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

Percentage Accurate: 91.2% → 95.7%

Time: 9.0s

Alternatives: 9

Speedup: 0.6×

• 28.2% 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: 91.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - t \cdot z\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+293} \lor \neg \left(t\_1 \leq 10^{+307}\right):\\ \;\;\;\;y \cdot \left(\frac{x}{a} - \frac{t}{a} \cdot \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* t z))))
   (if (or (<= t_1 -2e+293) (not (<= t_1 1e+307)))
     (* y (- (/ x a) (* (/ t a) (/ z y))))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (t * z);
	double tmp;
	if ((t_1 <= -2e+293) || !(t_1 <= 1e+307)) {
		tmp = y * ((x / a) - ((t / a) * (z / y)));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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) :: tmp
    t_1 = (x * y) - (t * z)
    if ((t_1 <= (-2d+293)) .or. (.not. (t_1 <= 1d+307))) then
        tmp = y * ((x / a) - ((t / a) * (z / y)))
    else
        tmp = t_1 / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (t * z);
	double tmp;
	if ((t_1 <= -2e+293) || !(t_1 <= 1e+307)) {
		tmp = y * ((x / a) - ((t / a) * (z / y)));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (t * z)
	tmp = 0
	if (t_1 <= -2e+293) or not (t_1 <= 1e+307):
		tmp = y * ((x / a) - ((t / a) * (z / y)))
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(t * z))
	tmp = 0.0
	if ((t_1 <= -2e+293) || !(t_1 <= 1e+307))
		tmp = Float64(y * Float64(Float64(x / a) - Float64(Float64(t / a) * Float64(z / y))));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (t * z);
	tmp = 0.0;
	if ((t_1 <= -2e+293) || ~((t_1 <= 1e+307)))
		tmp = y * ((x / a) - ((t / a) * (z / y)));
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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[(t * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+293], N[Not[LessEqual[t$95$1, 1e+307]], $MachinePrecision]], N[(y * N[(N[(x / a), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $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)) < -1.9999999999999998e293 or 9.99999999999999986e306 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 67.3%

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

   3. Taylor expanded in y around inf 77.9%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \frac{t \cdot z}{a \cdot y} + \frac{x}{a}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 77.9%

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

      2. mul-1-neg 77.9%

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

      3. unsub-neg 77.9%

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

      4. times-frac 84.6%

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

   5. Simplified 84.6%

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

   if -1.9999999999999998e293 < (-.f64 (*.f64 x y) (*.f64 z t)) < 9.99999999999999986e306

   1. Initial program 98.7%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - t \cdot z \leq -2 \cdot 10^{+293} \lor \neg \left(x \cdot y - t \cdot z \leq 10^{+307}\right):\\ \;\;\;\;y \cdot \left(\frac{x}{a} - \frac{t}{a} \cdot \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - t \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 7.6 \cdot 10^{+88}:\\ \;\;\;\;\frac{x \cdot \left(y - \frac{t \cdot z}{x}\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\sqrt{a}} \cdot \frac{y}{\sqrt{a}} - t \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= a 7.6e+88)
   (/ (* x (- y (/ (* t z) x))) a)
   (- (* (/ x (sqrt a)) (/ y (sqrt a))) (* t (/ z a)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 7.6e+88) {
		tmp = (x * (y - ((t * z) / x))) / a;
	} else {
		tmp = ((x / sqrt(a)) * (y / sqrt(a))) - (t * (z / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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 (a <= 7.6d+88) then
        tmp = (x * (y - ((t * z) / x))) / a
    else
        tmp = ((x / sqrt(a)) * (y / sqrt(a))) - (t * (z / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 7.6e+88) {
		tmp = (x * (y - ((t * z) / x))) / a;
	} else {
		tmp = ((x / Math.sqrt(a)) * (y / Math.sqrt(a))) - (t * (z / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if a <= 7.6e+88:
		tmp = (x * (y - ((t * z) / x))) / a
	else:
		tmp = ((x / math.sqrt(a)) * (y / math.sqrt(a))) - (t * (z / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 7.6e+88)
		tmp = Float64(Float64(x * Float64(y - Float64(Float64(t * z) / x))) / a);
	else
		tmp = Float64(Float64(Float64(x / sqrt(a)) * Float64(y / sqrt(a))) - Float64(t * Float64(z / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= 7.6e+88)
		tmp = (x * (y - ((t * z) / x))) / a;
	else
		tmp = ((x / sqrt(a)) * (y / sqrt(a))) - (t * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[a, 7.6e+88], N[(N[(x * N[(y - N[(N[(t * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(N[(x / N[Sqrt[a], $MachinePrecision]), $MachinePrecision] * N[(y / N[Sqrt[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 7.5999999999999993e88

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 91.5%

      \[\leadsto \frac{\color{blue}{x \cdot \left(y + -1 \cdot \frac{t \cdot z}{x}\right)}}{a} \]
   4. Step-by-step derivation

      1. associate-*r/ 91.5%

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

      2. mul-1-neg 91.5%

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

   5. Simplified 91.5%

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

   if 7.5999999999999993e88 < a

   1. Initial program 81.3%

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

      1. div-sub 81.3%

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

      2. *-un-lft-identity 81.3%

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

      3. add-sqr-sqrt 81.1%

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

      4. times-frac 81.1%

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

      5. fmm-def 81.1%

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

      6. associate-/l* 84.5%

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

   4. Applied egg-rr 84.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{\sqrt{a}}, \frac{x \cdot y}{\sqrt{a}}, -z \cdot \frac{t}{a}\right)} \]
   5. Step-by-step derivation

      1. fmm-undef 84.5%

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

      2. associate-*r/ 81.1%

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

      3. *-commutative 81.1%

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

      4. associate-/l* 87.4%

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

      5. associate-*l/ 87.4%

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

      6. *-lft-identity 87.4%

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

      7. associate-/l* 87.5%

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

      8. associate-*l/ 92.8%

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

   6. Simplified 92.8%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 7.6 \cdot 10^{+88}:\\ \;\;\;\;\frac{x \cdot \left(y - \frac{t \cdot z}{x}\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\sqrt{a}} \cdot \frac{y}{\sqrt{a}} - t \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - t \cdot z\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t \cdot \left(x \cdot \frac{y}{a \cdot t} - \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

   1. Initial program 66.2%

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

   3. Taylor expanded in t around inf 79.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \frac{z}{a} + \frac{x \cdot y}{a \cdot t}\right)} \]
   4. Step-by-step derivation

      1. +-commutative 79.4%

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

      2. mul-1-neg 79.4%

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

      3. unsub-neg 79.4%

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

      4. associate-/l* 92.8%

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

      5. *-commutative 92.8%

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

   5. Simplified 92.8%

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

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

   1. Initial program 94.7%

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

4. Final simplification 94.5%

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

Alternative 4: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+52}:\\ \;\;\;\;\frac{t \cdot z}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e-5)
   (/ x (/ a y))
   (if (<= (* x y) 5e+52) (/ (* t z) (- a)) (/ y (/ a x)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e-5) {
		tmp = x / (a / y);
	} else if ((x * y) <= 5e+52) {
		tmp = (t * z) / -a;
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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) <= (-5d-5)) then
        tmp = x / (a / y)
    else if ((x * y) <= 5d+52) then
        tmp = (t * z) / -a
    else
        tmp = y / (a / x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e-5) {
		tmp = x / (a / y);
	} else if ((x * y) <= 5e+52) {
		tmp = (t * z) / -a;
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e-5:
		tmp = x / (a / y)
	elif (x * y) <= 5e+52:
		tmp = (t * z) / -a
	else:
		tmp = y / (a / x)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e-5)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 5e+52)
		tmp = Float64(Float64(t * z) / Float64(-a));
	else
		tmp = Float64(y / Float64(a / x));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e-5)
		tmp = x / (a / y);
	elseif ((x * y) <= 5e+52)
		tmp = (t * z) / -a;
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e-5], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+52], N[(N[(t * z), $MachinePrecision] / (-a)), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.00000000000000024e-5

   1. Initial program 90.0%

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

   3. Taylor expanded in x around inf 74.0%

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

      1. associate-*r/ 71.0%

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

   5. Simplified 71.0%

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

      1. clear-num 70.2%

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

      2. un-div-inv 71.3%

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

   7. Applied egg-rr 71.3%

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

   if -5.00000000000000024e-5 < (*.f64 x y) < 5e52

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0 72.0%

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

      1. mul-1-neg 72.0%

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

      2. *-commutative 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

   5. Simplified 72.0%

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

   if 5e52 < (*.f64 x y)

   1. Initial program 85.3%

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

      1. add-cube-cbrt 84.6%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x \cdot y} \cdot \sqrt[3]{x \cdot y}\right) \cdot \sqrt[3]{x \cdot y}} - z \cdot t}{a} \]

      2. pow3 84.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x \cdot y}\right)}^{3}} - z \cdot t}{a} \]

   4. Applied egg-rr 84.6%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x \cdot y}\right)}^{3}} - z \cdot t}{a} \]

   5. Taylor expanded in x around inf 87.0%

      \[\leadsto \frac{\color{blue}{x \cdot \left(y + -1 \cdot \frac{t \cdot z}{x}\right)}}{a} \]
   6. Step-by-step derivation

      1. associate-*r/ 87.0%

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

      2. mul-1-neg 87.0%

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

      3. distribute-rgt-neg-in 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in x around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*r/ 83.2%

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

   10. Simplified 83.2%

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

       1. clear-num 83.1%

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

       2. un-div-inv 83.2%

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

   12. Applied egg-rr 83.2%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+52}:\\ \;\;\;\;\frac{t \cdot z}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e-5)
   (/ x (/ a y))
   (if (<= (* x y) 5e+52) (* z (/ (- t) a)) (/ y (/ a x)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e-5) {
		tmp = x / (a / y);
	} else if ((x * y) <= 5e+52) {
		tmp = z * (-t / a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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) <= (-5d-5)) then
        tmp = x / (a / y)
    else if ((x * y) <= 5d+52) then
        tmp = z * (-t / a)
    else
        tmp = y / (a / x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e-5) {
		tmp = x / (a / y);
	} else if ((x * y) <= 5e+52) {
		tmp = z * (-t / a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e-5:
		tmp = x / (a / y)
	elif (x * y) <= 5e+52:
		tmp = z * (-t / a)
	else:
		tmp = y / (a / x)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e-5)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 5e+52)
		tmp = Float64(z * Float64(Float64(-t) / a));
	else
		tmp = Float64(y / Float64(a / x));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e-5)
		tmp = x / (a / y);
	elseif ((x * y) <= 5e+52)
		tmp = z * (-t / a);
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e-5], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+52], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.00000000000000024e-5

   1. Initial program 90.0%

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

   3. Taylor expanded in x around inf 74.0%

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

      1. associate-*r/ 71.0%

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

   5. Simplified 71.0%

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

      1. clear-num 70.2%

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

      2. un-div-inv 71.3%

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

   7. Applied egg-rr 71.3%

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

   if -5.00000000000000024e-5 < (*.f64 x y) < 5e52

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0 72.0%

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

      1. mul-1-neg 72.0%

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

      2. *-commutative 72.0%

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

      3. associate-*r/ 70.3%

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

      4. distribute-rgt-neg-in 70.3%

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

      5. distribute-frac-neg 70.3%

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

   5. Simplified 70.3%

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

   if 5e52 < (*.f64 x y)

   1. Initial program 85.3%

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

      1. add-cube-cbrt 84.6%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x \cdot y} \cdot \sqrt[3]{x \cdot y}\right) \cdot \sqrt[3]{x \cdot y}} - z \cdot t}{a} \]

      2. pow3 84.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x \cdot y}\right)}^{3}} - z \cdot t}{a} \]

   4. Applied egg-rr 84.6%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x \cdot y}\right)}^{3}} - z \cdot t}{a} \]

   5. Taylor expanded in x around inf 87.0%

      \[\leadsto \frac{\color{blue}{x \cdot \left(y + -1 \cdot \frac{t \cdot z}{x}\right)}}{a} \]
   6. Step-by-step derivation

      1. associate-*r/ 87.0%

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

      2. mul-1-neg 87.0%

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

      3. distribute-rgt-neg-in 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in x around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*r/ 83.2%

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

   10. Simplified 83.2%

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

       1. clear-num 83.1%

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

       2. un-div-inv 83.2%

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

   12. Applied egg-rr 83.2%

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

Alternative 6: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-90}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e-5)
   (/ x (/ a y))
   (if (<= (* x y) 2e-90) (/ (- t) (/ a z)) (/ y (/ a x)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e-5) {
		tmp = x / (a / y);
	} else if ((x * y) <= 2e-90) {
		tmp = -t / (a / z);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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) <= (-5d-5)) then
        tmp = x / (a / y)
    else if ((x * y) <= 2d-90) then
        tmp = -t / (a / z)
    else
        tmp = y / (a / x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e-5) {
		tmp = x / (a / y);
	} else if ((x * y) <= 2e-90) {
		tmp = -t / (a / z);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e-5:
		tmp = x / (a / y)
	elif (x * y) <= 2e-90:
		tmp = -t / (a / z)
	else:
		tmp = y / (a / x)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e-5)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 2e-90)
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = Float64(y / Float64(a / x));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e-5)
		tmp = x / (a / y);
	elseif ((x * y) <= 2e-90)
		tmp = -t / (a / z);
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e-5], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-90], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.00000000000000024e-5

   1. Initial program 90.0%

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

   3. Taylor expanded in x around inf 74.0%

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

      1. associate-*r/ 71.0%

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

   5. Simplified 71.0%

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

      1. clear-num 70.2%

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

      2. un-div-inv 71.3%

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

   7. Applied egg-rr 71.3%

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

   if -5.00000000000000024e-5 < (*.f64 x y) < 1.99999999999999999e-90

   1. Initial program 94.9%

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

   3. Taylor expanded in x around 0 76.0%

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

      1. mul-1-neg 76.0%

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

      2. *-commutative 76.0%

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

      3. associate-*r/ 75.3%

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

      4. distribute-rgt-neg-in 75.3%

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

      5. distribute-frac-neg 75.3%

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

   5. Simplified 75.3%

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

      1. clear-num 75.2%

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

      2. un-div-inv 75.2%

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

      3. add-sqr-sqrt 37.4%

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

      4. sqrt-unprod 36.2%

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

      5. sqr-neg 36.2%

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

      6. sqrt-unprod 5.4%

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

      7. add-sqr-sqrt 9.4%

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

   7. Applied egg-rr 9.4%

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

      1. associate-/r/ 9.4%

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

   9. Simplified 9.4%

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

       1. add-sqr-sqrt 8.2%

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

       2. sqrt-unprod 38.3%

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

       3. *-commutative 38.3%

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

       4. *-commutative 38.3%

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

       5. swap-sqr 34.0%

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

       6. sqr-neg 34.0%

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

       7. distribute-frac-neg 34.0%

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

       8. distribute-frac-neg 34.0%

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

       9. swap-sqr 38.3%

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

       10. sqrt-unprod 39.6%

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

       11. add-sqr-sqrt 71.2%

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

       12. distribute-frac-neg 71.2%

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

       13. distribute-rgt-neg-out 71.2%

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

       14. clear-num 71.2%

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

       15. un-div-inv 72.1%

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

   11. Applied egg-rr 72.1%

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

   if 1.99999999999999999e-90 < (*.f64 x y)

   1. Initial program 89.0%

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

      1. add-cube-cbrt 88.2%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x \cdot y} \cdot \sqrt[3]{x \cdot y}\right) \cdot \sqrt[3]{x \cdot y}} - z \cdot t}{a} \]

      2. pow3 88.3%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x \cdot y}\right)}^{3}} - z \cdot t}{a} \]

   4. Applied egg-rr 88.3%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x \cdot y}\right)}^{3}} - z \cdot t}{a} \]

   5. Taylor expanded in x around inf 88.9%

      \[\leadsto \frac{\color{blue}{x \cdot \left(y + -1 \cdot \frac{t \cdot z}{x}\right)}}{a} \]
   6. Step-by-step derivation

      1. associate-*r/ 88.9%

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

      2. mul-1-neg 88.9%

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

      3. distribute-rgt-neg-in 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in x around inf 71.7%

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

      1. *-commutative 71.7%

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

      2. associate-*r/ 75.1%

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

   10. Simplified 75.1%

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

       1. clear-num 75.0%

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

       2. un-div-inv 75.1%

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

   12. Applied egg-rr 75.1%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-90}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \cdot z \leq 4 \cdot 10^{+299}:\\ \;\;\;\;\frac{x \cdot y - t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* t z) 4e+299) (/ (- (* x y) (* t z)) a) (* z (/ (- t) a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t * z) <= 4e+299) {
		tmp = ((x * y) - (t * z)) / a;
	} else {
		tmp = z * (-t / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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 ((t * z) <= 4d+299) then
        tmp = ((x * y) - (t * z)) / a
    else
        tmp = z * (-t / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t * z) <= 4e+299) {
		tmp = ((x * y) - (t * z)) / a;
	} else {
		tmp = z * (-t / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (t * z) <= 4e+299:
		tmp = ((x * y) - (t * z)) / a
	else:
		tmp = z * (-t / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(t * z) <= 4e+299)
		tmp = Float64(Float64(Float64(x * y) - Float64(t * z)) / a);
	else
		tmp = Float64(z * Float64(Float64(-t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t * z) <= 4e+299)
		tmp = ((x * y) - (t * z)) / a;
	else
		tmp = z * (-t / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(t * z), $MachinePrecision], 4e+299], N[(N[(N[(x * y), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < 4.0000000000000002e299

   1. Initial program 93.8%

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

   if 4.0000000000000002e299 < (*.f64 z t)

   1. Initial program 62.4%

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

   3. Taylor expanded in x around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. *-commutative 67.9%

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

      3. associate-*r/ 94.4%

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

      4. distribute-rgt-neg-in 94.4%

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

      5. distribute-frac-neg 94.4%

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

   5. Simplified 94.4%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq 4 \cdot 10^{+299}:\\ \;\;\;\;\frac{x \cdot y - t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.3% accurate, 1.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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 && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return y * (x / a);
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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 && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return y * (x / a);
}

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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 91.6%

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

   1. add-cube-cbrt 91.1%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x \cdot y} \cdot \sqrt[3]{x \cdot y}\right) \cdot \sqrt[3]{x \cdot y}} - z \cdot t}{a} \]

   2. pow3 91.0%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x \cdot y}\right)}^{3}} - z \cdot t}{a} \]

4. Applied egg-rr 91.0%

   \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x \cdot y}\right)}^{3}} - z \cdot t}{a} \]

5. Taylor expanded in x around inf 88.6%

   \[\leadsto \frac{\color{blue}{x \cdot \left(y + -1 \cdot \frac{t \cdot z}{x}\right)}}{a} \]
6. Step-by-step derivation

   1. associate-*r/ 88.6%

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

   2. mul-1-neg 88.6%

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

   3. distribute-rgt-neg-in 88.6%

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

7. Simplified 88.6%

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

8. Taylor expanded in x around inf 55.2%

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

   1. *-commutative 55.2%

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

   2. associate-*r/ 56.3%

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

10. Simplified 56.3%

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

Alternative 9: 51.0% accurate, 1.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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 && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return x * (y / a);
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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 && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return x * (y / a);
}

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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 91.6%

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

3. Taylor expanded in x around inf 55.2%

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

   1. associate-*r/ 54.3%

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

5. Simplified 54.3%

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

Developer Target 1: 91.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y / a) * x) - ((t / a) * z)
    if (z < (-2.468684968699548d+170)) then
        tmp = t_1
    else if (z < 6.309831121978371d-71) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

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

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