Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 90.0% → 97.8%

Time: 8.8s

Alternatives: 13

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot 2}{y \cdot z - t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x 2.0) (- (* y z) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * 2.0d0) / ((y * z) - (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Python

def code(x, y, z, t):
	return (x * 2.0) / ((y * z) - (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * 2.0) / ((y * z) - (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 90.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot 2}{y \cdot z - t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x 2.0) (- (* y z) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * 2.0d0) / ((y * z) - (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Python

def code(x, y, z, t):
	return (x * 2.0) / ((y * z) - (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * 2.0) / ((y * z) - (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - z \cdot t\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+222}:\\ \;\;\;\;\frac{\frac{2}{y - t}}{\frac{z}{x}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+199}:\\ \;\;\;\;\frac{2 \cdot x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) (* z t))))
   (if (<= t_1 -1e+222)
     (/ (/ 2.0 (- y t)) (/ z x))
     (if (<= t_1 2e+199) (/ (* 2.0 x) t_1) (* 2.0 (/ (/ x z) (- y t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if (t_1 <= -1e+222) {
		tmp = (2.0 / (y - t)) / (z / x);
	} else if (t_1 <= 2e+199) {
		tmp = (2.0 * x) / t_1;
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * z) - (z * t)
    if (t_1 <= (-1d+222)) then
        tmp = (2.0d0 / (y - t)) / (z / x)
    else if (t_1 <= 2d+199) then
        tmp = (2.0d0 * x) / t_1
    else
        tmp = 2.0d0 * ((x / z) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if (t_1 <= -1e+222) {
		tmp = (2.0 / (y - t)) / (z / x);
	} else if (t_1 <= 2e+199) {
		tmp = (2.0 * x) / t_1;
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - (z * t)
	tmp = 0
	if t_1 <= -1e+222:
		tmp = (2.0 / (y - t)) / (z / x)
	elif t_1 <= 2e+199:
		tmp = (2.0 * x) / t_1
	else:
		tmp = 2.0 * ((x / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= -1e+222)
		tmp = Float64(Float64(2.0 / Float64(y - t)) / Float64(z / x));
	elseif (t_1 <= 2e+199)
		tmp = Float64(Float64(2.0 * x) / t_1);
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) - (z * t);
	tmp = 0.0;
	if (t_1 <= -1e+222)
		tmp = (2.0 / (y - t)) / (z / x);
	elseif (t_1 <= 2e+199)
		tmp = (2.0 * x) / t_1;
	else
		tmp = 2.0 * ((x / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+222], N[(N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+199], N[(N[(2.0 * x), $MachinePrecision] / t$95$1), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 y z) (*.f64 t z)) < -1e222

   1. Initial program 77.8%

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

      1. *-commutative 77.8%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 77.7%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 77.7%

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

      4. associate-/r* 99.7%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.7%

         \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{z}}{y - t}} \]

      2. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{\frac{x}{z} \cdot 2}}{y - t} \]

      3. associate-*r/ 99.7%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

      4. clear-num 99.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \cdot \frac{2}{y - t} \]

      5. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{2}{y - t}}{\frac{z}{x}}} \]

      6. *-un-lft-identity 99.8%

         \[\leadsto \frac{\color{blue}{\frac{2}{y - t}}}{\frac{z}{x}} \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{\frac{2}{y - t}}{\frac{z}{x}}} \]

   if -1e222 < (-.f64 (*.f64 y z) (*.f64 t z)) < 2.00000000000000019e199

   1. Initial program 98.3%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]

   if 2.00000000000000019e199 < (-.f64 (*.f64 y z) (*.f64 t z))

   1. Initial program 70.8%

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

      1. *-commutative 70.8%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 70.8%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 79.1%

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

      4. associate-/r* 99.9%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - z \cdot t \leq -1 \cdot 10^{+222}:\\ \;\;\;\;\frac{\frac{2}{y - t}}{\frac{z}{x}}\\ \mathbf{elif}\;y \cdot z - z \cdot t \leq 2 \cdot 10^{+199}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 2: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \frac{\frac{x}{z}}{y}\\ t_2 := -2 \cdot \frac{x}{z \cdot t}\\ \mathbf{if}\;t \leq -1.68 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{2}{z}}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (/ (/ x z) y))) (t_2 (* -2.0 (/ x (* z t)))))
   (if (<= t -1.68e+44)
     (* x (/ (/ -2.0 z) t))
     (if (<= t -3.8e-17)
       t_1
       (if (<= t -2.55e-80)
         t_2
         (if (<= t 9e-87)
           (/ (/ x y) (* z 0.5))
           (if (<= t 7.8e-37)
             t_2
             (if (<= t 7.6e+52) t_1 (/ (* x (/ 2.0 z)) (- t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((x / z) / y);
	double t_2 = -2.0 * (x / (z * t));
	double tmp;
	if (t <= -1.68e+44) {
		tmp = x * ((-2.0 / z) / t);
	} else if (t <= -3.8e-17) {
		tmp = t_1;
	} else if (t <= -2.55e-80) {
		tmp = t_2;
	} else if (t <= 9e-87) {
		tmp = (x / y) / (z * 0.5);
	} else if (t <= 7.8e-37) {
		tmp = t_2;
	} else if (t <= 7.6e+52) {
		tmp = t_1;
	} else {
		tmp = (x * (2.0 / z)) / -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x / z) / y)
    t_2 = (-2.0d0) * (x / (z * t))
    if (t <= (-1.68d+44)) then
        tmp = x * (((-2.0d0) / z) / t)
    else if (t <= (-3.8d-17)) then
        tmp = t_1
    else if (t <= (-2.55d-80)) then
        tmp = t_2
    else if (t <= 9d-87) then
        tmp = (x / y) / (z * 0.5d0)
    else if (t <= 7.8d-37) then
        tmp = t_2
    else if (t <= 7.6d+52) then
        tmp = t_1
    else
        tmp = (x * (2.0d0 / z)) / -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((x / z) / y);
	double t_2 = -2.0 * (x / (z * t));
	double tmp;
	if (t <= -1.68e+44) {
		tmp = x * ((-2.0 / z) / t);
	} else if (t <= -3.8e-17) {
		tmp = t_1;
	} else if (t <= -2.55e-80) {
		tmp = t_2;
	} else if (t <= 9e-87) {
		tmp = (x / y) / (z * 0.5);
	} else if (t <= 7.8e-37) {
		tmp = t_2;
	} else if (t <= 7.6e+52) {
		tmp = t_1;
	} else {
		tmp = (x * (2.0 / z)) / -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * ((x / z) / y)
	t_2 = -2.0 * (x / (z * t))
	tmp = 0
	if t <= -1.68e+44:
		tmp = x * ((-2.0 / z) / t)
	elif t <= -3.8e-17:
		tmp = t_1
	elif t <= -2.55e-80:
		tmp = t_2
	elif t <= 9e-87:
		tmp = (x / y) / (z * 0.5)
	elif t <= 7.8e-37:
		tmp = t_2
	elif t <= 7.6e+52:
		tmp = t_1
	else:
		tmp = (x * (2.0 / z)) / -t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(Float64(x / z) / y))
	t_2 = Float64(-2.0 * Float64(x / Float64(z * t)))
	tmp = 0.0
	if (t <= -1.68e+44)
		tmp = Float64(x * Float64(Float64(-2.0 / z) / t));
	elseif (t <= -3.8e-17)
		tmp = t_1;
	elseif (t <= -2.55e-80)
		tmp = t_2;
	elseif (t <= 9e-87)
		tmp = Float64(Float64(x / y) / Float64(z * 0.5));
	elseif (t <= 7.8e-37)
		tmp = t_2;
	elseif (t <= 7.6e+52)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * Float64(2.0 / z)) / Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * ((x / z) / y);
	t_2 = -2.0 * (x / (z * t));
	tmp = 0.0;
	if (t <= -1.68e+44)
		tmp = x * ((-2.0 / z) / t);
	elseif (t <= -3.8e-17)
		tmp = t_1;
	elseif (t <= -2.55e-80)
		tmp = t_2;
	elseif (t <= 9e-87)
		tmp = (x / y) / (z * 0.5);
	elseif (t <= 7.8e-37)
		tmp = t_2;
	elseif (t <= 7.6e+52)
		tmp = t_1;
	else
		tmp = (x * (2.0 / z)) / -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.68e+44], N[(x * N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-17], t$95$1, If[LessEqual[t, -2.55e-80], t$95$2, If[LessEqual[t, 9e-87], N[(N[(x / y), $MachinePrecision] / N[(z * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-37], t$95$2, If[LessEqual[t, 7.6e+52], t$95$1, N[(N[(x * N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / (-t)), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.68000000000000001e44

   1. Initial program 86.2%

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

      1. *-commutative 86.2%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 86.1%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 90.3%

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

      4. associate-/r* 92.2%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around 0 88.1%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 88.2%

         \[\leadsto -2 \cdot \color{blue}{\frac{\frac{x}{t}}{z}} \]

      2. clear-num 86.9%

         \[\leadsto -2 \cdot \color{blue}{\frac{1}{\frac{z}{\frac{x}{t}}}} \]

      3. un-div-inv 86.9%

         \[\leadsto \color{blue}{\frac{-2}{\frac{z}{\frac{x}{t}}}} \]

      4. div-inv 85.8%

         \[\leadsto \frac{-2}{\color{blue}{z \cdot \frac{1}{\frac{x}{t}}}} \]

      5. clear-num 85.9%

         \[\leadsto \frac{-2}{z \cdot \color{blue}{\frac{t}{x}}} \]

   6. Applied egg-rr 85.9%

      \[\leadsto \color{blue}{\frac{-2}{z \cdot \frac{t}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 87.1%

         \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{\frac{t}{x}}} \]

      2. associate-/r/ 88.3%

         \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{t} \cdot x} \]

   8. Applied egg-rr 88.3%

      \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{t} \cdot x} \]

   if -1.68000000000000001e44 < t < -3.8000000000000001e-17 or 7.79999999999999981e-37 < t < 7.5999999999999999e52

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 92.7%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 92.7%

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

      4. associate-/r* 99.7%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.7%

         \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{z}}{y - t}} \]

      2. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{\frac{x}{z} \cdot 2}}{y - t} \]

      3. associate-*r/ 99.5%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

      4. clear-num 99.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \cdot \frac{2}{y - t} \]

      5. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{2}{y - t}}{\frac{z}{x}}} \]

      6. *-un-lft-identity 99.7%

         \[\leadsto \frac{\color{blue}{\frac{2}{y - t}}}{\frac{z}{x}} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{\frac{2}{y - t}}{\frac{z}{x}}} \]

   6. Taylor expanded in y around inf 58.7%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

      2. associate-/r* 76.1%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y}} \]

   8. Simplified 76.1%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y}} \]

   if -3.8000000000000001e-17 < t < -2.55000000000000004e-80 or 8.99999999999999915e-87 < t < 7.79999999999999981e-37

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 96.3%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 96.3%

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

      4. associate-/r* 89.7%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around 0 73.1%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]

   if -2.55000000000000004e-80 < t < 8.99999999999999915e-87

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 92.5%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 92.5%

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

      4. associate-/r* 92.1%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 92.1%

         \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{z}}{y - t}} \]

      2. *-commutative 92.1%

         \[\leadsto \frac{\color{blue}{\frac{x}{z} \cdot 2}}{y - t} \]

      3. associate-*r/ 92.0%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

      4. clear-num 92.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \cdot \frac{2}{y - t} \]

      5. associate-*l/ 92.0%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{2}{y - t}}{\frac{z}{x}}} \]

      6. *-un-lft-identity 92.0%

         \[\leadsto \frac{\color{blue}{\frac{2}{y - t}}}{\frac{z}{x}} \]

   5. Applied egg-rr 92.0%

      \[\leadsto \color{blue}{\frac{\frac{2}{y - t}}{\frac{z}{x}}} \]

   6. Taylor expanded in y around inf 85.5%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 85.5%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

      2. associate-/r* 83.7%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y}} \]

   8. Simplified 83.7%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y}} \]
   9. Step-by-step derivation

      1. associate-/r* 85.5%

         \[\leadsto 2 \cdot \color{blue}{\frac{x}{z \cdot y}} \]

      2. associate-*r/ 85.5%

         \[\leadsto \color{blue}{\frac{2 \cdot x}{z \cdot y}} \]

      3. frac-times 86.2%

         \[\leadsto \color{blue}{\frac{2}{z} \cdot \frac{x}{y}} \]

      4. clear-num 86.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{2}}} \cdot \frac{x}{y} \]

      5. associate-*l/ 87.2%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{y}}{\frac{z}{2}}} \]

      6. *-un-lft-identity 87.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{\frac{z}{2}} \]

      7. div-inv 87.2%

         \[\leadsto \frac{\frac{x}{y}}{\color{blue}{z \cdot \frac{1}{2}}} \]

      8. metadata-eval 87.2%

         \[\leadsto \frac{\frac{x}{y}}{z \cdot \color{blue}{0.5}} \]

   10. Applied egg-rr 87.2%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{z \cdot 0.5}} \]

   if 7.5999999999999999e52 < t

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 84.8%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 88.4%

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

      4. associate-/r* 91.5%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around 0 81.8%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 81.8%

         \[\leadsto \color{blue}{\frac{-2 \cdot x}{t \cdot z}} \]

      2. metadata-eval 81.8%

         \[\leadsto \frac{\color{blue}{\left(2 \cdot -1\right)} \cdot x}{t \cdot z} \]

      3. associate-*r* 81.8%

         \[\leadsto \frac{\color{blue}{2 \cdot \left(-1 \cdot x\right)}}{t \cdot z} \]

      4. neg-mul-1 81.8%

         \[\leadsto \frac{2 \cdot \color{blue}{\left(-x\right)}}{t \cdot z} \]

      5. *-commutative 81.8%

         \[\leadsto \frac{\color{blue}{\left(-x\right) \cdot 2}}{t \cdot z} \]

      6. frac-times 80.0%

         \[\leadsto \color{blue}{\frac{-x}{t} \cdot \frac{2}{z}} \]

      7. frac-2neg 80.0%

         \[\leadsto \color{blue}{\frac{-\left(-x\right)}{-t}} \cdot \frac{2}{z} \]

      8. remove-double-neg 80.0%

         \[\leadsto \frac{\color{blue}{x}}{-t} \cdot \frac{2}{z} \]

      9. associate-*l/ 83.3%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{2}{z}}{-t}} \]

   6. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\frac{x \cdot \frac{2}{z}}{-t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.68 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-17}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-80}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-87}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-37}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{2}{z}}{-t}\\ \end{array} \]

Alternative 3: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \frac{\frac{x}{z}}{y}\\ t_2 := -2 \cdot \frac{x}{z \cdot t}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-37} \lor \neg \left(t \leq 9.6 \cdot 10^{+50}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (/ (/ x z) y))) (t_2 (* -2.0 (/ x (* z t)))))
   (if (<= t -1.6e+44)
     t_2
     (if (<= t -1.06e-18)
       t_1
       (if (<= t -6.4e-75)
         t_2
         (if (<= t 8.5e-87)
           (* x (/ 2.0 (* y z)))
           (if (or (<= t 8.2e-37) (not (<= t 9.6e+50))) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((x / z) / y);
	double t_2 = -2.0 * (x / (z * t));
	double tmp;
	if (t <= -1.6e+44) {
		tmp = t_2;
	} else if (t <= -1.06e-18) {
		tmp = t_1;
	} else if (t <= -6.4e-75) {
		tmp = t_2;
	} else if (t <= 8.5e-87) {
		tmp = x * (2.0 / (y * z));
	} else if ((t <= 8.2e-37) || !(t <= 9.6e+50)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x / z) / y)
    t_2 = (-2.0d0) * (x / (z * t))
    if (t <= (-1.6d+44)) then
        tmp = t_2
    else if (t <= (-1.06d-18)) then
        tmp = t_1
    else if (t <= (-6.4d-75)) then
        tmp = t_2
    else if (t <= 8.5d-87) then
        tmp = x * (2.0d0 / (y * z))
    else if ((t <= 8.2d-37) .or. (.not. (t <= 9.6d+50))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((x / z) / y);
	double t_2 = -2.0 * (x / (z * t));
	double tmp;
	if (t <= -1.6e+44) {
		tmp = t_2;
	} else if (t <= -1.06e-18) {
		tmp = t_1;
	} else if (t <= -6.4e-75) {
		tmp = t_2;
	} else if (t <= 8.5e-87) {
		tmp = x * (2.0 / (y * z));
	} else if ((t <= 8.2e-37) || !(t <= 9.6e+50)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * ((x / z) / y)
	t_2 = -2.0 * (x / (z * t))
	tmp = 0
	if t <= -1.6e+44:
		tmp = t_2
	elif t <= -1.06e-18:
		tmp = t_1
	elif t <= -6.4e-75:
		tmp = t_2
	elif t <= 8.5e-87:
		tmp = x * (2.0 / (y * z))
	elif (t <= 8.2e-37) or not (t <= 9.6e+50):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(Float64(x / z) / y))
	t_2 = Float64(-2.0 * Float64(x / Float64(z * t)))
	tmp = 0.0
	if (t <= -1.6e+44)
		tmp = t_2;
	elseif (t <= -1.06e-18)
		tmp = t_1;
	elseif (t <= -6.4e-75)
		tmp = t_2;
	elseif (t <= 8.5e-87)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	elseif ((t <= 8.2e-37) || !(t <= 9.6e+50))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * ((x / z) / y);
	t_2 = -2.0 * (x / (z * t));
	tmp = 0.0;
	if (t <= -1.6e+44)
		tmp = t_2;
	elseif (t <= -1.06e-18)
		tmp = t_1;
	elseif (t <= -6.4e-75)
		tmp = t_2;
	elseif (t <= 8.5e-87)
		tmp = x * (2.0 / (y * z));
	elseif ((t <= 8.2e-37) || ~((t <= 9.6e+50)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+44], t$95$2, If[LessEqual[t, -1.06e-18], t$95$1, If[LessEqual[t, -6.4e-75], t$95$2, If[LessEqual[t, 8.5e-87], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 8.2e-37], N[Not[LessEqual[t, 9.6e+50]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.60000000000000002e44 or -1.05999999999999994e-18 < t < -6.39999999999999953e-75 or 8.5000000000000001e-87 < t < 8.1999999999999996e-37 or 9.6000000000000007e50 < t

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 87.6%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 90.7%

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

      4. associate-/r* 91.4%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around 0 82.3%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]

   if -1.60000000000000002e44 < t < -1.05999999999999994e-18 or 8.1999999999999996e-37 < t < 9.6000000000000007e50

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 92.7%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 92.7%

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

      4. associate-/r* 99.7%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.7%

         \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{z}}{y - t}} \]

      2. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{\frac{x}{z} \cdot 2}}{y - t} \]

      3. associate-*r/ 99.5%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

      4. clear-num 99.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \cdot \frac{2}{y - t} \]

      5. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{2}{y - t}}{\frac{z}{x}}} \]

      6. *-un-lft-identity 99.7%

         \[\leadsto \frac{\color{blue}{\frac{2}{y - t}}}{\frac{z}{x}} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{\frac{2}{y - t}}{\frac{z}{x}}} \]

   6. Taylor expanded in y around inf 58.7%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

      2. associate-/r* 76.1%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y}} \]

   8. Simplified 76.1%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y}} \]

   if -6.39999999999999953e-75 < t < 8.5000000000000001e-87

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 92.5%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 92.5%

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

      4. associate-/r* 92.1%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in x around 0 92.5%

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

      1. *-commutative 92.5%

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

      2. associate-/r/ 92.5%

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

      3. associate-/l* 92.4%

         \[\leadsto \frac{x}{\color{blue}{\frac{z}{\frac{2}{y - t}}}} \]

      4. associate-/l* 94.7%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{2}{y - t}}{z}} \]

      5. associate-*r/ 91.9%

         \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]

   6. Simplified 91.9%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]

   7. Taylor expanded in y around inf 85.4%

      \[\leadsto x \cdot \color{blue}{\frac{2}{y \cdot z}} \]
   8. Step-by-step derivation

      1. *-commutative 85.4%

         \[\leadsto x \cdot \frac{2}{\color{blue}{z \cdot y}} \]

   9. Simplified 85.4%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+44}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{-18}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-75}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-87}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-37} \lor \neg \left(t \leq 9.6 \cdot 10^{+50}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \end{array} \]

Alternative 4: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \frac{\frac{x}{z}}{y}\\ t_2 := -2 \cdot \frac{x}{z \cdot t}\\ \mathbf{if}\;t \leq -1.68 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-89}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-38} \lor \neg \left(t \leq 1.32 \cdot 10^{+51}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (/ (/ x z) y))) (t_2 (* -2.0 (/ x (* z t)))))
   (if (<= t -1.68e+44)
     t_2
     (if (<= t -1.22e-17)
       t_1
       (if (<= t -7.2e-88)
         t_2
         (if (<= t 6e-89)
           (* (/ 2.0 z) (/ x y))
           (if (or (<= t 4.5e-38) (not (<= t 1.32e+51))) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((x / z) / y);
	double t_2 = -2.0 * (x / (z * t));
	double tmp;
	if (t <= -1.68e+44) {
		tmp = t_2;
	} else if (t <= -1.22e-17) {
		tmp = t_1;
	} else if (t <= -7.2e-88) {
		tmp = t_2;
	} else if (t <= 6e-89) {
		tmp = (2.0 / z) * (x / y);
	} else if ((t <= 4.5e-38) || !(t <= 1.32e+51)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x / z) / y)
    t_2 = (-2.0d0) * (x / (z * t))
    if (t <= (-1.68d+44)) then
        tmp = t_2
    else if (t <= (-1.22d-17)) then
        tmp = t_1
    else if (t <= (-7.2d-88)) then
        tmp = t_2
    else if (t <= 6d-89) then
        tmp = (2.0d0 / z) * (x / y)
    else if ((t <= 4.5d-38) .or. (.not. (t <= 1.32d+51))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((x / z) / y);
	double t_2 = -2.0 * (x / (z * t));
	double tmp;
	if (t <= -1.68e+44) {
		tmp = t_2;
	} else if (t <= -1.22e-17) {
		tmp = t_1;
	} else if (t <= -7.2e-88) {
		tmp = t_2;
	} else if (t <= 6e-89) {
		tmp = (2.0 / z) * (x / y);
	} else if ((t <= 4.5e-38) || !(t <= 1.32e+51)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * ((x / z) / y)
	t_2 = -2.0 * (x / (z * t))
	tmp = 0
	if t <= -1.68e+44:
		tmp = t_2
	elif t <= -1.22e-17:
		tmp = t_1
	elif t <= -7.2e-88:
		tmp = t_2
	elif t <= 6e-89:
		tmp = (2.0 / z) * (x / y)
	elif (t <= 4.5e-38) or not (t <= 1.32e+51):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(Float64(x / z) / y))
	t_2 = Float64(-2.0 * Float64(x / Float64(z * t)))
	tmp = 0.0
	if (t <= -1.68e+44)
		tmp = t_2;
	elseif (t <= -1.22e-17)
		tmp = t_1;
	elseif (t <= -7.2e-88)
		tmp = t_2;
	elseif (t <= 6e-89)
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	elseif ((t <= 4.5e-38) || !(t <= 1.32e+51))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * ((x / z) / y);
	t_2 = -2.0 * (x / (z * t));
	tmp = 0.0;
	if (t <= -1.68e+44)
		tmp = t_2;
	elseif (t <= -1.22e-17)
		tmp = t_1;
	elseif (t <= -7.2e-88)
		tmp = t_2;
	elseif (t <= 6e-89)
		tmp = (2.0 / z) * (x / y);
	elseif ((t <= 4.5e-38) || ~((t <= 1.32e+51)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.68e+44], t$95$2, If[LessEqual[t, -1.22e-17], t$95$1, If[LessEqual[t, -7.2e-88], t$95$2, If[LessEqual[t, 6e-89], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 4.5e-38], N[Not[LessEqual[t, 1.32e+51]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.68000000000000001e44 or -1.22e-17 < t < -7.1999999999999999e-88 or 5.9999999999999999e-89 < t < 4.50000000000000009e-38 or 1.32e51 < t

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 87.6%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 90.7%

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

      4. associate-/r* 91.4%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around 0 82.3%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]

   if -1.68000000000000001e44 < t < -1.22e-17 or 4.50000000000000009e-38 < t < 1.32e51

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 92.7%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 92.7%

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

      4. associate-/r* 99.7%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.7%

         \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{z}}{y - t}} \]

      2. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{\frac{x}{z} \cdot 2}}{y - t} \]

      3. associate-*r/ 99.5%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

      4. clear-num 99.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \cdot \frac{2}{y - t} \]

      5. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{2}{y - t}}{\frac{z}{x}}} \]

      6. *-un-lft-identity 99.7%

         \[\leadsto \frac{\color{blue}{\frac{2}{y - t}}}{\frac{z}{x}} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{\frac{2}{y - t}}{\frac{z}{x}}} \]

   6. Taylor expanded in y around inf 58.7%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

      2. associate-/r* 76.1%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y}} \]

   8. Simplified 76.1%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y}} \]

   if -7.1999999999999999e-88 < t < 5.9999999999999999e-89

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 92.5%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 92.5%

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

      4. associate-/r* 92.1%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around inf 85.5%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 85.5%

         \[\leadsto \color{blue}{\frac{2 \cdot x}{y \cdot z}} \]

      2. *-commutative 85.5%

         \[\leadsto \frac{\color{blue}{x \cdot 2}}{y \cdot z} \]

      3. times-frac 86.2%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]

   6. Simplified 86.2%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.68 \cdot 10^{+44}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-17}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-88}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-89}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-38} \lor \neg \left(t \leq 1.32 \cdot 10^{+51}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \end{array} \]

Alternative 5: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \frac{\frac{x}{z}}{y}\\ t_2 := -2 \cdot \frac{x}{z \cdot t}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-88}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-38} \lor \neg \left(t \leq 3.8 \cdot 10^{+51}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (/ (/ x z) y))) (t_2 (* -2.0 (/ x (* z t)))))
   (if (<= t -1.6e+44)
     (* x (/ (/ -2.0 z) t))
     (if (<= t -2.75e-18)
       t_1
       (if (<= t -3e-79)
         t_2
         (if (<= t 2.1e-88)
           (* (/ 2.0 z) (/ x y))
           (if (or (<= t 4.3e-38) (not (<= t 3.8e+51))) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((x / z) / y);
	double t_2 = -2.0 * (x / (z * t));
	double tmp;
	if (t <= -1.6e+44) {
		tmp = x * ((-2.0 / z) / t);
	} else if (t <= -2.75e-18) {
		tmp = t_1;
	} else if (t <= -3e-79) {
		tmp = t_2;
	} else if (t <= 2.1e-88) {
		tmp = (2.0 / z) * (x / y);
	} else if ((t <= 4.3e-38) || !(t <= 3.8e+51)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x / z) / y)
    t_2 = (-2.0d0) * (x / (z * t))
    if (t <= (-1.6d+44)) then
        tmp = x * (((-2.0d0) / z) / t)
    else if (t <= (-2.75d-18)) then
        tmp = t_1
    else if (t <= (-3d-79)) then
        tmp = t_2
    else if (t <= 2.1d-88) then
        tmp = (2.0d0 / z) * (x / y)
    else if ((t <= 4.3d-38) .or. (.not. (t <= 3.8d+51))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((x / z) / y);
	double t_2 = -2.0 * (x / (z * t));
	double tmp;
	if (t <= -1.6e+44) {
		tmp = x * ((-2.0 / z) / t);
	} else if (t <= -2.75e-18) {
		tmp = t_1;
	} else if (t <= -3e-79) {
		tmp = t_2;
	} else if (t <= 2.1e-88) {
		tmp = (2.0 / z) * (x / y);
	} else if ((t <= 4.3e-38) || !(t <= 3.8e+51)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * ((x / z) / y)
	t_2 = -2.0 * (x / (z * t))
	tmp = 0
	if t <= -1.6e+44:
		tmp = x * ((-2.0 / z) / t)
	elif t <= -2.75e-18:
		tmp = t_1
	elif t <= -3e-79:
		tmp = t_2
	elif t <= 2.1e-88:
		tmp = (2.0 / z) * (x / y)
	elif (t <= 4.3e-38) or not (t <= 3.8e+51):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(Float64(x / z) / y))
	t_2 = Float64(-2.0 * Float64(x / Float64(z * t)))
	tmp = 0.0
	if (t <= -1.6e+44)
		tmp = Float64(x * Float64(Float64(-2.0 / z) / t));
	elseif (t <= -2.75e-18)
		tmp = t_1;
	elseif (t <= -3e-79)
		tmp = t_2;
	elseif (t <= 2.1e-88)
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	elseif ((t <= 4.3e-38) || !(t <= 3.8e+51))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * ((x / z) / y);
	t_2 = -2.0 * (x / (z * t));
	tmp = 0.0;
	if (t <= -1.6e+44)
		tmp = x * ((-2.0 / z) / t);
	elseif (t <= -2.75e-18)
		tmp = t_1;
	elseif (t <= -3e-79)
		tmp = t_2;
	elseif (t <= 2.1e-88)
		tmp = (2.0 / z) * (x / y);
	elseif ((t <= 4.3e-38) || ~((t <= 3.8e+51)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+44], N[(x * N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.75e-18], t$95$1, If[LessEqual[t, -3e-79], t$95$2, If[LessEqual[t, 2.1e-88], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 4.3e-38], N[Not[LessEqual[t, 3.8e+51]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.60000000000000002e44

   1. Initial program 86.2%

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

      1. *-commutative 86.2%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 86.1%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 90.3%

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

      4. associate-/r* 92.2%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around 0 88.1%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 88.2%

         \[\leadsto -2 \cdot \color{blue}{\frac{\frac{x}{t}}{z}} \]

      2. clear-num 86.9%

         \[\leadsto -2 \cdot \color{blue}{\frac{1}{\frac{z}{\frac{x}{t}}}} \]

      3. un-div-inv 86.9%

         \[\leadsto \color{blue}{\frac{-2}{\frac{z}{\frac{x}{t}}}} \]

      4. div-inv 85.8%

         \[\leadsto \frac{-2}{\color{blue}{z \cdot \frac{1}{\frac{x}{t}}}} \]

      5. clear-num 85.9%

         \[\leadsto \frac{-2}{z \cdot \color{blue}{\frac{t}{x}}} \]

   6. Applied egg-rr 85.9%

      \[\leadsto \color{blue}{\frac{-2}{z \cdot \frac{t}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 87.1%

         \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{\frac{t}{x}}} \]

      2. associate-/r/ 88.3%

         \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{t} \cdot x} \]

   8. Applied egg-rr 88.3%

      \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{t} \cdot x} \]

   if -1.60000000000000002e44 < t < -2.75e-18 or 4.3000000000000002e-38 < t < 3.7999999999999997e51

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 92.7%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 92.7%

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

      4. associate-/r* 99.7%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.7%

         \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{z}}{y - t}} \]

      2. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{\frac{x}{z} \cdot 2}}{y - t} \]

      3. associate-*r/ 99.5%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

      4. clear-num 99.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \cdot \frac{2}{y - t} \]

      5. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{2}{y - t}}{\frac{z}{x}}} \]

      6. *-un-lft-identity 99.7%

         \[\leadsto \frac{\color{blue}{\frac{2}{y - t}}}{\frac{z}{x}} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{\frac{2}{y - t}}{\frac{z}{x}}} \]

   6. Taylor expanded in y around inf 58.7%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

      2. associate-/r* 76.1%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y}} \]

   8. Simplified 76.1%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y}} \]

   if -2.75e-18 < t < -3e-79 or 2.1e-88 < t < 4.3000000000000002e-38 or 3.7999999999999997e51 < t

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 88.5%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 90.9%

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

      4. associate-/r* 90.9%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 90.9%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around 0 79.0%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]

   if -3e-79 < t < 2.1e-88

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 92.5%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 92.5%

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

      4. associate-/r* 92.1%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around inf 85.5%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 85.5%

         \[\leadsto \color{blue}{\frac{2 \cdot x}{y \cdot z}} \]

      2. *-commutative 85.5%

         \[\leadsto \frac{\color{blue}{x \cdot 2}}{y \cdot z} \]

      3. times-frac 86.2%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]

   6. Simplified 86.2%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-18}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-79}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-88}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-38} \lor \neg \left(t \leq 3.8 \cdot 10^{+51}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \end{array} \]

Alternative 6: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \frac{\frac{x}{z}}{y}\\ t_2 := -2 \cdot \frac{x}{z \cdot t}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-89}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-2}{\frac{z}{x}}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (/ (/ x z) y))) (t_2 (* -2.0 (/ x (* z t)))))
   (if (<= t -1.7e+44)
     (* x (/ (/ -2.0 z) t))
     (if (<= t -3.3e-15)
       t_1
       (if (<= t -2e-76)
         t_2
         (if (<= t 8e-89)
           (* (/ 2.0 z) (/ x y))
           (if (<= t 4.6e-38)
             t_2
             (if (<= t 2.1e+52) t_1 (/ (/ -2.0 (/ z x)) t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((x / z) / y);
	double t_2 = -2.0 * (x / (z * t));
	double tmp;
	if (t <= -1.7e+44) {
		tmp = x * ((-2.0 / z) / t);
	} else if (t <= -3.3e-15) {
		tmp = t_1;
	} else if (t <= -2e-76) {
		tmp = t_2;
	} else if (t <= 8e-89) {
		tmp = (2.0 / z) * (x / y);
	} else if (t <= 4.6e-38) {
		tmp = t_2;
	} else if (t <= 2.1e+52) {
		tmp = t_1;
	} else {
		tmp = (-2.0 / (z / x)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x / z) / y)
    t_2 = (-2.0d0) * (x / (z * t))
    if (t <= (-1.7d+44)) then
        tmp = x * (((-2.0d0) / z) / t)
    else if (t <= (-3.3d-15)) then
        tmp = t_1
    else if (t <= (-2d-76)) then
        tmp = t_2
    else if (t <= 8d-89) then
        tmp = (2.0d0 / z) * (x / y)
    else if (t <= 4.6d-38) then
        tmp = t_2
    else if (t <= 2.1d+52) then
        tmp = t_1
    else
        tmp = ((-2.0d0) / (z / x)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((x / z) / y);
	double t_2 = -2.0 * (x / (z * t));
	double tmp;
	if (t <= -1.7e+44) {
		tmp = x * ((-2.0 / z) / t);
	} else if (t <= -3.3e-15) {
		tmp = t_1;
	} else if (t <= -2e-76) {
		tmp = t_2;
	} else if (t <= 8e-89) {
		tmp = (2.0 / z) * (x / y);
	} else if (t <= 4.6e-38) {
		tmp = t_2;
	} else if (t <= 2.1e+52) {
		tmp = t_1;
	} else {
		tmp = (-2.0 / (z / x)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * ((x / z) / y)
	t_2 = -2.0 * (x / (z * t))
	tmp = 0
	if t <= -1.7e+44:
		tmp = x * ((-2.0 / z) / t)
	elif t <= -3.3e-15:
		tmp = t_1
	elif t <= -2e-76:
		tmp = t_2
	elif t <= 8e-89:
		tmp = (2.0 / z) * (x / y)
	elif t <= 4.6e-38:
		tmp = t_2
	elif t <= 2.1e+52:
		tmp = t_1
	else:
		tmp = (-2.0 / (z / x)) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(Float64(x / z) / y))
	t_2 = Float64(-2.0 * Float64(x / Float64(z * t)))
	tmp = 0.0
	if (t <= -1.7e+44)
		tmp = Float64(x * Float64(Float64(-2.0 / z) / t));
	elseif (t <= -3.3e-15)
		tmp = t_1;
	elseif (t <= -2e-76)
		tmp = t_2;
	elseif (t <= 8e-89)
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	elseif (t <= 4.6e-38)
		tmp = t_2;
	elseif (t <= 2.1e+52)
		tmp = t_1;
	else
		tmp = Float64(Float64(-2.0 / Float64(z / x)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * ((x / z) / y);
	t_2 = -2.0 * (x / (z * t));
	tmp = 0.0;
	if (t <= -1.7e+44)
		tmp = x * ((-2.0 / z) / t);
	elseif (t <= -3.3e-15)
		tmp = t_1;
	elseif (t <= -2e-76)
		tmp = t_2;
	elseif (t <= 8e-89)
		tmp = (2.0 / z) * (x / y);
	elseif (t <= 4.6e-38)
		tmp = t_2;
	elseif (t <= 2.1e+52)
		tmp = t_1;
	else
		tmp = (-2.0 / (z / x)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+44], N[(x * N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.3e-15], t$95$1, If[LessEqual[t, -2e-76], t$95$2, If[LessEqual[t, 8e-89], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-38], t$95$2, If[LessEqual[t, 2.1e+52], t$95$1, N[(N[(-2.0 / N[(z / x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.7e44

   1. Initial program 86.2%

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

      1. *-commutative 86.2%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 86.1%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 90.3%

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

      4. associate-/r* 92.2%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around 0 88.1%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 88.2%

         \[\leadsto -2 \cdot \color{blue}{\frac{\frac{x}{t}}{z}} \]

      2. clear-num 86.9%

         \[\leadsto -2 \cdot \color{blue}{\frac{1}{\frac{z}{\frac{x}{t}}}} \]

      3. un-div-inv 86.9%

         \[\leadsto \color{blue}{\frac{-2}{\frac{z}{\frac{x}{t}}}} \]

      4. div-inv 85.8%

         \[\leadsto \frac{-2}{\color{blue}{z \cdot \frac{1}{\frac{x}{t}}}} \]

      5. clear-num 85.9%

         \[\leadsto \frac{-2}{z \cdot \color{blue}{\frac{t}{x}}} \]

   6. Applied egg-rr 85.9%

      \[\leadsto \color{blue}{\frac{-2}{z \cdot \frac{t}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 87.1%

         \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{\frac{t}{x}}} \]

      2. associate-/r/ 88.3%

         \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{t} \cdot x} \]

   8. Applied egg-rr 88.3%

      \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{t} \cdot x} \]

   if -1.7e44 < t < -3.3e-15 or 4.60000000000000003e-38 < t < 2.1e52

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 92.7%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 92.7%

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

      4. associate-/r* 99.7%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.7%

         \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{z}}{y - t}} \]

      2. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{\frac{x}{z} \cdot 2}}{y - t} \]

      3. associate-*r/ 99.5%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

      4. clear-num 99.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \cdot \frac{2}{y - t} \]

      5. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{2}{y - t}}{\frac{z}{x}}} \]

      6. *-un-lft-identity 99.7%

         \[\leadsto \frac{\color{blue}{\frac{2}{y - t}}}{\frac{z}{x}} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{\frac{2}{y - t}}{\frac{z}{x}}} \]

   6. Taylor expanded in y around inf 58.7%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

      2. associate-/r* 76.1%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y}} \]

   8. Simplified 76.1%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y}} \]

   if -3.3e-15 < t < -1.99999999999999985e-76 or 8.00000000000000031e-89 < t < 4.60000000000000003e-38

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 96.3%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 96.3%

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

      4. associate-/r* 89.7%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around 0 73.1%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]

   if -1.99999999999999985e-76 < t < 8.00000000000000031e-89

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 92.5%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 92.5%

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

      4. associate-/r* 92.1%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around inf 85.5%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 85.5%

         \[\leadsto \color{blue}{\frac{2 \cdot x}{y \cdot z}} \]

      2. *-commutative 85.5%

         \[\leadsto \frac{\color{blue}{x \cdot 2}}{y \cdot z} \]

      3. times-frac 86.2%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]

   6. Simplified 86.2%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]

   if 2.1e52 < t

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 84.8%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 88.4%

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

      4. associate-/r* 91.5%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around 0 81.8%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 80.1%

         \[\leadsto -2 \cdot \color{blue}{\frac{\frac{x}{t}}{z}} \]

      2. clear-num 79.4%

         \[\leadsto -2 \cdot \color{blue}{\frac{1}{\frac{z}{\frac{x}{t}}}} \]

      3. un-div-inv 79.4%

         \[\leadsto \color{blue}{\frac{-2}{\frac{z}{\frac{x}{t}}}} \]

      4. div-inv 79.3%

         \[\leadsto \frac{-2}{\color{blue}{z \cdot \frac{1}{\frac{x}{t}}}} \]

      5. clear-num 79.4%

         \[\leadsto \frac{-2}{z \cdot \color{blue}{\frac{t}{x}}} \]

   6. Applied egg-rr 79.4%

      \[\leadsto \color{blue}{\frac{-2}{z \cdot \frac{t}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 79.4%

         \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{\frac{t}{x}}} \]

      2. associate-/r/ 81.6%

         \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{t} \cdot x} \]

   8. Applied egg-rr 81.6%

      \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{t} \cdot x} \]
   9. Step-by-step derivation

      1. associate-/l/ 81.7%

         \[\leadsto \color{blue}{\frac{-2}{t \cdot z}} \cdot x \]

      2. associate-*l/ 81.8%

         \[\leadsto \color{blue}{\frac{-2 \cdot x}{t \cdot z}} \]

      3. times-frac 83.1%

         \[\leadsto \color{blue}{\frac{-2}{t} \cdot \frac{x}{z}} \]

      4. associate-*l/ 83.3%

         \[\leadsto \color{blue}{\frac{-2 \cdot \frac{x}{z}}{t}} \]

      5. metadata-eval 83.3%

         \[\leadsto \frac{\color{blue}{\left(-2\right)} \cdot \frac{x}{z}}{t} \]

      6. distribute-lft-neg-in 83.3%

         \[\leadsto \frac{\color{blue}{-2 \cdot \frac{x}{z}}}{t} \]

      7. clear-num 83.2%

         \[\leadsto \frac{-2 \cdot \color{blue}{\frac{1}{\frac{z}{x}}}}{t} \]

      8. div-inv 83.2%

         \[\leadsto \frac{-\color{blue}{\frac{2}{\frac{z}{x}}}}{t} \]

      9. distribute-neg-frac 83.2%

         \[\leadsto \frac{\color{blue}{\frac{-2}{\frac{z}{x}}}}{t} \]

      10. metadata-eval 83.2%

          \[\leadsto \frac{\frac{\color{blue}{-2}}{\frac{z}{x}}}{t} \]

   10. Applied egg-rr 83.2%

       \[\leadsto \color{blue}{\frac{\frac{-2}{\frac{z}{x}}}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-15}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-76}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-89}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-38}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+52}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-2}{\frac{z}{x}}}{t}\\ \end{array} \]

Alternative 7: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \frac{\frac{x}{z}}{y}\\ t_2 := -2 \cdot \frac{x}{z \cdot t}\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-2}{\frac{z}{x}}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (/ (/ x z) y))) (t_2 (* -2.0 (/ x (* z t)))))
   (if (<= t -1.65e+44)
     (* x (/ (/ -2.0 z) t))
     (if (<= t -6e-15)
       t_1
       (if (<= t -3.1e-80)
         t_2
         (if (<= t 1.05e-86)
           (/ (/ x y) (* z 0.5))
           (if (<= t 9.2e-38)
             t_2
             (if (<= t 9.6e+50) t_1 (/ (/ -2.0 (/ z x)) t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((x / z) / y);
	double t_2 = -2.0 * (x / (z * t));
	double tmp;
	if (t <= -1.65e+44) {
		tmp = x * ((-2.0 / z) / t);
	} else if (t <= -6e-15) {
		tmp = t_1;
	} else if (t <= -3.1e-80) {
		tmp = t_2;
	} else if (t <= 1.05e-86) {
		tmp = (x / y) / (z * 0.5);
	} else if (t <= 9.2e-38) {
		tmp = t_2;
	} else if (t <= 9.6e+50) {
		tmp = t_1;
	} else {
		tmp = (-2.0 / (z / x)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * ((x / z) / y)
    t_2 = (-2.0d0) * (x / (z * t))
    if (t <= (-1.65d+44)) then
        tmp = x * (((-2.0d0) / z) / t)
    else if (t <= (-6d-15)) then
        tmp = t_1
    else if (t <= (-3.1d-80)) then
        tmp = t_2
    else if (t <= 1.05d-86) then
        tmp = (x / y) / (z * 0.5d0)
    else if (t <= 9.2d-38) then
        tmp = t_2
    else if (t <= 9.6d+50) then
        tmp = t_1
    else
        tmp = ((-2.0d0) / (z / x)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((x / z) / y);
	double t_2 = -2.0 * (x / (z * t));
	double tmp;
	if (t <= -1.65e+44) {
		tmp = x * ((-2.0 / z) / t);
	} else if (t <= -6e-15) {
		tmp = t_1;
	} else if (t <= -3.1e-80) {
		tmp = t_2;
	} else if (t <= 1.05e-86) {
		tmp = (x / y) / (z * 0.5);
	} else if (t <= 9.2e-38) {
		tmp = t_2;
	} else if (t <= 9.6e+50) {
		tmp = t_1;
	} else {
		tmp = (-2.0 / (z / x)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * ((x / z) / y)
	t_2 = -2.0 * (x / (z * t))
	tmp = 0
	if t <= -1.65e+44:
		tmp = x * ((-2.0 / z) / t)
	elif t <= -6e-15:
		tmp = t_1
	elif t <= -3.1e-80:
		tmp = t_2
	elif t <= 1.05e-86:
		tmp = (x / y) / (z * 0.5)
	elif t <= 9.2e-38:
		tmp = t_2
	elif t <= 9.6e+50:
		tmp = t_1
	else:
		tmp = (-2.0 / (z / x)) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(Float64(x / z) / y))
	t_2 = Float64(-2.0 * Float64(x / Float64(z * t)))
	tmp = 0.0
	if (t <= -1.65e+44)
		tmp = Float64(x * Float64(Float64(-2.0 / z) / t));
	elseif (t <= -6e-15)
		tmp = t_1;
	elseif (t <= -3.1e-80)
		tmp = t_2;
	elseif (t <= 1.05e-86)
		tmp = Float64(Float64(x / y) / Float64(z * 0.5));
	elseif (t <= 9.2e-38)
		tmp = t_2;
	elseif (t <= 9.6e+50)
		tmp = t_1;
	else
		tmp = Float64(Float64(-2.0 / Float64(z / x)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * ((x / z) / y);
	t_2 = -2.0 * (x / (z * t));
	tmp = 0.0;
	if (t <= -1.65e+44)
		tmp = x * ((-2.0 / z) / t);
	elseif (t <= -6e-15)
		tmp = t_1;
	elseif (t <= -3.1e-80)
		tmp = t_2;
	elseif (t <= 1.05e-86)
		tmp = (x / y) / (z * 0.5);
	elseif (t <= 9.2e-38)
		tmp = t_2;
	elseif (t <= 9.6e+50)
		tmp = t_1;
	else
		tmp = (-2.0 / (z / x)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e+44], N[(x * N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6e-15], t$95$1, If[LessEqual[t, -3.1e-80], t$95$2, If[LessEqual[t, 1.05e-86], N[(N[(x / y), $MachinePrecision] / N[(z * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-38], t$95$2, If[LessEqual[t, 9.6e+50], t$95$1, N[(N[(-2.0 / N[(z / x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.65000000000000007e44

   1. Initial program 86.2%

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

      1. *-commutative 86.2%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 86.1%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 90.3%

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

      4. associate-/r* 92.2%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around 0 88.1%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 88.2%

         \[\leadsto -2 \cdot \color{blue}{\frac{\frac{x}{t}}{z}} \]

      2. clear-num 86.9%

         \[\leadsto -2 \cdot \color{blue}{\frac{1}{\frac{z}{\frac{x}{t}}}} \]

      3. un-div-inv 86.9%

         \[\leadsto \color{blue}{\frac{-2}{\frac{z}{\frac{x}{t}}}} \]

      4. div-inv 85.8%

         \[\leadsto \frac{-2}{\color{blue}{z \cdot \frac{1}{\frac{x}{t}}}} \]

      5. clear-num 85.9%

         \[\leadsto \frac{-2}{z \cdot \color{blue}{\frac{t}{x}}} \]

   6. Applied egg-rr 85.9%

      \[\leadsto \color{blue}{\frac{-2}{z \cdot \frac{t}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 87.1%

         \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{\frac{t}{x}}} \]

      2. associate-/r/ 88.3%

         \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{t} \cdot x} \]

   8. Applied egg-rr 88.3%

      \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{t} \cdot x} \]

   if -1.65000000000000007e44 < t < -6e-15 or 9.20000000000000007e-38 < t < 9.6000000000000007e50

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 92.7%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 92.7%

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

      4. associate-/r* 99.7%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.7%

         \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{z}}{y - t}} \]

      2. *-commutative 99.7%

         \[\leadsto \frac{\color{blue}{\frac{x}{z} \cdot 2}}{y - t} \]

      3. associate-*r/ 99.5%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

      4. clear-num 99.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \cdot \frac{2}{y - t} \]

      5. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{2}{y - t}}{\frac{z}{x}}} \]

      6. *-un-lft-identity 99.7%

         \[\leadsto \frac{\color{blue}{\frac{2}{y - t}}}{\frac{z}{x}} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{\frac{2}{y - t}}{\frac{z}{x}}} \]

   6. Taylor expanded in y around inf 58.7%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

      2. associate-/r* 76.1%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y}} \]

   8. Simplified 76.1%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y}} \]

   if -6e-15 < t < -3.10000000000000016e-80 or 1.05e-86 < t < 9.20000000000000007e-38

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 96.3%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 96.3%

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

      4. associate-/r* 89.7%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around 0 73.1%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]

   if -3.10000000000000016e-80 < t < 1.05e-86

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 92.5%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 92.5%

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

      4. associate-/r* 92.1%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 92.1%

         \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{z}}{y - t}} \]

      2. *-commutative 92.1%

         \[\leadsto \frac{\color{blue}{\frac{x}{z} \cdot 2}}{y - t} \]

      3. associate-*r/ 92.0%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

      4. clear-num 92.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \cdot \frac{2}{y - t} \]

      5. associate-*l/ 92.0%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{2}{y - t}}{\frac{z}{x}}} \]

      6. *-un-lft-identity 92.0%

         \[\leadsto \frac{\color{blue}{\frac{2}{y - t}}}{\frac{z}{x}} \]

   5. Applied egg-rr 92.0%

      \[\leadsto \color{blue}{\frac{\frac{2}{y - t}}{\frac{z}{x}}} \]

   6. Taylor expanded in y around inf 85.5%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 85.5%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

      2. associate-/r* 83.7%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y}} \]

   8. Simplified 83.7%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y}} \]
   9. Step-by-step derivation

      1. associate-/r* 85.5%

         \[\leadsto 2 \cdot \color{blue}{\frac{x}{z \cdot y}} \]

      2. associate-*r/ 85.5%

         \[\leadsto \color{blue}{\frac{2 \cdot x}{z \cdot y}} \]

      3. frac-times 86.2%

         \[\leadsto \color{blue}{\frac{2}{z} \cdot \frac{x}{y}} \]

      4. clear-num 86.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{2}}} \cdot \frac{x}{y} \]

      5. associate-*l/ 87.2%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{y}}{\frac{z}{2}}} \]

      6. *-un-lft-identity 87.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{\frac{z}{2}} \]

      7. div-inv 87.2%

         \[\leadsto \frac{\frac{x}{y}}{\color{blue}{z \cdot \frac{1}{2}}} \]

      8. metadata-eval 87.2%

         \[\leadsto \frac{\frac{x}{y}}{z \cdot \color{blue}{0.5}} \]

   10. Applied egg-rr 87.2%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{z \cdot 0.5}} \]

   if 9.6000000000000007e50 < t

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 84.8%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 88.4%

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

      4. associate-/r* 91.5%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around 0 81.8%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   5. Step-by-step derivation

      1. associate-/r* 80.1%

         \[\leadsto -2 \cdot \color{blue}{\frac{\frac{x}{t}}{z}} \]

      2. clear-num 79.4%

         \[\leadsto -2 \cdot \color{blue}{\frac{1}{\frac{z}{\frac{x}{t}}}} \]

      3. un-div-inv 79.4%

         \[\leadsto \color{blue}{\frac{-2}{\frac{z}{\frac{x}{t}}}} \]

      4. div-inv 79.3%

         \[\leadsto \frac{-2}{\color{blue}{z \cdot \frac{1}{\frac{x}{t}}}} \]

      5. clear-num 79.4%

         \[\leadsto \frac{-2}{z \cdot \color{blue}{\frac{t}{x}}} \]

   6. Applied egg-rr 79.4%

      \[\leadsto \color{blue}{\frac{-2}{z \cdot \frac{t}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 79.4%

         \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{\frac{t}{x}}} \]

      2. associate-/r/ 81.6%

         \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{t} \cdot x} \]

   8. Applied egg-rr 81.6%

      \[\leadsto \color{blue}{\frac{\frac{-2}{z}}{t} \cdot x} \]
   9. Step-by-step derivation

      1. associate-/l/ 81.7%

         \[\leadsto \color{blue}{\frac{-2}{t \cdot z}} \cdot x \]

      2. associate-*l/ 81.8%

         \[\leadsto \color{blue}{\frac{-2 \cdot x}{t \cdot z}} \]

      3. times-frac 83.1%

         \[\leadsto \color{blue}{\frac{-2}{t} \cdot \frac{x}{z}} \]

      4. associate-*l/ 83.3%

         \[\leadsto \color{blue}{\frac{-2 \cdot \frac{x}{z}}{t}} \]

      5. metadata-eval 83.3%

         \[\leadsto \frac{\color{blue}{\left(-2\right)} \cdot \frac{x}{z}}{t} \]

      6. distribute-lft-neg-in 83.3%

         \[\leadsto \frac{\color{blue}{-2 \cdot \frac{x}{z}}}{t} \]

      7. clear-num 83.2%

         \[\leadsto \frac{-2 \cdot \color{blue}{\frac{1}{\frac{z}{x}}}}{t} \]

      8. div-inv 83.2%

         \[\leadsto \frac{-\color{blue}{\frac{2}{\frac{z}{x}}}}{t} \]

      9. distribute-neg-frac 83.2%

         \[\leadsto \frac{\color{blue}{\frac{-2}{\frac{z}{x}}}}{t} \]

      10. metadata-eval 83.2%

          \[\leadsto \frac{\frac{\color{blue}{-2}}{\frac{z}{x}}}{t} \]

   10. Applied egg-rr 83.2%

       \[\leadsto \color{blue}{\frac{\frac{-2}{\frac{z}{x}}}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-15}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-80}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-38}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+50}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-2}{\frac{z}{x}}}{t}\\ \end{array} \]

Alternative 8: 73.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+44} \lor \neg \left(t \leq 1.05 \cdot 10^{-86}\right) \land \left(t \leq 8.4 \cdot 10^{-38} \lor \neg \left(t \leq 1.3 \cdot 10^{+52}\right)\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.65e+44)
         (and (not (<= t 1.05e-86)) (or (<= t 8.4e-38) (not (<= t 1.3e+52)))))
   (* -2.0 (/ x (* z t)))
   (* 2.0 (/ (/ x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.65e+44) || (!(t <= 1.05e-86) && ((t <= 8.4e-38) || !(t <= 1.3e+52)))) {
		tmp = -2.0 * (x / (z * t));
	} else {
		tmp = 2.0 * ((x / z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.65d+44)) .or. (.not. (t <= 1.05d-86)) .and. (t <= 8.4d-38) .or. (.not. (t <= 1.3d+52))) then
        tmp = (-2.0d0) * (x / (z * t))
    else
        tmp = 2.0d0 * ((x / z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.65e+44) || (!(t <= 1.05e-86) && ((t <= 8.4e-38) || !(t <= 1.3e+52)))) {
		tmp = -2.0 * (x / (z * t));
	} else {
		tmp = 2.0 * ((x / z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.65e+44) or (not (t <= 1.05e-86) and ((t <= 8.4e-38) or not (t <= 1.3e+52))):
		tmp = -2.0 * (x / (z * t))
	else:
		tmp = 2.0 * ((x / z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.65e+44) || (!(t <= 1.05e-86) && ((t <= 8.4e-38) || !(t <= 1.3e+52))))
		tmp = Float64(-2.0 * Float64(x / Float64(z * t)));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.65e+44) || (~((t <= 1.05e-86)) && ((t <= 8.4e-38) || ~((t <= 1.3e+52)))))
		tmp = -2.0 * (x / (z * t));
	else
		tmp = 2.0 * ((x / z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.65e+44], And[N[Not[LessEqual[t, 1.05e-86]], $MachinePrecision], Or[LessEqual[t, 8.4e-38], N[Not[LessEqual[t, 1.3e+52]], $MachinePrecision]]]], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.65000000000000007e44 or 1.05e-86 < t < 8.40000000000000052e-38 or 1.3e52 < t

   1. Initial program 86.5%

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

      1. *-commutative 86.5%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 86.4%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 89.8%

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

      4. associate-/r* 91.3%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in y around 0 82.9%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]

   if -1.65000000000000007e44 < t < 1.05e-86 or 8.40000000000000052e-38 < t < 1.3e52

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 93.2%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 93.2%

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

      4. associate-/r* 93.6%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 93.6%

         \[\leadsto \color{blue}{\frac{2 \cdot \frac{x}{z}}{y - t}} \]

      2. *-commutative 93.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{z} \cdot 2}}{y - t} \]

      3. associate-*r/ 93.5%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

      4. clear-num 93.5%

         \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \cdot \frac{2}{y - t} \]

      5. associate-*l/ 93.6%

         \[\leadsto \color{blue}{\frac{1 \cdot \frac{2}{y - t}}{\frac{z}{x}}} \]

      6. *-un-lft-identity 93.6%

         \[\leadsto \frac{\color{blue}{\frac{2}{y - t}}}{\frac{z}{x}} \]

   5. Applied egg-rr 93.6%

      \[\leadsto \color{blue}{\frac{\frac{2}{y - t}}{\frac{z}{x}}} \]

   6. Taylor expanded in y around inf 75.9%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 75.9%

         \[\leadsto 2 \cdot \frac{x}{\color{blue}{z \cdot y}} \]

      2. associate-/r* 78.9%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y}} \]

   8. Simplified 78.9%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+44} \lor \neg \left(t \leq 1.05 \cdot 10^{-86}\right) \land \left(t \leq 8.4 \cdot 10^{-38} \lor \neg \left(t \leq 1.3 \cdot 10^{+52}\right)\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \end{array} \]

Alternative 9: 96.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+81} \lor \neg \left(z \leq 2.2 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.8e+81) (not (<= z 2.2e+29)))
   (* (/ 2.0 z) (/ x (- y t)))
   (* x (/ (/ 2.0 (- y t)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e+81) || !(z <= 2.2e+29)) {
		tmp = (2.0 / z) * (x / (y - t));
	} else {
		tmp = x * ((2.0 / (y - t)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.8d+81)) .or. (.not. (z <= 2.2d+29))) then
        tmp = (2.0d0 / z) * (x / (y - t))
    else
        tmp = x * ((2.0d0 / (y - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e+81) || !(z <= 2.2e+29)) {
		tmp = (2.0 / z) * (x / (y - t));
	} else {
		tmp = x * ((2.0 / (y - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.8e+81) or not (z <= 2.2e+29):
		tmp = (2.0 / z) * (x / (y - t))
	else:
		tmp = x * ((2.0 / (y - t)) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.8e+81) || !(z <= 2.2e+29))
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	else
		tmp = Float64(x * Float64(Float64(2.0 / Float64(y - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.8e+81) || ~((z <= 2.2e+29)))
		tmp = (2.0 / z) * (x / (y - t));
	else
		tmp = x * ((2.0 / (y - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.8e+81], N[Not[LessEqual[z, 2.2e+29]], $MachinePrecision]], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8e81 or 2.2000000000000001e29 < z

   1. Initial program 80.0%

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

      1. *-commutative 80.0%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. distribute-rgt-out-- 83.5%

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

      3. times-frac 98.1%

         \[\leadsto \color{blue}{\frac{2}{z} \cdot \frac{x}{y - t}} \]

   3. Simplified 98.1%

      \[\leadsto \color{blue}{\frac{2}{z} \cdot \frac{x}{y - t}} \]

   if -3.8e81 < z < 2.2000000000000001e29

   1. Initial program 98.0%

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

      1. *-commutative 98.0%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 98.0%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 98.0%

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

      4. associate-/r* 91.8%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 91.8%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in x around 0 98.0%

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

      1. *-commutative 98.0%

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

      2. associate-/r/ 98.0%

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

      3. associate-/l* 98.0%

         \[\leadsto \frac{x}{\color{blue}{\frac{z}{\frac{2}{y - t}}}} \]

      4. associate-/l* 87.6%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{2}{y - t}}{z}} \]

      5. associate-*r/ 97.5%

         \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]

   6. Simplified 97.5%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+81} \lor \neg \left(z \leq 2.2 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \end{array} \]

Alternative 10: 96.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+53} \lor \neg \left(z \leq 8.8 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3e+53) (not (<= z 8.8e+30)))
   (* (/ 2.0 z) (/ x (- y t)))
   (/ (* 2.0 x) (* z (- y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3e+53) || !(z <= 8.8e+30)) {
		tmp = (2.0 / z) * (x / (y - t));
	} else {
		tmp = (2.0 * x) / (z * (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3d+53)) .or. (.not. (z <= 8.8d+30))) then
        tmp = (2.0d0 / z) * (x / (y - t))
    else
        tmp = (2.0d0 * x) / (z * (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3e+53) || !(z <= 8.8e+30)) {
		tmp = (2.0 / z) * (x / (y - t));
	} else {
		tmp = (2.0 * x) / (z * (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3e+53) or not (z <= 8.8e+30):
		tmp = (2.0 / z) * (x / (y - t))
	else:
		tmp = (2.0 * x) / (z * (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3e+53) || !(z <= 8.8e+30))
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	else
		tmp = Float64(Float64(2.0 * x) / Float64(z * Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3e+53) || ~((z <= 8.8e+30)))
		tmp = (2.0 / z) * (x / (y - t));
	else
		tmp = (2.0 * x) / (z * (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3e+53], N[Not[LessEqual[z, 8.8e+30]], $MachinePrecision]], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999998e53 or 8.7999999999999999e30 < z

   1. Initial program 80.6%

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

      1. *-commutative 80.6%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. distribute-rgt-out-- 84.1%

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

      3. times-frac 98.2%

         \[\leadsto \color{blue}{\frac{2}{z} \cdot \frac{x}{y - t}} \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{2}{z} \cdot \frac{x}{y - t}} \]

   if -2.99999999999999998e53 < z < 8.7999999999999999e30

   1. Initial program 98.0%

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

      1. distribute-rgt-out-- 98.0%

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

   3. Simplified 98.0%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+53} \lor \neg \left(z \leq 8.8 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 11: 92.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.65e-216)
   (* x (/ (/ 2.0 (- y t)) z))
   (* 2.0 (/ (/ x z) (- y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e-216) {
		tmp = x * ((2.0 / (y - t)) / z);
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.65d-216)) then
        tmp = x * ((2.0d0 / (y - t)) / z)
    else
        tmp = 2.0d0 * ((x / z) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e-216) {
		tmp = x * ((2.0 / (y - t)) / z);
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.65e-216:
		tmp = x * ((2.0 / (y - t)) / z)
	else:
		tmp = 2.0 * ((x / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.65e-216)
		tmp = Float64(x * Float64(Float64(2.0 / Float64(y - t)) / z));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.65e-216)
		tmp = x * ((2.0 / (y - t)) / z);
	else
		tmp = 2.0 * ((x / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.65e-216], N[(x * N[(N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.64999999999999984e-216

   1. Initial program 93.5%

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

      1. *-commutative 93.5%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 93.5%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 95.4%

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

      4. associate-/r* 88.9%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

   4. Taylor expanded in x around 0 95.4%

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

      1. *-commutative 95.4%

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

      2. associate-/r/ 95.4%

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

      3. associate-/l* 95.4%

         \[\leadsto \frac{x}{\color{blue}{\frac{z}{\frac{2}{y - t}}}} \]

      4. associate-/l* 95.8%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{2}{y - t}}{z}} \]

      5. associate-*r/ 95.7%

         \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]

   6. Simplified 95.7%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]

   if -1.64999999999999984e-216 < y

   1. Initial program 87.3%

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

      1. *-commutative 87.3%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*r/ 87.3%

         \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

      3. distribute-rgt-out-- 88.7%

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

      4. associate-/r* 95.3%

         \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

   3. Simplified 95.3%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 12: 91.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \frac{\frac{x}{z}}{y - t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* 2.0 (/ (/ x z) (- y t))))

C

double code(double x, double y, double z, double t) {
	return 2.0 * ((x / z) / (y - t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 2.0d0 * ((x / z) / (y - t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return 2.0 * ((x / z) / (y - t));
}

Python

def code(x, y, z, t):
	return 2.0 * ((x / z) / (y - t))

Julia

function code(x, y, z, t)
	return Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 2.0 * ((x / z) / (y - t));
end

Wolfram

code[x_, y_, z_, t_] := N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.0%

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

   1. *-commutative 90.0%

      \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

   2. associate-*r/ 90.0%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

   3. distribute-rgt-out-- 91.6%

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

   4. associate-/r* 92.5%

      \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

3. Simplified 92.5%

   \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

4. Final simplification 92.5%

   \[\leadsto 2 \cdot \frac{\frac{x}{z}}{y - t} \]

Alternative 13: 53.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ -2 \cdot \frac{x}{z \cdot t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* -2.0 (/ x (* z t))))

C

double code(double x, double y, double z, double t) {
	return -2.0 * (x / (z * t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (-2.0d0) * (x / (z * t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return -2.0 * (x / (z * t));
}

Python

def code(x, y, z, t):
	return -2.0 * (x / (z * t))

Julia

function code(x, y, z, t)
	return Float64(-2.0 * Float64(x / Float64(z * t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = -2.0 * (x / (z * t));
end

Wolfram

code[x_, y_, z_, t_] := N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.0%

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

   1. *-commutative 90.0%

      \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

   2. associate-*r/ 90.0%

      \[\leadsto \color{blue}{2 \cdot \frac{x}{y \cdot z - t \cdot z}} \]

   3. distribute-rgt-out-- 91.6%

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

   4. associate-/r* 92.5%

      \[\leadsto 2 \cdot \color{blue}{\frac{\frac{x}{z}}{y - t}} \]

3. Simplified 92.5%

   \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]

4. Taylor expanded in y around 0 54.1%

   \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]

5. Final simplification 54.1%

   \[\leadsto -2 \cdot \frac{x}{z \cdot t} \]

Developer target: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ t_2 := \frac{x \cdot 2}{y \cdot z - t \cdot z}\\ \mathbf{if}\;t_2 < -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 1.045027827330126 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x (* (- y t) z)) 2.0))
        (t_2 (/ (* x 2.0) (- (* y z) (* t z)))))
   (if (< t_2 -2.559141628295061e-13)
     t_1
     (if (< t_2 1.045027827330126e-269) (/ (* (/ x z) 2.0) (- y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / ((y - t) * z)) * 2.0;
	double t_2 = (x * 2.0) / ((y * z) - (t * z));
	double tmp;
	if (t_2 < -2.559141628295061e-13) {
		tmp = t_1;
	} else if (t_2 < 1.045027827330126e-269) {
		tmp = ((x / z) * 2.0) / (y - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / ((y - t) * z)) * 2.0d0
    t_2 = (x * 2.0d0) / ((y * z) - (t * z))
    if (t_2 < (-2.559141628295061d-13)) then
        tmp = t_1
    else if (t_2 < 1.045027827330126d-269) then
        tmp = ((x / z) * 2.0d0) / (y - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / ((y - t) * z)) * 2.0;
	double t_2 = (x * 2.0) / ((y * z) - (t * z));
	double tmp;
	if (t_2 < -2.559141628295061e-13) {
		tmp = t_1;
	} else if (t_2 < 1.045027827330126e-269) {
		tmp = ((x / z) * 2.0) / (y - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / ((y - t) * z)) * 2.0
	t_2 = (x * 2.0) / ((y * z) - (t * z))
	tmp = 0
	if t_2 < -2.559141628295061e-13:
		tmp = t_1
	elif t_2 < 1.045027827330126e-269:
		tmp = ((x / z) * 2.0) / (y - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(Float64(y - t) * z)) * 2.0)
	t_2 = Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
	tmp = 0.0
	if (t_2 < -2.559141628295061e-13)
		tmp = t_1;
	elseif (t_2 < 1.045027827330126e-269)
		tmp = Float64(Float64(Float64(x / z) * 2.0) / Float64(y - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / ((y - t) * z)) * 2.0;
	t_2 = (x * 2.0) / ((y * z) - (t * z));
	tmp = 0.0;
	if (t_2 < -2.559141628295061e-13)
		tmp = t_1;
	elseif (t_2 < 1.045027827330126e-269)
		tmp = ((x / z) * 2.0) / (y - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -2.559141628295061e-13], t$95$1, If[Less[t$95$2, 1.045027827330126e-269], N[(N[(N[(x / z), $MachinePrecision] * 2.0), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023290 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (if (< (/ (* x 2.0) (- (* y z) (* t z))) -2.559141628295061e-13) (* (/ x (* (- y t) z)) 2.0) (if (< (/ (* x 2.0) (- (* y z) (* t z))) 1.045027827330126e-269) (/ (* (/ x z) 2.0) (- y t)) (* (/ x (* (- y t) z)) 2.0)))

  (/ (* x 2.0) (- (* y z) (* t z))))