Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 90.0% → 98.1%

Time: 10.1s

Alternatives: 11

Speedup: 1.0×

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: 98.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+157}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) (* z t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+157)))
     (* 2.0 (/ (/ x z) (- y t)))
     (/ (* 2.0 x) (* z (- y t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+157)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = (2.0 * x) / (z * (y - t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+157)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = (2.0 * x) / (z * (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - (z * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+157):
		tmp = 2.0 * ((x / z) / (y - t))
	else:
		tmp = (2.0 * x) / (z * (y - t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+157))
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(Float64(2.0 * x) / Float64(z * Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+157)))
		tmp = 2.0 * ((x / z) / (y - t));
	else
		tmp = (2.0 * x) / (z * (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+157]], $MachinePrecision]], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 y z) (*.f64 t z)) < -inf.0 or 4.99999999999999976e157 < (-.f64 (*.f64 y z) (*.f64 t z))

   1. Initial program 80.4%

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

      1. *-commutative 80.4%

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

      2. associate-*r/ 80.4%

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

      3. distribute-rgt-out-- 81.7%

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

      4. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (-.f64 (*.f64 y z) (*.f64 t z)) < 4.99999999999999976e157

   1. Initial program 98.0%

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

      1. distribute-rgt-out-- 99.2%

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

   3. Simplified 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - z \cdot t \leq -\infty \lor \neg \left(y \cdot z - z \cdot t \leq 5 \cdot 10^{+157}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 2: 72.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z} \cdot \frac{x}{y}\\ t_2 := \frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -180000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2900000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ 2.0 z) (/ x y))) (t_2 (* (/ x t) (/ -2.0 z))))
   (if (<= t -1.7e+31)
     t_2
     (if (<= t -180000.0)
       t_1
       (if (<= t -5e-62)
         t_2
         (if (<= t 2900000.0) t_1 (* x (/ -2.0 (* z t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double t_2 = (x / t) * (-2.0 / z);
	double tmp;
	if (t <= -1.7e+31) {
		tmp = t_2;
	} else if (t <= -180000.0) {
		tmp = t_1;
	} else if (t <= -5e-62) {
		tmp = t_2;
	} else if (t <= 2900000.0) {
		tmp = t_1;
	} else {
		tmp = x * (-2.0 / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (2.0d0 / z) * (x / y)
    t_2 = (x / t) * ((-2.0d0) / z)
    if (t <= (-1.7d+31)) then
        tmp = t_2
    else if (t <= (-180000.0d0)) then
        tmp = t_1
    else if (t <= (-5d-62)) then
        tmp = t_2
    else if (t <= 2900000.0d0) then
        tmp = t_1
    else
        tmp = x * ((-2.0d0) / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double t_2 = (x / t) * (-2.0 / z);
	double tmp;
	if (t <= -1.7e+31) {
		tmp = t_2;
	} else if (t <= -180000.0) {
		tmp = t_1;
	} else if (t <= -5e-62) {
		tmp = t_2;
	} else if (t <= 2900000.0) {
		tmp = t_1;
	} else {
		tmp = x * (-2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / z) * (x / y)
	t_2 = (x / t) * (-2.0 / z)
	tmp = 0
	if t <= -1.7e+31:
		tmp = t_2
	elif t <= -180000.0:
		tmp = t_1
	elif t <= -5e-62:
		tmp = t_2
	elif t <= 2900000.0:
		tmp = t_1
	else:
		tmp = x * (-2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / z) * Float64(x / y))
	t_2 = Float64(Float64(x / t) * Float64(-2.0 / z))
	tmp = 0.0
	if (t <= -1.7e+31)
		tmp = t_2;
	elseif (t <= -180000.0)
		tmp = t_1;
	elseif (t <= -5e-62)
		tmp = t_2;
	elseif (t <= 2900000.0)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / z) * (x / y);
	t_2 = (x / t) * (-2.0 / z);
	tmp = 0.0;
	if (t <= -1.7e+31)
		tmp = t_2;
	elseif (t <= -180000.0)
		tmp = t_1;
	elseif (t <= -5e-62)
		tmp = t_2;
	elseif (t <= 2900000.0)
		tmp = t_1;
	else
		tmp = x * (-2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+31], t$95$2, If[LessEqual[t, -180000.0], t$95$1, If[LessEqual[t, -5e-62], t$95$2, If[LessEqual[t, 2900000.0], t$95$1, N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6999999999999999e31 or -1.8e5 < t < -5.0000000000000002e-62

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-*r/ 90.5%

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

      3. distribute-rgt-out-- 90.5%

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

      4. associate-/r* 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in y around 0 75.0%

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

      1. associate-*r/ 75.0%

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

      2. *-commutative 75.0%

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

      3. *-commutative 75.0%

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

   6. Simplified 75.0%

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

      1. *-commutative 75.0%

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

      2. times-frac 82.8%

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

   8. Applied egg-rr 82.8%

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

   if -1.6999999999999999e31 < t < -1.8e5 or -5.0000000000000002e-62 < t < 2.9e6

   1. Initial program 94.2%

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

      1. *-commutative 94.2%

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

      2. distribute-rgt-out-- 96.7%

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

      3. times-frac 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around inf 81.9%

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

   if 2.9e6 < t

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

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

      2. associate-*r/ 92.5%

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

      3. distribute-rgt-out-- 92.4%

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

      4. associate-/r* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in x around 0 92.4%

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

      1. associate-*r/ 92.5%

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

      2. *-commutative 92.5%

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

      3. times-frac 94.8%

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

      4. associate-*l/ 89.2%

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

      5. associate-*r/ 93.9%

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

   6. Simplified 93.9%

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

   7. Taylor expanded in y around 0 81.6%

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

      1. *-commutative 81.6%

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

   9. Simplified 81.6%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq -180000:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq 2900000:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \]

Alternative 3: 72.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{if}\;t \leq -1.62 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{x}{t}}{z} \cdot -2\\ \mathbf{elif}\;t \leq -90000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq 200:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ 2.0 z) (/ x y))))
   (if (<= t -1.62e+31)
     (* (/ (/ x t) z) -2.0)
     (if (<= t -90000.0)
       t_1
       (if (<= t -6.6e-63)
         (* (/ x t) (/ -2.0 z))
         (if (<= t 200.0) t_1 (* x (/ -2.0 (* z t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (t <= -1.62e+31) {
		tmp = ((x / t) / z) * -2.0;
	} else if (t <= -90000.0) {
		tmp = t_1;
	} else if (t <= -6.6e-63) {
		tmp = (x / t) * (-2.0 / z);
	} else if (t <= 200.0) {
		tmp = t_1;
	} else {
		tmp = x * (-2.0 / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 / z) * (x / y)
    if (t <= (-1.62d+31)) then
        tmp = ((x / t) / z) * (-2.0d0)
    else if (t <= (-90000.0d0)) then
        tmp = t_1
    else if (t <= (-6.6d-63)) then
        tmp = (x / t) * ((-2.0d0) / z)
    else if (t <= 200.0d0) then
        tmp = t_1
    else
        tmp = x * ((-2.0d0) / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (t <= -1.62e+31) {
		tmp = ((x / t) / z) * -2.0;
	} else if (t <= -90000.0) {
		tmp = t_1;
	} else if (t <= -6.6e-63) {
		tmp = (x / t) * (-2.0 / z);
	} else if (t <= 200.0) {
		tmp = t_1;
	} else {
		tmp = x * (-2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / z) * (x / y)
	tmp = 0
	if t <= -1.62e+31:
		tmp = ((x / t) / z) * -2.0
	elif t <= -90000.0:
		tmp = t_1
	elif t <= -6.6e-63:
		tmp = (x / t) * (-2.0 / z)
	elif t <= 200.0:
		tmp = t_1
	else:
		tmp = x * (-2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / z) * Float64(x / y))
	tmp = 0.0
	if (t <= -1.62e+31)
		tmp = Float64(Float64(Float64(x / t) / z) * -2.0);
	elseif (t <= -90000.0)
		tmp = t_1;
	elseif (t <= -6.6e-63)
		tmp = Float64(Float64(x / t) * Float64(-2.0 / z));
	elseif (t <= 200.0)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / z) * (x / y);
	tmp = 0.0;
	if (t <= -1.62e+31)
		tmp = ((x / t) / z) * -2.0;
	elseif (t <= -90000.0)
		tmp = t_1;
	elseif (t <= -6.6e-63)
		tmp = (x / t) * (-2.0 / z);
	elseif (t <= 200.0)
		tmp = t_1;
	else
		tmp = x * (-2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.62e+31], N[(N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[t, -90000.0], t$95$1, If[LessEqual[t, -6.6e-63], N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 200.0], t$95$1, N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.6199999999999999e31

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

      2. associate-*r/ 89.5%

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

      3. distribute-rgt-out-- 89.5%

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

      4. associate-/r* 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in y around 0 75.9%

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

      1. *-commutative 75.9%

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

      2. associate-/r* 86.1%

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

   6. Simplified 86.1%

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

   if -1.6199999999999999e31 < t < -9e4 or -6.59999999999999987e-63 < t < 200

   1. Initial program 94.2%

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

      1. *-commutative 94.2%

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

      2. distribute-rgt-out-- 96.7%

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

      3. times-frac 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around inf 81.9%

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

   if -9e4 < t < -6.59999999999999987e-63

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-*r/ 93.9%

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

      3. distribute-rgt-out-- 94.0%

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

      4. associate-/r* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around 0 71.5%

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

      1. associate-*r/ 71.5%

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

      2. *-commutative 71.5%

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

      3. *-commutative 71.5%

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

   6. Simplified 71.5%

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

      1. *-commutative 71.5%

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

      2. times-frac 71.6%

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

   8. Applied egg-rr 71.6%

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

   if 200 < t

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

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

      2. associate-*r/ 92.5%

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

      3. distribute-rgt-out-- 92.4%

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

      4. associate-/r* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in x around 0 92.4%

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

      1. associate-*r/ 92.5%

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

      2. *-commutative 92.5%

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

      3. times-frac 94.8%

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

      4. associate-*l/ 89.2%

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

      5. associate-*r/ 93.9%

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

   6. Simplified 93.9%

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

   7. Taylor expanded in y around 0 81.6%

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

      1. *-commutative 81.6%

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

   9. Simplified 81.6%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.62 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{x}{t}}{z} \cdot -2\\ \mathbf{elif}\;t \leq -90000:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq 200:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \]

Alternative 4: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{if}\;t \leq -1.86 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{x}{t}}{z} \cdot -2\\ \mathbf{elif}\;t \leq -180000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq 11000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ 2.0 z) (/ x y))))
   (if (<= t -1.86e+31)
     (* (/ (/ x t) z) -2.0)
     (if (<= t -180000.0)
       t_1
       (if (<= t -4.5e-62)
         (* (/ x t) (/ -2.0 z))
         (if (<= t 11000.0) t_1 (/ (* x -2.0) (* z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (t <= -1.86e+31) {
		tmp = ((x / t) / z) * -2.0;
	} else if (t <= -180000.0) {
		tmp = t_1;
	} else if (t <= -4.5e-62) {
		tmp = (x / t) * (-2.0 / z);
	} else if (t <= 11000.0) {
		tmp = t_1;
	} else {
		tmp = (x * -2.0) / (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 / z) * (x / y)
    if (t <= (-1.86d+31)) then
        tmp = ((x / t) / z) * (-2.0d0)
    else if (t <= (-180000.0d0)) then
        tmp = t_1
    else if (t <= (-4.5d-62)) then
        tmp = (x / t) * ((-2.0d0) / z)
    else if (t <= 11000.0d0) then
        tmp = t_1
    else
        tmp = (x * (-2.0d0)) / (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (t <= -1.86e+31) {
		tmp = ((x / t) / z) * -2.0;
	} else if (t <= -180000.0) {
		tmp = t_1;
	} else if (t <= -4.5e-62) {
		tmp = (x / t) * (-2.0 / z);
	} else if (t <= 11000.0) {
		tmp = t_1;
	} else {
		tmp = (x * -2.0) / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / z) * (x / y)
	tmp = 0
	if t <= -1.86e+31:
		tmp = ((x / t) / z) * -2.0
	elif t <= -180000.0:
		tmp = t_1
	elif t <= -4.5e-62:
		tmp = (x / t) * (-2.0 / z)
	elif t <= 11000.0:
		tmp = t_1
	else:
		tmp = (x * -2.0) / (z * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / z) * Float64(x / y))
	tmp = 0.0
	if (t <= -1.86e+31)
		tmp = Float64(Float64(Float64(x / t) / z) * -2.0);
	elseif (t <= -180000.0)
		tmp = t_1;
	elseif (t <= -4.5e-62)
		tmp = Float64(Float64(x / t) * Float64(-2.0 / z));
	elseif (t <= 11000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * -2.0) / Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / z) * (x / y);
	tmp = 0.0;
	if (t <= -1.86e+31)
		tmp = ((x / t) / z) * -2.0;
	elseif (t <= -180000.0)
		tmp = t_1;
	elseif (t <= -4.5e-62)
		tmp = (x / t) * (-2.0 / z);
	elseif (t <= 11000.0)
		tmp = t_1;
	else
		tmp = (x * -2.0) / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.86e+31], N[(N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[t, -180000.0], t$95$1, If[LessEqual[t, -4.5e-62], N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 11000.0], t$95$1, N[(N[(x * -2.0), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.86000000000000008e31

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

      2. associate-*r/ 89.5%

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

      3. distribute-rgt-out-- 89.5%

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

      4. associate-/r* 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in y around 0 75.9%

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

      1. *-commutative 75.9%

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

      2. associate-/r* 86.1%

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

   6. Simplified 86.1%

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

   if -1.86000000000000008e31 < t < -1.8e5 or -4.50000000000000018e-62 < t < 11000

   1. Initial program 94.2%

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

      1. *-commutative 94.2%

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

      2. distribute-rgt-out-- 96.7%

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

      3. times-frac 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around inf 81.9%

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

   if -1.8e5 < t < -4.50000000000000018e-62

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-*r/ 93.9%

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

      3. distribute-rgt-out-- 94.0%

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

      4. associate-/r* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around 0 71.5%

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

      1. associate-*r/ 71.5%

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

      2. *-commutative 71.5%

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

      3. *-commutative 71.5%

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

   6. Simplified 71.5%

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

      1. *-commutative 71.5%

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

      2. times-frac 71.6%

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

   8. Applied egg-rr 71.6%

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

   if 11000 < t

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

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

      2. associate-*r/ 92.5%

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

      3. distribute-rgt-out-- 92.4%

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

      4. associate-/r* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in y around 0 81.6%

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

      1. associate-*r/ 81.6%

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

      2. *-commutative 81.6%

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

      3. *-commutative 81.6%

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

   6. Simplified 81.6%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.86 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{x}{t}}{z} \cdot -2\\ \mathbf{elif}\;t \leq -180000:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq 11000:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -2}{z \cdot t}\\ \end{array} \]

Alternative 5: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{if}\;t \leq -1.62 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{x}{t}}{z} \cdot -2\\ \mathbf{elif}\;t \leq -92000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-64}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot -2}{t}\\ \mathbf{elif}\;t \leq 1960:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ 2.0 z) (/ x y))))
   (if (<= t -1.62e+31)
     (* (/ (/ x t) z) -2.0)
     (if (<= t -92000.0)
       t_1
       (if (<= t -9e-64)
         (/ (* (/ x z) -2.0) t)
         (if (<= t 1960.0) t_1 (/ (* x -2.0) (* z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (t <= -1.62e+31) {
		tmp = ((x / t) / z) * -2.0;
	} else if (t <= -92000.0) {
		tmp = t_1;
	} else if (t <= -9e-64) {
		tmp = ((x / z) * -2.0) / t;
	} else if (t <= 1960.0) {
		tmp = t_1;
	} else {
		tmp = (x * -2.0) / (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 / z) * (x / y)
    if (t <= (-1.62d+31)) then
        tmp = ((x / t) / z) * (-2.0d0)
    else if (t <= (-92000.0d0)) then
        tmp = t_1
    else if (t <= (-9d-64)) then
        tmp = ((x / z) * (-2.0d0)) / t
    else if (t <= 1960.0d0) then
        tmp = t_1
    else
        tmp = (x * (-2.0d0)) / (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (t <= -1.62e+31) {
		tmp = ((x / t) / z) * -2.0;
	} else if (t <= -92000.0) {
		tmp = t_1;
	} else if (t <= -9e-64) {
		tmp = ((x / z) * -2.0) / t;
	} else if (t <= 1960.0) {
		tmp = t_1;
	} else {
		tmp = (x * -2.0) / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / z) * (x / y)
	tmp = 0
	if t <= -1.62e+31:
		tmp = ((x / t) / z) * -2.0
	elif t <= -92000.0:
		tmp = t_1
	elif t <= -9e-64:
		tmp = ((x / z) * -2.0) / t
	elif t <= 1960.0:
		tmp = t_1
	else:
		tmp = (x * -2.0) / (z * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / z) * Float64(x / y))
	tmp = 0.0
	if (t <= -1.62e+31)
		tmp = Float64(Float64(Float64(x / t) / z) * -2.0);
	elseif (t <= -92000.0)
		tmp = t_1;
	elseif (t <= -9e-64)
		tmp = Float64(Float64(Float64(x / z) * -2.0) / t);
	elseif (t <= 1960.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * -2.0) / Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / z) * (x / y);
	tmp = 0.0;
	if (t <= -1.62e+31)
		tmp = ((x / t) / z) * -2.0;
	elseif (t <= -92000.0)
		tmp = t_1;
	elseif (t <= -9e-64)
		tmp = ((x / z) * -2.0) / t;
	elseif (t <= 1960.0)
		tmp = t_1;
	else
		tmp = (x * -2.0) / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.62e+31], N[(N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[t, -92000.0], t$95$1, If[LessEqual[t, -9e-64], N[(N[(N[(x / z), $MachinePrecision] * -2.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1960.0], t$95$1, N[(N[(x * -2.0), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.6199999999999999e31

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

      2. associate-*r/ 89.5%

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

      3. distribute-rgt-out-- 89.5%

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

      4. associate-/r* 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in y around 0 75.9%

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

      1. *-commutative 75.9%

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

      2. associate-/r* 86.1%

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

   6. Simplified 86.1%

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

   if -1.6199999999999999e31 < t < -92000 or -9.00000000000000019e-64 < t < 1960

   1. Initial program 94.2%

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

      1. *-commutative 94.2%

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

      2. distribute-rgt-out-- 96.7%

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

      3. times-frac 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around inf 81.9%

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

   if -92000 < t < -9.00000000000000019e-64

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-*r/ 93.9%

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

      3. distribute-rgt-out-- 94.0%

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

      4. associate-/r* 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around 0 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-/r* 71.6%

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

   6. Simplified 71.6%

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

      1. *-commutative 71.6%

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

      2. associate-/l/ 71.5%

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

      3. associate-*r/ 71.5%

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

      4. *-commutative 71.5%

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

      5. times-frac 77.2%

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

      6. associate-*r/ 77.3%

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

   8. Applied egg-rr 77.3%

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

   if 1960 < t

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

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

      2. associate-*r/ 92.5%

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

      3. distribute-rgt-out-- 92.4%

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

      4. associate-/r* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in y around 0 81.6%

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

      1. associate-*r/ 81.6%

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

      2. *-commutative 81.6%

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

      3. *-commutative 81.6%

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

   6. Simplified 81.6%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.62 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{x}{t}}{z} \cdot -2\\ \mathbf{elif}\;t \leq -92000:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-64}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot -2}{t}\\ \mathbf{elif}\;t \leq 1960:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -2}{z \cdot t}\\ \end{array} \]

Alternative 6: 96.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-27} \lor \neg \left(z \leq 1.4 \cdot 10^{-47}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.5e-27) (not (<= z 1.4e-47)))
   (* 2.0 (/ (/ x z) (- y t)))
   (* x (/ (/ 2.0 (- y t)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.5e-27) || !(z <= 1.4e-47)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = x * ((2.0 / (y - t)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-9.5d-27)) .or. (.not. (z <= 1.4d-47))) then
        tmp = 2.0d0 * ((x / z) / (y - t))
    else
        tmp = x * ((2.0d0 / (y - t)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.5e-27) || !(z <= 1.4e-47)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = x * ((2.0 / (y - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.5e-27) or not (z <= 1.4e-47):
		tmp = 2.0 * ((x / z) / (y - t))
	else:
		tmp = x * ((2.0 / (y - t)) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.5e-27) || !(z <= 1.4e-47))
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(x * Float64(Float64(2.0 / Float64(y - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.5e-27) || ~((z <= 1.4e-47)))
		tmp = 2.0 * ((x / z) / (y - t));
	else
		tmp = x * ((2.0 / (y - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.5e-27], N[Not[LessEqual[z, 1.4e-47]], $MachinePrecision]], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000037e-27 or 1.39999999999999996e-47 < z

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*r/ 89.8%

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

      3. distribute-rgt-out-- 90.4%

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

      4. associate-/r* 99.0%

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

   3. Simplified 99.0%

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

   if -9.50000000000000037e-27 < z < 1.39999999999999996e-47

   1. Initial program 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*r/ 96.8%

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

      3. distribute-rgt-out-- 98.7%

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

      4. associate-/r* 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in x around 0 98.7%

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

      1. associate-*r/ 98.8%

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

      2. *-commutative 98.8%

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

      3. times-frac 76.5%

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

      4. associate-*l/ 90.4%

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

      5. associate-*r/ 98.7%

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

   6. Simplified 98.7%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-27} \lor \neg \left(z \leq 1.4 \cdot 10^{-47}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \end{array} \]

Alternative 7: 96.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-23}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.1e-23)
   (* 2.0 (/ (/ x z) (- y t)))
   (if (<= z 1.5e+35)
     (* x (/ (/ 2.0 (- y t)) z))
     (* (/ 2.0 z) (/ x (- y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e-23) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else if (z <= 1.5e+35) {
		tmp = x * ((2.0 / (y - t)) / z);
	} else {
		tmp = (2.0 / z) * (x / (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.1d-23)) then
        tmp = 2.0d0 * ((x / z) / (y - t))
    else if (z <= 1.5d+35) then
        tmp = x * ((2.0d0 / (y - t)) / z)
    else
        tmp = (2.0d0 / z) * (x / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e-23) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else if (z <= 1.5e+35) {
		tmp = x * ((2.0 / (y - t)) / z);
	} else {
		tmp = (2.0 / z) * (x / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.1e-23:
		tmp = 2.0 * ((x / z) / (y - t))
	elif z <= 1.5e+35:
		tmp = x * ((2.0 / (y - t)) / z)
	else:
		tmp = (2.0 / z) * (x / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.1e-23)
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	elseif (z <= 1.5e+35)
		tmp = Float64(x * Float64(Float64(2.0 / Float64(y - t)) / z));
	else
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.1e-23)
		tmp = 2.0 * ((x / z) / (y - t));
	elseif (z <= 1.5e+35)
		tmp = x * ((2.0 / (y - t)) / z);
	else
		tmp = (2.0 / z) * (x / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.1e-23], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+35], N[(x * N[(N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e-23

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

      2. associate-*r/ 92.6%

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

      3. distribute-rgt-out-- 92.6%

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

      4. associate-/r* 98.6%

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

   3. Simplified 98.6%

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

   if -1.1e-23 < z < 1.49999999999999995e35

   1. Initial program 97.3%

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

      1. *-commutative 97.3%

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

      2. associate-*r/ 97.3%

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

      3. distribute-rgt-out-- 98.9%

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

      4. associate-/r* 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in x around 0 98.9%

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

      1. associate-*r/ 98.9%

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

      2. *-commutative 98.9%

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

      3. times-frac 80.5%

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

      4. associate-*l/ 91.8%

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

      5. associate-*r/ 98.9%

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

   6. Simplified 98.9%

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

   if 1.49999999999999995e35 < z

   1. Initial program 81.1%

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

      1. *-commutative 81.1%

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

      2. distribute-rgt-out-- 83.1%

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

      3. times-frac 99.7%

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

   3. Simplified 99.7%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-23}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \end{array} \]

Alternative 8: 73.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-63} \lor \neg \left(t \leq 2300\right):\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.8e-63) (not (<= t 2300.0)))
   (* x (/ -2.0 (* z t)))
   (* x (/ (/ 2.0 y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.8e-63) || !(t <= 2300.0)) {
		tmp = x * (-2.0 / (z * t));
	} else {
		tmp = x * ((2.0 / y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.8d-63)) .or. (.not. (t <= 2300.0d0))) then
        tmp = x * ((-2.0d0) / (z * t))
    else
        tmp = x * ((2.0d0 / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.8e-63) || !(t <= 2300.0)) {
		tmp = x * (-2.0 / (z * t));
	} else {
		tmp = x * ((2.0 / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.8e-63) or not (t <= 2300.0):
		tmp = x * (-2.0 / (z * t))
	else:
		tmp = x * ((2.0 / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.8e-63) || !(t <= 2300.0))
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	else
		tmp = Float64(x * Float64(Float64(2.0 / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.8e-63) || ~((t <= 2300.0)))
		tmp = x * (-2.0 / (z * t));
	else
		tmp = x * ((2.0 / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.8e-63], N[Not[LessEqual[t, 2300.0]], $MachinePrecision]], N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.80000000000000004e-63 or 2300 < t

   1. Initial program 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-*r/ 90.4%

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

      3. distribute-rgt-out-- 91.1%

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

      4. associate-/r* 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in x around 0 91.1%

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

      1. associate-*r/ 91.1%

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

      2. *-commutative 91.1%

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

      3. times-frac 91.2%

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

      4. associate-*l/ 93.4%

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

      5. associate-*r/ 91.6%

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

   6. Simplified 91.6%

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

   7. Taylor expanded in y around 0 75.5%

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

      1. *-commutative 75.5%

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

   9. Simplified 75.5%

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

   if -1.80000000000000004e-63 < t < 2300

   1. Initial program 95.5%

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

      1. *-commutative 95.5%

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

      2. associate-*r/ 95.5%

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

      3. distribute-rgt-out-- 97.3%

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

      4. associate-/r* 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in x around 0 97.3%

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

      1. associate-*r/ 97.3%

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

      2. *-commutative 97.3%

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

      3. times-frac 87.8%

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

      4. associate-*l/ 97.1%

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

      5. associate-*r/ 97.2%

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

   6. Simplified 97.2%

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

   7. Taylor expanded in y around inf 80.9%

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

      1. associate-/r* 80.9%

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

   9. Simplified 80.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-63} \lor \neg \left(t \leq 2300\right):\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \]

Alternative 9: 72.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-63} \lor \neg \left(t \leq 115000\right):\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.4e-63) (not (<= t 115000.0)))
   (* x (/ -2.0 (* z t)))
   (* (/ 2.0 z) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.4e-63) || !(t <= 115000.0)) {
		tmp = x * (-2.0 / (z * t));
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.4d-63)) .or. (.not. (t <= 115000.0d0))) then
        tmp = x * ((-2.0d0) / (z * t))
    else
        tmp = (2.0d0 / z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.4e-63) || !(t <= 115000.0)) {
		tmp = x * (-2.0 / (z * t));
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.4e-63) or not (t <= 115000.0):
		tmp = x * (-2.0 / (z * t))
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.4e-63) || !(t <= 115000.0))
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	else
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.4e-63) || ~((t <= 115000.0)))
		tmp = x * (-2.0 / (z * t));
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.4e-63], N[Not[LessEqual[t, 115000.0]], $MachinePrecision]], N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.39999999999999998e-63 or 115000 < t

   1. Initial program 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-*r/ 90.4%

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

      3. distribute-rgt-out-- 91.1%

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

      4. associate-/r* 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in x around 0 91.1%

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

      1. associate-*r/ 91.1%

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

      2. *-commutative 91.1%

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

      3. times-frac 91.2%

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

      4. associate-*l/ 93.4%

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

      5. associate-*r/ 91.6%

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

   6. Simplified 91.6%

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

   7. Taylor expanded in y around 0 75.5%

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

      1. *-commutative 75.5%

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

   9. Simplified 75.5%

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

   if -3.39999999999999998e-63 < t < 115000

   1. Initial program 95.5%

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

      1. *-commutative 95.5%

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

      2. distribute-rgt-out-- 97.3%

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

      3. times-frac 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in y around inf 81.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-63} \lor \neg \left(t \leq 115000\right):\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 10: 91.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{+149}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 8.5e+149) (* 2.0 (/ (/ x z) (- y t))) (/ (* 2.0 x) (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 8.5e+149) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = (2.0 * x) / (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 8.5d+149) then
        tmp = 2.0d0 * ((x / z) / (y - t))
    else
        tmp = (2.0d0 * x) / (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 8.5e+149) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = (2.0 * x) / (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 8.5e+149:
		tmp = 2.0 * ((x / z) / (y - t))
	else:
		tmp = (2.0 * x) / (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 8.5e+149)
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(Float64(2.0 * x) / Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 8.5e+149)
		tmp = 2.0 * ((x / z) / (y - t));
	else
		tmp = (2.0 * x) / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 8.5e+149], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.49999999999999956e149

   1. Initial program 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-*r/ 91.9%

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

      3. distribute-rgt-out-- 93.2%

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

      4. associate-/r* 92.4%

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

   3. Simplified 92.4%

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

   if 8.49999999999999956e149 < y

   1. Initial program 99.8%

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

      1. distribute-rgt-out-- 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 91.4%

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

      1. *-commutative 91.4%

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

   6. Simplified 91.4%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{+149}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z}\\ \end{array} \]

Alternative 11: 52.0% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.7%

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

   1. *-commutative 92.7%

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

   2. associate-*r/ 92.7%

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

   3. distribute-rgt-out-- 93.8%

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

   4. associate-/r* 89.8%

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

3. Simplified 89.8%

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

4. Taylor expanded in x around 0 93.8%

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

   1. associate-*r/ 93.8%

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

   2. *-commutative 93.8%

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

   3. times-frac 89.7%

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

   4. associate-*l/ 95.0%

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

   5. associate-*r/ 94.1%

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

6. Simplified 94.1%

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

7. Taylor expanded in y around 0 56.0%

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

   1. *-commutative 56.0%

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

9. Simplified 56.0%

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

10. Final simplification 56.0%

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

Developer target: 96.8% 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 2023275 
(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))))