Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.3% → 96.0%

Time: 7.8s

Alternatives: 9

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: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 2}{y \cdot z - z \cdot t}\\ \mathbf{if}\;t_1 \leq -100000 \lor \neg \left(t_1 \leq 2 \cdot 10^{-150}\right):\\ \;\;\;\;\frac{\frac{2}{z}}{\frac{y - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x 2.0) (- (* y z) (* z t)))))
   (if (or (<= t_1 -100000.0) (not (<= t_1 2e-150)))
     (/ (/ 2.0 z) (/ (- y t) x))
     (* 2.0 (/ (/ x z) (- y t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * 2.0) / ((y * z) - (z * t));
	double tmp;
	if ((t_1 <= -100000.0) || !(t_1 <= 2e-150)) {
		tmp = (2.0 / z) / ((y - t) / x);
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) / ((y * z) - (z * t))
    if ((t_1 <= (-100000.0d0)) .or. (.not. (t_1 <= 2d-150))) then
        tmp = (2.0d0 / z) / ((y - t) / x)
    else
        tmp = 2.0d0 * ((x / z) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * 2.0) / ((y * z) - (z * t));
	double tmp;
	if ((t_1 <= -100000.0) || !(t_1 <= 2e-150)) {
		tmp = (2.0 / z) / ((y - t) / x);
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * 2.0) / ((y * z) - (z * t))
	tmp = 0
	if (t_1 <= -100000.0) or not (t_1 <= 2e-150):
		tmp = (2.0 / z) / ((y - t) / x)
	else:
		tmp = 2.0 * ((x / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(z * t)))
	tmp = 0.0
	if ((t_1 <= -100000.0) || !(t_1 <= 2e-150))
		tmp = Float64(Float64(2.0 / z) / Float64(Float64(y - t) / x));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * 2.0) / ((y * z) - (z * t));
	tmp = 0.0;
	if ((t_1 <= -100000.0) || ~((t_1 <= 2e-150)))
		tmp = (2.0 / z) / ((y - t) / x);
	else
		tmp = 2.0 * ((x / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -100000.0], N[Not[LessEqual[t$95$1, 2e-150]], $MachinePrecision]], N[(N[(2.0 / z), $MachinePrecision] / N[(N[(y - t), $MachinePrecision] / x), $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 (*.f64 x 2) (-.f64 (*.f64 y z) (*.f64 t z))) < -1e5 or 2.00000000000000001e-150 < (/.f64 (*.f64 x 2) (-.f64 (*.f64 y z) (*.f64 t z)))

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

      2. associate-*r/ 88.3%

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

      3. distribute-rgt-out-- 92.9%

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

      4. associate-/r* 86.6%

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

   3. Simplified 86.6%

      \[\leadsto \color{blue}{2 \cdot \frac{\frac{x}{z}}{y - t}} \]
   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. frac-times 96.7%

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

      4. clear-num 96.7%

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

      5. un-div-inv 97.1%

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

   5. Applied egg-rr 97.1%

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

   if -1e5 < (/.f64 (*.f64 x 2) (-.f64 (*.f64 y z) (*.f64 t z))) < 2.00000000000000001e-150

   1. Initial program 87.1%

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

      1. *-commutative 87.1%

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

      2. associate-*r/ 87.1%

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

      3. distribute-rgt-out-- 87.1%

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

      4. associate-/r* 98.1%

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

   3. Simplified 98.1%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - z \cdot t} \leq -100000 \lor \neg \left(\frac{x \cdot 2}{y \cdot z - z \cdot t} \leq 2 \cdot 10^{-150}\right):\\ \;\;\;\;\frac{\frac{2}{z}}{\frac{y - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 2: 96.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -4 \cdot 10^{+51} \lor \neg \left(x \cdot 2 \leq 10^{-58}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* x 2.0) -4e+51) (not (<= (* x 2.0) 1e-58)))
   (* (/ 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) <= -4e+51) || !((x * 2.0) <= 1e-58)) {
		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) <= (-4d+51)) .or. (.not. ((x * 2.0d0) <= 1d-58))) 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) <= -4e+51) || !((x * 2.0) <= 1e-58)) {
		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) <= -4e+51) or not ((x * 2.0) <= 1e-58):
		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) <= -4e+51) || !(Float64(x * 2.0) <= 1e-58))
		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) <= -4e+51) || ~(((x * 2.0) <= 1e-58)))
		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], -4e+51], N[Not[LessEqual[N[(x * 2.0), $MachinePrecision], 1e-58]], $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) < -4e51 or 1e-58 < (*.f64 x 2)

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

      2. distribute-rgt-out-- 86.5%

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

      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 -4e51 < (*.f64 x 2) < 1e-58

   1. Initial program 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*r/ 91.8%

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

      3. distribute-rgt-out-- 94.4%

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

      4. associate-/r* 97.6%

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

   3. Simplified 97.6%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -4 \cdot 10^{+51} \lor \neg \left(x \cdot 2 \leq 10^{-58}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 3: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{-101} \lor \neg \left(t \leq 2.8 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{-2}{z} \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.32e-101) (not (<= t 2.8e-29)))
   (* (/ -2.0 z) (/ x t))
   (* (/ 2.0 z) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.32e-101) || !(t <= 2.8e-29)) {
		tmp = (-2.0 / z) * (x / 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 <= (-1.32d-101)) .or. (.not. (t <= 2.8d-29))) then
        tmp = ((-2.0d0) / z) * (x / 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 <= -1.32e-101) || !(t <= 2.8e-29)) {
		tmp = (-2.0 / z) * (x / t);
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.32e-101) or not (t <= 2.8e-29):
		tmp = (-2.0 / z) * (x / t)
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.32e-101) || !(t <= 2.8e-29))
		tmp = Float64(Float64(-2.0 / z) * Float64(x / 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 <= -1.32e-101) || ~((t <= 2.8e-29)))
		tmp = (-2.0 / z) * (x / t);
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.32e-101], N[Not[LessEqual[t, 2.8e-29]], $MachinePrecision]], N[(N[(-2.0 / z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.32e-101 or 2.8000000000000002e-29 < t

   1. Initial program 88.7%

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

      1. *-commutative 88.7%

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

      2. associate-*r/ 88.7%

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

      3. distribute-rgt-out-- 90.8%

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

      4. associate-/r* 90.4%

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

   3. Simplified 90.4%

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

      1. associate-/r* 90.8%

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

      2. associate-*r/ 90.8%

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

      3. frac-times 93.0%

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

      4. clear-num 93.0%

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

      5. un-div-inv 93.1%

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

   5. Applied egg-rr 93.1%

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

   6. Taylor expanded in y around 0 74.7%

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

      1. associate-*r/ 74.7%

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

      2. *-commutative 74.7%

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

      3. times-frac 75.7%

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

   8. Simplified 75.7%

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

   if -1.32e-101 < t < 2.8000000000000002e-29

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-*r/ 86.3%

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

      3. distribute-rgt-out-- 89.5%

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

      4. associate-/r* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around inf 74.7%

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

      1. associate-*r/ 74.7%

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

      2. *-commutative 74.7%

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

      3. times-frac 80.0%

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

   6. Simplified 80.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{-101} \lor \neg \left(t \leq 2.8 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{-2}{z} \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 4: 72.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{-100} \lor \neg \left(t \leq 5.6 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.16e-100) (not (<= t 5.6e-31)))
   (/ -2.0 (* z (/ t x)))
   (* (/ 2.0 z) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.16e-100) || !(t <= 5.6e-31)) {
		tmp = -2.0 / (z * (t / x));
	} 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 <= (-1.16d-100)) .or. (.not. (t <= 5.6d-31))) then
        tmp = (-2.0d0) / (z * (t / x))
    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 <= -1.16e-100) || !(t <= 5.6e-31)) {
		tmp = -2.0 / (z * (t / x));
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.16e-100) or not (t <= 5.6e-31):
		tmp = -2.0 / (z * (t / x))
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.16e-100) || !(t <= 5.6e-31))
		tmp = Float64(-2.0 / Float64(z * Float64(t / x)));
	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 <= -1.16e-100) || ~((t <= 5.6e-31)))
		tmp = -2.0 / (z * (t / x));
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.16e-100], N[Not[LessEqual[t, 5.6e-31]], $MachinePrecision]], N[(-2.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.16e-100 or 5.5999999999999998e-31 < t

   1. Initial program 88.7%

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

      1. *-commutative 88.7%

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

      2. associate-*r/ 88.7%

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

      3. distribute-rgt-out-- 90.8%

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

      4. associate-/r* 90.4%

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

   3. Simplified 90.4%

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

      1. associate-/r* 90.8%

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

      2. associate-*r/ 90.8%

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

      3. frac-times 93.0%

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

      4. clear-num 93.0%

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

      5. un-div-inv 93.1%

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

   5. Applied egg-rr 93.1%

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

   6. Taylor expanded in y around 0 74.7%

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

      1. associate-*r/ 74.7%

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

      2. *-commutative 74.7%

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

      3. times-frac 75.7%

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

   8. Simplified 75.7%

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

      1. *-commutative 75.7%

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

      2. clear-num 75.7%

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

      3. frac-times 75.8%

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

      4. metadata-eval 75.8%

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

   10. Applied egg-rr 75.8%

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

   if -1.16e-100 < t < 5.5999999999999998e-31

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-*r/ 86.3%

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

      3. distribute-rgt-out-- 89.5%

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

      4. associate-/r* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around inf 74.7%

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

      1. associate-*r/ 74.7%

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

      2. *-commutative 74.7%

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

      3. times-frac 80.0%

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

   6. Simplified 80.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{-100} \lor \neg \left(t \leq 5.6 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 72.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-101} \lor \neg \left(t \leq 7 \cdot 10^{-111}\right):\\ \;\;\;\;\frac{\frac{-2}{t}}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.8e-101) (not (<= t 7e-111)))
   (/ (/ -2.0 t) (/ z x))
   (* (/ 2.0 z) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.8e-101) || !(t <= 7e-111)) {
		tmp = (-2.0 / t) / (z / x);
	} 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 <= (-8.8d-101)) .or. (.not. (t <= 7d-111))) then
        tmp = ((-2.0d0) / t) / (z / x)
    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 <= -8.8e-101) || !(t <= 7e-111)) {
		tmp = (-2.0 / t) / (z / x);
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.8e-101) or not (t <= 7e-111):
		tmp = (-2.0 / t) / (z / x)
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.8e-101) || !(t <= 7e-111))
		tmp = Float64(Float64(-2.0 / t) / Float64(z / x));
	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 <= -8.8e-101) || ~((t <= 7e-111)))
		tmp = (-2.0 / t) / (z / x);
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.8e-101], N[Not[LessEqual[t, 7e-111]], $MachinePrecision]], N[(N[(-2.0 / t), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.7999999999999996e-101 or 7.0000000000000001e-111 < t

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

      2. associate-*r/ 89.2%

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

      3. distribute-rgt-out-- 91.1%

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

      4. associate-/r* 90.9%

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

   3. Simplified 90.9%

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

      1. associate-*r/ 90.9%

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

      2. *-commutative 90.9%

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

      3. associate-*r/ 90.8%

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

      4. clear-num 90.7%

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

      5. associate-*l/ 91.6%

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

      6. *-un-lft-identity 91.6%

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

   5. Applied egg-rr 91.6%

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

   6. Taylor expanded in y around 0 76.8%

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

   if -8.7999999999999996e-101 < t < 7.0000000000000001e-111

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

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

      2. associate-*r/ 84.8%

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

      3. distribute-rgt-out-- 88.5%

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

      4. associate-/r* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around inf 77.7%

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

      1. associate-*r/ 77.8%

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

      2. *-commutative 77.8%

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

      3. times-frac 83.9%

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

   6. Simplified 83.9%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-101} \lor \neg \left(t \leq 7 \cdot 10^{-111}\right):\\ \;\;\;\;\frac{\frac{-2}{t}}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 6: 72.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-100}:\\ \;\;\;\;\frac{-2}{\frac{t}{\frac{x}{z}}}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.2e-100)
   (/ -2.0 (/ t (/ x z)))
   (if (<= t 4.6e-27) (* (/ 2.0 z) (/ x y)) (/ -2.0 (* z (/ t x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.2e-100) {
		tmp = -2.0 / (t / (x / z));
	} else if (t <= 4.6e-27) {
		tmp = (2.0 / z) * (x / y);
	} else {
		tmp = -2.0 / (z * (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 (t <= (-1.2d-100)) then
        tmp = (-2.0d0) / (t / (x / z))
    else if (t <= 4.6d-27) then
        tmp = (2.0d0 / z) * (x / y)
    else
        tmp = (-2.0d0) / (z * (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.2e-100) {
		tmp = -2.0 / (t / (x / z));
	} else if (t <= 4.6e-27) {
		tmp = (2.0 / z) * (x / y);
	} else {
		tmp = -2.0 / (z * (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.2e-100:
		tmp = -2.0 / (t / (x / z))
	elif t <= 4.6e-27:
		tmp = (2.0 / z) * (x / y)
	else:
		tmp = -2.0 / (z * (t / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.2e-100)
		tmp = Float64(-2.0 / Float64(t / Float64(x / z)));
	elseif (t <= 4.6e-27)
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	else
		tmp = Float64(-2.0 / Float64(z * Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.2e-100)
		tmp = -2.0 / (t / (x / z));
	elseif (t <= 4.6e-27)
		tmp = (2.0 / z) * (x / y);
	else
		tmp = -2.0 / (z * (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.2e-100], N[(-2.0 / N[(t / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-27], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(-2.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2000000000000001e-100

   1. Initial program 87.1%

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

      1. *-commutative 87.1%

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

      2. associate-*r/ 87.1%

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

      3. distribute-rgt-out-- 89.6%

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

      4. associate-/r* 88.3%

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

   3. Simplified 88.3%

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

      1. associate-/r* 89.6%

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

      2. associate-*r/ 89.6%

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

      3. frac-times 90.8%

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

      4. clear-num 90.8%

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

      5. un-div-inv 90.9%

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

   5. Applied egg-rr 90.9%

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

   6. Taylor expanded in y around 0 71.7%

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

      1. associate-*r/ 71.7%

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

      2. *-commutative 71.7%

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

      3. times-frac 71.7%

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

   8. Simplified 71.7%

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

      1. frac-times 71.7%

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

      2. *-commutative 71.7%

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

      3. associate-/l* 70.9%

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

      4. associate-/l* 74.0%

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

   10. Applied egg-rr 74.0%

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

   if -1.2000000000000001e-100 < t < 4.5999999999999999e-27

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-*r/ 86.3%

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

      3. distribute-rgt-out-- 89.5%

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

      4. associate-/r* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around inf 74.7%

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

      1. associate-*r/ 74.7%

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

      2. *-commutative 74.7%

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

      3. times-frac 80.0%

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

   6. Simplified 80.0%

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

   if 4.5999999999999999e-27 < t

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-*r/ 90.6%

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

      3. distribute-rgt-out-- 92.2%

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

      4. associate-/r* 93.0%

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

   3. Simplified 93.0%

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

      1. associate-/r* 92.2%

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

      2. associate-*r/ 92.2%

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

      3. frac-times 95.6%

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

      4. clear-num 95.6%

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

      5. un-div-inv 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in y around 0 78.2%

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

      1. associate-*r/ 78.2%

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

      2. *-commutative 78.2%

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

      3. times-frac 80.5%

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

   8. Simplified 80.5%

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

      1. *-commutative 80.5%

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

      2. clear-num 80.4%

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

      3. frac-times 80.5%

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

      4. metadata-eval 80.5%

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

   10. Applied egg-rr 80.5%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-100}:\\ \;\;\;\;\frac{-2}{\frac{t}{\frac{x}{z}}}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x}}\\ \end{array} \]

Alternative 7: 72.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.9 \cdot 10^{-101}:\\ \;\;\;\;\frac{x \cdot \frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9.9e-101)
   (/ (* x (/ -2.0 z)) t)
   (if (<= t 2.2e-24) (* (/ 2.0 z) (/ x y)) (/ -2.0 (* z (/ t x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.9e-101) {
		tmp = (x * (-2.0 / z)) / t;
	} else if (t <= 2.2e-24) {
		tmp = (2.0 / z) * (x / y);
	} else {
		tmp = -2.0 / (z * (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 (t <= (-9.9d-101)) then
        tmp = (x * ((-2.0d0) / z)) / t
    else if (t <= 2.2d-24) then
        tmp = (2.0d0 / z) * (x / y)
    else
        tmp = (-2.0d0) / (z * (t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.9e-101) {
		tmp = (x * (-2.0 / z)) / t;
	} else if (t <= 2.2e-24) {
		tmp = (2.0 / z) * (x / y);
	} else {
		tmp = -2.0 / (z * (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -9.9e-101:
		tmp = (x * (-2.0 / z)) / t
	elif t <= 2.2e-24:
		tmp = (2.0 / z) * (x / y)
	else:
		tmp = -2.0 / (z * (t / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9.9e-101)
		tmp = Float64(Float64(x * Float64(-2.0 / z)) / t);
	elseif (t <= 2.2e-24)
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	else
		tmp = Float64(-2.0 / Float64(z * Float64(t / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -9.9e-101)
		tmp = (x * (-2.0 / z)) / t;
	elseif (t <= 2.2e-24)
		tmp = (2.0 / z) * (x / y);
	else
		tmp = -2.0 / (z * (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -9.9e-101], N[(N[(x * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 2.2e-24], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(-2.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.90000000000000015e-101

   1. Initial program 87.1%

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

      1. *-commutative 87.1%

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

      2. distribute-rgt-out-- 89.6%

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

      3. times-frac 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in y around 0 71.7%

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

      1. associate-*r/ 71.7%

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

      2. neg-mul-1 71.7%

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

   6. Simplified 71.7%

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

      1. associate-*r/ 74.6%

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

      2. distribute-rgt-neg-in 74.6%

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

      3. *-commutative 74.6%

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

      4. distribute-rgt-neg-in 74.6%

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

      5. distribute-neg-frac 74.6%

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

      6. metadata-eval 74.6%

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

   8. Applied egg-rr 74.6%

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

   if -9.90000000000000015e-101 < t < 2.20000000000000002e-24

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-*r/ 86.3%

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

      3. distribute-rgt-out-- 89.5%

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

      4. associate-/r* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around inf 74.7%

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

      1. associate-*r/ 74.7%

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

      2. *-commutative 74.7%

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

      3. times-frac 80.0%

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

   6. Simplified 80.0%

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

   if 2.20000000000000002e-24 < t

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-*r/ 90.6%

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

      3. distribute-rgt-out-- 92.2%

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

      4. associate-/r* 93.0%

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

   3. Simplified 93.0%

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

      1. associate-/r* 92.2%

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

      2. associate-*r/ 92.2%

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

      3. frac-times 95.6%

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

      4. clear-num 95.6%

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

      5. un-div-inv 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in y around 0 78.2%

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

      1. associate-*r/ 78.2%

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

      2. *-commutative 78.2%

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

      3. times-frac 80.5%

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

   8. Simplified 80.5%

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

      1. *-commutative 80.5%

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

      2. clear-num 80.4%

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

      3. frac-times 80.5%

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

      4. metadata-eval 80.5%

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

   10. Applied egg-rr 80.5%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.9 \cdot 10^{-101}:\\ \;\;\;\;\frac{x \cdot \frac{-2}{z}}{t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x}}\\ \end{array} \]

Alternative 8: 91.9% 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 87.8%

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

   1. *-commutative 87.8%

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

   2. associate-*r/ 87.7%

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

   3. distribute-rgt-out-- 90.2%

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

   4. associate-/r* 91.9%

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

3. Simplified 91.9%

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

4. Final simplification 91.9%

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

Alternative 9: 52.5% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.8%

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

   1. *-commutative 87.8%

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

   2. associate-*r/ 87.7%

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

   3. distribute-rgt-out-- 90.2%

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

   4. associate-/r* 91.9%

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

3. Simplified 91.9%

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

   1. associate-/r* 90.2%

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

   2. associate-*r/ 90.3%

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

   3. frac-times 93.4%

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

   4. clear-num 93.1%

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

   5. un-div-inv 93.3%

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

5. Applied egg-rr 93.3%

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

6. Taylor expanded in y around 0 56.0%

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

   1. associate-*r/ 56.0%

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

   2. *-commutative 56.0%

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

   3. times-frac 56.2%

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

8. Simplified 56.2%

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

9. Final simplification 56.2%

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

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 2023268 
(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))))