Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 90.0% → 96.7%

Time: 8.9s

Alternatives: 8

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: 96.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -2 \cdot 10^{+40} \lor \neg \left(x \cdot 2 \leq 5 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* x 2.0) -2e+40) (not (<= (* x 2.0) 5e+40)))
   (* (/ 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 (((x * 2.0) <= -2e+40) || !((x * 2.0) <= 5e+40)) {
		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 (((x * 2.0d0) <= (-2d+40)) .or. (.not. ((x * 2.0d0) <= 5d+40))) 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 (((x * 2.0) <= -2e+40) || !((x * 2.0) <= 5e+40)) {
		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 ((x * 2.0) <= -2e+40) or not ((x * 2.0) <= 5e+40):
		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 ((Float64(x * 2.0) <= -2e+40) || !(Float64(x * 2.0) <= 5e+40))
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	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 (((x * 2.0) <= -2e+40) || ~(((x * 2.0) <= 5e+40)))
		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[N[(x * 2.0), $MachinePrecision], -2e+40], N[Not[LessEqual[N[(x * 2.0), $MachinePrecision], 5e+40]], $MachinePrecision]], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $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 (*.f64 x 2) < -2.00000000000000006e40 or 5.00000000000000003e40 < (*.f64 x 2)

   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. distribute-rgt-out-- 88.1%

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

      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 -2.00000000000000006e40 < (*.f64 x 2) < 5.00000000000000003e40

   1. Initial program 94.1%

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

      1. *-commutative 94.1%

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

      2. associate-*r/ 94.1%

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

      3. distribute-rgt-out-- 95.4%

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

      4. associate-/r* 98.5%

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

   3. Simplified 98.5%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -2 \cdot 10^{+40} \lor \neg \left(x \cdot 2 \leq 5 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 2: 74.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{x \cdot \frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-30}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{-x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.4e-17)
   (/ (* x (/ -2.0 z)) t)
   (if (<= t 5e-30) (/ (* 2.0 (/ x z)) y) (* (/ 2.0 z) (/ (- x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.4e-17) {
		tmp = (x * (-2.0 / z)) / t;
	} else if (t <= 5e-30) {
		tmp = (2.0 * (x / z)) / y;
	} 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) :: tmp
    if (t <= (-1.4d-17)) then
        tmp = (x * ((-2.0d0) / z)) / t
    else if (t <= 5d-30) then
        tmp = (2.0d0 * (x / z)) / y
    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 tmp;
	if (t <= -1.4e-17) {
		tmp = (x * (-2.0 / z)) / t;
	} else if (t <= 5e-30) {
		tmp = (2.0 * (x / z)) / y;
	} else {
		tmp = (2.0 / z) * (-x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.4e-17:
		tmp = (x * (-2.0 / z)) / t
	elif t <= 5e-30:
		tmp = (2.0 * (x / z)) / y
	else:
		tmp = (2.0 / z) * (-x / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.4e-17)
		tmp = Float64(Float64(x * Float64(-2.0 / z)) / t);
	elseif (t <= 5e-30)
		tmp = Float64(Float64(2.0 * Float64(x / z)) / y);
	else
		tmp = Float64(Float64(2.0 / z) * Float64(Float64(-x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.4e-17)
		tmp = (x * (-2.0 / z)) / t;
	elseif (t <= 5e-30)
		tmp = (2.0 * (x / z)) / y;
	else
		tmp = (2.0 / z) * (-x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.4e-17], N[(N[(x * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 5e-30], N[(N[(2.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[((-x) / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3999999999999999e-17

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-*r/ 88.9%

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

      3. distribute-rgt-out-- 89.7%

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

      4. associate-/r* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around 0 75.7%

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

      1. associate-*r/ 75.7%

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

      2. *-commutative 75.7%

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

      3. *-commutative 75.7%

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

      4. associate-/r* 77.0%

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

      5. metadata-eval 77.0%

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

      6. distribute-rgt-neg-in 77.0%

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

      7. distribute-neg-frac 77.0%

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

      8. associate-*r/ 77.0%

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

      9. distribute-rgt-neg-in 77.0%

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

      10. distribute-neg-frac 77.0%

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

      11. metadata-eval 77.0%

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

   6. Simplified 77.0%

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

   if -1.3999999999999999e-17 < t < 4.99999999999999972e-30

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

      2. distribute-rgt-out-- 92.2%

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

      3. times-frac 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around inf 79.8%

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

      1. frac-times 80.7%

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

      2. *-commutative 80.7%

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

      3. times-frac 83.1%

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

      4. associate-*r/ 83.1%

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

   6. Applied egg-rr 83.1%

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

   if 4.99999999999999972e-30 < t

   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. distribute-rgt-out-- 95.6%

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

      3. times-frac 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in y around 0 76.3%

      \[\leadsto \frac{2}{z} \cdot \color{blue}{\left(-1 \cdot \frac{x}{t}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 76.3%

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

      2. neg-mul-1 76.3%

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

   6. Simplified 76.3%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{x \cdot \frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-30}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{-x}{t}\\ \end{array} \]

Alternative 3: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.45e-17)
   (* x (/ -2.0 (* z t)))
   (if (<= t 1.6e-26) (* x (/ 2.0 (* z y))) (* -2.0 (/ (/ x t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.45e-17) {
		tmp = x * (-2.0 / (z * t));
	} else if (t <= 1.6e-26) {
		tmp = x * (2.0 / (z * y));
	} else {
		tmp = -2.0 * ((x / 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 (t <= (-1.45d-17)) then
        tmp = x * ((-2.0d0) / (z * t))
    else if (t <= 1.6d-26) then
        tmp = x * (2.0d0 / (z * y))
    else
        tmp = (-2.0d0) * ((x / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.45e-17) {
		tmp = x * (-2.0 / (z * t));
	} else if (t <= 1.6e-26) {
		tmp = x * (2.0 / (z * y));
	} else {
		tmp = -2.0 * ((x / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.45e-17:
		tmp = x * (-2.0 / (z * t))
	elif t <= 1.6e-26:
		tmp = x * (2.0 / (z * y))
	else:
		tmp = -2.0 * ((x / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.45e-17)
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	elseif (t <= 1.6e-26)
		tmp = Float64(x * Float64(2.0 / Float64(z * y)));
	else
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.45e-17)
		tmp = x * (-2.0 / (z * t));
	elseif (t <= 1.6e-26)
		tmp = x * (2.0 / (z * y));
	else
		tmp = -2.0 * ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.45e-17], N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e-26], N[(x * N[(2.0 / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4500000000000001e-17

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-*r/ 88.9%

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

      3. distribute-rgt-out-- 89.7%

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

      4. associate-/r* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 89.7%

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

      1. associate-*r/ 89.7%

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

      2. associate-*l/ 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-/r* 90.8%

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

   6. Simplified 90.8%

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

   7. Taylor expanded in y around 0 75.7%

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

   if -1.4500000000000001e-17 < t < 1.6000000000000001e-26

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

      2. associate-*r/ 92.1%

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

      3. distribute-rgt-out-- 92.2%

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

      4. associate-/r* 95.9%

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

   3. Simplified 95.9%

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

      1. associate-*r/ 95.9%

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

      2. *-commutative 95.9%

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

      3. associate-*r/ 95.9%

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

      4. clear-num 95.9%

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

      5. associate-*l/ 95.9%

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

      6. *-un-lft-identity 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in y around inf 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-*l/ 80.7%

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

      3. associate-*r/ 80.6%

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

      4. *-commutative 80.6%

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

   8. Simplified 80.6%

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

   if 1.6000000000000001e-26 < t

   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/ 92.6%

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

      3. distribute-rgt-out-- 95.5%

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

      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. Step-by-step derivation

      1. associate-*r/ 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*r/ 91.4%

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

      4. clear-num 91.4%

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

      5. associate-*l/ 91.5%

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

      6. *-un-lft-identity 91.5%

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

   5. Applied egg-rr 91.5%

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

   6. Taylor expanded in y around 0 76.2%

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

      1. associate-/r* 76.3%

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

   8. Simplified 76.3%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \]

Alternative 4: 74.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-27}:\\ \;\;\;\;\frac{2}{y \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.5e-17)
   (* x (/ -2.0 (* z t)))
   (if (<= t 8e-27) (/ 2.0 (* y (/ z x))) (* -2.0 (/ (/ x t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e-17) {
		tmp = x * (-2.0 / (z * t));
	} else if (t <= 8e-27) {
		tmp = 2.0 / (y * (z / x));
	} else {
		tmp = -2.0 * ((x / 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 (t <= (-1.5d-17)) then
        tmp = x * ((-2.0d0) / (z * t))
    else if (t <= 8d-27) then
        tmp = 2.0d0 / (y * (z / x))
    else
        tmp = (-2.0d0) * ((x / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e-17) {
		tmp = x * (-2.0 / (z * t));
	} else if (t <= 8e-27) {
		tmp = 2.0 / (y * (z / x));
	} else {
		tmp = -2.0 * ((x / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.5e-17:
		tmp = x * (-2.0 / (z * t))
	elif t <= 8e-27:
		tmp = 2.0 / (y * (z / x))
	else:
		tmp = -2.0 * ((x / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.5e-17)
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	elseif (t <= 8e-27)
		tmp = Float64(2.0 / Float64(y * Float64(z / x)));
	else
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.5e-17)
		tmp = x * (-2.0 / (z * t));
	elseif (t <= 8e-27)
		tmp = 2.0 / (y * (z / x));
	else
		tmp = -2.0 * ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.5e-17], N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e-27], N[(2.0 / N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.50000000000000003e-17

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-*r/ 88.9%

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

      3. distribute-rgt-out-- 89.7%

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

      4. associate-/r* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 89.7%

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

      1. associate-*r/ 89.7%

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

      2. associate-*l/ 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-/r* 90.8%

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

   6. Simplified 90.8%

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

   7. Taylor expanded in y around 0 75.7%

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

   if -1.50000000000000003e-17 < t < 8.0000000000000003e-27

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

      2. associate-*r/ 92.1%

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

      3. distribute-rgt-out-- 92.2%

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

      4. associate-/r* 95.9%

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

   3. Simplified 95.9%

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

      1. associate-*r/ 95.9%

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

      2. *-commutative 95.9%

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

      3. associate-*r/ 95.9%

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

      4. clear-num 95.9%

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

      5. frac-times 96.0%

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

      6. metadata-eval 96.0%

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

   5. Applied egg-rr 96.0%

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

   6. Taylor expanded in y around inf 80.5%

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

      1. associate-*r/ 83.1%

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

   8. Simplified 83.1%

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

   if 8.0000000000000003e-27 < t

   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/ 92.6%

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

      3. distribute-rgt-out-- 95.5%

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

      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. Step-by-step derivation

      1. associate-*r/ 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*r/ 91.4%

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

      4. clear-num 91.4%

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

      5. associate-*l/ 91.5%

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

      6. *-un-lft-identity 91.5%

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

   5. Applied egg-rr 91.5%

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

   6. Taylor expanded in y around 0 76.2%

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

      1. associate-/r* 76.3%

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

   8. Simplified 76.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-27}:\\ \;\;\;\;\frac{2}{y \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \]

Alternative 5: 74.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{x \cdot \frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-27}:\\ \;\;\;\;\frac{2}{y \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.5e-17)
   (/ (* x (/ -2.0 z)) t)
   (if (<= t 2.75e-27) (/ 2.0 (* y (/ z x))) (* -2.0 (/ (/ x t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e-17) {
		tmp = (x * (-2.0 / z)) / t;
	} else if (t <= 2.75e-27) {
		tmp = 2.0 / (y * (z / x));
	} else {
		tmp = -2.0 * ((x / 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 (t <= (-1.5d-17)) then
        tmp = (x * ((-2.0d0) / z)) / t
    else if (t <= 2.75d-27) then
        tmp = 2.0d0 / (y * (z / x))
    else
        tmp = (-2.0d0) * ((x / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e-17) {
		tmp = (x * (-2.0 / z)) / t;
	} else if (t <= 2.75e-27) {
		tmp = 2.0 / (y * (z / x));
	} else {
		tmp = -2.0 * ((x / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.5e-17:
		tmp = (x * (-2.0 / z)) / t
	elif t <= 2.75e-27:
		tmp = 2.0 / (y * (z / x))
	else:
		tmp = -2.0 * ((x / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.5e-17)
		tmp = Float64(Float64(x * Float64(-2.0 / z)) / t);
	elseif (t <= 2.75e-27)
		tmp = Float64(2.0 / Float64(y * Float64(z / x)));
	else
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.5e-17)
		tmp = (x * (-2.0 / z)) / t;
	elseif (t <= 2.75e-27)
		tmp = 2.0 / (y * (z / x));
	else
		tmp = -2.0 * ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.5e-17], N[(N[(x * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 2.75e-27], N[(2.0 / N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.50000000000000003e-17

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-*r/ 88.9%

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

      3. distribute-rgt-out-- 89.7%

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

      4. associate-/r* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around 0 75.7%

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

      1. associate-*r/ 75.7%

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

      2. *-commutative 75.7%

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

      3. *-commutative 75.7%

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

      4. associate-/r* 77.0%

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

      5. metadata-eval 77.0%

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

      6. distribute-rgt-neg-in 77.0%

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

      7. distribute-neg-frac 77.0%

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

      8. associate-*r/ 77.0%

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

      9. distribute-rgt-neg-in 77.0%

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

      10. distribute-neg-frac 77.0%

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

      11. metadata-eval 77.0%

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

   6. Simplified 77.0%

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

   if -1.50000000000000003e-17 < t < 2.7500000000000001e-27

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

      2. associate-*r/ 92.1%

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

      3. distribute-rgt-out-- 92.2%

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

      4. associate-/r* 95.9%

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

   3. Simplified 95.9%

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

      1. associate-*r/ 95.9%

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

      2. *-commutative 95.9%

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

      3. associate-*r/ 95.9%

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

      4. clear-num 95.9%

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

      5. frac-times 96.0%

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

      6. metadata-eval 96.0%

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

   5. Applied egg-rr 96.0%

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

   6. Taylor expanded in y around inf 80.5%

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

      1. associate-*r/ 83.1%

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

   8. Simplified 83.1%

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

   if 2.7500000000000001e-27 < t

   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/ 92.6%

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

      3. distribute-rgt-out-- 95.5%

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

      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. Step-by-step derivation

      1. associate-*r/ 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*r/ 91.4%

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

      4. clear-num 91.4%

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

      5. associate-*l/ 91.5%

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

      6. *-un-lft-identity 91.5%

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

   5. Applied egg-rr 91.5%

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

   6. Taylor expanded in y around 0 76.2%

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

      1. associate-/r* 76.3%

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

   8. Simplified 76.3%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{x \cdot \frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-27}:\\ \;\;\;\;\frac{2}{y \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \]

Alternative 6: 74.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{x \cdot \frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-26}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.5e-17)
   (/ (* x (/ -2.0 z)) t)
   (if (<= t 2.25e-26) (/ (* 2.0 (/ x z)) y) (* -2.0 (/ (/ x t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e-17) {
		tmp = (x * (-2.0 / z)) / t;
	} else if (t <= 2.25e-26) {
		tmp = (2.0 * (x / z)) / y;
	} else {
		tmp = -2.0 * ((x / 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 (t <= (-1.5d-17)) then
        tmp = (x * ((-2.0d0) / z)) / t
    else if (t <= 2.25d-26) then
        tmp = (2.0d0 * (x / z)) / y
    else
        tmp = (-2.0d0) * ((x / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e-17) {
		tmp = (x * (-2.0 / z)) / t;
	} else if (t <= 2.25e-26) {
		tmp = (2.0 * (x / z)) / y;
	} else {
		tmp = -2.0 * ((x / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.5e-17:
		tmp = (x * (-2.0 / z)) / t
	elif t <= 2.25e-26:
		tmp = (2.0 * (x / z)) / y
	else:
		tmp = -2.0 * ((x / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.5e-17)
		tmp = Float64(Float64(x * Float64(-2.0 / z)) / t);
	elseif (t <= 2.25e-26)
		tmp = Float64(Float64(2.0 * Float64(x / z)) / y);
	else
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.5e-17)
		tmp = (x * (-2.0 / z)) / t;
	elseif (t <= 2.25e-26)
		tmp = (2.0 * (x / z)) / y;
	else
		tmp = -2.0 * ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.5e-17], N[(N[(x * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 2.25e-26], N[(N[(2.0 * N[(x / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.50000000000000003e-17

   1. Initial program 88.9%

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

      1. *-commutative 88.9%

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

      2. associate-*r/ 88.9%

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

      3. distribute-rgt-out-- 89.7%

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

      4. associate-/r* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around 0 75.7%

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

      1. associate-*r/ 75.7%

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

      2. *-commutative 75.7%

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

      3. *-commutative 75.7%

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

      4. associate-/r* 77.0%

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

      5. metadata-eval 77.0%

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

      6. distribute-rgt-neg-in 77.0%

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

      7. distribute-neg-frac 77.0%

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

      8. associate-*r/ 77.0%

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

      9. distribute-rgt-neg-in 77.0%

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

      10. distribute-neg-frac 77.0%

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

      11. metadata-eval 77.0%

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

   6. Simplified 77.0%

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

   if -1.50000000000000003e-17 < t < 2.2499999999999999e-26

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

      2. distribute-rgt-out-- 92.2%

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

      3. times-frac 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around inf 79.8%

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

      1. frac-times 80.7%

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

      2. *-commutative 80.7%

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

      3. times-frac 83.1%

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

      4. associate-*r/ 83.1%

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

   6. Applied egg-rr 83.1%

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

   if 2.2499999999999999e-26 < t

   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/ 92.6%

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

      3. distribute-rgt-out-- 95.5%

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

      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. Step-by-step derivation

      1. associate-*r/ 91.5%

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

      2. *-commutative 91.5%

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

      3. associate-*r/ 91.4%

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

      4. clear-num 91.4%

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

      5. associate-*l/ 91.5%

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

      6. *-un-lft-identity 91.5%

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

   5. Applied egg-rr 91.5%

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

   6. Taylor expanded in y around 0 76.2%

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

      1. associate-/r* 76.3%

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

   8. Simplified 76.3%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{x \cdot \frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-26}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \]

Alternative 7: 92.1% 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 91.5%

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

   1. *-commutative 91.5%

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

   2. associate-*r/ 91.5%

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

   3. distribute-rgt-out-- 92.5%

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

   4. associate-/r* 93.8%

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

3. Simplified 93.8%

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

4. Final simplification 93.8%

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

Alternative 8: 52.4% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.5%

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

   1. *-commutative 91.5%

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

   2. associate-*r/ 91.5%

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

   3. distribute-rgt-out-- 92.5%

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

   4. associate-/r* 93.8%

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

3. Simplified 93.8%

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

   1. associate-*r/ 93.9%

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

   2. *-commutative 93.9%

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

   3. associate-*r/ 93.8%

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

   4. clear-num 93.8%

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

   5. associate-*l/ 93.8%

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

   6. *-un-lft-identity 93.8%

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

5. Applied egg-rr 93.8%

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

6. Taylor expanded in y around 0 51.8%

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

   1. associate-/r* 52.6%

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

8. Simplified 52.6%

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

9. Final simplification 52.6%

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

Developer target: 97.1% 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 2023310 
(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))))