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

Percentage Accurate: 92.0% → 93.7%

Time: 6.1s

Alternatives: 8

Speedup: 0.7×

• 28.7% 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: 92.0% 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: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 4 \cdot 10^{+304}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) 4e+304) (/ (- (* x y) (* z t)) a) (* x (/ y a))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 4e+304) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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) <= 4d+304) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 4e+304) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= 4e+304:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = x * (y / a)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= 4e+304)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= 4e+304)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], 4e+304], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 3.9999999999999998e304

   1. Initial program 96.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   if 3.9999999999999998e304 < (*.f64 x y)

   1. Initial program 57.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 63.2%

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

      1. associate-/l* 99.8%

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

      2. associate-/r/ 99.8%

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

   4. Applied egg-rr 99.8%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 4 \cdot 10^{+304}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 2: 92.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, x \cdot y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a} - t \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (- (* x y) (* z t)) INFINITY)
   (/ (fma (- z) t (* x y)) a)
   (- (* y (/ x a)) (* t (/ z a)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) - (z * t)) <= ((double) INFINITY)) {
		tmp = fma(-z, t, (x * y)) / a;
	} else {
		tmp = (y * (x / a)) - (t * (z / a));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(x * y) - Float64(z * t)) <= Inf)
		tmp = Float64(fma(Float64(-z), t, Float64(x * y)) / a);
	else
		tmp = Float64(Float64(y * Float64(x / a)) - Float64(t * Float64(z / a)));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[((-z) * t + N[(x * y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < +inf.0

   1. Initial program 94.6%

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

      1. sub-neg 94.6%

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

      2. +-commutative 94.6%

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

      3. distribute-lft-neg-in 94.6%

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

      4. fma-def 94.6%

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

   3. Applied egg-rr 94.6%

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

   if +inf.0 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 0.0%

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

      1. sub-neg 0.0%

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

      2. +-commutative 0.0%

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

      3. distribute-lft-neg-in 0.0%

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

      4. fma-def 53.5%

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

   3. Applied egg-rr 53.5%

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

   4. Taylor expanded in z around 0 0.0%

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

      1. associate-*l/ 0.1%

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

      2. +-commutative 0.1%

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

      3. mul-1-neg 0.1%

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

      4. associate-*r/ 50.0%

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

      5. distribute-lft-neg-in 50.0%

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

      6. cancel-sign-sub-inv 50.0%

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

      7. associate-*l/ 3.5%

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

      8. associate-*r/ 50.0%

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

   6. Simplified 50.0%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(-z, t, x \cdot y\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a} - t \cdot \frac{z}{a}\\ \end{array} \]

Alternative 3: 92.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;\frac{t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a} - t \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 INFINITY) (/ t_1 a) (- (* y (/ x a)) (* t (/ z a))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1 / a;
	} else {
		tmp = (y * (x / a)) - (t * (z / a));
	}
	return tmp;
}

Java

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

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1 / a
	else:
		tmp = (y * (x / a)) - (t * (z / a))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(y * Float64(x / a)) - Float64(t * Float64(z / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1 / a;
	else
		tmp = (y * (x / a)) - (t * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 / a), $MachinePrecision], N[(N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < +inf.0

   1. Initial program 94.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   if +inf.0 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 0.0%

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

      1. sub-neg 0.0%

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

      2. +-commutative 0.0%

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

      3. distribute-lft-neg-in 0.0%

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

      4. fma-def 53.5%

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

   3. Applied egg-rr 53.5%

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

   4. Taylor expanded in z around 0 0.0%

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

      1. associate-*l/ 0.1%

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

      2. +-commutative 0.1%

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

      3. mul-1-neg 0.1%

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

      4. associate-*r/ 50.0%

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

      5. distribute-lft-neg-in 50.0%

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

      6. cancel-sign-sub-inv 50.0%

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

      7. associate-*l/ 3.5%

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

      8. associate-*r/ 50.0%

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

   6. Simplified 50.0%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq \infty:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a} - t \cdot \frac{z}{a}\\ \end{array} \]

Alternative 4: 67.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \frac{z \cdot \left(-t\right)}{a}\\ t_2 := x \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -4.7 \cdot 10^{-90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+88}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* z (- t)) a)) (t_2 (* x (/ y a))))
   (if (<= y -4.7e-90)
     t_2
     (if (<= y -1.75e-168)
       t_1
       (if (<= y -4e-200)
         t_2
         (if (<= y 4.9e+20)
           t_1
           (if (<= y 1.15e+88)
             (/ (* x y) a)
             (if (<= y 2.25e+130) t_1 (* y (/ x a))))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * -t) / a;
	double t_2 = x * (y / a);
	double tmp;
	if (y <= -4.7e-90) {
		tmp = t_2;
	} else if (y <= -1.75e-168) {
		tmp = t_1;
	} else if (y <= -4e-200) {
		tmp = t_2;
	} else if (y <= 4.9e+20) {
		tmp = t_1;
	} else if (y <= 1.15e+88) {
		tmp = (x * y) / a;
	} else if (y <= 2.25e+130) {
		tmp = t_1;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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) :: t_2
    real(8) :: tmp
    t_1 = (z * -t) / a
    t_2 = x * (y / a)
    if (y <= (-4.7d-90)) then
        tmp = t_2
    else if (y <= (-1.75d-168)) then
        tmp = t_1
    else if (y <= (-4d-200)) then
        tmp = t_2
    else if (y <= 4.9d+20) then
        tmp = t_1
    else if (y <= 1.15d+88) then
        tmp = (x * y) / a
    else if (y <= 2.25d+130) then
        tmp = t_1
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * -t) / a;
	double t_2 = x * (y / a);
	double tmp;
	if (y <= -4.7e-90) {
		tmp = t_2;
	} else if (y <= -1.75e-168) {
		tmp = t_1;
	} else if (y <= -4e-200) {
		tmp = t_2;
	} else if (y <= 4.9e+20) {
		tmp = t_1;
	} else if (y <= 1.15e+88) {
		tmp = (x * y) / a;
	} else if (y <= 2.25e+130) {
		tmp = t_1;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	t_1 = (z * -t) / a
	t_2 = x * (y / a)
	tmp = 0
	if y <= -4.7e-90:
		tmp = t_2
	elif y <= -1.75e-168:
		tmp = t_1
	elif y <= -4e-200:
		tmp = t_2
	elif y <= 4.9e+20:
		tmp = t_1
	elif y <= 1.15e+88:
		tmp = (x * y) / a
	elif y <= 2.25e+130:
		tmp = t_1
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * Float64(-t)) / a)
	t_2 = Float64(x * Float64(y / a))
	tmp = 0.0
	if (y <= -4.7e-90)
		tmp = t_2;
	elseif (y <= -1.75e-168)
		tmp = t_1;
	elseif (y <= -4e-200)
		tmp = t_2;
	elseif (y <= 4.9e+20)
		tmp = t_1;
	elseif (y <= 1.15e+88)
		tmp = Float64(Float64(x * y) / a);
	elseif (y <= 2.25e+130)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * -t) / a;
	t_2 = x * (y / a);
	tmp = 0.0;
	if (y <= -4.7e-90)
		tmp = t_2;
	elseif (y <= -1.75e-168)
		tmp = t_1;
	elseif (y <= -4e-200)
		tmp = t_2;
	elseif (y <= 4.9e+20)
		tmp = t_1;
	elseif (y <= 1.15e+88)
		tmp = (x * y) / a;
	elseif (y <= 2.25e+130)
		tmp = t_1;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * (-t)), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.7e-90], t$95$2, If[LessEqual[y, -1.75e-168], t$95$1, If[LessEqual[y, -4e-200], t$95$2, If[LessEqual[y, 4.9e+20], t$95$1, If[LessEqual[y, 1.15e+88], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 2.25e+130], t$95$1, N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.7e-90 or -1.74999999999999991e-168 < y < -3.9999999999999999e-200

   1. Initial program 93.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 62.5%

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

      1. associate-/l* 67.5%

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

      2. associate-/r/ 63.7%

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

   4. Applied egg-rr 63.7%

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

   if -4.7e-90 < y < -1.74999999999999991e-168 or -3.9999999999999999e-200 < y < 4.9e20 or 1.1500000000000001e88 < y < 2.2500000000000002e130

   1. Initial program 97.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around 0 75.6%

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

      1. associate-*r/ 75.6%

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

      2. associate-*r* 75.6%

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

      3. neg-mul-1 75.6%

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

   4. Simplified 75.6%

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

   if 4.9e20 < y < 1.1500000000000001e88

   1. Initial program 99.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 75.1%

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

   if 2.2500000000000002e130 < y

   1. Initial program 84.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 63.9%

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

      1. associate-*r/ 71.4%

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

   4. Simplified 71.4%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-168}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-200}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+20}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+88}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+130}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 5: 67.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-24} \lor \neg \left(z \leq 5.4 \cdot 10^{-129}\right):\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.5e-24) (not (<= z 5.4e-129)))
   (/ (- t) (/ a z))
   (/ (* x y) a)))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.5e-24) || !(z <= 5.4e-129)) {
		tmp = -t / (a / z);
	} else {
		tmp = (x * y) / a;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-7.5d-24)) .or. (.not. (z <= 5.4d-129))) then
        tmp = -t / (a / z)
    else
        tmp = (x * y) / a
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.5e-24) || !(z <= 5.4e-129)) {
		tmp = -t / (a / z);
	} else {
		tmp = (x * y) / a;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.5e-24) or not (z <= 5.4e-129):
		tmp = -t / (a / z)
	else:
		tmp = (x * y) / a
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.5e-24) || !(z <= 5.4e-129))
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = Float64(Float64(x * y) / a);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.5e-24) || ~((z <= 5.4e-129)))
		tmp = -t / (a / z);
	else
		tmp = (x * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.5e-24], N[Not[LessEqual[z, 5.4e-129]], $MachinePrecision]], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.50000000000000007e-24 or 5.39999999999999998e-129 < z

   1. Initial program 92.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around 0 65.7%

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

      1. associate-*r/ 65.7%

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

      2. associate-*r* 65.7%

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

      3. neg-mul-1 65.7%

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

   4. Simplified 65.7%

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

      1. associate-/l* 63.9%

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

      2. distribute-frac-neg 63.9%

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

   6. Applied egg-rr 63.9%

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

   if -7.50000000000000007e-24 < z < 5.39999999999999998e-129

   1. Initial program 96.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 70.2%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-24} \lor \neg \left(z \leq 5.4 \cdot 10^{-129}\right):\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]

Alternative 6: 66.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-24}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-129}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.55e-24)
   (/ (- t) (/ a z))
   (if (<= z 5.4e-129) (/ (* x y) a) (* z (/ (- t) a)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e-24) {
		tmp = -t / (a / z);
	} else if (z <= 5.4e-129) {
		tmp = (x * y) / a;
	} else {
		tmp = z * (-t / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 <= (-1.55d-24)) then
        tmp = -t / (a / z)
    else if (z <= 5.4d-129) then
        tmp = (x * y) / a
    else
        tmp = z * (-t / a)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e-24) {
		tmp = -t / (a / z);
	} else if (z <= 5.4e-129) {
		tmp = (x * y) / a;
	} else {
		tmp = z * (-t / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.55e-24:
		tmp = -t / (a / z)
	elif z <= 5.4e-129:
		tmp = (x * y) / a
	else:
		tmp = z * (-t / a)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.55e-24)
		tmp = Float64(Float64(-t) / Float64(a / z));
	elseif (z <= 5.4e-129)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(z * Float64(Float64(-t) / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.55e-24)
		tmp = -t / (a / z);
	elseif (z <= 5.4e-129)
		tmp = (x * y) / a;
	else
		tmp = z * (-t / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.55e-24], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-129], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55e-24

   1. Initial program 93.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around 0 72.7%

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

      1. associate-*r/ 72.7%

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

      2. associate-*r* 72.7%

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

      3. neg-mul-1 72.7%

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

   4. Simplified 72.7%

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

      1. associate-/l* 71.3%

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

      2. distribute-frac-neg 71.3%

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

   6. Applied egg-rr 71.3%

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

   if -1.55e-24 < z < 5.39999999999999998e-129

   1. Initial program 96.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 70.2%

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

   if 5.39999999999999998e-129 < z

   1. Initial program 91.3%

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

      1. sub-neg 91.3%

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

      2. +-commutative 91.3%

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

      3. distribute-lft-neg-in 91.3%

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

      4. fma-def 91.4%

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

   3. Applied egg-rr 91.4%

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

   4. Taylor expanded in z around inf 60.2%

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

      1. mul-1-neg 60.2%

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

      2. associate-*l/ 59.1%

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

      3. *-commutative 59.1%

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

      4. distribute-rgt-neg-in 59.1%

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

   6. Simplified 59.1%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-24}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-129}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \]

Alternative 7: 52.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ y \cdot \frac{x}{a} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* y (/ x a)))

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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

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

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	return y * (x / a)

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	return Float64(y * Float64(x / a))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z, t, a)
	tmp = y * (x / a);
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.9%

   \[\frac{x \cdot y - z \cdot t}{a} \]

2. Taylor expanded in x around inf 47.1%

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

   1. associate-*r/ 48.5%

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

4. Simplified 48.5%

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

5. Final simplification 48.5%

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

Alternative 8: 52.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \frac{y}{\frac{a}{x}} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (/ y (/ a x)))

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
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 / (a / x)
end function

Java

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

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	return y / (a / x)

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	return Float64(y / Float64(a / x))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z, t, a)
	tmp = y / (a / x);
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.9%

   \[\frac{x \cdot y - z \cdot t}{a} \]

2. Taylor expanded in x around inf 47.1%

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

   1. associate-/l* 48.9%

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

4. Simplified 48.9%

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

5. Final simplification 48.9%

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

Developer target: 91.1% accurate, 0.6× 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 2023224 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (if (< z -2.468684968699548e+170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

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