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

Percentage Accurate: 97.8% → 98.9%

Time: 12.4s

Alternatives: 17

Speedup: 1.0×

• 32.9% 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

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. associate--l+ 98.4%

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

   2. fma-define 98.8%

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

   3. associate-/l* 98.8%

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

   4. fma-neg 99.2%

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

   5. distribute-neg-frac2 99.2%

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

   6. metadata-eval 99.2%

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

3. Simplified 99.2%

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

Alternative 2: 98.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. associate-+l- 98.4%

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

   2. *-commutative 98.4%

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

   3. associate-+l- 98.4%

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

   4. fma-define 98.8%

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

   5. *-commutative 98.8%

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

   6. associate-/l* 98.8%

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

   7. associate-/l* 98.8%

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

3. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 3: 65.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+299}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{+47}:\\ \;\;\;\;c + t\_2\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-311}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-212}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* 0.0625 (* z t)))) (t_2 (* b (* a -0.25))))
   (if (<= (* a b) -5e+299)
     t_2
     (if (<= (* a b) -2e+200)
       t_1
       (if (<= (* a b) -5e+47)
         (+ c t_2)
         (if (<= (* a b) -2e-311)
           t_1
           (if (<= (* a b) 2e-212)
             (+ c (* x y))
             (if (<= (* a b) 5e+36) 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 = (x * y) + (0.0625 * (z * t));
	double t_2 = b * (a * -0.25);
	double tmp;
	if ((a * b) <= -5e+299) {
		tmp = t_2;
	} else if ((a * b) <= -2e+200) {
		tmp = t_1;
	} else if ((a * b) <= -5e+47) {
		tmp = c + t_2;
	} else if ((a * b) <= -2e-311) {
		tmp = t_1;
	} else if ((a * b) <= 2e-212) {
		tmp = c + (x * y);
	} else if ((a * b) <= 5e+36) {
		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 = (x * y) + (0.0625d0 * (z * t))
    t_2 = b * (a * (-0.25d0))
    if ((a * b) <= (-5d+299)) then
        tmp = t_2
    else if ((a * b) <= (-2d+200)) then
        tmp = t_1
    else if ((a * b) <= (-5d+47)) then
        tmp = c + t_2
    else if ((a * b) <= (-2d-311)) then
        tmp = t_1
    else if ((a * b) <= 2d-212) then
        tmp = c + (x * y)
    else if ((a * b) <= 5d+36) 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 = (x * y) + (0.0625 * (z * t));
	double t_2 = b * (a * -0.25);
	double tmp;
	if ((a * b) <= -5e+299) {
		tmp = t_2;
	} else if ((a * b) <= -2e+200) {
		tmp = t_1;
	} else if ((a * b) <= -5e+47) {
		tmp = c + t_2;
	} else if ((a * b) <= -2e-311) {
		tmp = t_1;
	} else if ((a * b) <= 2e-212) {
		tmp = c + (x * y);
	} else if ((a * b) <= 5e+36) {
		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 = (x * y) + (0.0625 * (z * t))
	t_2 = b * (a * -0.25)
	tmp = 0
	if (a * b) <= -5e+299:
		tmp = t_2
	elif (a * b) <= -2e+200:
		tmp = t_1
	elif (a * b) <= -5e+47:
		tmp = c + t_2
	elif (a * b) <= -2e-311:
		tmp = t_1
	elif (a * b) <= 2e-212:
		tmp = c + (x * y)
	elif (a * b) <= 5e+36:
		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(Float64(x * y) + Float64(0.0625 * Float64(z * t)))
	t_2 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (Float64(a * b) <= -5e+299)
		tmp = t_2;
	elseif (Float64(a * b) <= -2e+200)
		tmp = t_1;
	elseif (Float64(a * b) <= -5e+47)
		tmp = Float64(c + t_2);
	elseif (Float64(a * b) <= -2e-311)
		tmp = t_1;
	elseif (Float64(a * b) <= 2e-212)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(a * b) <= 5e+36)
		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 = (x * y) + (0.0625 * (z * t));
	t_2 = b * (a * -0.25);
	tmp = 0.0;
	if ((a * b) <= -5e+299)
		tmp = t_2;
	elseif ((a * b) <= -2e+200)
		tmp = t_1;
	elseif ((a * b) <= -5e+47)
		tmp = c + t_2;
	elseif ((a * b) <= -2e-311)
		tmp = t_1;
	elseif ((a * b) <= 2e-212)
		tmp = c + (x * y);
	elseif ((a * b) <= 5e+36)
		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[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+299], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -2e+200], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -5e+47], N[(c + t$95$2), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -2e-311], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2e-212], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+36], t$95$1, N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a b) < -5.0000000000000003e299

   1. Initial program 93.3%

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

   3. Taylor expanded in a around inf 94.1%

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

      1. *-commutative 94.1%

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

      2. *-commutative 94.1%

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

      3. associate-*r* 94.1%

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

   5. Simplified 94.1%

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

   6. Taylor expanded in b around inf 94.1%

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

   7. Taylor expanded in a around inf 94.1%

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

      1. *-commutative 94.1%

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

   9. Simplified 94.1%

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

   if -5.0000000000000003e299 < (*.f64 a b) < -1.9999999999999999e200 or -5.00000000000000022e47 < (*.f64 a b) < -1.9999999999999e-311 or 1.99999999999999991e-212 < (*.f64 a b) < 4.99999999999999977e36

   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 a around 0 96.4%

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

   4. Taylor expanded in c around 0 79.4%

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

   if -1.9999999999999999e200 < (*.f64 a b) < -5.00000000000000022e47

   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 inf 65.6%

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

      1. *-commutative 65.6%

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

      2. *-commutative 65.6%

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

      3. associate-*r* 65.6%

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

   5. Simplified 65.6%

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

   if -1.9999999999999e-311 < (*.f64 a b) < 1.99999999999999991e-212

   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 x around inf 81.5%

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

   if 4.99999999999999977e36 < (*.f64 a b)

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0 95.6%

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

   4. Taylor expanded in c around 0 84.3%

      \[\leadsto \color{blue}{x \cdot y - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+299}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{+200}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq -5 \cdot 10^{+47}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-311}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-212}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+36}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 44.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -1.45 \cdot 10^{+154}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -8.5 \cdot 10^{-146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-305}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2.8 \cdot 10^{-130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.2 \cdot 10^{+15}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 7.5 \cdot 10^{+68}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))))
   (if (<= (* x y) -1.45e+154)
     (* x y)
     (if (<= (* x y) -8.5e-146)
       t_1
       (if (<= (* x y) -4e-305)
         c
         (if (<= (* x y) 2.8e-130)
           t_1
           (if (<= (* x y) 1.2e+15)
             c
             (if (<= (* x y) 7.5e+68) 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) <= -1.45e+154) {
		tmp = x * y;
	} else if ((x * y) <= -8.5e-146) {
		tmp = t_1;
	} else if ((x * y) <= -4e-305) {
		tmp = c;
	} else if ((x * y) <= 2.8e-130) {
		tmp = t_1;
	} else if ((x * y) <= 1.2e+15) {
		tmp = c;
	} else if ((x * y) <= 7.5e+68) {
		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) <= (-1.45d+154)) then
        tmp = x * y
    else if ((x * y) <= (-8.5d-146)) then
        tmp = t_1
    else if ((x * y) <= (-4d-305)) then
        tmp = c
    else if ((x * y) <= 2.8d-130) then
        tmp = t_1
    else if ((x * y) <= 1.2d+15) then
        tmp = c
    else if ((x * y) <= 7.5d+68) 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) <= -1.45e+154) {
		tmp = x * y;
	} else if ((x * y) <= -8.5e-146) {
		tmp = t_1;
	} else if ((x * y) <= -4e-305) {
		tmp = c;
	} else if ((x * y) <= 2.8e-130) {
		tmp = t_1;
	} else if ((x * y) <= 1.2e+15) {
		tmp = c;
	} else if ((x * y) <= 7.5e+68) {
		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) <= -1.45e+154:
		tmp = x * y
	elif (x * y) <= -8.5e-146:
		tmp = t_1
	elif (x * y) <= -4e-305:
		tmp = c
	elif (x * y) <= 2.8e-130:
		tmp = t_1
	elif (x * y) <= 1.2e+15:
		tmp = c
	elif (x * y) <= 7.5e+68:
		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) <= -1.45e+154)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -8.5e-146)
		tmp = t_1;
	elseif (Float64(x * y) <= -4e-305)
		tmp = c;
	elseif (Float64(x * y) <= 2.8e-130)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.2e+15)
		tmp = c;
	elseif (Float64(x * y) <= 7.5e+68)
		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) <= -1.45e+154)
		tmp = x * y;
	elseif ((x * y) <= -8.5e-146)
		tmp = t_1;
	elseif ((x * y) <= -4e-305)
		tmp = c;
	elseif ((x * y) <= 2.8e-130)
		tmp = t_1;
	elseif ((x * y) <= 1.2e+15)
		tmp = c;
	elseif ((x * y) <= 7.5e+68)
		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], -1.45e+154], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -8.5e-146], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -4e-305], c, If[LessEqual[N[(x * y), $MachinePrecision], 2.8e-130], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.2e+15], c, If[LessEqual[N[(x * y), $MachinePrecision], 7.5e+68], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.4499999999999999e154 or 7.49999999999999959e68 < (*.f64 x y)

   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 z around 0 84.1%

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

   4. Taylor expanded in x around inf 66.7%

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

   if -1.4499999999999999e154 < (*.f64 x y) < -8.4999999999999997e-146 or -3.99999999999999999e-305 < (*.f64 x y) < 2.80000000000000016e-130 or 1.2e15 < (*.f64 x y) < 7.49999999999999959e68

   1. Initial program 98.3%

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

   3. Taylor expanded in a around inf 64.2%

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

      1. *-commutative 64.2%

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

      2. *-commutative 64.2%

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

      3. associate-*r* 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in b around inf 58.9%

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

   7. Taylor expanded in a around inf 45.8%

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

      1. *-commutative 45.8%

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

   9. Simplified 45.8%

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

   if -8.4999999999999997e-146 < (*.f64 x y) < -3.99999999999999999e-305 or 2.80000000000000016e-130 < (*.f64 x y) < 1.2e15

   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 c around inf 46.4%

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

Alternative 5: 68.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := x \cdot y + t\_2\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+70}:\\ \;\;\;\;t\_2 + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-311}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+36}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* 0.0625 (* z t))) (t_3 (+ (* x y) t_2)))
   (if (<= (* a b) -2e+70)
     (+ t_2 (* (* a b) -0.25))
     (if (<= (* a b) -4e-20)
       t_1
       (if (<= (* a b) -2e-311)
         t_3
         (if (<= (* a b) 2e-212)
           t_1
           (if (<= (* a b) 5e+36) t_3 (- (* 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 = 0.0625 * (z * t);
	double t_3 = (x * y) + t_2;
	double tmp;
	if ((a * b) <= -2e+70) {
		tmp = t_2 + ((a * b) * -0.25);
	} else if ((a * b) <= -4e-20) {
		tmp = t_1;
	} else if ((a * b) <= -2e-311) {
		tmp = t_3;
	} else if ((a * b) <= 2e-212) {
		tmp = t_1;
	} else if ((a * b) <= 5e+36) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = 0.0625d0 * (z * t)
    t_3 = (x * y) + t_2
    if ((a * b) <= (-2d+70)) then
        tmp = t_2 + ((a * b) * (-0.25d0))
    else if ((a * b) <= (-4d-20)) then
        tmp = t_1
    else if ((a * b) <= (-2d-311)) then
        tmp = t_3
    else if ((a * b) <= 2d-212) then
        tmp = t_1
    else if ((a * b) <= 5d+36) then
        tmp = t_3
    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 = 0.0625 * (z * t);
	double t_3 = (x * y) + t_2;
	double tmp;
	if ((a * b) <= -2e+70) {
		tmp = t_2 + ((a * b) * -0.25);
	} else if ((a * b) <= -4e-20) {
		tmp = t_1;
	} else if ((a * b) <= -2e-311) {
		tmp = t_3;
	} else if ((a * b) <= 2e-212) {
		tmp = t_1;
	} else if ((a * b) <= 5e+36) {
		tmp = t_3;
	} 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 = 0.0625 * (z * t)
	t_3 = (x * y) + t_2
	tmp = 0
	if (a * b) <= -2e+70:
		tmp = t_2 + ((a * b) * -0.25)
	elif (a * b) <= -4e-20:
		tmp = t_1
	elif (a * b) <= -2e-311:
		tmp = t_3
	elif (a * b) <= 2e-212:
		tmp = t_1
	elif (a * b) <= 5e+36:
		tmp = t_3
	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(0.0625 * Float64(z * t))
	t_3 = Float64(Float64(x * y) + t_2)
	tmp = 0.0
	if (Float64(a * b) <= -2e+70)
		tmp = Float64(t_2 + Float64(Float64(a * b) * -0.25));
	elseif (Float64(a * b) <= -4e-20)
		tmp = t_1;
	elseif (Float64(a * b) <= -2e-311)
		tmp = t_3;
	elseif (Float64(a * b) <= 2e-212)
		tmp = t_1;
	elseif (Float64(a * b) <= 5e+36)
		tmp = t_3;
	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 = 0.0625 * (z * t);
	t_3 = (x * y) + t_2;
	tmp = 0.0;
	if ((a * b) <= -2e+70)
		tmp = t_2 + ((a * b) * -0.25);
	elseif ((a * b) <= -4e-20)
		tmp = t_1;
	elseif ((a * b) <= -2e-311)
		tmp = t_3;
	elseif ((a * b) <= 2e-212)
		tmp = t_1;
	elseif ((a * b) <= 5e+36)
		tmp = t_3;
	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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+70], N[(t$95$2 + N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -4e-20], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -2e-311], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 2e-212], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 5e+36], t$95$3, 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) < -2.00000000000000015e70

   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 0 89.4%

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

   4. Taylor expanded in z around inf 72.0%

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

   5. Taylor expanded in c around 0 70.3%

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

   6. Taylor expanded in z around 0 80.6%

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

   if -2.00000000000000015e70 < (*.f64 a b) < -3.99999999999999978e-20 or -1.9999999999999e-311 < (*.f64 a b) < 1.99999999999999991e-212

   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 x around inf 81.6%

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

   if -3.99999999999999978e-20 < (*.f64 a b) < -1.9999999999999e-311 or 1.99999999999999991e-212 < (*.f64 a b) < 4.99999999999999977e36

   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 a around 0 96.7%

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

   4. Taylor expanded in c around 0 79.7%

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

   if 4.99999999999999977e36 < (*.f64 a b)

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0 95.6%

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

   4. Taylor expanded in c around 0 84.3%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+70}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq -4 \cdot 10^{-20}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-311}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-212}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+36}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;y \leq -400:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-267}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+87}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625))))
        (t_2 (+ (* x y) (* 0.0625 (* z t))))
        (t_3 (+ c (* b (* a -0.25)))))
   (if (<= y -400.0)
     t_2
     (if (<= y -1.9e-184)
       t_1
       (if (<= y 6e-267)
         t_3
         (if (<= y 1.4e-101) t_1 (if (<= y 6.4e+87) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (t * (z * 0.0625));
	double t_2 = (x * y) + (0.0625 * (z * t));
	double t_3 = c + (b * (a * -0.25));
	double tmp;
	if (y <= -400.0) {
		tmp = t_2;
	} else if (y <= -1.9e-184) {
		tmp = t_1;
	} else if (y <= 6e-267) {
		tmp = t_3;
	} else if (y <= 1.4e-101) {
		tmp = t_1;
	} else if (y <= 6.4e+87) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = c + (t * (z * 0.0625d0))
    t_2 = (x * y) + (0.0625d0 * (z * t))
    t_3 = c + (b * (a * (-0.25d0)))
    if (y <= (-400.0d0)) then
        tmp = t_2
    else if (y <= (-1.9d-184)) then
        tmp = t_1
    else if (y <= 6d-267) then
        tmp = t_3
    else if (y <= 1.4d-101) then
        tmp = t_1
    else if (y <= 6.4d+87) then
        tmp = t_3
    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 + (t * (z * 0.0625));
	double t_2 = (x * y) + (0.0625 * (z * t));
	double t_3 = c + (b * (a * -0.25));
	double tmp;
	if (y <= -400.0) {
		tmp = t_2;
	} else if (y <= -1.9e-184) {
		tmp = t_1;
	} else if (y <= 6e-267) {
		tmp = t_3;
	} else if (y <= 1.4e-101) {
		tmp = t_1;
	} else if (y <= 6.4e+87) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (t * (z * 0.0625))
	t_2 = (x * y) + (0.0625 * (z * t))
	t_3 = c + (b * (a * -0.25))
	tmp = 0
	if y <= -400.0:
		tmp = t_2
	elif y <= -1.9e-184:
		tmp = t_1
	elif y <= 6e-267:
		tmp = t_3
	elif y <= 1.4e-101:
		tmp = t_1
	elif y <= 6.4e+87:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(t * Float64(z * 0.0625)))
	t_2 = Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t)))
	t_3 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (y <= -400.0)
		tmp = t_2;
	elseif (y <= -1.9e-184)
		tmp = t_1;
	elseif (y <= 6e-267)
		tmp = t_3;
	elseif (y <= 1.4e-101)
		tmp = t_1;
	elseif (y <= 6.4e+87)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (t * (z * 0.0625));
	t_2 = (x * y) + (0.0625 * (z * t));
	t_3 = c + (b * (a * -0.25));
	tmp = 0.0;
	if (y <= -400.0)
		tmp = t_2;
	elseif (y <= -1.9e-184)
		tmp = t_1;
	elseif (y <= 6e-267)
		tmp = t_3;
	elseif (y <= 1.4e-101)
		tmp = t_1;
	elseif (y <= 6.4e+87)
		tmp = t_3;
	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[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -400.0], t$95$2, If[LessEqual[y, -1.9e-184], t$95$1, If[LessEqual[y, 6e-267], t$95$3, If[LessEqual[y, 1.4e-101], t$95$1, If[LessEqual[y, 6.4e+87], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -400 or 6.4000000000000001e87 < y

   1. Initial program 97.2%

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

   3. Taylor expanded in a around 0 77.8%

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

   4. Taylor expanded in c around 0 65.6%

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

   if -400 < y < -1.90000000000000008e-184 or 5.9999999999999999e-267 < y < 1.39999999999999995e-101

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf 64.6%

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

      1. associate-*r* 64.6%

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

      2. *-commutative 64.6%

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

      3. associate-*r* 64.6%

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

   5. Simplified 64.6%

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

   if -1.90000000000000008e-184 < y < 5.9999999999999999e-267 or 1.39999999999999995e-101 < y < 6.4000000000000001e87

   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 a around inf 64.8%

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

      1. *-commutative 64.8%

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

      2. *-commutative 64.8%

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

      3. associate-*r* 64.8%

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

   5. Simplified 64.8%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -400:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-184}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-267}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-101}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+87}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ \mathbf{if}\;a \leq -1.52 \cdot 10^{+109}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-258}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 3.75 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25 + \frac{c}{b}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))))
   (if (<= a -1.52e+109)
     (+ c (* b (* a -0.25)))
     (if (<= a -5e+65)
       t_1
       (if (<= a -1.55e-258)
         (+ c (* t (* z 0.0625)))
         (if (<= a 3.75e-6) t_1 (* b (+ (* a -0.25) (/ c b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if (a <= -1.52e+109) {
		tmp = c + (b * (a * -0.25));
	} else if (a <= -5e+65) {
		tmp = t_1;
	} else if (a <= -1.55e-258) {
		tmp = c + (t * (z * 0.0625));
	} else if (a <= 3.75e-6) {
		tmp = t_1;
	} else {
		tmp = b * ((a * -0.25) + (c / b));
	}
	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 = c + (x * y)
    if (a <= (-1.52d+109)) then
        tmp = c + (b * (a * (-0.25d0)))
    else if (a <= (-5d+65)) then
        tmp = t_1
    else if (a <= (-1.55d-258)) then
        tmp = c + (t * (z * 0.0625d0))
    else if (a <= 3.75d-6) then
        tmp = t_1
    else
        tmp = b * ((a * (-0.25d0)) + (c / b))
    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 tmp;
	if (a <= -1.52e+109) {
		tmp = c + (b * (a * -0.25));
	} else if (a <= -5e+65) {
		tmp = t_1;
	} else if (a <= -1.55e-258) {
		tmp = c + (t * (z * 0.0625));
	} else if (a <= 3.75e-6) {
		tmp = t_1;
	} else {
		tmp = b * ((a * -0.25) + (c / b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	tmp = 0
	if a <= -1.52e+109:
		tmp = c + (b * (a * -0.25))
	elif a <= -5e+65:
		tmp = t_1
	elif a <= -1.55e-258:
		tmp = c + (t * (z * 0.0625))
	elif a <= 3.75e-6:
		tmp = t_1
	else:
		tmp = b * ((a * -0.25) + (c / b))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (a <= -1.52e+109)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (a <= -5e+65)
		tmp = t_1;
	elseif (a <= -1.55e-258)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (a <= 3.75e-6)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(Float64(a * -0.25) + Float64(c / b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	tmp = 0.0;
	if (a <= -1.52e+109)
		tmp = c + (b * (a * -0.25));
	elseif (a <= -5e+65)
		tmp = t_1;
	elseif (a <= -1.55e-258)
		tmp = c + (t * (z * 0.0625));
	elseif (a <= 3.75e-6)
		tmp = t_1;
	else
		tmp = b * ((a * -0.25) + (c / b));
	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]}, If[LessEqual[a, -1.52e+109], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5e+65], t$95$1, If[LessEqual[a, -1.55e-258], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.75e-6], t$95$1, N[(b * N[(N[(a * -0.25), $MachinePrecision] + N[(c / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.52000000000000003e109

   1. Initial program 96.1%

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

   3. Taylor expanded in a around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. *-commutative 75.4%

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

      3. associate-*r* 75.4%

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

   5. Simplified 75.4%

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

   if -1.52000000000000003e109 < a < -4.99999999999999973e65 or -1.54999999999999999e-258 < a < 3.7500000000000001e-6

   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 x around inf 58.6%

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

   if -4.99999999999999973e65 < a < -1.54999999999999999e-258

   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 inf 68.6%

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

      1. associate-*r* 68.6%

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

      2. *-commutative 68.6%

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

      3. associate-*r* 68.6%

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

   5. Simplified 68.6%

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

   if 3.7500000000000001e-6 < a

   1. Initial program 96.1%

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

   3. Taylor expanded in a around inf 57.7%

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

      1. *-commutative 57.7%

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

      2. *-commutative 57.7%

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

      3. associate-*r* 57.7%

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

   5. Simplified 57.7%

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

   6. Taylor expanded in b around inf 57.7%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.52 \cdot 10^{+109}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+65}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \leq -1.55 \cdot 10^{-258}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 3.75 \cdot 10^{-6}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25 + \frac{c}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-263}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 0.19:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (+ c (* b (* a -0.25)))))
   (if (<= a -1.7e+109)
     t_2
     (if (<= a -5.2e+64)
       t_1
       (if (<= a -4e-263)
         (+ c (* t (* z 0.0625)))
         (if (<= a 0.19) 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 + (x * y);
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if (a <= -1.7e+109) {
		tmp = t_2;
	} else if (a <= -5.2e+64) {
		tmp = t_1;
	} else if (a <= -4e-263) {
		tmp = c + (t * (z * 0.0625));
	} else if (a <= 0.19) {
		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 + (x * y)
    t_2 = c + (b * (a * (-0.25d0)))
    if (a <= (-1.7d+109)) then
        tmp = t_2
    else if (a <= (-5.2d+64)) then
        tmp = t_1
    else if (a <= (-4d-263)) then
        tmp = c + (t * (z * 0.0625d0))
    else if (a <= 0.19d0) 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 + (x * y);
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if (a <= -1.7e+109) {
		tmp = t_2;
	} else if (a <= -5.2e+64) {
		tmp = t_1;
	} else if (a <= -4e-263) {
		tmp = c + (t * (z * 0.0625));
	} else if (a <= 0.19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = c + (b * (a * -0.25))
	tmp = 0
	if a <= -1.7e+109:
		tmp = t_2
	elif a <= -5.2e+64:
		tmp = t_1
	elif a <= -4e-263:
		tmp = c + (t * (z * 0.0625))
	elif a <= 0.19:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (a <= -1.7e+109)
		tmp = t_2;
	elseif (a <= -5.2e+64)
		tmp = t_1;
	elseif (a <= -4e-263)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (a <= 0.19)
		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 + (x * y);
	t_2 = c + (b * (a * -0.25));
	tmp = 0.0;
	if (a <= -1.7e+109)
		tmp = t_2;
	elseif (a <= -5.2e+64)
		tmp = t_1;
	elseif (a <= -4e-263)
		tmp = c + (t * (z * 0.0625));
	elseif (a <= 0.19)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+109], t$95$2, If[LessEqual[a, -5.2e+64], t$95$1, If[LessEqual[a, -4e-263], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.19], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.70000000000000003e109 or 0.19 < a

   1. Initial program 96.1%

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

   3. Taylor expanded in a around inf 67.0%

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

      1. *-commutative 67.0%

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

      2. *-commutative 67.0%

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

      3. associate-*r* 67.0%

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

   5. Simplified 67.0%

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

   if -1.70000000000000003e109 < a < -5.19999999999999994e64 or -4e-263 < a < 0.19

   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 x around inf 57.9%

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

   if -5.19999999999999994e64 < a < -4e-263

   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 inf 68.6%

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

      1. associate-*r* 68.6%

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

      2. *-commutative 68.6%

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

      3. associate-*r* 68.6%

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

   5. Simplified 68.6%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+109}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{+64}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-263}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 0.19:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 6.8:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* b (* a -0.25))))
   (if (<= a -2.2e+162)
     t_2
     (if (<= a -2.8e+64)
       t_1
       (if (<= a -8.5e-11) (* z (* t 0.0625)) (if (<= a 6.8) 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 + (x * y);
	double t_2 = b * (a * -0.25);
	double tmp;
	if (a <= -2.2e+162) {
		tmp = t_2;
	} else if (a <= -2.8e+64) {
		tmp = t_1;
	} else if (a <= -8.5e-11) {
		tmp = z * (t * 0.0625);
	} else if (a <= 6.8) {
		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 + (x * y)
    t_2 = b * (a * (-0.25d0))
    if (a <= (-2.2d+162)) then
        tmp = t_2
    else if (a <= (-2.8d+64)) then
        tmp = t_1
    else if (a <= (-8.5d-11)) then
        tmp = z * (t * 0.0625d0)
    else if (a <= 6.8d0) 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 + (x * y);
	double t_2 = b * (a * -0.25);
	double tmp;
	if (a <= -2.2e+162) {
		tmp = t_2;
	} else if (a <= -2.8e+64) {
		tmp = t_1;
	} else if (a <= -8.5e-11) {
		tmp = z * (t * 0.0625);
	} else if (a <= 6.8) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = b * (a * -0.25)
	tmp = 0
	if a <= -2.2e+162:
		tmp = t_2
	elif a <= -2.8e+64:
		tmp = t_1
	elif a <= -8.5e-11:
		tmp = z * (t * 0.0625)
	elif a <= 6.8:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (a <= -2.2e+162)
		tmp = t_2;
	elseif (a <= -2.8e+64)
		tmp = t_1;
	elseif (a <= -8.5e-11)
		tmp = Float64(z * Float64(t * 0.0625));
	elseif (a <= 6.8)
		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 + (x * y);
	t_2 = b * (a * -0.25);
	tmp = 0.0;
	if (a <= -2.2e+162)
		tmp = t_2;
	elseif (a <= -2.8e+64)
		tmp = t_1;
	elseif (a <= -8.5e-11)
		tmp = z * (t * 0.0625);
	elseif (a <= 6.8)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e+162], t$95$2, If[LessEqual[a, -2.8e+64], t$95$1, If[LessEqual[a, -8.5e-11], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.2000000000000002e162 or 6.79999999999999982 < a

   1. Initial program 95.4%

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

   3. Taylor expanded in a around inf 66.3%

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

      1. *-commutative 66.3%

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

      2. *-commutative 66.3%

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

      3. associate-*r* 66.3%

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

   5. Simplified 66.3%

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

   6. Taylor expanded in b around inf 63.0%

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

   7. Taylor expanded in a around inf 55.1%

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

      1. *-commutative 55.1%

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

   9. Simplified 55.1%

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

   if -2.2000000000000002e162 < a < -2.80000000000000024e64 or -8.50000000000000037e-11 < a < 6.79999999999999982

   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 x around inf 57.2%

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

   if -2.80000000000000024e64 < a < -8.50000000000000037e-11

   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 x around 0 92.2%

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

   4. Taylor expanded in z around inf 84.4%

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

   5. Taylor expanded in t around inf 51.5%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+162}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{+64}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-11}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 6.8:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 40.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;a \leq -1.52 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{+64}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-262}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))))
   (if (<= a -1.52e+109)
     t_1
     (if (<= a -1.85e+64)
       (* x y)
       (if (<= a -4.1e-262)
         (* z (* t 0.0625))
         (if (<= a 1.04e-7) (* x y) t_1))))))

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 (a <= -1.52e+109) {
		tmp = t_1;
	} else if (a <= -1.85e+64) {
		tmp = x * y;
	} else if (a <= -4.1e-262) {
		tmp = z * (t * 0.0625);
	} else if (a <= 1.04e-7) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	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 (a <= (-1.52d+109)) then
        tmp = t_1
    else if (a <= (-1.85d+64)) then
        tmp = x * y
    else if (a <= (-4.1d-262)) then
        tmp = z * (t * 0.0625d0)
    else if (a <= 1.04d-7) then
        tmp = x * y
    else
        tmp = t_1
    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 (a <= -1.52e+109) {
		tmp = t_1;
	} else if (a <= -1.85e+64) {
		tmp = x * y;
	} else if (a <= -4.1e-262) {
		tmp = z * (t * 0.0625);
	} else if (a <= 1.04e-7) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * (a * -0.25)
	tmp = 0
	if a <= -1.52e+109:
		tmp = t_1
	elif a <= -1.85e+64:
		tmp = x * y
	elif a <= -4.1e-262:
		tmp = z * (t * 0.0625)
	elif a <= 1.04e-7:
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (a <= -1.52e+109)
		tmp = t_1;
	elseif (a <= -1.85e+64)
		tmp = Float64(x * y);
	elseif (a <= -4.1e-262)
		tmp = Float64(z * Float64(t * 0.0625));
	elseif (a <= 1.04e-7)
		tmp = Float64(x * y);
	else
		tmp = t_1;
	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 (a <= -1.52e+109)
		tmp = t_1;
	elseif (a <= -1.85e+64)
		tmp = x * y;
	elseif (a <= -4.1e-262)
		tmp = z * (t * 0.0625);
	elseif (a <= 1.04e-7)
		tmp = x * y;
	else
		tmp = t_1;
	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[a, -1.52e+109], t$95$1, If[LessEqual[a, -1.85e+64], N[(x * y), $MachinePrecision], If[LessEqual[a, -4.1e-262], N[(z * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.04e-7], N[(x * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.52000000000000003e109 or 1.04e-7 < a

   1. Initial program 96.1%

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

   3. Taylor expanded in a around inf 66.5%

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

      1. *-commutative 66.5%

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

      2. *-commutative 66.5%

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

      3. associate-*r* 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in b around inf 61.0%

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

   7. Taylor expanded in a around inf 52.8%

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

      1. *-commutative 52.8%

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

   9. Simplified 52.8%

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

   if -1.52000000000000003e109 < a < -1.84999999999999992e64 or -4.10000000000000026e-262 < a < 1.04e-7

   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 70.5%

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

   4. Taylor expanded in x around inf 38.8%

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

   if -1.84999999999999992e64 < a < -4.10000000000000026e-262

   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 x around 0 79.2%

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

   4. Taylor expanded in z around inf 61.7%

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

   5. Taylor expanded in t around inf 41.6%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.52 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{+64}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-262}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq 1.04 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+70}:\\ \;\;\;\;\left(c + t\_1\right) - t\_2\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+36}:\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (* (* a b) 0.25)))
   (if (<= (* a b) -2e+70)
     (- (+ c t_1) t_2)
     (if (<= (* a b) 5e+36) (+ 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 = 0.0625 * (z * t);
	double t_2 = (a * b) * 0.25;
	double tmp;
	if ((a * b) <= -2e+70) {
		tmp = (c + t_1) - t_2;
	} else if ((a * b) <= 5e+36) {
		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 = 0.0625d0 * (z * t)
    t_2 = (a * b) * 0.25d0
    if ((a * b) <= (-2d+70)) then
        tmp = (c + t_1) - t_2
    else if ((a * b) <= 5d+36) 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 = 0.0625 * (z * t);
	double t_2 = (a * b) * 0.25;
	double tmp;
	if ((a * b) <= -2e+70) {
		tmp = (c + t_1) - t_2;
	} else if ((a * b) <= 5e+36) {
		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 = 0.0625 * (z * t)
	t_2 = (a * b) * 0.25
	tmp = 0
	if (a * b) <= -2e+70:
		tmp = (c + t_1) - t_2
	elif (a * b) <= 5e+36:
		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(0.0625 * Float64(z * t))
	t_2 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if (Float64(a * b) <= -2e+70)
		tmp = Float64(Float64(c + t_1) - t_2);
	elseif (Float64(a * b) <= 5e+36)
		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 = 0.0625 * (z * t);
	t_2 = (a * b) * 0.25;
	tmp = 0.0;
	if ((a * b) <= -2e+70)
		tmp = (c + t_1) - t_2;
	elseif ((a * b) <= 5e+36)
		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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+70], N[(N[(c + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+36], 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) < -2.00000000000000015e70

   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 0 89.4%

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

   if -2.00000000000000015e70 < (*.f64 a b) < 4.99999999999999977e36

   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 a around 0 96.7%

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

   if 4.99999999999999977e36 < (*.f64 a b)

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0 95.6%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+70}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+36}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 88.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+141}:\\ \;\;\;\;t\_1 + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+36}:\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* a b) -5e+141)
     (+ t_1 (* (* a b) -0.25))
     (if (<= (* a b) 5e+36)
       (+ c (+ (* x y) t_1))
       (- (+ 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 t_1 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+141) {
		tmp = t_1 + ((a * b) * -0.25);
	} else if ((a * b) <= 5e+36) {
		tmp = c + ((x * y) + t_1);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if ((a * b) <= (-5d+141)) then
        tmp = t_1 + ((a * b) * (-0.25d0))
    else if ((a * b) <= 5d+36) then
        tmp = c + ((x * y) + t_1)
    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 t_1 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+141) {
		tmp = t_1 + ((a * b) * -0.25);
	} else if ((a * b) <= 5e+36) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -5e+141:
		tmp = t_1 + ((a * b) * -0.25)
	elif (a * b) <= 5e+36:
		tmp = c + ((x * y) + t_1)
	else:
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -5e+141)
		tmp = Float64(t_1 + Float64(Float64(a * b) * -0.25));
	elseif (Float64(a * b) <= 5e+36)
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	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)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -5e+141)
		tmp = t_1 + ((a * b) * -0.25);
	elseif ((a * b) <= 5e+36)
		tmp = c + ((x * y) + t_1);
	else
		tmp = (c + (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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+141], N[(t$95$1 + N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+36], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $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) < -5.00000000000000025e141

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0 91.6%

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

   4. Taylor expanded in z around inf 74.3%

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

   5. Taylor expanded in c around 0 77.8%

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

   6. Taylor expanded in z around 0 88.6%

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

   if -5.00000000000000025e141 < (*.f64 a b) < 4.99999999999999977e36

   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 a around 0 94.9%

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

   if 4.99999999999999977e36 < (*.f64 a b)

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0 95.6%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+141}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+36}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 87.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+141}:\\ \;\;\;\;t\_1 + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+66}:\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* a b) -5e+141)
     (+ t_1 (* (* a b) -0.25))
     (if (<= (* a b) 2e+66)
       (+ c (+ (* x y) 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 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+141) {
		tmp = t_1 + ((a * b) * -0.25);
	} else if ((a * b) <= 2e+66) {
		tmp = c + ((x * y) + 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) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if ((a * b) <= (-5d+141)) then
        tmp = t_1 + ((a * b) * (-0.25d0))
    else if ((a * b) <= 2d+66) then
        tmp = c + ((x * y) + 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 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+141) {
		tmp = t_1 + ((a * b) * -0.25);
	} else if ((a * b) <= 2e+66) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -5e+141:
		tmp = t_1 + ((a * b) * -0.25)
	elif (a * b) <= 2e+66:
		tmp = c + ((x * y) + 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(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -5e+141)
		tmp = Float64(t_1 + Float64(Float64(a * b) * -0.25));
	elseif (Float64(a * b) <= 2e+66)
		tmp = Float64(c + Float64(Float64(x * y) + 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 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -5e+141)
		tmp = t_1 + ((a * b) * -0.25);
	elseif ((a * b) <= 2e+66)
		tmp = c + ((x * y) + 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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+141], N[(t$95$1 + N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+66], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $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) < -5.00000000000000025e141

   1. Initial program 97.0%

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

   3. Taylor expanded in x around 0 91.6%

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

   4. Taylor expanded in z around inf 74.3%

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

   5. Taylor expanded in c around 0 77.8%

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

   6. Taylor expanded in z around 0 88.6%

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

   if -5.00000000000000025e141 < (*.f64 a b) < 1.99999999999999989e66

   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 a around 0 94.5%

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

   if 1.99999999999999989e66 < (*.f64 a b)

   1. Initial program 95.0%

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

   3. Taylor expanded in z around 0 95.2%

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

   4. Taylor expanded in c around 0 84.3%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+141}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+66}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 64.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+155} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+65}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1e+155) (not (<= (* x y) 2e+65)))
   (+ c (* x y))
   (+ c (* b (* a -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -1e+155) || !((x * y) <= 2e+65)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (b * (a * -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) <= (-1d+155)) .or. (.not. ((x * y) <= 2d+65))) then
        tmp = c + (x * y)
    else
        tmp = c + (b * (a * (-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) <= -1e+155) || !((x * y) <= 2e+65)) {
		tmp = c + (x * y);
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1e+155) or not ((x * y) <= 2e+65):
		tmp = c + (x * y)
	else:
		tmp = c + (b * (a * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -1e+155) || !(Float64(x * y) <= 2e+65))
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -1e+155) || ~(((x * y) <= 2e+65)))
		tmp = c + (x * y);
	else
		tmp = c + (b * (a * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+155], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+65]], $MachinePrecision]], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.00000000000000001e155 or 2e65 < (*.f64 x y)

   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 74.7%

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

   if -1.00000000000000001e155 < (*.f64 x y) < 2e65

   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 inf 62.5%

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

      1. *-commutative 62.5%

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

      2. *-commutative 62.5%

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

      3. associate-*r* 62.5%

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

   5. Simplified 62.5%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+155} \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+65}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1700 \lor \neg \left(x \cdot y \leq 7 \cdot 10^{+123}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -1700.0) (not (<= (* x y) 7e+123))) (* 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) <= -1700.0) || !((x * y) <= 7e+123)) {
		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) <= (-1700.0d0)) .or. (.not. ((x * y) <= 7d+123))) 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) <= -1700.0) || !((x * y) <= 7e+123)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -1700.0) or not ((x * y) <= 7e+123):
		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) <= -1700.0) || !(Float64(x * y) <= 7e+123))
		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) <= -1700.0) || ~(((x * y) <= 7e+123)))
		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], -1700.0], N[Not[LessEqual[N[(x * y), $MachinePrecision], 7e+123]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1700 or 6.99999999999999999e123 < (*.f64 x y)

   1. Initial program 97.0%

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

   3. Taylor expanded in z around 0 83.1%

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

   4. Taylor expanded in x around inf 60.3%

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

   if -1700 < (*.f64 x y) < 6.99999999999999999e123

   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 30.4%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1700 \lor \neg \left(x \cdot y \leq 7 \cdot 10^{+123}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Final simplification 98.4%

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

Alternative 17: 22.4% 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 98.4%

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

3. Taylor expanded in c around inf 21.4%

   \[\leadsto \color{blue}{c} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024100 
(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))