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

Percentage Accurate: 91.5% → 93.5%

Time: 9.1s

Alternatives: 11

Speedup: 0.7×

• 27.9% 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: 91.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.5% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (- (* x y) (* z t)) a) (- INFINITY))
   (- (/ x (/ a y)) (* t (/ z a)))
   (/ (fma x y (* z (- t))) a)))

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 85.7%

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

      1. div-sub 83.8%

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

      2. associate-/l* 92.7%

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

      3. associate-/l* 98.0%

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

   3. Applied egg-rr 98.0%

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

      1. associate-/r/ 98.1%

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

   5. Applied egg-rr 98.1%

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

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

   1. Initial program 95.9%

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

      1. fma-neg 96.4%

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

      2. distribute-rgt-neg-out 96.4%

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

   3. Simplified 96.4%

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

4. Final simplification 96.7%

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

Alternative 2: 71.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot \frac{t}{a}\\ t_2 := \frac{y}{\frac{a}{x}}\\ t_3 := \frac{-t}{\frac{a}{z}}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-289}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 400000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+42}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z) (/ t a))) (t_2 (/ y (/ a x))) (t_3 (/ (- t) (/ a z))))
   (if (<= (* x y) -2e-6)
     t_2
     (if (<= (* x y) -4e-39)
       t_1
       (if (<= (* x y) -1e-76)
         (* x (/ y a))
         (if (<= (* x y) -5e-289)
           t_3
           (if (<= (* x y) 2e-119)
             t_1
             (if (<= (* x y) 400000000000.0)
               (/ (* x y) a)
               (if (<= (* x y) 2e+42) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -z * (t / a);
	double t_2 = y / (a / x);
	double t_3 = -t / (a / z);
	double tmp;
	if ((x * y) <= -2e-6) {
		tmp = t_2;
	} else if ((x * y) <= -4e-39) {
		tmp = t_1;
	} else if ((x * y) <= -1e-76) {
		tmp = x * (y / a);
	} else if ((x * y) <= -5e-289) {
		tmp = t_3;
	} else if ((x * y) <= 2e-119) {
		tmp = t_1;
	} else if ((x * y) <= 400000000000.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 2e+42) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = -z * (t / a)
    t_2 = y / (a / x)
    t_3 = -t / (a / z)
    if ((x * y) <= (-2d-6)) then
        tmp = t_2
    else if ((x * y) <= (-4d-39)) then
        tmp = t_1
    else if ((x * y) <= (-1d-76)) then
        tmp = x * (y / a)
    else if ((x * y) <= (-5d-289)) then
        tmp = t_3
    else if ((x * y) <= 2d-119) then
        tmp = t_1
    else if ((x * y) <= 400000000000.0d0) then
        tmp = (x * y) / a
    else if ((x * y) <= 2d+42) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -z * (t / a);
	double t_2 = y / (a / x);
	double t_3 = -t / (a / z);
	double tmp;
	if ((x * y) <= -2e-6) {
		tmp = t_2;
	} else if ((x * y) <= -4e-39) {
		tmp = t_1;
	} else if ((x * y) <= -1e-76) {
		tmp = x * (y / a);
	} else if ((x * y) <= -5e-289) {
		tmp = t_3;
	} else if ((x * y) <= 2e-119) {
		tmp = t_1;
	} else if ((x * y) <= 400000000000.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 2e+42) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -z * (t / a)
	t_2 = y / (a / x)
	t_3 = -t / (a / z)
	tmp = 0
	if (x * y) <= -2e-6:
		tmp = t_2
	elif (x * y) <= -4e-39:
		tmp = t_1
	elif (x * y) <= -1e-76:
		tmp = x * (y / a)
	elif (x * y) <= -5e-289:
		tmp = t_3
	elif (x * y) <= 2e-119:
		tmp = t_1
	elif (x * y) <= 400000000000.0:
		tmp = (x * y) / a
	elif (x * y) <= 2e+42:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-z) * Float64(t / a))
	t_2 = Float64(y / Float64(a / x))
	t_3 = Float64(Float64(-t) / Float64(a / z))
	tmp = 0.0
	if (Float64(x * y) <= -2e-6)
		tmp = t_2;
	elseif (Float64(x * y) <= -4e-39)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e-76)
		tmp = Float64(x * Float64(y / a));
	elseif (Float64(x * y) <= -5e-289)
		tmp = t_3;
	elseif (Float64(x * y) <= 2e-119)
		tmp = t_1;
	elseif (Float64(x * y) <= 400000000000.0)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 2e+42)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -z * (t / a);
	t_2 = y / (a / x);
	t_3 = -t / (a / z);
	tmp = 0.0;
	if ((x * y) <= -2e-6)
		tmp = t_2;
	elseif ((x * y) <= -4e-39)
		tmp = t_1;
	elseif ((x * y) <= -1e-76)
		tmp = x * (y / a);
	elseif ((x * y) <= -5e-289)
		tmp = t_3;
	elseif ((x * y) <= 2e-119)
		tmp = t_1;
	elseif ((x * y) <= 400000000000.0)
		tmp = (x * y) / a;
	elseif ((x * y) <= 2e+42)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e-6], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -4e-39], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e-76], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e-289], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 2e-119], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 400000000000.0], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+42], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.99999999999999991e-6 or 2.00000000000000009e42 < (*.f64 x y)

   1. Initial program 89.7%

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

   2. Taylor expanded in x around inf 78.8%

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

      1. associate-*l/ 78.5%

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

   4. Simplified 78.5%

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

      1. *-commutative 78.5%

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

      2. clear-num 77.4%

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

      3. un-div-inv 77.5%

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

   6. Applied egg-rr 77.5%

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

   if -1.99999999999999991e-6 < (*.f64 x y) < -3.99999999999999972e-39 or -5.00000000000000029e-289 < (*.f64 x y) < 2.00000000000000003e-119

   1. Initial program 96.7%

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

   2. Taylor expanded in x around 0 89.1%

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

      1. mul-1-neg 89.1%

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

      2. associate-/l* 86.2%

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

   4. Simplified 86.2%

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

      1. associate-/r/ 77.7%

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

   6. Applied egg-rr 77.7%

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

   if -3.99999999999999972e-39 < (*.f64 x y) < -9.99999999999999927e-77

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 84.9%

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

      1. associate-*l/ 84.9%

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

   4. Simplified 84.9%

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

      1. expm1-log1p-u 59.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{a} \cdot y\right)\right)} \]

      2. expm1-udef 13.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{a} \cdot y\right)} - 1} \]

      3. *-commutative 13.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{y \cdot \frac{x}{a}}\right)} - 1 \]

      4. clear-num 13.1%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right)} - 1 \]

      5. un-div-inv 13.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a}{x}}}\right)} - 1 \]

   6. Applied egg-rr 13.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{a}{x}}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 59.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a}{x}}\right)\right)} \]

      2. expm1-log1p 84.5%

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

      3. associate-/r/ 84.5%

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

   8. Simplified 84.5%

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

   if -9.99999999999999927e-77 < (*.f64 x y) < -5.00000000000000029e-289 or 4e11 < (*.f64 x y) < 2.00000000000000009e42

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. associate-/l* 62.9%

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

   4. Simplified 62.9%

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

   if 2.00000000000000003e-119 < (*.f64 x y) < 4e11

   1. Initial program 99.4%

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

   2. Taylor expanded in x around inf 58.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-39}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-289}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-119}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y \leq 400000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+42}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 3: 71.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot \frac{t}{a}\\ t_2 := \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-289}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 400000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+42}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z) (/ t a))) (t_2 (/ y (/ a x))))
   (if (<= (* x y) -2e-6)
     t_2
     (if (<= (* x y) -4e-39)
       t_1
       (if (<= (* x y) -1e-76)
         (* x (/ y a))
         (if (<= (* x y) -5e-289)
           (* t (/ (- z) a))
           (if (<= (* x y) 2e-119)
             t_1
             (if (<= (* x y) 400000000000.0)
               (/ (* x y) a)
               (if (<= (* x y) 2e+42) (/ (- t) (/ a z)) t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -z * (t / a);
	double t_2 = y / (a / x);
	double tmp;
	if ((x * y) <= -2e-6) {
		tmp = t_2;
	} else if ((x * y) <= -4e-39) {
		tmp = t_1;
	} else if ((x * y) <= -1e-76) {
		tmp = x * (y / a);
	} else if ((x * y) <= -5e-289) {
		tmp = t * (-z / a);
	} else if ((x * y) <= 2e-119) {
		tmp = t_1;
	} else if ((x * y) <= 400000000000.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 2e+42) {
		tmp = -t / (a / z);
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = -z * (t / a)
    t_2 = y / (a / x)
    if ((x * y) <= (-2d-6)) then
        tmp = t_2
    else if ((x * y) <= (-4d-39)) then
        tmp = t_1
    else if ((x * y) <= (-1d-76)) then
        tmp = x * (y / a)
    else if ((x * y) <= (-5d-289)) then
        tmp = t * (-z / a)
    else if ((x * y) <= 2d-119) then
        tmp = t_1
    else if ((x * y) <= 400000000000.0d0) then
        tmp = (x * y) / a
    else if ((x * y) <= 2d+42) then
        tmp = -t / (a / z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -z * (t / a);
	double t_2 = y / (a / x);
	double tmp;
	if ((x * y) <= -2e-6) {
		tmp = t_2;
	} else if ((x * y) <= -4e-39) {
		tmp = t_1;
	} else if ((x * y) <= -1e-76) {
		tmp = x * (y / a);
	} else if ((x * y) <= -5e-289) {
		tmp = t * (-z / a);
	} else if ((x * y) <= 2e-119) {
		tmp = t_1;
	} else if ((x * y) <= 400000000000.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 2e+42) {
		tmp = -t / (a / z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -z * (t / a)
	t_2 = y / (a / x)
	tmp = 0
	if (x * y) <= -2e-6:
		tmp = t_2
	elif (x * y) <= -4e-39:
		tmp = t_1
	elif (x * y) <= -1e-76:
		tmp = x * (y / a)
	elif (x * y) <= -5e-289:
		tmp = t * (-z / a)
	elif (x * y) <= 2e-119:
		tmp = t_1
	elif (x * y) <= 400000000000.0:
		tmp = (x * y) / a
	elif (x * y) <= 2e+42:
		tmp = -t / (a / z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-z) * Float64(t / a))
	t_2 = Float64(y / Float64(a / x))
	tmp = 0.0
	if (Float64(x * y) <= -2e-6)
		tmp = t_2;
	elseif (Float64(x * y) <= -4e-39)
		tmp = t_1;
	elseif (Float64(x * y) <= -1e-76)
		tmp = Float64(x * Float64(y / a));
	elseif (Float64(x * y) <= -5e-289)
		tmp = Float64(t * Float64(Float64(-z) / a));
	elseif (Float64(x * y) <= 2e-119)
		tmp = t_1;
	elseif (Float64(x * y) <= 400000000000.0)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 2e+42)
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -z * (t / a);
	t_2 = y / (a / x);
	tmp = 0.0;
	if ((x * y) <= -2e-6)
		tmp = t_2;
	elseif ((x * y) <= -4e-39)
		tmp = t_1;
	elseif ((x * y) <= -1e-76)
		tmp = x * (y / a);
	elseif ((x * y) <= -5e-289)
		tmp = t * (-z / a);
	elseif ((x * y) <= 2e-119)
		tmp = t_1;
	elseif ((x * y) <= 400000000000.0)
		tmp = (x * y) / a;
	elseif ((x * y) <= 2e+42)
		tmp = -t / (a / z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e-6], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -4e-39], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -1e-76], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e-289], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-119], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 400000000000.0], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+42], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 x y) < -1.99999999999999991e-6 or 2.00000000000000009e42 < (*.f64 x y)

   1. Initial program 89.7%

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

   2. Taylor expanded in x around inf 78.8%

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

      1. associate-*l/ 78.5%

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

   4. Simplified 78.5%

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

      1. *-commutative 78.5%

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

      2. clear-num 77.4%

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

      3. un-div-inv 77.5%

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

   6. Applied egg-rr 77.5%

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

   if -1.99999999999999991e-6 < (*.f64 x y) < -3.99999999999999972e-39 or -5.00000000000000029e-289 < (*.f64 x y) < 2.00000000000000003e-119

   1. Initial program 96.7%

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

   2. Taylor expanded in x around 0 89.1%

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

      1. mul-1-neg 89.1%

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

      2. associate-/l* 86.2%

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

   4. Simplified 86.2%

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

      1. associate-/r/ 77.7%

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

   6. Applied egg-rr 77.7%

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

   if -3.99999999999999972e-39 < (*.f64 x y) < -9.99999999999999927e-77

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 84.9%

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

      1. associate-*l/ 84.9%

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

   4. Simplified 84.9%

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

      1. expm1-log1p-u 59.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{a} \cdot y\right)\right)} \]

      2. expm1-udef 13.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{a} \cdot y\right)} - 1} \]

      3. *-commutative 13.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{y \cdot \frac{x}{a}}\right)} - 1 \]

      4. clear-num 13.1%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right)} - 1 \]

      5. un-div-inv 13.1%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a}{x}}}\right)} - 1 \]

   6. Applied egg-rr 13.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{a}{x}}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 59.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a}{x}}\right)\right)} \]

      2. expm1-log1p 84.5%

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

      3. associate-/r/ 84.5%

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

   8. Simplified 84.5%

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

   if -9.99999999999999927e-77 < (*.f64 x y) < -5.00000000000000029e-289

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-*l/ 60.2%

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

      3. associate-*r* 60.2%

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

      4. neg-mul-1 60.2%

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

      5. distribute-frac-neg 60.2%

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

   4. Simplified 60.2%

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

   if 2.00000000000000003e-119 < (*.f64 x y) < 4e11

   1. Initial program 99.4%

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

   2. Taylor expanded in x around inf 58.0%

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

   if 4e11 < (*.f64 x y) < 2.00000000000000009e42

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 86.0%

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

      1. mul-1-neg 86.0%

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

      2. associate-/l* 70.0%

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

   4. Simplified 70.0%

      \[\leadsto \color{blue}{-\frac{t}{\frac{a}{z}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-39}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-289}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-119}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y \leq 400000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+42}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 4: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-1}{\frac{a}{z \cdot t}}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 400000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ -1.0 (/ a (* z t)))))
   (if (<= (* x y) -2e-6)
     (/ y (/ a x))
     (if (<= (* x y) 5e-56)
       t_1
       (if (<= (* x y) 400000000000.0)
         (/ (* x y) a)
         (if (<= (* x y) 1e+75) t_1 (* y (/ x a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -1.0 / (a / (z * t));
	double tmp;
	if ((x * y) <= -2e-6) {
		tmp = y / (a / x);
	} else if ((x * y) <= 5e-56) {
		tmp = t_1;
	} else if ((x * y) <= 400000000000.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 1e+75) {
		tmp = t_1;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-1.0d0) / (a / (z * t))
    if ((x * y) <= (-2d-6)) then
        tmp = y / (a / x)
    else if ((x * y) <= 5d-56) then
        tmp = t_1
    else if ((x * y) <= 400000000000.0d0) then
        tmp = (x * y) / a
    else if ((x * y) <= 1d+75) then
        tmp = t_1
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -1.0 / (a / (z * t));
	double tmp;
	if ((x * y) <= -2e-6) {
		tmp = y / (a / x);
	} else if ((x * y) <= 5e-56) {
		tmp = t_1;
	} else if ((x * y) <= 400000000000.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 1e+75) {
		tmp = t_1;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -1.0 / (a / (z * t))
	tmp = 0
	if (x * y) <= -2e-6:
		tmp = y / (a / x)
	elif (x * y) <= 5e-56:
		tmp = t_1
	elif (x * y) <= 400000000000.0:
		tmp = (x * y) / a
	elif (x * y) <= 1e+75:
		tmp = t_1
	else:
		tmp = y * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-1.0 / Float64(a / Float64(z * t)))
	tmp = 0.0
	if (Float64(x * y) <= -2e-6)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 5e-56)
		tmp = t_1;
	elseif (Float64(x * y) <= 400000000000.0)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 1e+75)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -1.0 / (a / (z * t));
	tmp = 0.0;
	if ((x * y) <= -2e-6)
		tmp = y / (a / x);
	elseif ((x * y) <= 5e-56)
		tmp = t_1;
	elseif ((x * y) <= 400000000000.0)
		tmp = (x * y) / a;
	elseif ((x * y) <= 1e+75)
		tmp = t_1;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-1.0 / N[(a / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e-6], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-56], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 400000000000.0], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+75], t$95$1, N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.99999999999999991e-6

   1. Initial program 91.9%

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

   2. Taylor expanded in x around inf 81.0%

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

      1. associate-*l/ 78.9%

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

   4. Simplified 78.9%

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

      1. *-commutative 78.9%

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

      2. clear-num 78.0%

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

      3. un-div-inv 77.9%

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

   6. Applied egg-rr 77.9%

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

   if -1.99999999999999991e-6 < (*.f64 x y) < 4.99999999999999997e-56 or 4e11 < (*.f64 x y) < 9.99999999999999927e74

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 77.6%

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

      1. *-commutative 77.6%

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

      2. associate-*l/ 69.0%

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

      3. associate-*r* 69.0%

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

      4. neg-mul-1 69.0%

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

      5. distribute-frac-neg 69.0%

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

   4. Simplified 69.0%

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

      1. associate-*l/ 77.6%

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

      2. associate-/l* 68.1%

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

      3. distribute-neg-frac 68.1%

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

      4. clear-num 68.1%

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

      5. distribute-neg-frac 68.1%

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

      6. metadata-eval 68.1%

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

      7. associate-/l/ 77.6%

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

   6. Applied egg-rr 77.6%

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

   if 4.99999999999999997e-56 < (*.f64 x y) < 4e11

   1. Initial program 99.4%

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

   2. Taylor expanded in x around inf 75.4%

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

   if 9.99999999999999927e74 < (*.f64 x y)

   1. Initial program 86.3%

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

   2. Taylor expanded in x around inf 79.9%

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

      1. associate-*l/ 84.4%

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

   4. Simplified 84.4%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-56}:\\ \;\;\;\;\frac{-1}{\frac{a}{z \cdot t}}\\ \mathbf{elif}\;x \cdot y \leq 400000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+75}:\\ \;\;\;\;\frac{-1}{\frac{a}{z \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 5: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(-t\right)}{a}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 400000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* z (- t)) a)))
   (if (<= (* x y) -2e-6)
     (/ y (/ a x))
     (if (<= (* x y) 5e-56)
       t_1
       (if (<= (* x y) 400000000000.0)
         (/ (* x y) a)
         (if (<= (* x y) 1e+75) t_1 (* y (/ x a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * -t) / a;
	double tmp;
	if ((x * y) <= -2e-6) {
		tmp = y / (a / x);
	} else if ((x * y) <= 5e-56) {
		tmp = t_1;
	} else if ((x * y) <= 400000000000.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 1e+75) {
		tmp = t_1;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * -t) / a
    if ((x * y) <= (-2d-6)) then
        tmp = y / (a / x)
    else if ((x * y) <= 5d-56) then
        tmp = t_1
    else if ((x * y) <= 400000000000.0d0) then
        tmp = (x * y) / a
    else if ((x * y) <= 1d+75) then
        tmp = t_1
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * -t) / a;
	double tmp;
	if ((x * y) <= -2e-6) {
		tmp = y / (a / x);
	} else if ((x * y) <= 5e-56) {
		tmp = t_1;
	} else if ((x * y) <= 400000000000.0) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 1e+75) {
		tmp = t_1;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * -t) / a
	tmp = 0
	if (x * y) <= -2e-6:
		tmp = y / (a / x)
	elif (x * y) <= 5e-56:
		tmp = t_1
	elif (x * y) <= 400000000000.0:
		tmp = (x * y) / a
	elif (x * y) <= 1e+75:
		tmp = t_1
	else:
		tmp = y * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * Float64(-t)) / a)
	tmp = 0.0
	if (Float64(x * y) <= -2e-6)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 5e-56)
		tmp = t_1;
	elseif (Float64(x * y) <= 400000000000.0)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 1e+75)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * -t) / a;
	tmp = 0.0;
	if ((x * y) <= -2e-6)
		tmp = y / (a / x);
	elseif ((x * y) <= 5e-56)
		tmp = t_1;
	elseif ((x * y) <= 400000000000.0)
		tmp = (x * y) / a;
	elseif ((x * y) <= 1e+75)
		tmp = t_1;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * (-t)), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e-6], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-56], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 400000000000.0], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+75], t$95$1, N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.99999999999999991e-6

   1. Initial program 91.9%

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

   2. Taylor expanded in x around inf 81.0%

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

      1. associate-*l/ 78.9%

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

   4. Simplified 78.9%

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

      1. *-commutative 78.9%

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

      2. clear-num 78.0%

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

      3. un-div-inv 77.9%

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

   6. Applied egg-rr 77.9%

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

   if -1.99999999999999991e-6 < (*.f64 x y) < 4.99999999999999997e-56 or 4e11 < (*.f64 x y) < 9.99999999999999927e74

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. distribute-rgt-neg-in 77.6%

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

   4. Simplified 77.6%

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

   if 4.99999999999999997e-56 < (*.f64 x y) < 4e11

   1. Initial program 99.4%

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

   2. Taylor expanded in x around inf 75.4%

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

   if 9.99999999999999927e74 < (*.f64 x y)

   1. Initial program 86.3%

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

   2. Taylor expanded in x around inf 79.9%

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

      1. associate-*l/ 84.4%

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

   4. Simplified 84.4%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-56}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 400000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+75}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 6: 93.3% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- (* x y) (* z t)) a)))
   (if (<= t_1 (- INFINITY)) (- (/ x (/ a y)) (* t (/ z a))) t_1)))

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x * y) - (z * t)) / a;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x / (a / y)) - (t * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 85.7%

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

      1. div-sub 83.8%

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

      2. associate-/l* 92.7%

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

      3. associate-/l* 98.0%

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

   3. Applied egg-rr 98.0%

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

      1. associate-/r/ 98.1%

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

   5. Applied egg-rr 98.1%

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

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

   1. Initial program 95.9%

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

4. Final simplification 96.4%

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

Alternative 7: 73.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-119}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+240}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e-6)
   (/ y (/ a x))
   (if (<= (* x y) 2e-119)
     (* (- z) (/ t a))
     (if (<= (* x y) 1e+240) (/ (* x y) a) (* x (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-6) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e-119) {
		tmp = -z * (t / a);
	} else if ((x * y) <= 1e+240) {
		tmp = (x * y) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-2d-6)) then
        tmp = y / (a / x)
    else if ((x * y) <= 2d-119) then
        tmp = -z * (t / a)
    else if ((x * y) <= 1d+240) then
        tmp = (x * y) / a
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e-6) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e-119) {
		tmp = -z * (t / a);
	} else if ((x * y) <= 1e+240) {
		tmp = (x * y) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e-6:
		tmp = y / (a / x)
	elif (x * y) <= 2e-119:
		tmp = -z * (t / a)
	elif (x * y) <= 1e+240:
		tmp = (x * y) / a
	else:
		tmp = x * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e-6)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 2e-119)
		tmp = Float64(Float64(-z) * Float64(t / a));
	elseif (Float64(x * y) <= 1e+240)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e-6)
		tmp = y / (a / x);
	elseif ((x * y) <= 2e-119)
		tmp = -z * (t / a);
	elseif ((x * y) <= 1e+240)
		tmp = (x * y) / a;
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e-6], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-119], N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+240], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.99999999999999991e-6

   1. Initial program 91.9%

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

   2. Taylor expanded in x around inf 81.0%

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

      1. associate-*l/ 78.9%

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

   4. Simplified 78.9%

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

      1. *-commutative 78.9%

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

      2. clear-num 78.0%

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

      3. un-div-inv 77.9%

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

   6. Applied egg-rr 77.9%

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

   if -1.99999999999999991e-6 < (*.f64 x y) < 2.00000000000000003e-119

   1. Initial program 97.4%

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

   2. Taylor expanded in x around 0 84.3%

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

      1. mul-1-neg 84.3%

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

      2. associate-/l* 77.0%

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

   4. Simplified 77.0%

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

      1. associate-/r/ 74.8%

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

   6. Applied egg-rr 74.8%

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

   if 2.00000000000000003e-119 < (*.f64 x y) < 1.00000000000000001e240

   1. Initial program 98.4%

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

   2. Taylor expanded in x around inf 63.2%

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

   if 1.00000000000000001e240 < (*.f64 x y)

   1. Initial program 77.5%

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

   2. Taylor expanded in x around inf 77.5%

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

      1. associate-*l/ 91.4%

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

   4. Simplified 91.4%

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

      1. expm1-log1p-u 36.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{a} \cdot y\right)\right)} \]

      2. expm1-udef 36.7%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{a} \cdot y\right)} - 1} \]

      3. *-commutative 36.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{y \cdot \frac{x}{a}}\right)} - 1 \]

      4. clear-num 36.7%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right)} - 1 \]

      5. un-div-inv 36.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a}{x}}}\right)} - 1 \]

   6. Applied egg-rr 36.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{a}{x}}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 36.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a}{x}}\right)\right)} \]

      2. expm1-log1p 91.3%

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

      3. associate-/r/ 91.2%

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

   8. Simplified 91.2%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-119}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+240}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 10^{+240}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) 1e+240) (/ (- (* x y) (* z t)) a) (* x (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 1e+240) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= 1d+240) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 1e+240) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= 1e+240:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = x * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= 1e+240)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= 1e+240)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], 1e+240], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 1.00000000000000001e240

   1. Initial program 96.3%

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

   if 1.00000000000000001e240 < (*.f64 x y)

   1. Initial program 77.5%

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

   2. Taylor expanded in x around inf 77.5%

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

      1. associate-*l/ 91.4%

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

   4. Simplified 91.4%

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

      1. expm1-log1p-u 36.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{a} \cdot y\right)\right)} \]

      2. expm1-udef 36.7%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{a} \cdot y\right)} - 1} \]

      3. *-commutative 36.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{y \cdot \frac{x}{a}}\right)} - 1 \]

      4. clear-num 36.7%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right)} - 1 \]

      5. un-div-inv 36.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a}{x}}}\right)} - 1 \]

   6. Applied egg-rr 36.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{a}{x}}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 36.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a}{x}}\right)\right)} \]

      2. expm1-log1p 91.3%

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

      3. associate-/r/ 91.2%

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

   8. Simplified 91.2%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 10^{+240}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9: 51.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.7 \cdot 10^{+41}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 2.7e+41) (/ (* x y) a) (* x (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.7e+41) {
		tmp = (x * y) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 2.7d+41) then
        tmp = (x * y) / a
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.7e+41) {
		tmp = (x * y) / a;
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 2.7e+41:
		tmp = (x * y) / a
	else:
		tmp = x * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2.7e+41)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 2.7e+41)
		tmp = (x * y) / a;
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2.7e+41], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.7e41

   1. Initial program 93.9%

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

   2. Taylor expanded in x around inf 62.1%

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

   if 2.7e41 < t

   1. Initial program 93.4%

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

   2. Taylor expanded in x around inf 32.8%

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

      1. associate-*l/ 33.0%

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

   4. Simplified 33.0%

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

      1. expm1-log1p-u 20.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{a} \cdot y\right)\right)} \]

      2. expm1-udef 18.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{a} \cdot y\right)} - 1} \]

      3. *-commutative 18.6%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{y \cdot \frac{x}{a}}\right)} - 1 \]

      4. clear-num 18.6%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right)} - 1 \]

      5. un-div-inv 18.6%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a}{x}}}\right)} - 1 \]

   6. Applied egg-rr 18.6%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{a}{x}}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 20.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a}{x}}\right)\right)} \]

      2. expm1-log1p 32.9%

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

      3. associate-/r/ 36.2%

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

   8. Simplified 36.2%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.7 \cdot 10^{+41}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10: 51.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

2. Taylor expanded in x around inf 55.5%

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

   1. associate-*l/ 54.2%

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

4. Simplified 54.2%

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

5. Final simplification 54.2%

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

Alternative 11: 51.8% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

2. Taylor expanded in x around inf 55.5%

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

   1. associate-*l/ 54.2%

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

4. Simplified 54.2%

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

   1. expm1-log1p-u 30.8%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{a} \cdot y\right)\right)} \]

   2. expm1-udef 23.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{a} \cdot y\right)} - 1} \]

   3. *-commutative 23.0%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{y \cdot \frac{x}{a}}\right)} - 1 \]

   4. clear-num 23.0%

      \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right)} - 1 \]

   5. un-div-inv 23.0%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{\frac{a}{x}}}\right)} - 1 \]

6. Applied egg-rr 23.0%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{a}{x}}\right)} - 1} \]
7. Step-by-step derivation

   1. expm1-def 30.2%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{a}{x}}\right)\right)} \]

   2. expm1-log1p 53.6%

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

   3. associate-/r/ 55.7%

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

8. Simplified 55.7%

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

9. Final simplification 55.7%

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

Developer target: 91.2% 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 2023310 
(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))