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

Percentage Accurate: 91.7% → 97.3%

Time: 8.9s

Alternatives: 11

Speedup: 0.5×

• Unsound rule application detected in e-graph. Results may not be sound.

• 28.5% 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: 91.7% 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: 97.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{a}, \frac{-z}{\frac{a}{t}}\right)\\ \end{array} \end{array} \]

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))
     (- (* x (/ y a)) (/ z (/ a t)))
     (if (<= t_1 5e+292) (/ t_1 a) (fma x (/ y a) (/ (- z) (/ a t)))))))

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 = (x * (y / a)) - (z / (a / t));
	} else if (t_1 <= 5e+292) {
		tmp = t_1 / a;
	} else {
		tmp = fma(x, (y / a), (-z / (a / t)));
	}
	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 <= Float64(-Inf))
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(z / Float64(a / t)));
	elseif (t_1 <= 5e+292)
		tmp = Float64(t_1 / a);
	else
		tmp = fma(x, Float64(y / a), Float64(Float64(-z) / Float64(a / t)));
	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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+292], N[(t$95$1 / a), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision] + N[((-z) / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 60.6%

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

      1. div-sub 56.4%

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

      2. associate-/l* 64.2%

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

      3. associate-/l* 95.5%

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

   3. Applied egg-rr 95.5%

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

      1. clear-num 95.6%

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

      2. associate-/r/ 95.5%

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

      3. clear-num 95.5%

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

   5. Applied egg-rr 95.5%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999996e292

   1. Initial program 97.7%

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

   if 4.9999999999999996e292 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 66.6%

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

      1. div-sub 61.6%

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

      2. *-un-lft-identity 61.6%

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

      3. times-frac 78.1%

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

      4. fma-neg 80.6%

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

      5. associate-/l* 92.3%

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

   3. Applied egg-rr 92.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{1}, \frac{y}{a}, -\frac{z}{\frac{a}{t}}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{a}, \frac{-z}{\frac{a}{t}}\right)\\ \end{array} \]

Alternative 2: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+292}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

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 (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+292)))
     (- (* x (/ y a)) (/ z (/ a t)))
     (/ t_1 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)) || !(t_1 <= 5e+292)) {
		tmp = (x * (y / a)) - (z / (a / t));
	} else {
		tmp = t_1 / 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) || !(t_1 <= 5e+292)) {
		tmp = (x * (y / a)) - (z / (a / t));
	} else {
		tmp = t_1 / 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) or not (t_1 <= 5e+292):
		tmp = (x * (y / a)) - (z / (a / t))
	else:
		tmp = t_1 / 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 <= Float64(-Inf)) || !(t_1 <= 5e+292))
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(z / Float64(a / t)));
	else
		tmp = Float64(t_1 / 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) || ~((t_1 <= 5e+292)))
		tmp = (x * (y / a)) - (z / (a / t));
	else
		tmp = t_1 / 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[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+292]], $MachinePrecision]], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 4.9999999999999996e292 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 64.3%

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

      1. div-sub 59.7%

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

      2. associate-/l* 72.9%

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

      3. associate-/l* 92.0%

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

   3. Applied egg-rr 92.0%

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

      1. clear-num 92.0%

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

      2. associate-/r/ 92.0%

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

      3. clear-num 92.0%

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

   5. Applied egg-rr 92.0%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999996e292

   1. Initial program 97.7%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+292}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 3: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := \frac{z}{\frac{a}{t}}\\ t_2 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{a} - t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{t_2}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t_1\\ \end{array} \end{array} \]

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 (/ a t))) (t_2 (- (* x y) (* z t))))
   (if (<= t_2 (- INFINITY))
     (- (* x (/ y a)) t_1)
     (if (<= t_2 5e+292) (/ t_2 a) (- (/ x (/ a y)) t_1)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a / t);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (x * (y / a)) - t_1;
	} else if (t_2 <= 5e+292) {
		tmp = t_2 / a;
	} else {
		tmp = (x / (a / y)) - t_1;
	}
	return tmp;
}

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a / t);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (x * (y / a)) - t_1;
	} else if (t_2 <= 5e+292) {
		tmp = t_2 / a;
	} else {
		tmp = (x / (a / y)) - t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	t_1 = z / (a / t)
	t_2 = (x * y) - (z * t)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (x * (y / a)) - t_1
	elif t_2 <= 5e+292:
		tmp = t_2 / a
	else:
		tmp = (x / (a / y)) - t_1
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(a / t))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(x * Float64(y / a)) - t_1);
	elseif (t_2 <= 5e+292)
		tmp = Float64(t_2 / a);
	else
		tmp = Float64(Float64(x / Float64(a / y)) - t_1);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = z / (a / t);
	t_2 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (x * (y / a)) - t_1;
	elseif (t_2 <= 5e+292)
		tmp = t_2 / a;
	else
		tmp = (x / (a / y)) - t_1;
	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[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 5e+292], N[(t$95$2 / a), $MachinePrecision], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 60.6%

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

      1. div-sub 56.4%

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

      2. associate-/l* 64.2%

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

      3. associate-/l* 95.5%

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

   3. Applied egg-rr 95.5%

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

      1. clear-num 95.6%

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

      2. associate-/r/ 95.5%

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

      3. clear-num 95.5%

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

   5. Applied egg-rr 95.5%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999996e292

   1. Initial program 97.7%

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

   if 4.9999999999999996e292 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 66.6%

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

      1. div-sub 61.6%

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

      2. associate-/l* 78.2%

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

      3. associate-/l* 89.9%

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

   3. Applied egg-rr 89.9%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 4: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+140}:\\ \;\;\;\;\frac{z}{-\frac{a}{t}}\\ \mathbf{elif}\;z \cdot t \leq -4 \cdot 10^{-53}:\\ \;\;\;\;\frac{-1}{\frac{a}{z \cdot t}}\\ \mathbf{elif}\;z \cdot t \leq 50000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) -2e+140)
   (/ z (- (/ a t)))
   (if (<= (* z t) -4e-53)
     (/ -1.0 (/ a (* z t)))
     (if (<= (* z t) 50000000000.0) (/ (* x y) a) (* (- t) (/ z a))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -2e+140) {
		tmp = z / -(a / t);
	} else if ((z * t) <= -4e-53) {
		tmp = -1.0 / (a / (z * t));
	} else if ((z * t) <= 50000000000.0) {
		tmp = (x * y) / a;
	} else {
		tmp = -t * (z / 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 * t) <= (-2d+140)) then
        tmp = z / -(a / t)
    else if ((z * t) <= (-4d-53)) then
        tmp = (-1.0d0) / (a / (z * t))
    else if ((z * t) <= 50000000000.0d0) then
        tmp = (x * y) / a
    else
        tmp = -t * (z / 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 * t) <= -2e+140) {
		tmp = z / -(a / t);
	} else if ((z * t) <= -4e-53) {
		tmp = -1.0 / (a / (z * t));
	} else if ((z * t) <= 50000000000.0) {
		tmp = (x * y) / a;
	} else {
		tmp = -t * (z / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -2e+140:
		tmp = z / -(a / t)
	elif (z * t) <= -4e-53:
		tmp = -1.0 / (a / (z * t))
	elif (z * t) <= 50000000000.0:
		tmp = (x * y) / a
	else:
		tmp = -t * (z / a)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= -2e+140)
		tmp = Float64(z / Float64(-Float64(a / t)));
	elseif (Float64(z * t) <= -4e-53)
		tmp = Float64(-1.0 / Float64(a / Float64(z * t)));
	elseif (Float64(z * t) <= 50000000000.0)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(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)
	tmp = 0.0;
	if ((z * t) <= -2e+140)
		tmp = z / -(a / t);
	elseif ((z * t) <= -4e-53)
		tmp = -1.0 / (a / (z * t));
	elseif ((z * t) <= 50000000000.0)
		tmp = (x * y) / a;
	else
		tmp = -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_] := If[LessEqual[N[(z * t), $MachinePrecision], -2e+140], N[(z / (-N[(a / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -4e-53], N[(-1.0 / N[(a / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 50000000000.0], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -2.00000000000000012e140

   1. Initial program 80.7%

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

   2. Taylor expanded in x around 0 78.0%

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

      1. associate-*r/ 78.0%

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

      2. associate-*r* 78.0%

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

      3. neg-mul-1 78.0%

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

   4. Simplified 78.0%

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

      1. associate-/l* 91.3%

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

      2. associate-/r/ 88.7%

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

      3. add-sqr-sqrt 40.0%

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

      4. sqrt-unprod 32.4%

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

      5. sqr-neg 32.4%

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

      6. sqrt-unprod 3.1%

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

      7. add-sqr-sqrt 3.3%

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

   6. Applied egg-rr 3.3%

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

      1. *-commutative 3.3%

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

      2. clear-num 3.3%

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

      3. div-inv 3.3%

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

      4. frac-2neg 3.3%

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

      5. add-sqr-sqrt 3.1%

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

      6. sqrt-unprod 43.3%

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

      7. sqr-neg 43.3%

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

      8. sqrt-unprod 40.1%

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

      9. add-sqr-sqrt 88.7%

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

      10. distribute-neg-frac 88.7%

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

   8. Applied egg-rr 88.7%

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

   if -2.00000000000000012e140 < (*.f64 z t) < -4.00000000000000012e-53

   1. Initial program 94.5%

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

   2. Taylor expanded in x around 0 71.5%

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

      1. associate-*r/ 71.5%

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

      2. associate-*r* 71.5%

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

      3. neg-mul-1 71.5%

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

   4. Simplified 71.5%

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

      1. associate-/l* 59.5%

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

      2. associate-/r/ 57.3%

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

      3. add-sqr-sqrt 29.8%

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

      4. sqrt-unprod 13.1%

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

      5. sqr-neg 13.1%

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

      6. sqrt-unprod 1.0%

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

      7. add-sqr-sqrt 2.0%

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

   6. Applied egg-rr 2.0%

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

      1. *-commutative 2.0%

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

      2. clear-num 2.0%

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

      3. div-inv 2.0%

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

      4. frac-2neg 2.0%

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

      5. neg-mul-1 2.0%

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

      6. associate-/l* 2.0%

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

      7. add-sqr-sqrt 1.1%

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

      8. sqrt-unprod 27.9%

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

      9. sqr-neg 27.9%

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

      10. sqrt-unprod 27.2%

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

      11. add-sqr-sqrt 57.6%

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

      12. frac-2neg 57.6%

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

      13. associate-/l/ 71.6%

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

   8. Applied egg-rr 71.6%

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

   if -4.00000000000000012e-53 < (*.f64 z t) < 5e10

   1. Initial program 94.2%

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

   2. Taylor expanded in x around inf 76.5%

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

   if 5e10 < (*.f64 z t)

   1. Initial program 81.8%

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

   2. Taylor expanded in x around 0 69.1%

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

      1. associate-*r/ 69.1%

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

      2. mul-1-neg 69.1%

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

      3. distribute-rgt-neg-out 69.1%

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

      4. *-commutative 69.1%

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

      5. associate-/l* 77.0%

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

      6. associate-/r/ 79.1%

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

   4. Simplified 79.1%

      \[\leadsto \color{blue}{\frac{-z}{a} \cdot t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+140}:\\ \;\;\;\;\frac{z}{-\frac{a}{t}}\\ \mathbf{elif}\;z \cdot t \leq -4 \cdot 10^{-53}:\\ \;\;\;\;\frac{-1}{\frac{a}{z \cdot t}}\\ \mathbf{elif}\;z \cdot t \leq 50000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \end{array} \]

Alternative 5: 95.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{z}{-\frac{a}{t}}\\ \mathbf{elif}\;z \cdot t \leq 10^{+306}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \end{array} \]

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 t) (- INFINITY))
   (/ z (- (/ a t)))
   (if (<= (* z t) 1e+306) (/ (- (* x y) (* z t)) a) (* z (/ (- t) a)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -((double) INFINITY)) {
		tmp = z / -(a / t);
	} else if ((z * t) <= 1e+306) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = z * (-t / a);
	}
	return tmp;
}

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = z / -(a / t);
	} else if ((z * t) <= 1e+306) {
		tmp = ((x * y) - (z * t)) / 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 * t) <= -math.inf:
		tmp = z / -(a / t)
	elif (z * t) <= 1e+306:
		tmp = ((x * y) - (z * t)) / 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 (Float64(z * t) <= Float64(-Inf))
		tmp = Float64(z / Float64(-Float64(a / t)));
	elseif (Float64(z * t) <= 1e+306)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / 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 * t) <= -Inf)
		tmp = z / -(a / t);
	elseif ((z * t) <= 1e+306)
		tmp = ((x * y) - (z * t)) / 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[N[(z * t), $MachinePrecision], (-Infinity)], N[(z / (-N[(a / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e+306], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 71.1%

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

   2. Taylor expanded in x around 0 76.1%

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

      1. associate-*r/ 76.1%

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

      2. associate-*r* 76.1%

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

      3. neg-mul-1 76.1%

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

   4. Simplified 76.1%

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

      1. associate-/l* 94.9%

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

      2. associate-/r/ 94.8%

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

      3. add-sqr-sqrt 34.8%

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

      4. sqrt-unprod 30.4%

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

      5. sqr-neg 30.4%

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

      6. sqrt-unprod 5.0%

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

      7. add-sqr-sqrt 5.1%

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

   6. Applied egg-rr 5.1%

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

      1. *-commutative 5.1%

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

      2. clear-num 5.1%

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

      3. div-inv 5.1%

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

      4. frac-2neg 5.1%

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

      5. add-sqr-sqrt 5.0%

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

      6. sqrt-unprod 35.3%

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

      7. sqr-neg 35.3%

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

      8. sqrt-unprod 34.9%

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

      9. add-sqr-sqrt 94.9%

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

      10. distribute-neg-frac 94.9%

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

   8. Applied egg-rr 94.9%

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

   if -inf.0 < (*.f64 z t) < 1.00000000000000002e306

   1. Initial program 94.1%

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

   if 1.00000000000000002e306 < (*.f64 z t)

   1. Initial program 52.4%

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

      1. clear-num 52.4%

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

      2. inv-pow 52.4%

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

      3. fma-neg 52.7%

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

      4. *-commutative 52.7%

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

      5. distribute-rgt-neg-in 52.7%

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

   3. Applied egg-rr 52.7%

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

   4. Taylor expanded in x around 0 52.7%

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

      1. mul-1-neg 52.7%

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

      2. associate-*l/ 96.3%

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

      3. distribute-rgt-neg-in 96.3%

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

   6. Simplified 96.3%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;\frac{z}{-\frac{a}{t}}\\ \mathbf{elif}\;z \cdot t \leq 10^{+306}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \]

Alternative 6: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-14}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-26}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -1e-14)
   (/ (* x y) a)
   (if (<= (* x y) 4e-26) (/ (* z (- t)) a) (* y (/ x a)))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e-14) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 4e-26) {
		tmp = (z * -t) / a;
	} 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) :: tmp
    if ((x * y) <= (-1d-14)) then
        tmp = (x * y) / a
    else if ((x * y) <= 4d-26) then
        tmp = (z * -t) / a
    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 tmp;
	if ((x * y) <= -1e-14) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 4e-26) {
		tmp = (z * -t) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -1e-14:
		tmp = (x * y) / a
	elif (x * y) <= 4e-26:
		tmp = (z * -t) / a
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -1e-14)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 4e-26)
		tmp = Float64(Float64(z * Float64(-t)) / a);
	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)
	tmp = 0.0;
	if ((x * y) <= -1e-14)
		tmp = (x * y) / a;
	elseif ((x * y) <= 4e-26)
		tmp = (z * -t) / a;
	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_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e-14], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-26], N[(N[(z * (-t)), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999999e-15

   1. Initial program 89.0%

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

   2. Taylor expanded in x around inf 69.6%

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

   if -9.99999999999999999e-15 < (*.f64 x y) < 4.0000000000000002e-26

   1. Initial program 91.8%

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

   2. Taylor expanded in x around 0 79.4%

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

      1. associate-*r/ 79.4%

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

      2. associate-*r* 79.4%

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

      3. neg-mul-1 79.4%

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

   4. Simplified 79.4%

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

   if 4.0000000000000002e-26 < (*.f64 x y)

   1. Initial program 84.5%

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

   2. Taylor expanded in x around inf 69.7%

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

      1. associate-*r/ 77.4%

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

   4. Simplified 77.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-14}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-26}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 7: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-84} \lor \neg \left(y \leq 1.7 \cdot 10^{+103}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.5e-84) (not (<= y 1.7e+103)))
   (* y (/ x a))
   (* z (/ (- t) a))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.5e-84) || !(y <= 1.7e+103)) {
		tmp = y * (x / 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 ((y <= (-5.5d-84)) .or. (.not. (y <= 1.7d+103))) then
        tmp = y * (x / 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 ((y <= -5.5e-84) || !(y <= 1.7e+103)) {
		tmp = y * (x / a);
	} else {
		tmp = z * (-t / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.5e-84) or not (y <= 1.7e+103):
		tmp = y * (x / 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 ((y <= -5.5e-84) || !(y <= 1.7e+103))
		tmp = Float64(y * Float64(x / 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 ((y <= -5.5e-84) || ~((y <= 1.7e+103)))
		tmp = y * (x / 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[Or[LessEqual[y, -5.5e-84], N[Not[LessEqual[y, 1.7e+103]], $MachinePrecision]], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.50000000000000019e-84 or 1.6999999999999999e103 < y

   1. Initial program 88.4%

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

   2. Taylor expanded in x around inf 61.7%

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

      1. associate-*r/ 66.2%

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

   4. Simplified 66.2%

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

   if -5.50000000000000019e-84 < y < 1.6999999999999999e103

   1. Initial program 90.2%

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

      1. clear-num 90.2%

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

      2. inv-pow 90.2%

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

      3. fma-neg 90.2%

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

      4. *-commutative 90.2%

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

      5. distribute-rgt-neg-in 90.2%

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

   3. Applied egg-rr 90.2%

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

   4. Taylor expanded in x around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. associate-*l/ 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

   6. Simplified 70.9%

      \[\leadsto \color{blue}{\frac{t}{a} \cdot \left(-z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-84} \lor \neg \left(y \leq 1.7 \cdot 10^{+103}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \]

Alternative 8: 66.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-23} \lor \neg \left(y \leq 4.8 \cdot 10^{+103}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -7.6e-23) (not (<= y 4.8e+103)))
   (* 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 ((y <= -7.6e-23) || !(y <= 4.8e+103)) {
		tmp = y * (x / a);
	} else {
		tmp = -t * (z / 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 ((y <= (-7.6d-23)) .or. (.not. (y <= 4.8d+103))) then
        tmp = y * (x / a)
    else
        tmp = -t * (z / 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 ((y <= -7.6e-23) || !(y <= 4.8e+103)) {
		tmp = y * (x / a);
	} else {
		tmp = -t * (z / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (y <= -7.6e-23) or not (y <= 4.8e+103):
		tmp = y * (x / a)
	else:
		tmp = -t * (z / a)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -7.6e-23) || !(y <= 4.8e+103))
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(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)
	tmp = 0.0;
	if ((y <= -7.6e-23) || ~((y <= 4.8e+103)))
		tmp = y * (x / a);
	else
		tmp = -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_] := If[Or[LessEqual[y, -7.6e-23], N[Not[LessEqual[y, 4.8e+103]], $MachinePrecision]], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.60000000000000023e-23 or 4.7999999999999997e103 < y

   1. Initial program 87.8%

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

   2. Taylor expanded in x around inf 64.4%

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

      1. associate-*r/ 69.4%

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

   4. Simplified 69.4%

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

   if -7.60000000000000023e-23 < y < 4.7999999999999997e103

   1. Initial program 90.6%

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

   2. Taylor expanded in x around 0 69.2%

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

      1. associate-*r/ 69.2%

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

      2. mul-1-neg 69.2%

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

      3. distribute-rgt-neg-out 69.2%

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

      4. *-commutative 69.2%

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

      5. associate-/l* 70.0%

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

      6. associate-/r/ 68.6%

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

   4. Simplified 68.6%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-23} \lor \neg \left(y \leq 4.8 \cdot 10^{+103}\right):\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \end{array} \]

Alternative 9: 51.8% 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 89.3%

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

2. Taylor expanded in x around inf 46.2%

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

   1. associate-*r/ 48.2%

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

4. Simplified 48.2%

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

5. Final simplification 48.2%

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

Alternative 10: 51.9% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

2. Taylor expanded in x around inf 46.2%

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

   1. associate-/l* 47.8%

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

   2. associate-/r/ 47.3%

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

4. Applied egg-rr 47.3%

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

5. Final simplification 47.3%

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

Alternative 11: 51.9% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

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 = x / (a / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

2. Taylor expanded in x around inf 46.2%

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

   1. associate-*r/ 48.2%

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

4. Simplified 48.2%

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

   1. associate-*r/ 46.2%

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

   2. *-commutative 46.2%

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

   3. associate-/l* 47.1%

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

6. Applied egg-rr 47.1%

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

7. Final simplification 47.1%

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

Developer target: 91.0% 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 2023176 
(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))