Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.3% → 97.9%

Time: 10.3s

Alternatives: 10

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: 89.3% 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: 97.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - z \cdot t\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+268} \lor \neg \left(t_1 \leq 5 \cdot 10^{+244}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) (* z t))))
   (if (or (<= t_1 -2e+268) (not (<= t_1 5e+244)))
     (* 2.0 (/ (/ x z) (- y t)))
     (/ (* 2.0 x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if ((t_1 <= -2e+268) || !(t_1 <= 5e+244)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = (2.0 * x) / 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) :: tmp
    t_1 = (y * z) - (z * t)
    if ((t_1 <= (-2d+268)) .or. (.not. (t_1 <= 5d+244))) then
        tmp = 2.0d0 * ((x / z) / (y - t))
    else
        tmp = (2.0d0 * x) / t_1
    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 <= -2e+268) || !(t_1 <= 5e+244)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = (2.0 * x) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - (z * t)
	tmp = 0
	if (t_1 <= -2e+268) or not (t_1 <= 5e+244):
		tmp = 2.0 * ((x / z) / (y - t))
	else:
		tmp = (2.0 * x) / t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= -2e+268) || !(t_1 <= 5e+244))
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(Float64(2.0 * x) / t_1);
	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 <= -2e+268) || ~((t_1 <= 5e+244)))
		tmp = 2.0 * ((x / z) / (y - t));
	else
		tmp = (2.0 * x) / t_1;
	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[Or[LessEqual[t$95$1, -2e+268], N[Not[LessEqual[t$95$1, 5e+244]], $MachinePrecision]], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] / t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 y z) (*.f64 t z)) < -1.9999999999999999e268 or 5.00000000000000022e244 < (-.f64 (*.f64 y z) (*.f64 t z))

   1. Initial program 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-*r/ 71.2%

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

      3. distribute-rgt-out-- 81.6%

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

      4. associate-/r* 100.0%

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

   3. Simplified 100.0%

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

   if -1.9999999999999999e268 < (-.f64 (*.f64 y z) (*.f64 t z)) < 5.00000000000000022e244

   1. Initial program 98.7%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - z \cdot t \leq -2 \cdot 10^{+268} \lor \neg \left(y \cdot z - z \cdot t \leq 5 \cdot 10^{+244}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z - z \cdot t}\\ \end{array} \]

Alternative 2: 96.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot x \leq -1 \cdot 10^{-96}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{elif}\;2 \cdot x \leq 5 \cdot 10^{-61}:\\ \;\;\;\;\frac{2}{\frac{z \cdot \left(y - t\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y - t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* 2.0 x) -1e-96)
   (* (/ 2.0 z) (/ x (- y t)))
   (if (<= (* 2.0 x) 5e-61)
     (/ 2.0 (/ (* z (- y t)) x))
     (/ 2.0 (* z (/ (- y t) x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((2.0 * x) <= -1e-96) {
		tmp = (2.0 / z) * (x / (y - t));
	} else if ((2.0 * x) <= 5e-61) {
		tmp = 2.0 / ((z * (y - t)) / x);
	} else {
		tmp = 2.0 / (z * ((y - t) / x));
	}
	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 ((2.0d0 * x) <= (-1d-96)) then
        tmp = (2.0d0 / z) * (x / (y - t))
    else if ((2.0d0 * x) <= 5d-61) then
        tmp = 2.0d0 / ((z * (y - t)) / x)
    else
        tmp = 2.0d0 / (z * ((y - t) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((2.0 * x) <= -1e-96) {
		tmp = (2.0 / z) * (x / (y - t));
	} else if ((2.0 * x) <= 5e-61) {
		tmp = 2.0 / ((z * (y - t)) / x);
	} else {
		tmp = 2.0 / (z * ((y - t) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (2.0 * x) <= -1e-96:
		tmp = (2.0 / z) * (x / (y - t))
	elif (2.0 * x) <= 5e-61:
		tmp = 2.0 / ((z * (y - t)) / x)
	else:
		tmp = 2.0 / (z * ((y - t) / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(2.0 * x) <= -1e-96)
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	elseif (Float64(2.0 * x) <= 5e-61)
		tmp = Float64(2.0 / Float64(Float64(z * Float64(y - t)) / x));
	else
		tmp = Float64(2.0 / Float64(z * Float64(Float64(y - t) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((2.0 * x) <= -1e-96)
		tmp = (2.0 / z) * (x / (y - t));
	elseif ((2.0 * x) <= 5e-61)
		tmp = 2.0 / ((z * (y - t)) / x);
	else
		tmp = 2.0 / (z * ((y - t) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(2.0 * x), $MachinePrecision], -1e-96], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(2.0 * x), $MachinePrecision], 5e-61], N[(2.0 / N[(N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(z * N[(N[(y - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x 2) < -9.9999999999999991e-97

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

      2. distribute-rgt-out-- 91.6%

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

      3. times-frac 97.4%

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

   3. Simplified 97.4%

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

   if -9.9999999999999991e-97 < (*.f64 x 2) < 4.9999999999999999e-61

   1. Initial program 96.9%

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

      1. *-commutative 96.9%

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

      2. associate-*r/ 96.9%

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

      3. distribute-rgt-out-- 98.8%

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

      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. Step-by-step derivation

      1. associate-/r* 98.8%

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

      2. associate-*r/ 98.8%

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

      3. associate-/l* 98.1%

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

   5. Applied egg-rr 98.1%

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

   if 4.9999999999999999e-61 < (*.f64 x 2)

   1. Initial program 83.9%

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

      1. *-commutative 83.9%

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

      2. associate-*r/ 83.9%

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

      3. distribute-rgt-out-- 88.1%

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

      4. associate-/r* 93.3%

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

   3. Simplified 93.3%

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

      1. associate-/r* 88.1%

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

      2. associate-*r/ 88.1%

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

      3. frac-times 98.3%

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

      4. clear-num 98.2%

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

      5. frac-times 98.7%

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

      6. metadata-eval 98.7%

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

   5. Applied egg-rr 98.7%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x \leq -1 \cdot 10^{-96}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{elif}\;2 \cdot x \leq 5 \cdot 10^{-61}:\\ \;\;\;\;\frac{2}{\frac{z \cdot \left(y - t\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y - t}{x}}\\ \end{array} \]

Alternative 3: 96.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot x \leq -5 \cdot 10^{-37}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{elif}\;2 \cdot x \leq 10^{+33}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y - t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* 2.0 x) -5e-37)
   (* (/ 2.0 z) (/ x (- y t)))
   (if (<= (* 2.0 x) 1e+33)
     (/ (* 2.0 x) (* z (- y t)))
     (/ 2.0 (* z (/ (- y t) x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((2.0 * x) <= -5e-37) {
		tmp = (2.0 / z) * (x / (y - t));
	} else if ((2.0 * x) <= 1e+33) {
		tmp = (2.0 * x) / (z * (y - t));
	} else {
		tmp = 2.0 / (z * ((y - t) / x));
	}
	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 ((2.0d0 * x) <= (-5d-37)) then
        tmp = (2.0d0 / z) * (x / (y - t))
    else if ((2.0d0 * x) <= 1d+33) then
        tmp = (2.0d0 * x) / (z * (y - t))
    else
        tmp = 2.0d0 / (z * ((y - t) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((2.0 * x) <= -5e-37) {
		tmp = (2.0 / z) * (x / (y - t));
	} else if ((2.0 * x) <= 1e+33) {
		tmp = (2.0 * x) / (z * (y - t));
	} else {
		tmp = 2.0 / (z * ((y - t) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (2.0 * x) <= -5e-37:
		tmp = (2.0 / z) * (x / (y - t))
	elif (2.0 * x) <= 1e+33:
		tmp = (2.0 * x) / (z * (y - t))
	else:
		tmp = 2.0 / (z * ((y - t) / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(2.0 * x) <= -5e-37)
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	elseif (Float64(2.0 * x) <= 1e+33)
		tmp = Float64(Float64(2.0 * x) / Float64(z * Float64(y - t)));
	else
		tmp = Float64(2.0 / Float64(z * Float64(Float64(y - t) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((2.0 * x) <= -5e-37)
		tmp = (2.0 / z) * (x / (y - t));
	elseif ((2.0 * x) <= 1e+33)
		tmp = (2.0 * x) / (z * (y - t));
	else
		tmp = 2.0 / (z * ((y - t) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(2.0 * x), $MachinePrecision], -5e-37], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(2.0 * x), $MachinePrecision], 1e+33], N[(N[(2.0 * x), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(z * N[(N[(y - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x 2) < -4.9999999999999997e-37

   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. distribute-rgt-out-- 90.4%

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

      3. times-frac 97.0%

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

   3. Simplified 97.0%

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

   if -4.9999999999999997e-37 < (*.f64 x 2) < 9.9999999999999995e32

   1. Initial program 96.1%

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

      1. distribute-rgt-out-- 99.1%

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

   3. Simplified 99.1%

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

   if 9.9999999999999995e32 < (*.f64 x 2)

   1. Initial program 80.2%

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

      1. *-commutative 80.2%

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

      2. associate-*r/ 80.2%

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

      3. distribute-rgt-out-- 82.2%

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

      4. associate-/r* 90.1%

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

   3. Simplified 90.1%

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

      1. associate-/r* 82.2%

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

      2. associate-*r/ 82.2%

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

      3. frac-times 97.7%

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

      4. clear-num 97.6%

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

      5. frac-times 98.9%

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

      6. metadata-eval 98.9%

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

   5. Applied egg-rr 98.9%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x \leq -5 \cdot 10^{-37}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{elif}\;2 \cdot x \leq 10^{+33}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y - t}{x}}\\ \end{array} \]

Alternative 4: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-67} \lor \neg \left(t \leq 3.8 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.2e-67) (not (<= t 3.8e-40)))
   (* x (/ (/ -2.0 z) t))
   (* x (/ 2.0 (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.2e-67) || !(t <= 3.8e-40)) {
		tmp = x * ((-2.0 / z) / t);
	} else {
		tmp = x * (2.0 / (y * 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 ((t <= (-6.2d-67)) .or. (.not. (t <= 3.8d-40))) then
        tmp = x * (((-2.0d0) / z) / t)
    else
        tmp = x * (2.0d0 / (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.2e-67) || !(t <= 3.8e-40)) {
		tmp = x * ((-2.0 / z) / t);
	} else {
		tmp = x * (2.0 / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.2e-67) or not (t <= 3.8e-40):
		tmp = x * ((-2.0 / z) / t)
	else:
		tmp = x * (2.0 / (y * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.2e-67) || !(t <= 3.8e-40))
		tmp = Float64(x * Float64(Float64(-2.0 / z) / t));
	else
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.2e-67) || ~((t <= 3.8e-40)))
		tmp = x * ((-2.0 / z) / t);
	else
		tmp = x * (2.0 / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.2e-67], N[Not[LessEqual[t, 3.8e-40]], $MachinePrecision]], N[(x * N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2000000000000005e-67 or 3.7999999999999999e-40 < t

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

      2. associate-*r/ 87.5%

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

      3. distribute-rgt-out-- 92.9%

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

      4. associate-/r* 92.8%

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

   3. Simplified 92.8%

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

      1. associate-/r* 92.9%

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

      2. associate-*r/ 92.9%

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

      3. associate-/l* 92.6%

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

   5. Applied egg-rr 92.6%

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

   6. Taylor expanded in y around 0 78.8%

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

      1. *-commutative 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*l/ 78.8%

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

      4. associate-*r/ 78.6%

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

      5. associate-/r* 79.5%

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

   8. Simplified 79.5%

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

   if -6.2000000000000005e-67 < t < 3.7999999999999999e-40

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

      2. associate-*r/ 94.4%

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

      3. distribute-rgt-out-- 94.4%

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

      4. associate-/r* 91.0%

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

   3. Simplified 91.0%

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

      1. associate-/r* 94.4%

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

      2. associate-*r/ 94.4%

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

      3. associate-/l* 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in y around inf 77.1%

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

      1. *-commutative 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-/r/ 77.1%

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

      4. associate-/l* 77.1%

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

   8. Simplified 77.1%

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

      1. clear-num 76.5%

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

      2. associate-/r/ 77.1%

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

      3. clear-num 77.9%

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

      4. associate-/l/ 77.1%

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

   10. Applied egg-rr 77.1%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-67} \lor \neg \left(t \leq 3.8 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \end{array} \]

Alternative 5: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-66} \lor \neg \left(t \leq 5.2 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7.2e-66) (not (<= t 5.2e-38)))
   (* x (/ (/ -2.0 z) t))
   (* (/ 2.0 z) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.2e-66) || !(t <= 5.2e-38)) {
		tmp = x * ((-2.0 / z) / t);
	} else {
		tmp = (2.0 / z) * (x / 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 <= (-7.2d-66)) .or. (.not. (t <= 5.2d-38))) then
        tmp = x * (((-2.0d0) / z) / t)
    else
        tmp = (2.0d0 / z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.2e-66) || !(t <= 5.2e-38)) {
		tmp = x * ((-2.0 / z) / t);
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7.2e-66) or not (t <= 5.2e-38):
		tmp = x * ((-2.0 / z) / t)
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7.2e-66) || !(t <= 5.2e-38))
		tmp = Float64(x * Float64(Float64(-2.0 / z) / t));
	else
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -7.2e-66) || ~((t <= 5.2e-38)))
		tmp = x * ((-2.0 / z) / t);
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7.2e-66], N[Not[LessEqual[t, 5.2e-38]], $MachinePrecision]], N[(x * N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.20000000000000025e-66 or 5.20000000000000022e-38 < t

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

      2. associate-*r/ 87.5%

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

      3. distribute-rgt-out-- 92.9%

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

      4. associate-/r* 92.8%

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

   3. Simplified 92.8%

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

      1. associate-/r* 92.9%

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

      2. associate-*r/ 92.9%

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

      3. associate-/l* 92.6%

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

   5. Applied egg-rr 92.6%

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

   6. Taylor expanded in y around 0 78.8%

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

      1. *-commutative 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*l/ 78.8%

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

      4. associate-*r/ 78.6%

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

      5. associate-/r* 79.5%

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

   8. Simplified 79.5%

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

   if -7.20000000000000025e-66 < t < 5.20000000000000022e-38

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

      2. associate-*r/ 94.4%

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

      3. distribute-rgt-out-- 94.4%

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

      4. associate-/r* 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in y around inf 77.1%

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

      1. associate-*r/ 77.1%

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

      2. *-commutative 77.1%

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

      3. times-frac 79.0%

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

   6. Simplified 79.0%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-66} \lor \neg \left(t \leq 5.2 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 6: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot -2}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-38}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.9e-67)
   (/ (* x -2.0) (* z t))
   (if (<= t 1.35e-38) (* (/ 2.0 z) (/ x y)) (* x (/ (/ -2.0 z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.9e-67) {
		tmp = (x * -2.0) / (z * t);
	} else if (t <= 1.35e-38) {
		tmp = (2.0 / z) * (x / y);
	} 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) :: tmp
    if (t <= (-3.9d-67)) then
        tmp = (x * (-2.0d0)) / (z * t)
    else if (t <= 1.35d-38) then
        tmp = (2.0d0 / z) * (x / y)
    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 tmp;
	if (t <= -3.9e-67) {
		tmp = (x * -2.0) / (z * t);
	} else if (t <= 1.35e-38) {
		tmp = (2.0 / z) * (x / y);
	} else {
		tmp = x * ((-2.0 / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.9e-67:
		tmp = (x * -2.0) / (z * t)
	elif t <= 1.35e-38:
		tmp = (2.0 / z) * (x / y)
	else:
		tmp = x * ((-2.0 / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.9e-67)
		tmp = Float64(Float64(x * -2.0) / Float64(z * t));
	elseif (t <= 1.35e-38)
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	else
		tmp = Float64(x * Float64(Float64(-2.0 / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.9e-67)
		tmp = (x * -2.0) / (z * t);
	elseif (t <= 1.35e-38)
		tmp = (2.0 / z) * (x / y);
	else
		tmp = x * ((-2.0 / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.9e-67], N[(N[(x * -2.0), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-38], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8999999999999998e-67

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*r/ 90.3%

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

      3. distribute-rgt-out-- 94.5%

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

      4. associate-/r* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around 0 77.1%

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

      1. associate-*r/ 77.1%

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

      2. *-commutative 77.1%

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

      3. *-commutative 77.1%

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

   6. Simplified 77.1%

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

   if -3.8999999999999998e-67 < t < 1.35000000000000003e-38

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

      2. associate-*r/ 94.4%

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

      3. distribute-rgt-out-- 94.4%

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

      4. associate-/r* 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in y around inf 77.1%

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

      1. associate-*r/ 77.1%

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

      2. *-commutative 77.1%

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

      3. times-frac 79.0%

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

   6. Simplified 79.0%

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

   if 1.35000000000000003e-38 < t

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*r/ 85.0%

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

      3. distribute-rgt-out-- 91.4%

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

      4. associate-/r* 92.7%

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

   3. Simplified 92.7%

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

      1. associate-/r* 91.4%

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

      2. associate-*r/ 91.4%

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

      3. associate-/l* 91.4%

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

   5. Applied egg-rr 91.4%

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

   6. Taylor expanded in y around 0 80.2%

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

      1. *-commutative 80.2%

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

      2. *-commutative 80.2%

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

      3. associate-*l/ 80.2%

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

      4. associate-*r/ 80.1%

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

      5. associate-/r* 81.9%

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

   8. Simplified 81.9%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-67}:\\ \;\;\;\;\frac{x \cdot -2}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-38}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \end{array} \]

Alternative 7: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x \cdot -2}{z \cdot t}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.5e-65)
   (/ (* x -2.0) (* z t))
   (if (<= t 2.05e-38) (/ (/ x y) (* z 0.5)) (* x (/ (/ -2.0 z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.5e-65) {
		tmp = (x * -2.0) / (z * t);
	} else if (t <= 2.05e-38) {
		tmp = (x / y) / (z * 0.5);
	} 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) :: tmp
    if (t <= (-5.5d-65)) then
        tmp = (x * (-2.0d0)) / (z * t)
    else if (t <= 2.05d-38) then
        tmp = (x / y) / (z * 0.5d0)
    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 tmp;
	if (t <= -5.5e-65) {
		tmp = (x * -2.0) / (z * t);
	} else if (t <= 2.05e-38) {
		tmp = (x / y) / (z * 0.5);
	} else {
		tmp = x * ((-2.0 / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.5e-65:
		tmp = (x * -2.0) / (z * t)
	elif t <= 2.05e-38:
		tmp = (x / y) / (z * 0.5)
	else:
		tmp = x * ((-2.0 / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.5e-65)
		tmp = Float64(Float64(x * -2.0) / Float64(z * t));
	elseif (t <= 2.05e-38)
		tmp = Float64(Float64(x / y) / Float64(z * 0.5));
	else
		tmp = Float64(x * Float64(Float64(-2.0 / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.5e-65)
		tmp = (x * -2.0) / (z * t);
	elseif (t <= 2.05e-38)
		tmp = (x / y) / (z * 0.5);
	else
		tmp = x * ((-2.0 / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.5e-65], N[(N[(x * -2.0), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e-38], N[(N[(x / y), $MachinePrecision] / N[(z * 0.5), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.4999999999999999e-65

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*r/ 90.3%

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

      3. distribute-rgt-out-- 94.5%

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

      4. associate-/r* 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around 0 77.1%

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

      1. associate-*r/ 77.1%

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

      2. *-commutative 77.1%

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

      3. *-commutative 77.1%

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

   6. Simplified 77.1%

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

   if -5.4999999999999999e-65 < t < 2.0499999999999999e-38

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

      2. associate-*r/ 94.4%

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

      3. distribute-rgt-out-- 94.4%

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

      4. associate-/r* 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in y around inf 77.1%

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

      1. associate-*r/ 77.1%

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

      2. *-commutative 77.1%

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

      3. times-frac 79.0%

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

   6. Simplified 79.0%

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

      1. clear-num 79.0%

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

      2. un-div-inv 79.2%

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

      3. div-inv 79.2%

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

      4. metadata-eval 79.2%

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

   8. Applied egg-rr 79.2%

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

   if 2.0499999999999999e-38 < t

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-*r/ 85.0%

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

      3. distribute-rgt-out-- 91.4%

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

      4. associate-/r* 92.7%

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

   3. Simplified 92.7%

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

      1. associate-/r* 91.4%

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

      2. associate-*r/ 91.4%

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

      3. associate-/l* 91.4%

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

   5. Applied egg-rr 91.4%

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

   6. Taylor expanded in y around 0 80.2%

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

      1. *-commutative 80.2%

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

      2. *-commutative 80.2%

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

      3. associate-*l/ 80.2%

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

      4. associate-*r/ 80.1%

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

      5. associate-/r* 81.9%

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

   8. Simplified 81.9%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x \cdot -2}{z \cdot t}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \end{array} \]

Alternative 8: 92.3% 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 90.4%

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

   1. *-commutative 90.4%

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

   2. associate-*r/ 90.4%

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

   3. distribute-rgt-out-- 93.5%

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

   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. Final simplification 92.1%

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

Alternative 9: 91.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.4%

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

   1. *-commutative 90.4%

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

   2. distribute-rgt-out-- 93.5%

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

   3. times-frac 93.5%

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

3. Simplified 93.5%

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

4. Final simplification 93.5%

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

Alternative 10: 53.2% accurate, 1.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x * ((-2.0 / 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 = x * (((-2.0d0) / z) / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.4%

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

   1. *-commutative 90.4%

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

   2. associate-*r/ 90.4%

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

   3. distribute-rgt-out-- 93.5%

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

   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* 93.5%

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

   2. associate-*r/ 93.5%

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

   3. associate-/l* 93.1%

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

5. Applied egg-rr 93.1%

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

6. Taylor expanded in y around 0 58.9%

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

   1. *-commutative 58.9%

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

   2. *-commutative 58.9%

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

   3. associate-*l/ 58.9%

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

   4. associate-*r/ 58.8%

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

   5. associate-/r* 59.3%

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

8. Simplified 59.3%

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

9. Final simplification 59.3%

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

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 2023336 
(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))))