Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, C

Percentage Accurate: 97.8% → 98.9%

Time: 12.7s

Alternatives: 14

Speedup: 0.5×

• 33.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Initial Program: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Alternative 1: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (fma x y (fma (/ z 16.0) t (fma (/ a -4.0) b c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return fma(x, y, fma((z / 16.0), t, fma((a / -4.0), b, c)));
}

Julia

function code(x, y, z, t, a, b, c)
	return fma(x, y, fma(Float64(z / 16.0), t, fma(Float64(a / -4.0), b, c)))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x * y + N[(N[(z / 16.0), $MachinePrecision] * t + N[(N[(a / -4.0), $MachinePrecision] * b + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Step-by-step derivation

   1. associate-+l- 96.4%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

   2. associate--l+ 96.4%

      \[\leadsto \color{blue}{x \cdot y + \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

   3. fma-def 98.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

   4. associate-*l/ 98.4%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{z}{16} \cdot t} - \left(\frac{a \cdot b}{4} - c\right)\right) \]

   5. fma-neg 99.6%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\mathsf{fma}\left(\frac{z}{16}, t, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

   6. sub-neg 99.6%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, -\color{blue}{\left(\frac{a \cdot b}{4} + \left(-c\right)\right)}\right)\right) \]

   7. distribute-neg-in 99.6%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\left(-\frac{a \cdot b}{4}\right) + \left(-\left(-c\right)\right)}\right)\right) \]

   8. remove-double-neg 99.6%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\frac{a \cdot b}{4}\right) + \color{blue}{c}\right)\right) \]

   9. associate-/l* 99.6%

      \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \left(-\color{blue}{\frac{a}{\frac{4}{b}}}\right) + c\right)\right) \]

   10. distribute-frac-neg 99.6%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{\frac{4}{b}}} + c\right)\right) \]

   11. associate-/r/ 99.6%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\frac{-a}{4} \cdot b} + c\right)\right) \]

   12. fma-def 99.6%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \color{blue}{\mathsf{fma}\left(\frac{-a}{4}, b, c\right)}\right)\right) \]

   13. neg-mul-1 99.6%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

   14. *-commutative 99.6%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

   15. associate-/l* 99.6%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

   16. metadata-eval 99.6%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{\color{blue}{-4}}, b, c\right)\right)\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right)} \]
4. Add Preprocessing

5. Final simplification 99.6%

   \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{a}{-4}, b, c\right)\right)\right) \]
6. Add Preprocessing

Alternative 2: 68.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+120}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-229}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-127}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (+ (* x y) (* (* z t) 0.0625))))
   (if (<= (* a b) -2e+120)
     (+ c (* a (* b -0.25)))
     (if (<= (* a b) -2e-229)
       t_2
       (if (<= (* a b) 2e-220)
         t_1
         (if (<= (* a b) 5e-127)
           t_2
           (if (<= (* a b) 2e-58)
             t_1
             (if (<= (* a b) 2e+40)
               t_2
               (if (<= (* a b) 1e+114)
                 t_1
                 (- (* x y) (* (* a b) 0.25)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = (x * y) + ((z * t) * 0.0625);
	double tmp;
	if ((a * b) <= -2e+120) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= -2e-229) {
		tmp = t_2;
	} else if ((a * b) <= 2e-220) {
		tmp = t_1;
	} else if ((a * b) <= 5e-127) {
		tmp = t_2;
	} else if ((a * b) <= 2e-58) {
		tmp = t_1;
	} else if ((a * b) <= 2e+40) {
		tmp = t_2;
	} else if ((a * b) <= 1e+114) {
		tmp = t_1;
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = (x * y) + ((z * t) * 0.0625d0)
    if ((a * b) <= (-2d+120)) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((a * b) <= (-2d-229)) then
        tmp = t_2
    else if ((a * b) <= 2d-220) then
        tmp = t_1
    else if ((a * b) <= 5d-127) then
        tmp = t_2
    else if ((a * b) <= 2d-58) then
        tmp = t_1
    else if ((a * b) <= 2d+40) then
        tmp = t_2
    else if ((a * b) <= 1d+114) then
        tmp = t_1
    else
        tmp = (x * y) - ((a * b) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = (x * y) + ((z * t) * 0.0625);
	double tmp;
	if ((a * b) <= -2e+120) {
		tmp = c + (a * (b * -0.25));
	} else if ((a * b) <= -2e-229) {
		tmp = t_2;
	} else if ((a * b) <= 2e-220) {
		tmp = t_1;
	} else if ((a * b) <= 5e-127) {
		tmp = t_2;
	} else if ((a * b) <= 2e-58) {
		tmp = t_1;
	} else if ((a * b) <= 2e+40) {
		tmp = t_2;
	} else if ((a * b) <= 1e+114) {
		tmp = t_1;
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = (x * y) + ((z * t) * 0.0625)
	tmp = 0
	if (a * b) <= -2e+120:
		tmp = c + (a * (b * -0.25))
	elif (a * b) <= -2e-229:
		tmp = t_2
	elif (a * b) <= 2e-220:
		tmp = t_1
	elif (a * b) <= 5e-127:
		tmp = t_2
	elif (a * b) <= 2e-58:
		tmp = t_1
	elif (a * b) <= 2e+40:
		tmp = t_2
	elif (a * b) <= 1e+114:
		tmp = t_1
	else:
		tmp = (x * y) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625))
	tmp = 0.0
	if (Float64(a * b) <= -2e+120)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(a * b) <= -2e-229)
		tmp = t_2;
	elseif (Float64(a * b) <= 2e-220)
		tmp = t_1;
	elseif (Float64(a * b) <= 5e-127)
		tmp = t_2;
	elseif (Float64(a * b) <= 2e-58)
		tmp = t_1;
	elseif (Float64(a * b) <= 2e+40)
		tmp = t_2;
	elseif (Float64(a * b) <= 1e+114)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = (x * y) + ((z * t) * 0.0625);
	tmp = 0.0;
	if ((a * b) <= -2e+120)
		tmp = c + (a * (b * -0.25));
	elseif ((a * b) <= -2e-229)
		tmp = t_2;
	elseif ((a * b) <= 2e-220)
		tmp = t_1;
	elseif ((a * b) <= 5e-127)
		tmp = t_2;
	elseif ((a * b) <= 2e-58)
		tmp = t_1;
	elseif ((a * b) <= 2e+40)
		tmp = t_2;
	elseif ((a * b) <= 1e+114)
		tmp = t_1;
	else
		tmp = (x * y) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+120], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2e-229], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 2e-220], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 5e-127], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 2e-58], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2e+40], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 1e+114], t$95$1, N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -2e120

   1. Initial program 92.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 86.5%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 86.5%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

      2. associate-*r* 86.5%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   5. Simplified 86.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   if -2e120 < (*.f64 a b) < -2.00000000000000014e-229 or 1.99999999999999998e-220 < (*.f64 a b) < 4.9999999999999997e-127 or 2.0000000000000001e-58 < (*.f64 a b) < 2.00000000000000006e40

   1. Initial program 99.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 94.9%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. +-commutative 94.9%

         \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right) + c} \]

      2. associate-*r* 94.9%

         \[\leadsto \left(\color{blue}{\left(0.0625 \cdot t\right) \cdot z} + x \cdot y\right) + c \]

      3. *-commutative 94.9%

         \[\leadsto \left(\color{blue}{\left(t \cdot 0.0625\right)} \cdot z + x \cdot y\right) + c \]

      4. *-commutative 94.9%

         \[\leadsto \left(\color{blue}{z \cdot \left(t \cdot 0.0625\right)} + x \cdot y\right) + c \]

      5. +-commutative 94.9%

         \[\leadsto \color{blue}{\left(x \cdot y + z \cdot \left(t \cdot 0.0625\right)\right)} + c \]

      6. associate-+l+ 94.9%

         \[\leadsto \color{blue}{x \cdot y + \left(z \cdot \left(t \cdot 0.0625\right) + c\right)} \]

      7. *-commutative 94.9%

         \[\leadsto x \cdot y + \left(z \cdot \color{blue}{\left(0.0625 \cdot t\right)} + c\right) \]

      8. associate-*r* 94.9%

         \[\leadsto x \cdot y + \left(\color{blue}{\left(z \cdot 0.0625\right) \cdot t} + c\right) \]

      9. *-commutative 94.9%

         \[\leadsto x \cdot y + \left(\color{blue}{t \cdot \left(z \cdot 0.0625\right)} + c\right) \]

      10. fma-def 95.0%

          \[\leadsto x \cdot y + \color{blue}{\mathsf{fma}\left(t, z \cdot 0.0625, c\right)} \]

      11. *-commutative 95.0%

          \[\leadsto x \cdot y + \mathsf{fma}\left(t, \color{blue}{0.0625 \cdot z}, c\right) \]

   5. Simplified 95.0%

      \[\leadsto \color{blue}{x \cdot y + \mathsf{fma}\left(t, 0.0625 \cdot z, c\right)} \]

   6. Taylor expanded in c around 0 79.1%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) + x \cdot y} \]

   if -2.00000000000000014e-229 < (*.f64 a b) < 1.99999999999999998e-220 or 4.9999999999999997e-127 < (*.f64 a b) < 2.0000000000000001e-58 or 2.00000000000000006e40 < (*.f64 a b) < 1e114

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 81.3%

      \[\leadsto \color{blue}{x \cdot y} + c \]

   if 1e114 < (*.f64 a b)

   1. Initial program 91.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 86.5%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 81.8%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+120}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-229}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-220}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-127}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-58}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+40}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;a \cdot b \leq 10^{+114}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 43.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -3.4 \cdot 10^{+121}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.15 \cdot 10^{-196}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2.05 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 35:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 1.02 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))))
   (if (<= (* x y) -3.4e+121)
     (* x y)
     (if (<= (* x y) 1.15e-196)
       c
       (if (<= (* x y) 2.05e-42)
         t_1
         (if (<= (* x y) 35.0)
           (* z (* t 0.0625))
           (if (<= (* x y) 1.02e+62) t_1 (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (a * -0.25);
	double tmp;
	if ((x * y) <= -3.4e+121) {
		tmp = x * y;
	} else if ((x * y) <= 1.15e-196) {
		tmp = c;
	} else if ((x * y) <= 2.05e-42) {
		tmp = t_1;
	} else if ((x * y) <= 35.0) {
		tmp = z * (t * 0.0625);
	} else if ((x * y) <= 1.02e+62) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * (-0.25d0))
    if ((x * y) <= (-3.4d+121)) then
        tmp = x * y
    else if ((x * y) <= 1.15d-196) then
        tmp = c
    else if ((x * y) <= 2.05d-42) then
        tmp = t_1
    else if ((x * y) <= 35.0d0) then
        tmp = z * (t * 0.0625d0)
    else if ((x * y) <= 1.02d+62) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (a * -0.25);
	double tmp;
	if ((x * y) <= -3.4e+121) {
		tmp = x * y;
	} else if ((x * y) <= 1.15e-196) {
		tmp = c;
	} else if ((x * y) <= 2.05e-42) {
		tmp = t_1;
	} else if ((x * y) <= 35.0) {
		tmp = z * (t * 0.0625);
	} else if ((x * y) <= 1.02e+62) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * (a * -0.25)
	tmp = 0
	if (x * y) <= -3.4e+121:
		tmp = x * y
	elif (x * y) <= 1.15e-196:
		tmp = c
	elif (x * y) <= 2.05e-42:
		tmp = t_1
	elif (x * y) <= 35.0:
		tmp = z * (t * 0.0625)
	elif (x * y) <= 1.02e+62:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (Float64(x * y) <= -3.4e+121)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 1.15e-196)
		tmp = c;
	elseif (Float64(x * y) <= 2.05e-42)
		tmp = t_1;
	elseif (Float64(x * y) <= 35.0)
		tmp = Float64(z * Float64(t * 0.0625));
	elseif (Float64(x * y) <= 1.02e+62)
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b * (a * -0.25);
	tmp = 0.0;
	if ((x * y) <= -3.4e+121)
		tmp = x * y;
	elseif ((x * y) <= 1.15e-196)
		tmp = c;
	elseif ((x * y) <= 2.05e-42)
		tmp = t_1;
	elseif ((x * y) <= 35.0)
		tmp = z * (t * 0.0625);
	elseif ((x * y) <= 1.02e+62)
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -3.4e+121], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.15e-196], c, If[LessEqual[N[(x * y), $MachinePrecision], 2.05e-42], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 35.0], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.02e+62], t$95$1, N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -3.4000000000000001e121 or 1.02000000000000002e62 < (*.f64 x y)

   1. Initial program 91.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 82.5%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 75.9%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]

   5. Taylor expanded in x around inf 68.9%

      \[\leadsto \color{blue}{x \cdot y} \]

   if -3.4000000000000001e121 < (*.f64 x y) < 1.1500000000000001e-196

   1. Initial program 99.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 41.9%

      \[\leadsto \color{blue}{c} \]

   if 1.1500000000000001e-196 < (*.f64 x y) < 2.0500000000000001e-42 or 35 < (*.f64 x y) < 1.02000000000000002e62

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 80.7%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 59.3%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]

   5. Taylor expanded in x around 0 56.8%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 56.8%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} \]

      2. *-commutative 56.8%

         \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} \]

   7. Simplified 56.8%

      \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} \]

   if 2.0500000000000001e-42 < (*.f64 x y) < 35

   1. Initial program 99.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x \cdot y + \frac{\color{blue}{t \cdot z}}{16}\right) - \left(\frac{a \cdot b}{4} - c\right) \]

      3. associate-+l- 99.9%

         \[\leadsto \color{blue}{\left(\left(x \cdot y + \frac{t \cdot z}{16}\right) - \frac{a \cdot b}{4}\right) + c} \]

      4. fma-def 99.9%

         \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, y, \frac{t \cdot z}{16}\right)} - \frac{a \cdot b}{4}\right) + c \]

      5. *-commutative 99.9%

         \[\leadsto \left(\mathsf{fma}\left(x, y, \frac{\color{blue}{z \cdot t}}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

      6. associate-/l* 99.4%

         \[\leadsto \left(\mathsf{fma}\left(x, y, \color{blue}{\frac{z}{\frac{16}{t}}}\right) - \frac{a \cdot b}{4}\right) + c \]

      7. associate-/l* 99.6%

         \[\leadsto \left(\mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \color{blue}{\frac{a}{\frac{4}{b}}}\right) + c \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, y, \frac{z}{\frac{16}{t}}\right) - \frac{a}{\frac{4}{b}}\right) + c} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 99.6%

         \[\leadsto \left(\color{blue}{\left(x \cdot y + \frac{z}{\frac{16}{t}}\right)} - \frac{a}{\frac{4}{b}}\right) + c \]

      2. associate-/l* 100.0%

         \[\leadsto \left(\left(x \cdot y + \color{blue}{\frac{z \cdot t}{16}}\right) - \frac{a}{\frac{4}{b}}\right) + c \]

      3. +-commutative 100.0%

         \[\leadsto \left(\color{blue}{\left(\frac{z \cdot t}{16} + x \cdot y\right)} - \frac{a}{\frac{4}{b}}\right) + c \]

      4. div-inv 100.0%

         \[\leadsto \left(\left(\color{blue}{\left(z \cdot t\right) \cdot \frac{1}{16}} + x \cdot y\right) - \frac{a}{\frac{4}{b}}\right) + c \]

      5. associate-*l* 100.0%

         \[\leadsto \left(\left(\color{blue}{z \cdot \left(t \cdot \frac{1}{16}\right)} + x \cdot y\right) - \frac{a}{\frac{4}{b}}\right) + c \]

      6. metadata-eval 100.0%

         \[\leadsto \left(\left(z \cdot \left(t \cdot \color{blue}{0.0625}\right) + x \cdot y\right) - \frac{a}{\frac{4}{b}}\right) + c \]

   6. Applied egg-rr 100.0%

      \[\leadsto \left(\color{blue}{\left(z \cdot \left(t \cdot 0.0625\right) + x \cdot y\right)} - \frac{a}{\frac{4}{b}}\right) + c \]

   7. Taylor expanded in z around inf 72.2%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   8. Step-by-step derivation

      1. *-commutative 72.2%

         \[\leadsto 0.0625 \cdot \color{blue}{\left(z \cdot t\right)} + c \]

      2. *-commutative 72.2%

         \[\leadsto \color{blue}{\left(z \cdot t\right) \cdot 0.0625} + c \]

      3. associate-*r* 72.2%

         \[\leadsto \color{blue}{z \cdot \left(t \cdot 0.0625\right)} + c \]

      4. *-commutative 72.2%

         \[\leadsto z \cdot \color{blue}{\left(0.0625 \cdot t\right)} + c \]

   9. Simplified 72.2%

      \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} + c \]

   10. Taylor expanded in z around inf 63.5%

       \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 63.5%

          \[\leadsto \color{blue}{\left(0.0625 \cdot t\right) \cdot z} \]

       2. *-commutative 63.5%

          \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} \]

   12. Simplified 63.5%

       \[\leadsto \color{blue}{z \cdot \left(0.0625 \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.4 \cdot 10^{+121}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.15 \cdot 10^{-196}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2.05 \cdot 10^{-42}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 35:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 1.02 \cdot 10^{+62}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{if}\;x \cdot y \leq -4.3 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 1.3 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.06:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 3.35 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25)))) (t_2 (+ (* x y) (* (* z t) 0.0625))))
   (if (<= (* x y) -4.3e+77)
     t_2
     (if (<= (* x y) 1.3e-46)
       t_1
       (if (<= (* x y) 1.06)
         (+ c (* t (* z 0.0625)))
         (if (<= (* x y) 3.35e+66) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = (x * y) + ((z * t) * 0.0625);
	double tmp;
	if ((x * y) <= -4.3e+77) {
		tmp = t_2;
	} else if ((x * y) <= 1.3e-46) {
		tmp = t_1;
	} else if ((x * y) <= 1.06) {
		tmp = c + (t * (z * 0.0625));
	} else if ((x * y) <= 3.35e+66) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (a * (b * (-0.25d0)))
    t_2 = (x * y) + ((z * t) * 0.0625d0)
    if ((x * y) <= (-4.3d+77)) then
        tmp = t_2
    else if ((x * y) <= 1.3d-46) then
        tmp = t_1
    else if ((x * y) <= 1.06d0) then
        tmp = c + (t * (z * 0.0625d0))
    else if ((x * y) <= 3.35d+66) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = (x * y) + ((z * t) * 0.0625);
	double tmp;
	if ((x * y) <= -4.3e+77) {
		tmp = t_2;
	} else if ((x * y) <= 1.3e-46) {
		tmp = t_1;
	} else if ((x * y) <= 1.06) {
		tmp = c + (t * (z * 0.0625));
	} else if ((x * y) <= 3.35e+66) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = (x * y) + ((z * t) * 0.0625)
	tmp = 0
	if (x * y) <= -4.3e+77:
		tmp = t_2
	elif (x * y) <= 1.3e-46:
		tmp = t_1
	elif (x * y) <= 1.06:
		tmp = c + (t * (z * 0.0625))
	elif (x * y) <= 3.35e+66:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625))
	tmp = 0.0
	if (Float64(x * y) <= -4.3e+77)
		tmp = t_2;
	elseif (Float64(x * y) <= 1.3e-46)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.06)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (Float64(x * y) <= 3.35e+66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (a * (b * -0.25));
	t_2 = (x * y) + ((z * t) * 0.0625);
	tmp = 0.0;
	if ((x * y) <= -4.3e+77)
		tmp = t_2;
	elseif ((x * y) <= 1.3e-46)
		tmp = t_1;
	elseif ((x * y) <= 1.06)
		tmp = c + (t * (z * 0.0625));
	elseif ((x * y) <= 3.35e+66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -4.3e+77], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 1.3e-46], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.06], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.35e+66], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.29999999999999991e77 or 3.34999999999999984e66 < (*.f64 x y)

   1. Initial program 92.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 88.1%

      \[\leadsto \color{blue}{c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} \]
   4. Step-by-step derivation

      1. +-commutative 88.1%

         \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right) + c} \]

      2. associate-*r* 88.1%

         \[\leadsto \left(\color{blue}{\left(0.0625 \cdot t\right) \cdot z} + x \cdot y\right) + c \]

      3. *-commutative 88.1%

         \[\leadsto \left(\color{blue}{\left(t \cdot 0.0625\right)} \cdot z + x \cdot y\right) + c \]

      4. *-commutative 88.1%

         \[\leadsto \left(\color{blue}{z \cdot \left(t \cdot 0.0625\right)} + x \cdot y\right) + c \]

      5. +-commutative 88.1%

         \[\leadsto \color{blue}{\left(x \cdot y + z \cdot \left(t \cdot 0.0625\right)\right)} + c \]

      6. associate-+l+ 88.1%

         \[\leadsto \color{blue}{x \cdot y + \left(z \cdot \left(t \cdot 0.0625\right) + c\right)} \]

      7. *-commutative 88.1%

         \[\leadsto x \cdot y + \left(z \cdot \color{blue}{\left(0.0625 \cdot t\right)} + c\right) \]

      8. associate-*r* 88.1%

         \[\leadsto x \cdot y + \left(\color{blue}{\left(z \cdot 0.0625\right) \cdot t} + c\right) \]

      9. *-commutative 88.1%

         \[\leadsto x \cdot y + \left(\color{blue}{t \cdot \left(z \cdot 0.0625\right)} + c\right) \]

      10. fma-def 88.1%

          \[\leadsto x \cdot y + \color{blue}{\mathsf{fma}\left(t, z \cdot 0.0625, c\right)} \]

      11. *-commutative 88.1%

          \[\leadsto x \cdot y + \mathsf{fma}\left(t, \color{blue}{0.0625 \cdot z}, c\right) \]

   5. Simplified 88.1%

      \[\leadsto \color{blue}{x \cdot y + \mathsf{fma}\left(t, 0.0625 \cdot z, c\right)} \]

   6. Taylor expanded in c around 0 77.9%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) + x \cdot y} \]

   if -4.29999999999999991e77 < (*.f64 x y) < 1.3000000000000001e-46 or 1.0600000000000001 < (*.f64 x y) < 3.34999999999999984e66

   1. Initial program 99.2%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 73.6%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 73.6%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

      2. associate-*r* 73.6%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   5. Simplified 73.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   if 1.3000000000000001e-46 < (*.f64 x y) < 1.0600000000000001

   1. Initial program 99.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 72.2%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   4. Step-by-step derivation

      1. associate-*r* 72.2%

         \[\leadsto \color{blue}{\left(0.0625 \cdot t\right) \cdot z} + c \]

      2. *-commutative 72.2%

         \[\leadsto \color{blue}{\left(t \cdot 0.0625\right)} \cdot z + c \]

      3. associate-*r* 72.2%

         \[\leadsto \color{blue}{t \cdot \left(0.0625 \cdot z\right)} + c \]

   5. Simplified 72.2%

      \[\leadsto \color{blue}{t \cdot \left(0.0625 \cdot z\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4.3 \cdot 10^{+77}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;x \cdot y \leq 1.3 \cdot 10^{-46}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.06:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 3.35 \cdot 10^{+66}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
   (if (<= t_1 INFINITY) (+ c t_1) (+ c (* a (* b -0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = c + t_1;
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)
	tmp = 0
	if t_1 <= math.inf:
		tmp = c + t_1
	else:
		tmp = c + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(c + t_1);
	else
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = c + t_1;
	else
		tmp = c + (a * (b * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4))

   1. Initial program 0.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 78.4%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 78.4%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

      2. associate-*r* 78.4%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   5. Simplified 78.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1.45 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 3.15 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 800:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25)))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -1.45e+80)
     t_2
     (if (<= (* x y) 3.15e-43)
       t_1
       (if (<= (* x y) 800.0)
         (+ c (* t (* z 0.0625)))
         (if (<= (* x y) 6e+72) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.45e+80) {
		tmp = t_2;
	} else if ((x * y) <= 3.15e-43) {
		tmp = t_1;
	} else if ((x * y) <= 800.0) {
		tmp = c + (t * (z * 0.0625));
	} else if ((x * y) <= 6e+72) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (a * (b * (-0.25d0)))
    t_2 = c + (x * y)
    if ((x * y) <= (-1.45d+80)) then
        tmp = t_2
    else if ((x * y) <= 3.15d-43) then
        tmp = t_1
    else if ((x * y) <= 800.0d0) then
        tmp = c + (t * (z * 0.0625d0))
    else if ((x * y) <= 6d+72) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.45e+80) {
		tmp = t_2;
	} else if ((x * y) <= 3.15e-43) {
		tmp = t_1;
	} else if ((x * y) <= 800.0) {
		tmp = c + (t * (z * 0.0625));
	} else if ((x * y) <= 6e+72) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = c + (x * y)
	tmp = 0
	if (x * y) <= -1.45e+80:
		tmp = t_2
	elif (x * y) <= 3.15e-43:
		tmp = t_1
	elif (x * y) <= 800.0:
		tmp = c + (t * (z * 0.0625))
	elif (x * y) <= 6e+72:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1.45e+80)
		tmp = t_2;
	elseif (Float64(x * y) <= 3.15e-43)
		tmp = t_1;
	elseif (Float64(x * y) <= 800.0)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (Float64(x * y) <= 6e+72)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (a * (b * -0.25));
	t_2 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -1.45e+80)
		tmp = t_2;
	elseif ((x * y) <= 3.15e-43)
		tmp = t_1;
	elseif ((x * y) <= 800.0)
		tmp = c + (t * (z * 0.0625));
	elseif ((x * y) <= 6e+72)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.45e+80], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 3.15e-43], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 800.0], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6e+72], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.44999999999999993e80 or 6.00000000000000006e72 < (*.f64 x y)

   1. Initial program 92.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.9%

      \[\leadsto \color{blue}{x \cdot y} + c \]

   if -1.44999999999999993e80 < (*.f64 x y) < 3.1500000000000001e-43 or 800 < (*.f64 x y) < 6.00000000000000006e72

   1. Initial program 99.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 72.0%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 72.0%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

      2. associate-*r* 72.0%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   5. Simplified 72.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   if 3.1500000000000001e-43 < (*.f64 x y) < 800

   1. Initial program 99.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 72.2%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   4. Step-by-step derivation

      1. associate-*r* 72.2%

         \[\leadsto \color{blue}{\left(0.0625 \cdot t\right) \cdot z} + c \]

      2. *-commutative 72.2%

         \[\leadsto \color{blue}{\left(t \cdot 0.0625\right)} \cdot z + c \]

      3. associate-*r* 72.2%

         \[\leadsto \color{blue}{t \cdot \left(0.0625 \cdot z\right)} + c \]

   5. Simplified 72.2%

      \[\leadsto \color{blue}{t \cdot \left(0.0625 \cdot z\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.45 \cdot 10^{+80}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 3.15 \cdot 10^{-43}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 800:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+72}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 43.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.3 \cdot 10^{+122}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.05 \cdot 10^{-196}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 7.3 \cdot 10^{+59}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -3.3e+122)
   (* x y)
   (if (<= (* x y) 1.05e-196)
     c
     (if (<= (* x y) 7.3e+59) (* b (* a -0.25)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -3.3e+122) {
		tmp = x * y;
	} else if ((x * y) <= 1.05e-196) {
		tmp = c;
	} else if ((x * y) <= 7.3e+59) {
		tmp = b * (a * -0.25);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x * y) <= (-3.3d+122)) then
        tmp = x * y
    else if ((x * y) <= 1.05d-196) then
        tmp = c
    else if ((x * y) <= 7.3d+59) then
        tmp = b * (a * (-0.25d0))
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -3.3e+122) {
		tmp = x * y;
	} else if ((x * y) <= 1.05e-196) {
		tmp = c;
	} else if ((x * y) <= 7.3e+59) {
		tmp = b * (a * -0.25);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -3.3e+122:
		tmp = x * y
	elif (x * y) <= 1.05e-196:
		tmp = c
	elif (x * y) <= 7.3e+59:
		tmp = b * (a * -0.25)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -3.3e+122)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 1.05e-196)
		tmp = c;
	elseif (Float64(x * y) <= 7.3e+59)
		tmp = Float64(b * Float64(a * -0.25));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -3.3e+122)
		tmp = x * y;
	elseif ((x * y) <= 1.05e-196)
		tmp = c;
	elseif ((x * y) <= 7.3e+59)
		tmp = b * (a * -0.25);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -3.3e+122], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.05e-196], c, If[LessEqual[N[(x * y), $MachinePrecision], 7.3e+59], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.2999999999999999e122 or 7.3000000000000003e59 < (*.f64 x y)

   1. Initial program 91.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 82.5%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 75.9%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]

   5. Taylor expanded in x around inf 68.9%

      \[\leadsto \color{blue}{x \cdot y} \]

   if -3.2999999999999999e122 < (*.f64 x y) < 1.04999999999999994e-196

   1. Initial program 99.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 41.9%

      \[\leadsto \color{blue}{c} \]

   if 1.04999999999999994e-196 < (*.f64 x y) < 7.3000000000000003e59

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 69.3%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 50.9%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]

   5. Taylor expanded in x around 0 48.9%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 48.9%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} \]

      2. *-commutative 48.9%

         \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} \]

   7. Simplified 48.9%

      \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.3 \cdot 10^{+122}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.05 \cdot 10^{-196}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 7.3 \cdot 10^{+59}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+209}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+114}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -2e+209)
   (* b (* a -0.25))
   (if (<= (* a b) 1e+114)
     (+ c (+ (* x y) (* (* z t) 0.0625)))
     (- (* x y) (* (* a b) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2e+209) {
		tmp = b * (a * -0.25);
	} else if ((a * b) <= 1e+114) {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= (-2d+209)) then
        tmp = b * (a * (-0.25d0))
    else if ((a * b) <= 1d+114) then
        tmp = c + ((x * y) + ((z * t) * 0.0625d0))
    else
        tmp = (x * y) - ((a * b) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2e+209) {
		tmp = b * (a * -0.25);
	} else if ((a * b) <= 1e+114) {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -2e+209:
		tmp = b * (a * -0.25)
	elif (a * b) <= 1e+114:
		tmp = c + ((x * y) + ((z * t) * 0.0625))
	else:
		tmp = (x * y) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -2e+209)
		tmp = Float64(b * Float64(a * -0.25));
	elseif (Float64(a * b) <= 1e+114)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625)));
	else
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -2e+209)
		tmp = b * (a * -0.25);
	elseif ((a * b) <= 1e+114)
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	else
		tmp = (x * y) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -2e+209], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+114], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.0000000000000001e209

   1. Initial program 87.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 93.8%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 93.8%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]

   5. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} \]

   if -2.0000000000000001e209 < (*.f64 a b) < 1e114

   1. Initial program 98.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 93.2%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} + c \]

   if 1e114 < (*.f64 a b)

   1. Initial program 91.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 86.5%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 81.8%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+209}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+114}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+209}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+99}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -2e+209)
   (* b (* a -0.25))
   (if (<= (* a b) 1e+99)
     (+ c (+ (* x y) (* (* z t) 0.0625)))
     (- (+ c (* x y)) (* (* a b) 0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2e+209) {
		tmp = b * (a * -0.25);
	} else if ((a * b) <= 1e+99) {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	} else {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= (-2d+209)) then
        tmp = b * (a * (-0.25d0))
    else if ((a * b) <= 1d+99) then
        tmp = c + ((x * y) + ((z * t) * 0.0625d0))
    else
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2e+209) {
		tmp = b * (a * -0.25);
	} else if ((a * b) <= 1e+99) {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	} else {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -2e+209:
		tmp = b * (a * -0.25)
	elif (a * b) <= 1e+99:
		tmp = c + ((x * y) + ((z * t) * 0.0625))
	else:
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -2e+209)
		tmp = Float64(b * Float64(a * -0.25));
	elseif (Float64(a * b) <= 1e+99)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625)));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -2e+209)
		tmp = b * (a * -0.25);
	elseif ((a * b) <= 1e+99)
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	else
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -2e+209], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+99], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.0000000000000001e209

   1. Initial program 87.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 93.8%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 93.8%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]

   5. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} \]

   if -2.0000000000000001e209 < (*.f64 a b) < 9.9999999999999997e98

   1. Initial program 98.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 93.2%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} + c \]

   if 9.9999999999999997e98 < (*.f64 a b)

   1. Initial program 91.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 86.9%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+209}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+99}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot t\right) \cdot 0.0625\\ t_2 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+121}:\\ \;\;\;\;\left(c + t\_1\right) - t\_2\\ \mathbf{elif}\;a \cdot b \leq 10^{+99}:\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* z t) 0.0625)) (t_2 (* (* a b) 0.25)))
   (if (<= (* a b) -1e+121)
     (- (+ c t_1) t_2)
     (if (<= (* a b) 1e+99) (+ c (+ (* x y) t_1)) (- (+ c (* x y)) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) * 0.0625;
	double t_2 = (a * b) * 0.25;
	double tmp;
	if ((a * b) <= -1e+121) {
		tmp = (c + t_1) - t_2;
	} else if ((a * b) <= 1e+99) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + (x * y)) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * t) * 0.0625d0
    t_2 = (a * b) * 0.25d0
    if ((a * b) <= (-1d+121)) then
        tmp = (c + t_1) - t_2
    else if ((a * b) <= 1d+99) then
        tmp = c + ((x * y) + t_1)
    else
        tmp = (c + (x * y)) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) * 0.0625;
	double t_2 = (a * b) * 0.25;
	double tmp;
	if ((a * b) <= -1e+121) {
		tmp = (c + t_1) - t_2;
	} else if ((a * b) <= 1e+99) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + (x * y)) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (z * t) * 0.0625
	t_2 = (a * b) * 0.25
	tmp = 0
	if (a * b) <= -1e+121:
		tmp = (c + t_1) - t_2
	elif (a * b) <= 1e+99:
		tmp = c + ((x * y) + t_1)
	else:
		tmp = (c + (x * y)) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) * 0.0625)
	t_2 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if (Float64(a * b) <= -1e+121)
		tmp = Float64(Float64(c + t_1) - t_2);
	elseif (Float64(a * b) <= 1e+99)
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (z * t) * 0.0625;
	t_2 = (a * b) * 0.25;
	tmp = 0.0;
	if ((a * b) <= -1e+121)
		tmp = (c + t_1) - t_2;
	elseif ((a * b) <= 1e+99)
		tmp = c + ((x * y) + t_1);
	else
		tmp = (c + (x * y)) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1e+121], N[(N[(c + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1e+99], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.00000000000000004e121

   1. Initial program 92.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.1%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if -1.00000000000000004e121 < (*.f64 a b) < 9.9999999999999997e98

   1. Initial program 98.8%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 95.8%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} + c \]

   if 9.9999999999999997e98 < (*.f64 a b)

   1. Initial program 91.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 86.9%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+121}:\\ \;\;\;\;\left(c + \left(z \cdot t\right) \cdot 0.0625\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 10^{+99}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.35 \cdot 10^{+80} \lor \neg \left(x \cdot y \leq 2.6 \cdot 10^{+71}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.35e+80) (not (<= (* x y) 2.6e+71)))
   (+ c (* x y))
   (+ c (* a (* b -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.35e+80) || !((x * y) <= 2.6e+71)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-1.35d+80)) .or. (.not. ((x * y) <= 2.6d+71))) then
        tmp = c + (x * y)
    else
        tmp = c + (a * (b * (-0.25d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.35e+80) || !((x * y) <= 2.6e+71)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.35e+80) or not ((x * y) <= 2.6e+71):
		tmp = c + (x * y)
	else:
		tmp = c + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.35e+80) || !(Float64(x * y) <= 2.6e+71))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.35e+80) || ~(((x * y) <= 2.6e+71)))
		tmp = c + (x * y);
	else
		tmp = c + (a * (b * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.35e+80], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.6e+71]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.34999999999999991e80 or 2.59999999999999991e71 < (*.f64 x y)

   1. Initial program 92.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.9%

      \[\leadsto \color{blue}{x \cdot y} + c \]

   if -1.34999999999999991e80 < (*.f64 x y) < 2.59999999999999991e71

   1. Initial program 99.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 69.1%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative 69.1%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]

      2. associate-*r* 69.1%

         \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]

   5. Simplified 69.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot -0.25\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.35 \cdot 10^{+80} \lor \neg \left(x \cdot y \leq 2.6 \cdot 10^{+71}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+122} \lor \neg \left(x \cdot y \leq 2.9 \cdot 10^{+67}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1.8e+122) (not (<= (* x y) 2.9e+67))) (* x y) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.8e+122) || !((x * y) <= 2.9e+67)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-1.8d+122)) .or. (.not. ((x * y) <= 2.9d+67))) then
        tmp = x * y
    else
        tmp = c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1.8e+122) || !((x * y) <= 2.9e+67)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1.8e+122) or not ((x * y) <= 2.9e+67):
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1.8e+122) || !(Float64(x * y) <= 2.9e+67))
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1.8e+122) || ~(((x * y) <= 2.9e+67)))
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.8e+122], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.9e+67]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.8000000000000001e122 or 2.90000000000000023e67 < (*.f64 x y)

   1. Initial program 91.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 83.2%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 77.5%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]

   5. Taylor expanded in x around inf 70.3%

      \[\leadsto \color{blue}{x \cdot y} \]

   if -1.8000000000000001e122 < (*.f64 x y) < 2.90000000000000023e67

   1. Initial program 99.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 35.8%

      \[\leadsto \color{blue}{c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.8 \cdot 10^{+122} \lor \neg \left(x \cdot y \leq 2.9 \cdot 10^{+67}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+105} \lor \neg \left(a \leq 2.4 \cdot 10^{-75}\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -1.2e+105) (not (<= a 2.4e-75)))
   (* b (* a -0.25))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.2e+105) || !(a <= 2.4e-75)) {
		tmp = b * (a * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-1.2d+105)) .or. (.not. (a <= 2.4d-75))) then
        tmp = b * (a * (-0.25d0))
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.2e+105) || !(a <= 2.4e-75)) {
		tmp = b * (a * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -1.2e+105) or not (a <= 2.4e-75):
		tmp = b * (a * -0.25)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -1.2e+105) || !(a <= 2.4e-75))
		tmp = Float64(b * Float64(a * -0.25));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -1.2e+105) || ~((a <= 2.4e-75)))
		tmp = b * (a * -0.25);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -1.2e+105], N[Not[LessEqual[a, 2.4e-75]], $MachinePrecision]], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.19999999999999987e105 or 2.40000000000000019e-75 < a

   1. Initial program 93.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 75.6%

      \[\leadsto \color{blue}{\left(c + x \cdot y\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   4. Taylor expanded in c around 0 60.6%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]

   5. Taylor expanded in x around 0 48.6%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 48.6%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} \]

      2. *-commutative 48.6%

         \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} \]

   7. Simplified 48.6%

      \[\leadsto \color{blue}{b \cdot \left(-0.25 \cdot a\right)} \]

   if -1.19999999999999987e105 < a < 2.40000000000000019e-75

   1. Initial program 98.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 70.2%

      \[\leadsto \color{blue}{x \cdot y} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+105} \lor \neg \left(a \leq 2.4 \cdot 10^{-75}\right):\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 22.1% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ c \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 c)

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return c;
}

Python

def code(x, y, z, t, a, b, c):
	return c

Julia

function code(x, y, z, t, a, b, c)
	return c
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := c

Derivation

1. Initial program 96.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Add Preprocessing

3. Taylor expanded in c around inf 25.2%

   \[\leadsto \color{blue}{c} \]

4. Final simplification 25.2%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024027 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))