7,8,9],
        '((y/x)*z)+((y/x)*y)' => [1,2,3,4,5,6,7,8,9],
        '(-12*y+36)/-8' => [1,2,3,4,5,6,7,8,9],
        '(1+2+x)*((y+z)*(p+q+c))' => [1,2,3,4,5,6,7,8,9],
        '(1+2+x)*((y+z)*(p-q-c))' => [1,2,3,4,5,6,7,8,9],
        '(1+2+x)*(sin(y)+z)' => [1,2,3,4,5,6,7,8,9],
        '(1+2+x)*(y+z)' => [1,2,3,4,5,6,7,8,9],
        '(1/(x+1))+(x/(4-x))-(1/(x-2))' => [1,2,3,4,5,6,7,9],
        '(1/14)*(x+x+y)' => [1,2,3,4,5,6,7,8,9],
        '(1/4)*2+(x/2)' => [1,2,3,4,5,6,7,8,9],
        '(1/sqrt(x))*(1/sqrt(x))' => [1,2,3,7,8,9],
        '(21*x+9)/15' => [1,2,3,4,5,6,7,8,9],
        '(3*(x^2))/(x^3)' => [1,2,3,4,5,6,7,8,9],
        '(5*x)/(1-(1/x))' => [1,2,3,4,5,6,8,9],
        '(5*z-30)/-5' => [1,2,3,4,5,6,7,8,9],
        '(5+y)*x^(2-z)' => [1,2,3,7,8,9],
        '(5+y)*x^(2-z)*(5+y)' => [1,2,3,7,8,9],
        '(5+y)*x^2' => [1,2,3,4,5,6,7,8,9],
        '(5+y)*x^2*(5+y)' => [1,2,3,4,5,6,7,8,9],
        '(5/(x+1))-((x-2)/(x+1))' => [1,2,3,4,5,6,7,8,9],
        '(6*x+4)/2' => [1,2,3,4,5,6,7,8,9],
        '(p*(q+c))/((q+c)*p)' => [1,2,3,4,5,6,7,8,9],
        '(p-p^2)/(3*p^3-3*p)' => [1,2,3,4,5,6,7,8,9],
        '(sin(x)*q + sin(x)*c)/(sin(x)*p + sin(x)*d)' => [1,2,4,5,7,8,9],
        '(sinh(sin(x)+cos(y))+cosh(sin(x)+cos(y)))*(sinh(x)-cosh(y))' => [1,2,3,4,5,6,7,8,9],
        '(sinh(x)+cosh(y))*(sinh(x)+cosh(y))' => [1,2,3,4,5,6,7,8,9],
        '(sinh(x)+cosh(y))*(sinh(x)-cosh(y))' => [1,2,3,4,5,6,7,8,9],
        '(x*p-x*q)/(x*p+x*q)' => [1,2,3,4,5,6,7,8,9],
        '(x+y)*(((x+y)/14) + ((x+y)/12))' => [1,2,3,4,5,6,7,8,9],
        '(x+y+z)*x' => [1,2,3,4,5,6,7,8,9],
        '(x+y+z)*x^2' => [1,2,3,4,5,6,7,8,9],
        '(x+y+z)/2' => [1,2,3,4,5,6,7,8,9],
        '(x^2+y^2)/(z^2+p^2)' => [1,2,3,4,5,6,7,8,9],
        '(x^p)^(q)' => [1,2,3,7,8,9],
        '(y+x)*(x+2*x)*(1+(y*x))' => [1,2,3,4,5,6,7,8,9],
        '-((((1/5)*(x+(z*y)))/2)*(((1/5)*(x+(z*y)))/3))/4' => [1,2,3,4,5,6,7,8,9],
        '-((((1/5)*(x-(z*y)))/2)*(((1/-5)*(x+(z*y)))/3))/4' => [1,2,3,4,5,6,7,8,9],
        '-(((x+y)/2)*((x+y)/3))/(x+y)' => [1,2,3,4,5,6,7,8,9],
        '-(((x+y)/2)*((x+y)/3))/4' => [1,2,3,4,5,6,7,8,9],
        '-(((x+y)/2)*((x-y)/3))/-4' => [1,2,3,4,5,6,7,8,9],
        '-((1/2)*x^2 + 2*x + (1/4))*x^2' => [1,2,3,4,5,6,7,8,9],
        '-((1/2)*x^2 + 2*x - (1/4))*2' => [1,2,3,4,5,6,7,8,9],
        '-((1/2)*x^2 - 2*x + (1/4))*(x+z+y)' => [1,2,3,4,5,6,7,8,9],
        '-((x*(2/14))+(x*y))*y' => [1,2,3,4,5,6,7,8,9],
        '-((x+y)^2)/-7' => [1,2,3,4,5,6,7,8,9],
        '-((x-y+z)*x^2)/5' => [1,2,3,4,5,6,7,8,9],
        '-((y/x)*z)+((y/x)*y)' => [1,2,3,4,5,6,7,8,9],
        '-(1+2+x)*((y+z)*(p+q+c))' => [1,2,3,4,5,6,7,8,9],
        '-(1+2+x)*((y+z)*(p-q-c))' => [1,2,3,4,5,6,7,8,9],
        '-(1+2+x)*(sin(y)-z)' => [1,2,3,4,5,6,7,8,9],
        '-(1-2+x)*(y-z)' => [1,2,3,4,5,6,7,8,9],
        '-(1/14)*(x+x+y)' => [1,2,3,4,5,6,7,8,9],
        '-(1/4)*(1/3)*(1/2)*5' => [1,2,3,4,5,6,7,8,9],
        '-(5/(x+1))-((x-2)/(x-1))' => [1,2,3,4,5,6,8,9],
        '-(sinh(sin(x)-cos(y))+cosh(sin(x)-cos(y)))*(sinh(x)-cosh(y))' => [1,2,3,4,5,6,7,8,9],
        '-(sinh(x)+cosh(y))*(sinh(x)-cosh(y))' => [1,2,3,4,5,6,7,8,9],
        '-(sinh(x)-cosh(y))*(sinh(x)+cosh(y))' => [1,2,3,4,5,6,7,8,9],
        '-(x*p-x*q)/(x*p-x*q)' => [1,2,3,4,5,6,7,8,9],
        '-(x+y)*(((x+y)/14) + ((x+y)/12))' => [1,2,3,4,5,6,7,8,9],
        '-(x+y)*(((x-y)/14) + ((x+y)/12))' => [1,2,3,4,5,6,7,8,9],
        '-(x+y-z)*x^2' => [1,2,3,4,5,6,7,8,9],
        '-(x-y-z)*x' => [1,2,3,4,5,6,7,8,9],
        '-(x^2+y^2)/(z^2+p^2)' => [1,2,3,4,5,6,7,8,9],
        '-(y+x)*(x+2*x)*(1+(y*x))' => [1,2,3,4,5,6,7,8,9],
        '-1*(x+1)*(x+1)+1' => [1,2,3,4,5,6,7,8,9],
        '-2/(-2*x)' => [1,2,3,4,5,6,7,8,9],
        '-2/-x' => [1,2,3,4,5,6,7,8,9],
        '-cos(((x+y)^2)/7)' => [1,2,3,4,5,6,7,8,9],
        '-cos((1+2+x)*((y+z)*(p-q-c)))' => [1,2,3,4,5,6,7,8,9],
        '-cos((1+2+x)*((y-z)*(p+q+c)))' => [1,2,3,4,5,6,7,8,9],
        '-cos((1+2-x)*(sin(y)+z))' => [1,2,3,4,5,6,7,8,9],
        '-cos((1-2+x)*(y+z))' => [1,2,3,4,5,6,7,8,9],
        '-cos(-1/-7)' => [1,2,3,4,5,6,7,8,9],
        '-cos(-1/7)' => [1,2,3,4,5,6,7,8,9],
        '-cos(1/-7)' => [1,2,3,4,5,6,7,8,9],
        '-cos(10/5)' => [1,2,3,4,5,6,7,8,9],
        '-cos(11/5)' => [1,2,3,4,5,6,7,8,9],
        '-cos(5/1)' => [1,2,3,4,5,6,7,8,9],
        '-cos(7/4)' => [1,2,3,4,5,6,7,8,9],
        '-cos(x^2+y^2)' => [1,2,3,4,5,6,7,8,9],
        '-sin(x)*(x+y+z)' => [1,2,3,4,5,6,7,8,9],
        '-x^2-y^2' => [1,2,3,4,5,6,7,8,9],
        '1/(1-(1/x))' => [1,2,3,4,5,6,8,9],
        '2/-x' => [1,2,3,4,5,6,7,8,9],
        '4*x*(1/4)' => [1,2,3,4,5,6,7,8,9],
        '5*x^(3+z)' => [1,2,3,7,8,9],
        '5*x^(3+z)*5' => [1,2,3,7,8,9],
        '5*x^3' => [1,2,3,4,5,6,7,8,9],
        '6*x^3*5' => [1,2,3,4,5,6,7,8,9],
        'cos(((x+y)^2)/7)' => [1,2,3,4,5,6,7,8,9],
        'cos((1+2+x)*((y+z)*(p+q+c)))' => [1,2,3,4,5,6,7,8,9],
        'cos((1+2+x)*((y+z)*(p-q-c)))' => [1,2,3,4,5,6,7,8,9],
        'cos((1+2+x)*(sin(y)+z))' => [1,2,3,4,5,6,7,8,9],
        'cos((1+2+x)*(y+z))' => [1,2,3,4,5,6,7,8,9],
        'cos(-1/-7)' => [1,2,3,4,5,6,7,8,9],
        'cos(-1/7)' => [1,2,3,4,5,6,7,8,9],
        'cos(1/-7)' => [1,2,3,4,5,6,7,8,9],
        'cos(10/5)' => [1,2,3,4,5,6,7,8,9],
        'cos(11/5)' => [1,2,3,4,5,6,7,8,9],
        'cos(5/1)' => [1,2,3,4,5,6,7,8,9],
        'cos(7/4)' => [1,2,3,4,5,6,7,8,9],
        'cos(x^2+y^2)' => [1,2,3,4,5,6,7,8,9],
        'sin((x+4)*(x+1))*sin((x+1)*(x+4))' => [1,2,3,4,5,6,7,8,9],
        'sin(x)*(x+y+z)' => [1,2,3,4,5,6,7,8,9],
        'sqrt(x)*sqrt(x)' => [1,2,3,7,8,9],
        'sqrt(x)*sqrt(x)*sqrt(x)' => [1,2,3,7,8,9],
        'sqrt(x)*sqrt(x)*sqrt(x)*sqrt(x)' => [1,2,3,7,8,9],
        'x/x' => [1,2,3,4,5,6,7,8,9],
        'x^(-2)' => [1,2,3,4,5,6,7,8,9],
        'x^(2-z)*(5+y)' => [1,2,3,7,8,9],
        'x^(3+z)*5' => [1,2,3,7,8,9],
        'x^(4*(x+y))' => [1,2,3,7,8,9],
        'x^-3 * x^2' => [1,2,3,4,5,6,7,8,9],
        'x^2 / x' => [1,2,3,4,5,6,7,8,9],
        'x^2*(5+y)' => [1,2,3,4,5,6,7,8,9],
        'x^2+4*x+4+((13*x+7)/(x^2-x-2))' => [1,2,3,4,5,6,7,9],
        'x^2+y^2' => [1,2,3,4,5,6,7,8,9],
        'x^3*5' => [1,2,3,4,5,6,7,8,9],
);
my %test_vectors = (
        1 => [0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1],
        2 => [0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1],
        3 => [0.1, 0.3, 0.5, 0.7, 0.9, 1.1],
        4 => [-0.5, -0.6, -0.7, -0.8, -0.9, -1, -1.1],
        5 => [-0.4, -0.5, -0.6, -0.7, -0.8, -0.9, -1],
        6 => [0.1, -0.3, -0.5, -0.7, -0.9, -1.1],
        7 => [1.0, 0.9, 0.8, 0.7, 0.8, 0.9, 1],
        8 => [2.0, 1.9, 1.8, 1.7, 1.8, 1.9, 2],
        9 => [0.1, 1.7, 0.4, 0.02, 1.8, -0.9, 1],
    );
TEST_VARIABLES: while ( my ($test, $valid_tests) = each %var_expr ) { 
    my $f1 = parse_from_string($test);
    ok( defined($f1), "parsing test string [$test]" );
    if (!defined $f1) {
        next TEST_VARIABLES;
    }  
    my $f2 = $f1->to_collected();
    ok( defined($f2), "to_collected() returns defined [$f2] ($test)" );
    if (!defined $f2) {
        next TEST_VARIABLES;
    }   
     
    # test for numerical equivalence with a known set of test vectors
    # Some expressions aren't valid for some input vectors
    foreach my $tv (@{$valid_tests}) {
        my ($x, $y, $z, $p, $q, $c, $d) = @{$test_vectors{$tv}};
        my $v1 = $f1->value( 'x' => $x, 'y' => $y, 'z' => $z, 'p' => $p, 'q' => $q, 'c' => $c, 'd' => $d );
        my $v2 = $f2->value( 'x' => $x, 'y' => $y, 'z' => $z, 'p' => $p, 'q' => $q, 'c' => $c, 'd' => $d );
        ok( sprintf("%.11f", $v1) == sprintf("%.11f", $v2), "[$f1]vs[$f2]/[$v1]vs[$v2] numerically equivalent to 11 dp with test $tv");
    }
}