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

Percentage Accurate: 91.1% → 94.6%

Time: 7.2s

Alternatives: 10

Speedup: 0.6×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.1% 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: 94.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{t}{a} \cdot z\\ \mathbf{if}\;a \leq -1.32 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+114}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}} - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ t a) z)))
   (if (<= a -1.32e+38)
     (- (* (/ y (pow (cbrt a) 2.0)) (/ x (cbrt a))) t_1)
     (if (<= a 2.2e+114) (/ (fma x y (* t (- z))) a) (- (/ y (/ a x)) t_1)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / a) * z;
	double tmp;
	if (a <= -1.32e+38) {
		tmp = ((y / pow(cbrt(a), 2.0)) * (x / cbrt(a))) - t_1;
	} else if (a <= 2.2e+114) {
		tmp = fma(x, y, (t * -z)) / a;
	} else {
		tmp = (y / (a / x)) - t_1;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / a) * z)
	tmp = 0.0
	if (a <= -1.32e+38)
		tmp = Float64(Float64(Float64(y / (cbrt(a) ^ 2.0)) * Float64(x / cbrt(a))) - t_1);
	elseif (a <= 2.2e+114)
		tmp = Float64(fma(x, y, Float64(t * Float64(-z))) / a);
	else
		tmp = Float64(Float64(y / Float64(a / x)) - t_1);
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[a, -1.32e+38], N[(N[(N[(y / N[Power[N[Power[a, 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(x / N[Power[a, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[a, 2.2e+114], N[(N[(x * y + N[(t * (-z)), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.32e38

   1. Initial program 79.7%

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

      1. div-sub 79.6%

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

      2. *-commutative 79.6%

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

      3. add-cube-cbrt 79.0%

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

      4. times-frac 90.7%

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

      5. fma-neg 90.7%

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

      6. pow2 90.7%

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{{\left(\sqrt[3]{a}\right)}^{2}}}, \frac{x}{\sqrt[3]{a}}, -\frac{z \cdot t}{a}\right) \]

      7. associate-/l* 92.4%

         \[\leadsto \mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\color{blue}{\frac{z}{\frac{a}{t}}}\right) \]

   3. Applied egg-rr 92.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\frac{z}{\frac{a}{t}}\right)} \]
   4. Step-by-step derivation

      1. fma-neg 92.3%

         \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{z}{\frac{a}{t}}} \]

      2. associate-/l* 90.7%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{z \cdot t}{a}} \]

      3. *-commutative 90.7%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{\color{blue}{t \cdot z}}{a} \]

      4. associate-/l* 98.0%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{t}{\frac{a}{z}}} \]

      5. associate-/r/ 93.7%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{t}{a} \cdot z} \]

   5. Simplified 93.7%

      \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{t}{a} \cdot z} \]

   if -1.32e38 < a < 2.2e114

   1. Initial program 99.2%

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

      1. fma-neg 99.2%

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

      2. distribute-lft-neg-out 99.2%

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

      3. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   if 2.2e114 < a

   1. Initial program 76.7%

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

      1. div-sub 76.7%

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

      2. *-commutative 76.7%

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

      3. add-cube-cbrt 76.2%

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

      4. times-frac 91.8%

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

      5. fma-neg 91.8%

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

      6. pow2 91.8%

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{{\left(\sqrt[3]{a}\right)}^{2}}}, \frac{x}{\sqrt[3]{a}}, -\frac{z \cdot t}{a}\right) \]

      7. associate-/l* 90.0%

         \[\leadsto \mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\color{blue}{\frac{z}{\frac{a}{t}}}\right) \]

   3. Applied egg-rr 90.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\frac{z}{\frac{a}{t}}\right)} \]
   4. Step-by-step derivation

      1. fma-neg 90.0%

         \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{z}{\frac{a}{t}}} \]

      2. associate-/l* 91.8%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{z \cdot t}{a}} \]

      3. *-commutative 91.8%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{\color{blue}{t \cdot z}}{a} \]

      4. associate-/l* 97.1%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{t}{\frac{a}{z}}} \]

      5. associate-/r/ 91.2%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{t}{a} \cdot z} \]

   5. Simplified 91.2%

      \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{t}{a} \cdot z} \]
   6. Step-by-step derivation

      1. frac-times 75.6%

         \[\leadsto \color{blue}{\frac{y \cdot x}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \sqrt[3]{a}}} - \frac{t}{a} \cdot z \]

      2. unpow2 75.6%

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

      3. add-cube-cbrt 76.1%

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

      4. *-un-lft-identity 76.1%

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

      5. frac-times 90.2%

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

      6. /-rgt-identity 90.2%

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

      7. clear-num 90.2%

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

      8. un-div-inv 90.2%

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

   7. Applied egg-rr 90.2%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.32 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{t}{a} \cdot z\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+114}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}} - \frac{t}{a} \cdot z\\ \end{array} \]

Alternative 2: 94.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-58} \lor \neg \left(a \leq 9 \cdot 10^{+110}\right):\\ \;\;\;\;\frac{y}{\frac{a}{x}} - \frac{t}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.7e-58) (not (<= a 9e+110)))
   (- (/ y (/ a x)) (* (/ t a) z))
   (/ (fma x y (* t (- z))) a)))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.7e-58) || !(a <= 9e+110)) {
		tmp = (y / (a / x)) - ((t / a) * z);
	} else {
		tmp = fma(x, y, (t * -z)) / a;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.7e-58) || !(a <= 9e+110))
		tmp = Float64(Float64(y / Float64(a / x)) - Float64(Float64(t / a) * z));
	else
		tmp = Float64(fma(x, y, Float64(t * Float64(-z))) / a);
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.7e-58], N[Not[LessEqual[a, 9e+110]], $MachinePrecision]], N[(N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(t * (-z)), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.69999999999999987e-58 or 9.0000000000000005e110 < a

   1. Initial program 80.2%

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

      1. div-sub 80.2%

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

      2. *-commutative 80.2%

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

      3. add-cube-cbrt 79.6%

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

      4. times-frac 92.0%

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

      5. fma-neg 92.0%

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

      6. pow2 92.0%

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{{\left(\sqrt[3]{a}\right)}^{2}}}, \frac{x}{\sqrt[3]{a}}, -\frac{z \cdot t}{a}\right) \]

      7. associate-/l* 91.9%

         \[\leadsto \mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\color{blue}{\frac{z}{\frac{a}{t}}}\right) \]

   3. Applied egg-rr 91.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\frac{z}{\frac{a}{t}}\right)} \]
   4. Step-by-step derivation

      1. fma-neg 91.9%

         \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{z}{\frac{a}{t}}} \]

      2. associate-/l* 92.0%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{z \cdot t}{a}} \]

      3. *-commutative 92.0%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{\color{blue}{t \cdot z}}{a} \]

      4. associate-/l* 97.7%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{t}{\frac{a}{z}}} \]

      5. associate-/r/ 93.1%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{t}{a} \cdot z} \]

   5. Simplified 93.1%

      \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{t}{a} \cdot z} \]
   6. Step-by-step derivation

      1. frac-times 80.7%

         \[\leadsto \color{blue}{\frac{y \cdot x}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \sqrt[3]{a}}} - \frac{t}{a} \cdot z \]

      2. unpow2 80.7%

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

      3. add-cube-cbrt 81.3%

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

      4. *-un-lft-identity 81.3%

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

      5. frac-times 91.7%

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

      6. /-rgt-identity 91.7%

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

      7. clear-num 91.7%

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

      8. un-div-inv 91.8%

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

   7. Applied egg-rr 91.8%

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

   if -1.69999999999999987e-58 < a < 9.0000000000000005e110

   1. Initial program 99.1%

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

      1. fma-neg 99.1%

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

      2. distribute-lft-neg-out 99.1%

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

      3. *-commutative 99.1%

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

   3. Simplified 99.1%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{-58} \lor \neg \left(a \leq 9 \cdot 10^{+110}\right):\\ \;\;\;\;\frac{y}{\frac{a}{x}} - \frac{t}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right)}{a}\\ \end{array} \]

Alternative 3: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -2 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;y \cdot x \leq 5 \cdot 10^{-75}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{elif}\;y \cdot x \leq 0.05:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \cdot x \leq 2 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y x) -2e+30)
   (* y (/ x a))
   (if (<= (* y x) 5e-75)
     (/ (- z) (/ a t))
     (if (<= (* y x) 0.05)
       (/ x (/ a y))
       (if (<= (* y x) 2e+28) (* t (/ (- z) a)) (/ y (/ a x)))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -2e+30) {
		tmp = y * (x / a);
	} else if ((y * x) <= 5e-75) {
		tmp = -z / (a / t);
	} else if ((y * x) <= 0.05) {
		tmp = x / (a / y);
	} else if ((y * x) <= 2e+28) {
		tmp = t * (-z / a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 * x) <= (-2d+30)) then
        tmp = y * (x / a)
    else if ((y * x) <= 5d-75) then
        tmp = -z / (a / t)
    else if ((y * x) <= 0.05d0) then
        tmp = x / (a / y)
    else if ((y * x) <= 2d+28) then
        tmp = t * (-z / a)
    else
        tmp = y / (a / x)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -2e+30) {
		tmp = y * (x / a);
	} else if ((y * x) <= 5e-75) {
		tmp = -z / (a / t);
	} else if ((y * x) <= 0.05) {
		tmp = x / (a / y);
	} else if ((y * x) <= 2e+28) {
		tmp = t * (-z / a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (y * x) <= -2e+30:
		tmp = y * (x / a)
	elif (y * x) <= 5e-75:
		tmp = -z / (a / t)
	elif (y * x) <= 0.05:
		tmp = x / (a / y)
	elif (y * x) <= 2e+28:
		tmp = t * (-z / a)
	else:
		tmp = y / (a / x)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(y * x) <= -2e+30)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(y * x) <= 5e-75)
		tmp = Float64(Float64(-z) / Float64(a / t));
	elseif (Float64(y * x) <= 0.05)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(y * x) <= 2e+28)
		tmp = Float64(t * Float64(Float64(-z) / a));
	else
		tmp = Float64(y / Float64(a / x));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y * x) <= -2e+30)
		tmp = y * (x / a);
	elseif ((y * x) <= 5e-75)
		tmp = -z / (a / t);
	elseif ((y * x) <= 0.05)
		tmp = x / (a / y);
	elseif ((y * x) <= 2e+28)
		tmp = t * (-z / a);
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], -2e+30], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 5e-75], N[((-z) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 0.05], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 2e+28], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -2e30

   1. Initial program 87.0%

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

   2. Taylor expanded in x around inf 71.1%

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

      1. associate-*l/ 75.9%

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

   4. Simplified 75.9%

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

   if -2e30 < (*.f64 x y) < 4.99999999999999979e-75

   1. Initial program 92.7%

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

      1. div-sub 92.7%

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

      2. *-commutative 92.7%

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

      3. add-cube-cbrt 92.4%

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

      4. times-frac 91.6%

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

      5. fma-neg 91.6%

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

      6. pow2 91.6%

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{{\left(\sqrt[3]{a}\right)}^{2}}}, \frac{x}{\sqrt[3]{a}}, -\frac{z \cdot t}{a}\right) \]

      7. associate-/l* 88.9%

         \[\leadsto \mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\color{blue}{\frac{z}{\frac{a}{t}}}\right) \]

   3. Applied egg-rr 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\frac{z}{\frac{a}{t}}\right)} \]
   4. Step-by-step derivation

      1. fma-neg 88.9%

         \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{z}{\frac{a}{t}}} \]

      2. associate-/l* 91.6%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{z \cdot t}{a}} \]

      3. *-commutative 91.6%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{\color{blue}{t \cdot z}}{a} \]

      4. associate-/l* 91.4%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{t}{\frac{a}{z}}} \]

      5. associate-/r/ 90.1%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{t}{a} \cdot z} \]

   5. Simplified 90.1%

      \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{t}{a} \cdot z} \]

   6. Taylor expanded in y around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. *-commutative 79.3%

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

      3. associate-/l* 76.6%

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

   8. Simplified 76.6%

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

   if 4.99999999999999979e-75 < (*.f64 x y) < 0.050000000000000003

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 80.5%

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

      1. associate-*l/ 74.1%

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

   4. Simplified 74.1%

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

      1. associate-/r/ 74.2%

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

   6. Applied egg-rr 74.2%

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

   if 0.050000000000000003 < (*.f64 x y) < 1.99999999999999992e28

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. *-commutative 77.8%

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

      3. associate-*l/ 78.0%

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

      4. *-commutative 78.0%

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

      5. distribute-rgt-neg-in 78.0%

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

      6. distribute-frac-neg 78.0%

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

   4. Simplified 78.0%

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

   if 1.99999999999999992e28 < (*.f64 x y)

   1. Initial program 87.3%

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

   2. Taylor expanded in x around inf 69.7%

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

      1. associate-*l/ 80.8%

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

   4. Simplified 80.8%

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

      1. *-commutative 80.8%

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

      2. clear-num 80.8%

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

      3. un-div-inv 81.1%

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

   6. Applied egg-rr 81.1%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -2 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;y \cdot x \leq 5 \cdot 10^{-75}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{elif}\;y \cdot x \leq 0.05:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \cdot x \leq 2 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 4: 93.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{y \cdot x - t \cdot z}{a}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+303}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- (* y x) (* t z)) a)))
   (if (<= t_1 -1e+303) (- (/ x (/ a y)) (/ z (/ a t))) t_1)))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y * x) - (t * z)) / a;
	double tmp;
	if (t_1 <= -1e+303) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 = ((y * x) - (t * z)) / a
    if (t_1 <= (-1d+303)) then
        tmp = (x / (a / y)) - (z / (a / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y * x) - (t * z)) / a;
	double tmp;
	if (t_1 <= -1e+303) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = ((y * x) - (t * z)) / a
	tmp = 0
	if t_1 <= -1e+303:
		tmp = (x / (a / y)) - (z / (a / t))
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y * x) - Float64(t * z)) / a)
	tmp = 0.0
	if (t_1 <= -1e+303)
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y * x) - (t * z)) / a;
	tmp = 0.0;
	if (t_1 <= -1e+303)
		tmp = (x / (a / y)) - (z / (a / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+303], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < -1e303

   1. Initial program 71.6%

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

      1. div-sub 69.7%

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

      2. associate-/l* 87.2%

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

      3. associate-/l* 96.1%

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

   3. Applied egg-rr 96.1%

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

   if -1e303 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

   1. Initial program 95.6%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot x - t \cdot z}{a} \leq -1 \cdot 10^{+303}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - t \cdot z}{a}\\ \end{array} \]

Alternative 5: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \cdot x \leq 10^{+305}:\\ \;\;\;\;\frac{y \cdot x - t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y x) (- INFINITY))
   (/ x (/ a y))
   (if (<= (* y x) 1e+305) (/ (- (* y x) (* t z)) a) (* x (/ y a)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -((double) INFINITY)) {
		tmp = x / (a / y);
	} else if ((y * x) <= 1e+305) {
		tmp = ((y * x) - (t * z)) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -Double.POSITIVE_INFINITY) {
		tmp = x / (a / y);
	} else if ((y * x) <= 1e+305) {
		tmp = ((y * x) - (t * z)) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (y * x) <= -math.inf:
		tmp = x / (a / y)
	elif (y * x) <= 1e+305:
		tmp = ((y * x) - (t * z)) / a
	else:
		tmp = x * (y / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(y * x) <= Float64(-Inf))
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(y * x) <= 1e+305)
		tmp = Float64(Float64(Float64(y * x) - Float64(t * z)) / a);
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y * x) <= -Inf)
		tmp = x / (a / y);
	elseif ((y * x) <= 1e+305)
		tmp = ((y * x) - (t * z)) / a;
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], (-Infinity)], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 1e+305], N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 67.4%

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

   2. Taylor expanded in x around inf 67.4%

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

      1. associate-*l/ 99.8%

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

   4. Simplified 99.8%

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

      1. associate-/r/ 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 x y) < 9.9999999999999994e304

   1. Initial program 95.8%

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

   if 9.9999999999999994e304 < (*.f64 x y)

   1. Initial program 57.7%

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

   2. Taylor expanded in x around inf 57.7%

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

      1. associate-*r/ 99.7%

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

   4. Simplified 99.7%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \cdot x \leq 10^{+305}:\\ \;\;\;\;\frac{y \cdot x - t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 94.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-58} \lor \neg \left(a \leq 1.5 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{y}{\frac{a}{x}} - \frac{t}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - t \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.8e-58) (not (<= a 1.5e+113)))
   (- (/ y (/ a x)) (* (/ t a) z))
   (/ (- (* y x) (* t z)) a)))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e-58) || !(a <= 1.5e+113)) {
		tmp = (y / (a / x)) - ((t / a) * z);
	} else {
		tmp = ((y * x) - (t * z)) / a;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 <= (-1.8d-58)) .or. (.not. (a <= 1.5d+113))) then
        tmp = (y / (a / x)) - ((t / a) * z)
    else
        tmp = ((y * x) - (t * z)) / a
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e-58) || !(a <= 1.5e+113)) {
		tmp = (y / (a / x)) - ((t / a) * z);
	} else {
		tmp = ((y * x) - (t * z)) / a;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.8e-58) or not (a <= 1.5e+113):
		tmp = (y / (a / x)) - ((t / a) * z)
	else:
		tmp = ((y * x) - (t * z)) / a
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.8e-58) || !(a <= 1.5e+113))
		tmp = Float64(Float64(y / Float64(a / x)) - Float64(Float64(t / a) * z));
	else
		tmp = Float64(Float64(Float64(y * x) - Float64(t * z)) / a);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.8e-58) || ~((a <= 1.5e+113)))
		tmp = (y / (a / x)) - ((t / a) * z);
	else
		tmp = ((y * x) - (t * z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.8e-58], N[Not[LessEqual[a, 1.5e+113]], $MachinePrecision]], N[(N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.80000000000000005e-58 or 1.5e113 < a

   1. Initial program 80.2%

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

      1. div-sub 80.2%

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

      2. *-commutative 80.2%

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

      3. add-cube-cbrt 79.6%

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

      4. times-frac 92.0%

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

      5. fma-neg 92.0%

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

      6. pow2 92.0%

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{{\left(\sqrt[3]{a}\right)}^{2}}}, \frac{x}{\sqrt[3]{a}}, -\frac{z \cdot t}{a}\right) \]

      7. associate-/l* 91.9%

         \[\leadsto \mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\color{blue}{\frac{z}{\frac{a}{t}}}\right) \]

   3. Applied egg-rr 91.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\frac{z}{\frac{a}{t}}\right)} \]
   4. Step-by-step derivation

      1. fma-neg 91.9%

         \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{z}{\frac{a}{t}}} \]

      2. associate-/l* 92.0%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{z \cdot t}{a}} \]

      3. *-commutative 92.0%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{\color{blue}{t \cdot z}}{a} \]

      4. associate-/l* 97.7%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{t}{\frac{a}{z}}} \]

      5. associate-/r/ 93.1%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{t}{a} \cdot z} \]

   5. Simplified 93.1%

      \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{t}{a} \cdot z} \]
   6. Step-by-step derivation

      1. frac-times 80.7%

         \[\leadsto \color{blue}{\frac{y \cdot x}{{\left(\sqrt[3]{a}\right)}^{2} \cdot \sqrt[3]{a}}} - \frac{t}{a} \cdot z \]

      2. unpow2 80.7%

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

      3. add-cube-cbrt 81.3%

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

      4. *-un-lft-identity 81.3%

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

      5. frac-times 91.7%

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

      6. /-rgt-identity 91.7%

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

      7. clear-num 91.7%

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

      8. un-div-inv 91.8%

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

   7. Applied egg-rr 91.8%

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

   if -1.80000000000000005e-58 < a < 1.5e113

   1. Initial program 99.1%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-58} \lor \neg \left(a \leq 1.5 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{y}{\frac{a}{x}} - \frac{t}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - t \cdot z}{a}\\ \end{array} \]

Alternative 7: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -2 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;y \cdot x \leq 5 \cdot 10^{-75}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y x) -2e+30)
   (* y (/ x a))
   (if (<= (* y x) 5e-75) (/ (- z) (/ a t)) (/ x (/ a y)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -2e+30) {
		tmp = y * (x / a);
	} else if ((y * x) <= 5e-75) {
		tmp = -z / (a / t);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 * x) <= (-2d+30)) then
        tmp = y * (x / a)
    else if ((y * x) <= 5d-75) then
        tmp = -z / (a / t)
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -2e+30) {
		tmp = y * (x / a);
	} else if ((y * x) <= 5e-75) {
		tmp = -z / (a / t);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (y * x) <= -2e+30:
		tmp = y * (x / a)
	elif (y * x) <= 5e-75:
		tmp = -z / (a / t)
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(y * x) <= -2e+30)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(y * x) <= 5e-75)
		tmp = Float64(Float64(-z) / Float64(a / t));
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y * x) <= -2e+30)
		tmp = y * (x / a);
	elseif ((y * x) <= 5e-75)
		tmp = -z / (a / t);
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], -2e+30], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 5e-75], N[((-z) / N[(a / t), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2e30

   1. Initial program 87.0%

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

   2. Taylor expanded in x around inf 71.1%

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

      1. associate-*l/ 75.9%

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

   4. Simplified 75.9%

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

   if -2e30 < (*.f64 x y) < 4.99999999999999979e-75

   1. Initial program 92.7%

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

      1. div-sub 92.7%

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

      2. *-commutative 92.7%

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

      3. add-cube-cbrt 92.4%

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

      4. times-frac 91.6%

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

      5. fma-neg 91.6%

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

      6. pow2 91.6%

         \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{{\left(\sqrt[3]{a}\right)}^{2}}}, \frac{x}{\sqrt[3]{a}}, -\frac{z \cdot t}{a}\right) \]

      7. associate-/l* 88.9%

         \[\leadsto \mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\color{blue}{\frac{z}{\frac{a}{t}}}\right) \]

   3. Applied egg-rr 88.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}}, \frac{x}{\sqrt[3]{a}}, -\frac{z}{\frac{a}{t}}\right)} \]
   4. Step-by-step derivation

      1. fma-neg 88.9%

         \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{z}{\frac{a}{t}}} \]

      2. associate-/l* 91.6%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{z \cdot t}{a}} \]

      3. *-commutative 91.6%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{\color{blue}{t \cdot z}}{a} \]

      4. associate-/l* 91.4%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{t}{\frac{a}{z}}} \]

      5. associate-/r/ 90.1%

         \[\leadsto \frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \color{blue}{\frac{t}{a} \cdot z} \]

   5. Simplified 90.1%

      \[\leadsto \color{blue}{\frac{y}{{\left(\sqrt[3]{a}\right)}^{2}} \cdot \frac{x}{\sqrt[3]{a}} - \frac{t}{a} \cdot z} \]

   6. Taylor expanded in y around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. *-commutative 79.3%

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

      3. associate-/l* 76.6%

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

   8. Simplified 76.6%

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

   if 4.99999999999999979e-75 < (*.f64 x y)

   1. Initial program 90.6%

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

   2. Taylor expanded in x around inf 67.1%

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

      1. associate-*l/ 74.3%

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

   4. Simplified 74.3%

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

      1. associate-/r/ 70.5%

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

   6. Applied egg-rr 70.5%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -2 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;y \cdot x \leq 5 \cdot 10^{-75}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 51.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e-144) (/ x (/ a y)) (* y (/ x a))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e-144) {
		tmp = x / (a / y);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 <= (-2.2d-144)) then
        tmp = x / (a / y)
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e-144) {
		tmp = x / (a / y);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e-144:
		tmp = x / (a / y)
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e-144)
		tmp = Float64(x / Float64(a / y));
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e-144)
		tmp = x / (a / y);
	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.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e-144], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.20000000000000006e-144

   1. Initial program 89.5%

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

   2. Taylor expanded in x around inf 43.9%

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

      1. associate-*l/ 46.6%

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

   4. Simplified 46.6%

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

      1. associate-/r/ 48.0%

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

   6. Applied egg-rr 48.0%

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

   if -2.20000000000000006e-144 < z

   1. Initial program 91.4%

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

   2. Taylor expanded in x around inf 52.7%

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

      1. associate-*l/ 54.7%

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

   4. Simplified 54.7%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 9: 52.1% accurate, 1.8× speedup

Math

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

FPCore

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

Python

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

Julia

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

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
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.
NOTE: z and t 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 90.6%

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

2. Taylor expanded in x around inf 49.3%

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

   1. associate-*r/ 53.0%

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

4. Simplified 53.0%

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

5. Final simplification 53.0%

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

Alternative 10: 52.1% accurate, 1.8× speedup

Math

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

FPCore

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

Python

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

Julia

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

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
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.
NOTE: z and t 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 90.6%

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

2. Taylor expanded in x around inf 49.3%

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

   1. associate-*l/ 51.6%

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

4. Simplified 51.6%

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

5. Final simplification 51.6%

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

Developer target: 91.5% 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 2023271 
(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))