Data.Colour.Matrix:inverse from colour-2.3.3, B

Percentage Accurate: 92.2% → 95.3%

Time: 11.2s

Alternatives: 7

Speedup: 0.4×

• 28.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - z \cdot t}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- (* x y) (* z t)) a))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = ((x * y) - (z * t)) / a
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Python

def code(x, y, z, t, a):
	return ((x * y) - (z * t)) / a

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (z * t)) / a;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]

Initial Program: 92.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - z \cdot t}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- (* x y) (* z t)) a))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = ((x * y) - (z * t)) / a
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Python

def code(x, y, z, t, a):
	return ((x * y) - (z * t)) / a

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (z * t)) / a;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]

Alternative 1: 95.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+271}:\\ \;\;\;\;0 - t \cdot \frac{z}{a}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+233}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(0 - z\right) \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) -2e+271)
   (- 0.0 (* t (/ z a)))
   (if (<= (* z t) 5e+233) (/ (- (* x y) (* z t)) a) (* (- 0.0 z) (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -2e+271) {
		tmp = 0.0 - (t * (z / a));
	} else if ((z * t) <= 5e+233) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (0.0 - z) * (t / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((z * t) <= (-2d+271)) then
        tmp = 0.0d0 - (t * (z / a))
    else if ((z * t) <= 5d+233) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = (0.0d0 - z) * (t / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -2e+271) {
		tmp = 0.0 - (t * (z / a));
	} else if ((z * t) <= 5e+233) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (0.0 - z) * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -2e+271:
		tmp = 0.0 - (t * (z / a))
	elif (z * t) <= 5e+233:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = (0.0 - z) * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= -2e+271)
		tmp = Float64(0.0 - Float64(t * Float64(z / a)));
	elseif (Float64(z * t) <= 5e+233)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(Float64(0.0 - z) * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z * t) <= -2e+271)
		tmp = 0.0 - (t * (z / a));
	elseif ((z * t) <= 5e+233)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = (0.0 - z) * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], -2e+271], N[(0.0 - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+233], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(0.0 - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.99999999999999991e271

   1. Initial program 65.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip-- N/A

         \[\leadsto \frac{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}{x \cdot y + z \cdot t}}{a} \]

      2. clear-num N/A

         \[\leadsto \frac{\frac{1}{\frac{x \cdot y + z \cdot t}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}}}{a} \]

      3. associate-/l/ N/A

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

      4. associate-/r* N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{a}\right), \color{blue}{\left(\frac{x \cdot y + z \cdot t}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}\right)}\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, a\right), \left(\frac{\color{blue}{x \cdot y + z \cdot t}}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}\right)\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, a\right), \left(\frac{1}{\color{blue}{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot t\right) \cdot \left(z \cdot t\right)}{x \cdot y + z \cdot t}}}\right)\right) \]

      8. flip-- N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, a\right), \left(\frac{1}{x \cdot y - \color{blue}{z \cdot t}}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{/.f64}\left(1, \color{blue}{\left(x \cdot y - z \cdot t\right)}\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(z \cdot t\right)}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{z} \cdot t\right)\right)\right)\right) \]

      12. *-lowering-*.f64 66.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, a\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right)\right)\right) \]

   4. Applied egg-rr 66.0%

      \[\leadsto \color{blue}{\frac{\frac{1}{a}}{\frac{1}{x \cdot y - z \cdot t}}} \]

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{t \cdot z}{a}\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{\frac{t \cdot z}{a}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(\frac{t \cdot z}{a}\right)}\right) \]

      4. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \left(t \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{z}{a}\right)}\right)\right) \]

      6. /-lowering-/.f64 99.9%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, \color{blue}{a}\right)\right)\right) \]

   7. Simplified 99.9%

      \[\leadsto \color{blue}{0 - t \cdot \frac{z}{a}} \]

   if -1.99999999999999991e271 < (*.f64 z t) < 5.00000000000000009e233

   1. Initial program 96.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   if 5.00000000000000009e233 < (*.f64 z t)

   1. Initial program 48.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot z\right)\right)}, a\right) \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot t\right) \cdot z\right), a\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \left(-1 \cdot t\right)\right), a\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot t\right)\right), a\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t\right)\right)\right), a\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(0 - t\right)\right), a\right) \]

      6. --lowering--.f64 62.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(0, t\right)\right), a\right) \]

   5. Simplified 62.1%

      \[\leadsto \frac{\color{blue}{z \cdot \left(0 - t\right)}}{a} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \frac{z \cdot \left(\mathsf{neg}\left(t\right)\right)}{a} \]

      2. associate-/l* N/A

         \[\leadsto z \cdot \color{blue}{\frac{\mathsf{neg}\left(t\right)}{a}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\mathsf{neg}\left(t\right)}{a} \cdot \color{blue}{z} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\mathsf{neg}\left(t\right)}{a}\right), \color{blue}{z}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(t\right)\right), a\right), z\right) \]

      6. sub0-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(0 - t\right), a\right), z\right) \]

      7. --lowering--.f64 93.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, t\right), a\right), z\right) \]

   7. Applied egg-rr 93.7%

      \[\leadsto \color{blue}{\frac{0 - t}{a} \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+271}:\\ \;\;\;\;0 - t \cdot \frac{z}{a}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+233}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(0 - z\right) \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -100000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-91}:\\ \;\;\;\;\frac{z \cdot t}{0 - a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -100000000000.0)
   (/ (* x y) a)
   (if (<= (* x y) 1e-91) (/ (* z t) (- 0.0 a)) (* x (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -100000000000.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 1e-91) {
		tmp = (z * t) / (0.0 - a);
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x * y) <= (-100000000000.0d0)) then
        tmp = (x * y) / a
    else if ((x * y) <= 1d-91) then
        tmp = (z * t) / (0.0d0 - a)
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -100000000000.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 1e-91) {
		tmp = (z * t) / (0.0 - a);
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -100000000000.0:
		tmp = (x * y) / a
	elif (x * y) <= 1e-91:
		tmp = (z * t) / (0.0 - a)
	else:
		tmp = x * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -100000000000.0)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 1e-91)
		tmp = Float64(Float64(z * t) / Float64(0.0 - a));
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -100000000000.0)
		tmp = (x * y) / a;
	elseif ((x * y) <= 1e-91)
		tmp = (z * t) / (0.0 - a);
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -100000000000.0], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-91], N[(N[(z * t), $MachinePrecision] / N[(0.0 - a), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1e11

   1. Initial program 91.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 78.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

   5. Simplified 78.2%

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

   if -1e11 < (*.f64 x y) < 1.00000000000000002e-91

   1. Initial program 93.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-1 \cdot \left(t \cdot z\right)\right)}, a\right) \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(-1 \cdot t\right) \cdot z\right), a\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(z \cdot \left(-1 \cdot t\right)\right), a\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(-1 \cdot t\right)\right), a\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t\right)\right)\right), a\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(0 - t\right)\right), a\right) \]

      6. --lowering--.f64 80.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(0, t\right)\right), a\right) \]

   5. Simplified 80.6%

      \[\leadsto \frac{\color{blue}{z \cdot \left(0 - t\right)}}{a} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(t\right)\right)\right), a\right) \]

      2. neg-lowering-neg.f64 80.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, \mathsf{neg.f64}\left(t\right)\right), a\right) \]

   7. Applied egg-rr 80.6%

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

   if 1.00000000000000002e-91 < (*.f64 x y)

   1. Initial program 86.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 72.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

   5. Simplified 72.9%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 75.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), x\right) \]

   7. Applied egg-rr 75.9%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -100000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-91}:\\ \;\;\;\;\frac{z \cdot t}{0 - a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 2 \cdot 10^{+244}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) 2e+244) (/ (* x y) a) (* y (/ x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 2e+244) {
		tmp = (x * y) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x * y) <= 2d+244) then
        tmp = (x * y) / a
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 2e+244) {
		tmp = (x * y) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= 2e+244:
		tmp = (x * y) / a
	else:
		tmp = y * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= 2e+244)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= 2e+244)
		tmp = (x * y) / a;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], 2e+244], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 2.00000000000000015e244

   1. Initial program 92.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 52.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

   5. Simplified 52.5%

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

   if 2.00000000000000015e244 < (*.f64 x y)

   1. Initial program 76.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 73.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

   5. Simplified 73.5%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{y \cdot x}{a} \]

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{a}\right)}\right) \]

      4. /-lowering-/.f64 89.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{a}\right)\right) \]

   7. Applied egg-rr 89.8%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.14 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1.14e-293) (* x (/ y a)) (/ y (/ a x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.14e-293) {
		tmp = x * (y / a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (t <= 1.14d-293) then
        tmp = x * (y / a)
    else
        tmp = y / (a / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.14e-293) {
		tmp = x * (y / a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.14e-293:
		tmp = x * (y / a)
	else:
		tmp = y / (a / x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.14e-293)
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(y / Float64(a / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 1.14e-293)
		tmp = x * (y / a);
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.14e-293], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.14000000000000006e-293

   1. Initial program 89.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 51.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

   5. Simplified 51.1%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 50.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), x\right) \]

   7. Applied egg-rr 50.5%

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

   if 1.14000000000000006e-293 < t

   1. Initial program 92.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 58.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

   5. Simplified 58.4%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{y \cdot x}{a} \]

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{a}\right)}\right) \]

      4. /-lowering-/.f64 54.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{a}\right)\right) \]

   7. Applied egg-rr 54.8%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]
   8. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto y \cdot \frac{1}{\color{blue}{\frac{a}{x}}} \]

      2. un-div-inv N/A

         \[\leadsto \frac{y}{\color{blue}{\frac{a}{x}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a}{x}\right)}\right) \]

      4. /-lowering-/.f64 55.9%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{x}\right)\right) \]

   9. Applied egg-rr 55.9%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.14 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4.4 \cdot 10^{-165}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 4.4e-165) (* x (/ y a)) (* y (/ x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 4.4e-165) {
		tmp = x * (y / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (t <= 4.4d-165) then
        tmp = x * (y / a)
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 4.4e-165) {
		tmp = x * (y / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 4.4e-165:
		tmp = x * (y / a)
	else:
		tmp = y * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 4.4e-165)
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 4.4e-165)
		tmp = x * (y / a);
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 4.4e-165], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 4.3999999999999998e-165

   1. Initial program 90.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 57.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

   5. Simplified 57.0%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{x}\right) \]

      4. /-lowering-/.f64 57.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), x\right) \]

   7. Applied egg-rr 57.1%

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

   if 4.3999999999999998e-165 < t

   1. Initial program 91.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 51.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

   5. Simplified 51.6%

      \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{y \cdot x}{a} \]

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{a}\right)}\right) \]

      4. /-lowering-/.f64 47.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{a}\right)\right) \]

   7. Applied egg-rr 47.8%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.4 \cdot 10^{-165}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{a}{y}} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ x (/ a y)))

C

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

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = x / (a / y)
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return Float64(x / Float64(a / y))
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.9%

   \[\frac{x \cdot y - z \cdot t}{a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
4. Step-by-step derivation

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

   2. *-lowering-*.f64 54.9%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

5. Simplified 54.9%

   \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
6. Step-by-step derivation

   1. associate-/l* N/A

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

   2. *-commutative N/A

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

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{x}\right) \]

   4. /-lowering-/.f64 54.7%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), x\right) \]

7. Applied egg-rr 54.7%

   \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]
8. Step-by-step derivation

   1. *-commutative N/A

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

   2. clear-num N/A

      \[\leadsto x \cdot \frac{1}{\color{blue}{\frac{a}{y}}} \]

   3. un-div-inv N/A

      \[\leadsto \frac{x}{\color{blue}{\frac{a}{y}}} \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{a}{y}\right)}\right) \]

   5. /-lowering-/.f64 54.5%

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(a, \color{blue}{y}\right)\right) \]

9. Applied egg-rr 54.5%

   \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]
10. Add Preprocessing

Alternative 7: 52.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ y \cdot \frac{x}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* y (/ x a)))

C

double code(double x, double y, double z, double t, double a) {
	return y * (x / a);
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = y * (x / a)
end function

Java

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

Python

def code(x, y, z, t, a):
	return y * (x / a)

Julia

function code(x, y, z, t, a)
	return Float64(y * Float64(x / a))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = y * (x / a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.9%

   \[\frac{x \cdot y - z \cdot t}{a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
4. Step-by-step derivation

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{a}\right) \]

   2. *-lowering-*.f64 54.9%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), a\right) \]

5. Simplified 54.9%

   \[\leadsto \color{blue}{\frac{x \cdot y}{a}} \]
6. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{y \cdot x}{a} \]

   2. associate-/l* N/A

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

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{a}\right)}\right) \]

   4. /-lowering-/.f64 53.8%

      \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{a}\right)\right) \]

7. Applied egg-rr 53.8%

   \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]
8. Add Preprocessing

Developer Target 1: 91.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* (/ y a) x) (* (/ t a) z))))
   (if (< z -2.468684968699548e+170)
     t_1
     (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = ((y / a) * x) - ((t / a) * z)
    if (z < (-2.468684968699548d+170)) then
        tmp = t_1
    else if (z < 6.309831121978371d-71) then
        tmp = ((x * y) - (z * t)) / a
    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 t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y / a) * x) - ((t / a) * z)
	tmp = 0
	if z < -2.468684968699548e+170:
		tmp = t_1
	elif z < 6.309831121978371e-71:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y / a) * x) - Float64(Float64(t / a) * z))
	tmp = 0.0
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y / a) * x) - ((t / a) * z);
	tmp = 0.0;
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -2.468684968699548e+170], t$95$1, If[Less[z, 6.309831121978371e-71], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024158 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -246868496869954800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6309831121978371/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z)))))

  (/ (- (* x y) (* z t)) a))