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

Percentage Accurate: 98.0% → 99.1%

Time: 11.8s

Alternatives: 14

Speedup: 1.0×

• 32.6% 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: 98.0% 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: 99.1% 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 97.6%

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

   1. associate--l+ 97.6%

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

   2. fma-define 98.4%

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

   3. associate-/l* 98.4%

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

   4. fma-neg 98.8%

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

   5. distribute-neg-frac2 98.8%

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

   6. metadata-eval 98.8%

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

3. Simplified 98.8%

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

Alternative 2: 98.5% 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 97.6%

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

   1. associate-+l- 97.6%

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

   2. *-commutative 97.6%

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

   3. associate-+l- 97.6%

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

   4. fma-define 98.0%

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

   5. *-commutative 98.0%

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

   6. associate-/l* 98.0%

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

   7. associate-/l* 98.0%

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

3. Simplified 98.0%

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

5. Final simplification 98.0%

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

Alternative 3: 66.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-43}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-315}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625 + \frac{x \cdot y}{z}\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+127}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* a b) 0.25))))
   (if (<= (* a b) -4e+46)
     t_1
     (if (<= (* a b) -2e-43)
       (+ c (* x y))
       (if (<= (* a b) -1e-315)
         (* z (+ (* t 0.0625) (/ (* x y) z)))
         (if (<= (* a b) 2e+127) (+ c (* t (* z 0.0625))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -4e+46) {
		tmp = t_1;
	} else if ((a * b) <= -2e-43) {
		tmp = c + (x * y);
	} else if ((a * b) <= -1e-315) {
		tmp = z * ((t * 0.0625) + ((x * y) / z));
	} else if ((a * b) <= 2e+127) {
		tmp = c + (t * (z * 0.0625));
	} 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 = (x * y) - ((a * b) * 0.25d0)
    if ((a * b) <= (-4d+46)) then
        tmp = t_1
    else if ((a * b) <= (-2d-43)) then
        tmp = c + (x * y)
    else if ((a * b) <= (-1d-315)) then
        tmp = z * ((t * 0.0625d0) + ((x * y) / z))
    else if ((a * b) <= 2d+127) then
        tmp = c + (t * (z * 0.0625d0))
    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 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -4e+46) {
		tmp = t_1;
	} else if ((a * b) <= -2e-43) {
		tmp = c + (x * y);
	} else if ((a * b) <= -1e-315) {
		tmp = z * ((t * 0.0625) + ((x * y) / z));
	} else if ((a * b) <= 2e+127) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) - ((a * b) * 0.25)
	tmp = 0
	if (a * b) <= -4e+46:
		tmp = t_1
	elif (a * b) <= -2e-43:
		tmp = c + (x * y)
	elif (a * b) <= -1e-315:
		tmp = z * ((t * 0.0625) + ((x * y) / z))
	elif (a * b) <= 2e+127:
		tmp = c + (t * (z * 0.0625))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25))
	tmp = 0.0
	if (Float64(a * b) <= -4e+46)
		tmp = t_1;
	elseif (Float64(a * b) <= -2e-43)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(a * b) <= -1e-315)
		tmp = Float64(z * Float64(Float64(t * 0.0625) + Float64(Float64(x * y) / z)));
	elseif (Float64(a * b) <= 2e+127)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) - ((a * b) * 0.25);
	tmp = 0.0;
	if ((a * b) <= -4e+46)
		tmp = t_1;
	elseif ((a * b) <= -2e-43)
		tmp = c + (x * y);
	elseif ((a * b) <= -1e-315)
		tmp = z * ((t * 0.0625) + ((x * y) / z));
	elseif ((a * b) <= 2e+127)
		tmp = c + (t * (z * 0.0625));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -4e+46], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -2e-43], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], -1e-315], N[(z * N[(N[(t * 0.0625), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+127], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -4e46 or 1.99999999999999991e127 < (*.f64 a b)

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 86.0%

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

   4. Taylor expanded in c around 0 78.4%

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

   if -4e46 < (*.f64 a b) < -2.00000000000000015e-43

   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 79.2%

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

   if -2.00000000000000015e-43 < (*.f64 a b) < -9.999999985e-316

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 90.6%

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

   4. Taylor expanded in a around 0 90.6%

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

   5. Taylor expanded in c around 0 71.6%

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

   if -9.999999985e-316 < (*.f64 a b) < 1.99999999999999991e127

   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 68.5%

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

      1. associate-*r* 68.5%

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

      2. *-commutative 68.5%

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

      3. associate-*r* 68.5%

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

   5. Simplified 68.5%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+46}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-43}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{-315}:\\ \;\;\;\;z \cdot \left(t \cdot 0.0625 + \frac{x \cdot y}{z}\right)\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+127}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1.66 \cdot 10^{+176}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -2.3 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5.8 \cdot 10^{-235}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 250:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625)))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -1.66e+176)
     t_2
     (if (<= (* x y) -2.3e-43)
       t_1
       (if (<= (* x y) -5.8e-235)
         (+ c (* a (* b -0.25)))
         (if (<= (* x y) 250.0) 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 + (t * (z * 0.0625));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.66e+176) {
		tmp = t_2;
	} else if ((x * y) <= -2.3e-43) {
		tmp = t_1;
	} else if ((x * y) <= -5.8e-235) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 250.0) {
		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 + (t * (z * 0.0625d0))
    t_2 = c + (x * y)
    if ((x * y) <= (-1.66d+176)) then
        tmp = t_2
    else if ((x * y) <= (-2.3d-43)) then
        tmp = t_1
    else if ((x * y) <= (-5.8d-235)) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 250.0d0) 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 + (t * (z * 0.0625));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.66e+176) {
		tmp = t_2;
	} else if ((x * y) <= -2.3e-43) {
		tmp = t_1;
	} else if ((x * y) <= -5.8e-235) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 250.0) {
		tmp = t_1;
	} 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 = c + (x * y)
	tmp = 0
	if (x * y) <= -1.66e+176:
		tmp = t_2
	elif (x * y) <= -2.3e-43:
		tmp = t_1
	elif (x * y) <= -5.8e-235:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 250.0:
		tmp = t_1
	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(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1.66e+176)
		tmp = t_2;
	elseif (Float64(x * y) <= -2.3e-43)
		tmp = t_1;
	elseif (Float64(x * y) <= -5.8e-235)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 250.0)
		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 + (t * (z * 0.0625));
	t_2 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -1.66e+176)
		tmp = t_2;
	elseif ((x * y) <= -2.3e-43)
		tmp = t_1;
	elseif ((x * y) <= -5.8e-235)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 250.0)
		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[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.66e+176], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -2.3e-43], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5.8e-235], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 250.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.6600000000000001e176 or 250 < (*.f64 x y)

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf 76.0%

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

   if -1.6600000000000001e176 < (*.f64 x y) < -2.2999999999999999e-43 or -5.80000000000000018e-235 < (*.f64 x y) < 250

   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 z around inf 67.2%

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

      1. associate-*r* 67.2%

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

      2. *-commutative 67.2%

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

      3. associate-*r* 67.2%

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

   5. Simplified 67.2%

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

   if -2.2999999999999999e-43 < (*.f64 x y) < -5.80000000000000018e-235

   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 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-*r* 73.5%

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

   5. Simplified 73.5%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.66 \cdot 10^{+176}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.3 \cdot 10^{-43}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -5.8 \cdot 10^{-235}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 250:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{if}\;x \cdot y \leq -1.5 \cdot 10^{+176}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.35 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2.6 \cdot 10^{-235}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 0.5:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* z 0.0625))))
   (if (<= (* x y) -1.5e+176)
     (* x y)
     (if (<= (* x y) -3.35e-46)
       t_1
       (if (<= (* x y) -2.6e-235)
         (* a (* b -0.25))
         (if (<= (* x y) 0.5) t_1 (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (z * 0.0625);
	double tmp;
	if ((x * y) <= -1.5e+176) {
		tmp = x * y;
	} else if ((x * y) <= -3.35e-46) {
		tmp = t_1;
	} else if ((x * y) <= -2.6e-235) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 0.5) {
		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 = t * (z * 0.0625d0)
    if ((x * y) <= (-1.5d+176)) then
        tmp = x * y
    else if ((x * y) <= (-3.35d-46)) then
        tmp = t_1
    else if ((x * y) <= (-2.6d-235)) then
        tmp = a * (b * (-0.25d0))
    else if ((x * y) <= 0.5d0) 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 = t * (z * 0.0625);
	double tmp;
	if ((x * y) <= -1.5e+176) {
		tmp = x * y;
	} else if ((x * y) <= -3.35e-46) {
		tmp = t_1;
	} else if ((x * y) <= -2.6e-235) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 0.5) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = t * (z * 0.0625)
	tmp = 0
	if (x * y) <= -1.5e+176:
		tmp = x * y
	elif (x * y) <= -3.35e-46:
		tmp = t_1
	elif (x * y) <= -2.6e-235:
		tmp = a * (b * -0.25)
	elif (x * y) <= 0.5:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(z * 0.0625))
	tmp = 0.0
	if (Float64(x * y) <= -1.5e+176)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3.35e-46)
		tmp = t_1;
	elseif (Float64(x * y) <= -2.6e-235)
		tmp = Float64(a * Float64(b * -0.25));
	elseif (Float64(x * y) <= 0.5)
		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 = t * (z * 0.0625);
	tmp = 0.0;
	if ((x * y) <= -1.5e+176)
		tmp = x * y;
	elseif ((x * y) <= -3.35e-46)
		tmp = t_1;
	elseif ((x * y) <= -2.6e-235)
		tmp = a * (b * -0.25);
	elseif ((x * y) <= 0.5)
		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[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.5e+176], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.35e-46], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2.6e-235], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.5], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.5e176 or 0.5 < (*.f64 x y)

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0 89.2%

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

   4. Taylor expanded in x around inf 66.0%

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

   if -1.5e176 < (*.f64 x y) < -3.35e-46 or -2.6e-235 < (*.f64 x y) < 0.5

   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 z around inf 67.2%

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

      1. associate-*r* 67.2%

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

      2. *-commutative 67.2%

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

      3. associate-*r* 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in t around inf 40.0%

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

      1. associate-*r* 40.0%

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

      2. *-commutative 40.0%

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

      3. associate-*r* 40.0%

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

   8. Simplified 40.0%

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

   if -3.35e-46 < (*.f64 x y) < -2.6e-235

   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 79.1%

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

   4. Taylor expanded in a around inf 48.5%

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

      1. *-commutative 48.5%

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

      2. associate-*r* 48.5%

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

   6. Simplified 48.5%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.5 \cdot 10^{+176}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.35 \cdot 10^{-46}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq -2.6 \cdot 10^{-235}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 0.5:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 10^{-267}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+127}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* a b) 0.25))))
   (if (<= (* a b) -4e+46)
     t_1
     (if (<= (* a b) 1e-267)
       (+ c (* x y))
       (if (<= (* a b) 2e+127) (+ c (* t (* z 0.0625))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -4e+46) {
		tmp = t_1;
	} else if ((a * b) <= 1e-267) {
		tmp = c + (x * y);
	} else if ((a * b) <= 2e+127) {
		tmp = c + (t * (z * 0.0625));
	} 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 = (x * y) - ((a * b) * 0.25d0)
    if ((a * b) <= (-4d+46)) then
        tmp = t_1
    else if ((a * b) <= 1d-267) then
        tmp = c + (x * y)
    else if ((a * b) <= 2d+127) then
        tmp = c + (t * (z * 0.0625d0))
    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 = (x * y) - ((a * b) * 0.25);
	double tmp;
	if ((a * b) <= -4e+46) {
		tmp = t_1;
	} else if ((a * b) <= 1e-267) {
		tmp = c + (x * y);
	} else if ((a * b) <= 2e+127) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) - ((a * b) * 0.25)
	tmp = 0
	if (a * b) <= -4e+46:
		tmp = t_1
	elif (a * b) <= 1e-267:
		tmp = c + (x * y)
	elif (a * b) <= 2e+127:
		tmp = c + (t * (z * 0.0625))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25))
	tmp = 0.0
	if (Float64(a * b) <= -4e+46)
		tmp = t_1;
	elseif (Float64(a * b) <= 1e-267)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(a * b) <= 2e+127)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) - ((a * b) * 0.25);
	tmp = 0.0;
	if ((a * b) <= -4e+46)
		tmp = t_1;
	elseif ((a * b) <= 1e-267)
		tmp = c + (x * y);
	elseif ((a * b) <= 2e+127)
		tmp = c + (t * (z * 0.0625));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -4e+46], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1e-267], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+127], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4e46 or 1.99999999999999991e127 < (*.f64 a b)

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 86.0%

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

   4. Taylor expanded in c around 0 78.4%

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

   if -4e46 < (*.f64 a b) < 9.9999999999999998e-268

   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 x around inf 69.0%

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

   if 9.9999999999999998e-268 < (*.f64 a b) < 1.99999999999999991e127

   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 68.2%

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

      1. associate-*r* 68.2%

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

      2. *-commutative 68.2%

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

      3. associate-*r* 68.2%

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

   5. Simplified 68.2%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4 \cdot 10^{+46}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 10^{-267}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+127}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+113} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+127}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -2e+113) (not (<= (* a b) 2e+127)))
   (- (+ c (* x y)) (* (* a b) 0.25))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -2e+113) || !((a * b) <= 2e+127)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	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+113)) .or. (.not. ((a * b) <= 2d+127))) then
        tmp = (c + (x * y)) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    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+113) || !((a * b) <= 2e+127)) {
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -2e+113) or not ((a * b) <= 2e+127):
		tmp = (c + (x * y)) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -2e+113) || !(Float64(a * b) <= 2e+127))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -2e+113) || ~(((a * b) <= 2e+127)))
		tmp = (c + (x * y)) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -2e+113], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+127]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -2e113 or 1.99999999999999991e127 < (*.f64 a b)

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 89.8%

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

   if -2e113 < (*.f64 a b) < 1.99999999999999991e127

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 94.1%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+113} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+127}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+131} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+127}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+131) (not (<= (* a b) 2e+127)))
   (- (* x y) (* (* a b) 0.25))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+131) || !((a * b) <= 2e+127)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	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) <= (-5d+131)) .or. (.not. ((a * b) <= 2d+127))) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    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) <= -5e+131) || !((a * b) <= 2e+127)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -5e+131) or not ((a * b) <= 2e+127):
		tmp = (x * y) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -5e+131) || !(Float64(a * b) <= 2e+127))
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -5e+131) || ~(((a * b) <= 2e+127)))
		tmp = (x * y) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+131], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+127]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4.99999999999999995e131 or 1.99999999999999991e127 < (*.f64 a b)

   1. Initial program 94.0%

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

   3. Taylor expanded in z around 0 89.5%

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

   4. Taylor expanded in c around 0 82.1%

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

   if -4.99999999999999995e131 < (*.f64 a b) < 1.99999999999999991e127

   1. Initial program 99.4%

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

   3. Taylor expanded in a around 0 93.6%

      \[\leadsto \color{blue}{\left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+131} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+127}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5.2 \cdot 10^{+46}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.9 \cdot 10^{-187}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 9.8 \cdot 10^{-37}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -5.2e+46)
   (* x y)
   (if (<= (* x y) 1.9e-187)
     (* a (* b -0.25))
     (if (<= (* x y) 9.8e-37) c (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -5.2e+46) {
		tmp = x * y;
	} else if ((x * y) <= 1.9e-187) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 9.8e-37) {
		tmp = c;
	} 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) <= (-5.2d+46)) then
        tmp = x * y
    else if ((x * y) <= 1.9d-187) then
        tmp = a * (b * (-0.25d0))
    else if ((x * y) <= 9.8d-37) then
        tmp = c
    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) <= -5.2e+46) {
		tmp = x * y;
	} else if ((x * y) <= 1.9e-187) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 9.8e-37) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -5.2e+46:
		tmp = x * y
	elif (x * y) <= 1.9e-187:
		tmp = a * (b * -0.25)
	elif (x * y) <= 9.8e-37:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -5.2e+46)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 1.9e-187)
		tmp = Float64(a * Float64(b * -0.25));
	elseif (Float64(x * y) <= 9.8e-37)
		tmp = c;
	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) <= -5.2e+46)
		tmp = x * y;
	elseif ((x * y) <= 1.9e-187)
		tmp = a * (b * -0.25);
	elseif ((x * y) <= 9.8e-37)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -5.2e+46], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.9e-187], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 9.8e-37], c, N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.20000000000000027e46 or 9.80000000000000036e-37 < (*.f64 x y)

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0 80.8%

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

   4. Taylor expanded in x around inf 54.1%

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

   if -5.20000000000000027e46 < (*.f64 x y) < 1.90000000000000013e-187

   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 65.7%

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

   4. Taylor expanded in a around inf 38.6%

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

      1. *-commutative 38.6%

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

      2. associate-*r* 38.6%

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

   6. Simplified 38.6%

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

   if 1.90000000000000013e-187 < (*.f64 x y) < 9.80000000000000036e-37

   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 47.8%

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

Alternative 10: 64.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.55 \cdot 10^{+165} \lor \neg \left(x \cdot y \leq 6.4 \cdot 10^{-17}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2.55e+165) (not (<= (* x y) 6.4e-17)))
   (+ 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) <= -2.55e+165) || !((x * y) <= 6.4e-17)) {
		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) <= (-2.55d+165)) .or. (.not. ((x * y) <= 6.4d-17))) 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) <= -2.55e+165) || !((x * y) <= 6.4e-17)) {
		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) <= -2.55e+165) or not ((x * y) <= 6.4e-17):
		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) <= -2.55e+165) || !(Float64(x * y) <= 6.4e-17))
		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) <= -2.55e+165) || ~(((x * y) <= 6.4e-17)))
		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], -2.55e+165], N[Not[LessEqual[N[(x * y), $MachinePrecision], 6.4e-17]], $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) < -2.5500000000000002e165 or 6.4000000000000005e-17 < (*.f64 x y)

   1. Initial program 94.9%

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

   3. Taylor expanded in x around inf 73.3%

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

   if -2.5500000000000002e165 < (*.f64 x y) < 6.4000000000000005e-17

   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 60.1%

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

      1. *-commutative 60.1%

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

      2. associate-*r* 60.1%

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

   5. Simplified 60.1%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.55 \cdot 10^{+165} \lor \neg \left(x \cdot y \leq 6.4 \cdot 10^{-17}\right):\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+59} \lor \neg \left(x \cdot y \leq 2.85 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -3.8e+59) (not (<= (* x y) 2.85e-36))) (* 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) <= -3.8e+59) || !((x * y) <= 2.85e-36)) {
		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) <= (-3.8d+59)) .or. (.not. ((x * y) <= 2.85d-36))) 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) <= -3.8e+59) || !((x * y) <= 2.85e-36)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -3.8e+59) or not ((x * y) <= 2.85e-36):
		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) <= -3.8e+59) || !(Float64(x * y) <= 2.85e-36))
		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) <= -3.8e+59) || ~(((x * y) <= 2.85e-36)))
		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], -3.8e+59], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.85e-36]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.8000000000000001e59 or 2.8499999999999999e-36 < (*.f64 x y)

   1. Initial program 95.2%

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

   3. Taylor expanded in z around 0 80.3%

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

   4. Taylor expanded in x around inf 54.6%

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

   if -3.8000000000000001e59 < (*.f64 x y) < 2.8499999999999999e-36

   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 31.9%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.8 \cdot 10^{+59} \lor \neg \left(x \cdot y \leq 2.85 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 98.0% 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 97.6%

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

3. Final simplification 97.6%

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

Alternative 13: 54.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+172} \lor \neg \left(a \leq 5.6 \cdot 10^{-18}\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -5.5e+172) (not (<= a 5.6e-18)))
   (* a (* b -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 <= -5.5e+172) || !(a <= 5.6e-18)) {
		tmp = a * (b * -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 <= (-5.5d+172)) .or. (.not. (a <= 5.6d-18))) then
        tmp = a * (b * (-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 <= -5.5e+172) || !(a <= 5.6e-18)) {
		tmp = a * (b * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -5.5e+172) or not (a <= 5.6e-18):
		tmp = a * (b * -0.25)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -5.5e+172) || !(a <= 5.6e-18))
		tmp = Float64(a * Float64(b * -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 <= -5.5e+172) || ~((a <= 5.6e-18)))
		tmp = a * (b * -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, -5.5e+172], N[Not[LessEqual[a, 5.6e-18]], $MachinePrecision]], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.4999999999999999e172 or 5.60000000000000025e-18 < a

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0 80.3%

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

   4. Taylor expanded in a around inf 49.2%

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

      1. *-commutative 49.2%

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

      2. associate-*r* 49.2%

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

   6. Simplified 49.2%

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

   if -5.4999999999999999e172 < a < 5.60000000000000025e-18

   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 x around inf 58.0%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+172} \lor \neg \left(a \leq 5.6 \cdot 10^{-18}\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 22.5% 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 97.6%

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

3. Taylor expanded in c around inf 22.1%

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

Reproduce

herbie shell --seed 2024123 
(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))