Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 90.0% → 97.7%

Time: 8.9s

Alternatives: 14

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - z \cdot t\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+215}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+96}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{t - y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) (* z t))))
   (if (<= t_1 -1e+215)
     (* (/ x z) (/ 2.0 (- y t)))
     (if (<= t_1 5e+96)
       (/ (* x 2.0) (* z (- y t)))
       (/ (/ (* x -2.0) (- t y)) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if (t_1 <= -1e+215) {
		tmp = (x / z) * (2.0 / (y - t));
	} else if (t_1 <= 5e+96) {
		tmp = (x * 2.0) / (z * (y - t));
	} else {
		tmp = ((x * -2.0) / (t - 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) :: t_1
    real(8) :: tmp
    t_1 = (y * z) - (z * t)
    if (t_1 <= (-1d+215)) then
        tmp = (x / z) * (2.0d0 / (y - t))
    else if (t_1 <= 5d+96) then
        tmp = (x * 2.0d0) / (z * (y - t))
    else
        tmp = ((x * (-2.0d0)) / (t - y)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if (t_1 <= -1e+215) {
		tmp = (x / z) * (2.0 / (y - t));
	} else if (t_1 <= 5e+96) {
		tmp = (x * 2.0) / (z * (y - t));
	} else {
		tmp = ((x * -2.0) / (t - y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - (z * t)
	tmp = 0
	if t_1 <= -1e+215:
		tmp = (x / z) * (2.0 / (y - t))
	elif t_1 <= 5e+96:
		tmp = (x * 2.0) / (z * (y - t))
	else:
		tmp = ((x * -2.0) / (t - y)) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= -1e+215)
		tmp = Float64(Float64(x / z) * Float64(2.0 / Float64(y - t)));
	elseif (t_1 <= 5e+96)
		tmp = Float64(Float64(x * 2.0) / Float64(z * Float64(y - t)));
	else
		tmp = Float64(Float64(Float64(x * -2.0) / Float64(t - y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) - (z * t);
	tmp = 0.0;
	if (t_1 <= -1e+215)
		tmp = (x / z) * (2.0 / (y - t));
	elseif (t_1 <= 5e+96)
		tmp = (x * 2.0) / (z * (y - t));
	else
		tmp = ((x * -2.0) / (t - y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+215], N[(N[(x / z), $MachinePrecision] * N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+96], N[(N[(x * 2.0), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * -2.0), $MachinePrecision] / N[(t - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 y z) (*.f64 t z)) < -9.99999999999999907e214

   1. Initial program 85.9%

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

      1. distribute-rgt-out-- 85.9%

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

      2. times-frac 100.0%

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

   3. Simplified 100.0%

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

   if -9.99999999999999907e214 < (-.f64 (*.f64 y z) (*.f64 t z)) < 5.0000000000000004e96

   1. Initial program 98.4%

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

      1. distribute-rgt-out-- 98.4%

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

   3. Simplified 98.4%

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

   if 5.0000000000000004e96 < (-.f64 (*.f64 y z) (*.f64 t z))

   1. Initial program 80.6%

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

      1. associate-*r/ 80.5%

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

      2. distribute-rgt-out-- 89.6%

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

      3. associate-/l/ 90.1%

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

      4. sub-neg 90.1%

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

      5. +-commutative 90.1%

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

      6. neg-sub0 90.1%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 90.1%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 90.1%

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

      9. neg-mul-1 90.1%

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

      10. associate-/r* 90.1%

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

      11. metadata-eval 90.1%

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

   3. Simplified 90.1%

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

      1. associate-*r/ 99.8%

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

      2. associate-*r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - z \cdot t \leq -1 \cdot 10^{+215}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{elif}\;y \cdot z - z \cdot t \leq 5 \cdot 10^{+96}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{t - y}}{z}\\ \end{array} \]

Alternative 2: 72.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-115} \lor \neg \left(y \leq 126000\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.1e-115) (not (<= y 126000.0)))
   (* 2.0 (/ (/ x z) y))
   (* x (/ -2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.1e-115) || !(y <= 126000.0)) {
		tmp = 2.0 * ((x / z) / y);
	} else {
		tmp = x * (-2.0 / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.1d-115)) .or. (.not. (y <= 126000.0d0))) then
        tmp = 2.0d0 * ((x / z) / y)
    else
        tmp = x * ((-2.0d0) / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.1e-115) || !(y <= 126000.0)) {
		tmp = 2.0 * ((x / z) / y);
	} else {
		tmp = x * (-2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.1e-115) or not (y <= 126000.0):
		tmp = 2.0 * ((x / z) / y)
	else:
		tmp = x * (-2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.1e-115) || !(y <= 126000.0))
		tmp = Float64(2.0 * Float64(Float64(x / z) / y));
	else
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.1e-115) || ~((y <= 126000.0)))
		tmp = 2.0 * ((x / z) / y);
	else
		tmp = x * (-2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.1e-115], N[Not[LessEqual[y, 126000.0]], $MachinePrecision]], N[(2.0 * N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.10000000000000002e-115 or 126000 < y

   1. Initial program 90.9%

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

      1. associate-*l/ 90.9%

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

      2. *-commutative 90.9%

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

      3. distribute-rgt-out-- 94.4%

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

      4. associate-/r* 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in x around 0 94.4%

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

      1. associate-*r/ 94.4%

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

      2. *-commutative 94.4%

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

      3. times-frac 93.0%

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

      4. associate-*l/ 89.6%

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

      5. associate-*r/ 94.4%

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

   6. Simplified 94.4%

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

   7. Taylor expanded in y around inf 77.9%

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

      1. associate-/l/ 76.5%

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

   9. Simplified 76.5%

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

   if -2.10000000000000002e-115 < y < 126000

   1. Initial program 94.6%

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

      1. associate-*r/ 93.9%

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

      2. distribute-rgt-out-- 93.9%

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

      3. associate-/l/ 94.0%

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

      4. sub-neg 94.0%

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

      5. +-commutative 94.0%

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

      6. neg-sub0 94.0%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 94.0%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 94.0%

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

      9. neg-mul-1 94.0%

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

      10. associate-/r* 94.0%

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

      11. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in t around inf 76.6%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-115} \lor \neg \left(y \leq 126000\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \]

Alternative 3: 72.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-112} \lor \neg \left(y \leq 1200\right):\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2e-112) (not (<= y 1200.0)))
   (* x (/ 2.0 (* y z)))
   (* x (/ -2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-112) || !(y <= 1200.0)) {
		tmp = x * (2.0 / (y * z));
	} else {
		tmp = x * (-2.0 / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2d-112)) .or. (.not. (y <= 1200.0d0))) then
        tmp = x * (2.0d0 / (y * z))
    else
        tmp = x * ((-2.0d0) / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-112) || !(y <= 1200.0)) {
		tmp = x * (2.0 / (y * z));
	} else {
		tmp = x * (-2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2e-112) or not (y <= 1200.0):
		tmp = x * (2.0 / (y * z))
	else:
		tmp = x * (-2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2e-112) || !(y <= 1200.0))
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	else
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2e-112) || ~((y <= 1200.0)))
		tmp = x * (2.0 / (y * z));
	else
		tmp = x * (-2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2e-112], N[Not[LessEqual[y, 1200.0]], $MachinePrecision]], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9999999999999999e-112 or 1200 < y

   1. Initial program 90.9%

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

      1. associate-*r/ 90.7%

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

      2. distribute-rgt-out-- 94.2%

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

      3. associate-/l/ 94.5%

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

      4. sub-neg 94.5%

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

      5. +-commutative 94.5%

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

      6. neg-sub0 94.5%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 94.5%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 94.5%

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

      9. neg-mul-1 94.5%

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

      10. associate-/r* 94.5%

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

      11. metadata-eval 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in t around 0 77.7%

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

   if -1.9999999999999999e-112 < y < 1200

   1. Initial program 94.6%

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

      1. associate-*r/ 93.9%

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

      2. distribute-rgt-out-- 93.9%

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

      3. associate-/l/ 94.0%

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

      4. sub-neg 94.0%

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

      5. +-commutative 94.0%

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

      6. neg-sub0 94.0%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 94.0%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 94.0%

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

      9. neg-mul-1 94.0%

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

      10. associate-/r* 94.0%

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

      11. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in t around inf 76.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-112} \lor \neg \left(y \leq 1200\right):\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \]

Alternative 4: 72.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-112} \lor \neg \left(y \leq 1550\right):\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2e-112) (not (<= y 1550.0)))
   (* x (/ 2.0 (* y z)))
   (* x (/ (/ -2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-112) || !(y <= 1550.0)) {
		tmp = x * (2.0 / (y * z));
	} else {
		tmp = x * ((-2.0 / 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 ((y <= (-2d-112)) .or. (.not. (y <= 1550.0d0))) then
        tmp = x * (2.0d0 / (y * z))
    else
        tmp = x * (((-2.0d0) / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e-112) || !(y <= 1550.0)) {
		tmp = x * (2.0 / (y * z));
	} else {
		tmp = x * ((-2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2e-112) or not (y <= 1550.0):
		tmp = x * (2.0 / (y * z))
	else:
		tmp = x * ((-2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2e-112) || !(y <= 1550.0))
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	else
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2e-112) || ~((y <= 1550.0)))
		tmp = x * (2.0 / (y * z));
	else
		tmp = x * ((-2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2e-112], N[Not[LessEqual[y, 1550.0]], $MachinePrecision]], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9999999999999999e-112 or 1550 < y

   1. Initial program 90.9%

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

      1. associate-*r/ 90.7%

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

      2. distribute-rgt-out-- 94.2%

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

      3. associate-/l/ 94.5%

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

      4. sub-neg 94.5%

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

      5. +-commutative 94.5%

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

      6. neg-sub0 94.5%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 94.5%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 94.5%

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

      9. neg-mul-1 94.5%

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

      10. associate-/r* 94.5%

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

      11. metadata-eval 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in t around 0 77.7%

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

   if -1.9999999999999999e-112 < y < 1550

   1. Initial program 94.6%

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

      1. associate-*r/ 93.9%

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

      2. distribute-rgt-out-- 93.9%

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

      3. associate-/l/ 94.0%

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

      4. sub-neg 94.0%

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

      5. +-commutative 94.0%

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

      6. neg-sub0 94.0%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 94.0%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 94.0%

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

      9. neg-mul-1 94.0%

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

      10. associate-/r* 94.0%

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

      11. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in t around inf 76.6%

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

      1. associate-/r* 76.7%

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

   6. Simplified 76.7%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-112} \lor \neg \left(y \leq 1550\right):\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \]

Alternative 5: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 1900:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2e-112)
   (* x (/ 2.0 (* y z)))
   (if (<= y 1900.0) (* x (/ (/ -2.0 t) z)) (* x (/ (/ 2.0 y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e-112) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 1900.0) {
		tmp = x * ((-2.0 / t) / z);
	} 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 (y <= (-2d-112)) then
        tmp = x * (2.0d0 / (y * z))
    else if (y <= 1900.0d0) then
        tmp = x * (((-2.0d0) / t) / z)
    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 (y <= -2e-112) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 1900.0) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = x * ((2.0 / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2e-112:
		tmp = x * (2.0 / (y * z))
	elif y <= 1900.0:
		tmp = x * ((-2.0 / t) / z)
	else:
		tmp = x * ((2.0 / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2e-112)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	elseif (y <= 1900.0)
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	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 (y <= -2e-112)
		tmp = x * (2.0 / (y * z));
	elseif (y <= 1900.0)
		tmp = x * ((-2.0 / t) / z);
	else
		tmp = x * ((2.0 / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2e-112], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1900.0], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9999999999999999e-112

   1. Initial program 92.8%

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

      1. associate-*r/ 92.7%

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

      2. distribute-rgt-out-- 96.3%

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

      3. associate-/l/ 96.3%

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

      4. sub-neg 96.3%

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

      5. +-commutative 96.3%

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

      6. neg-sub0 96.3%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 96.3%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 96.3%

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

      9. neg-mul-1 96.3%

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

      10. associate-/r* 96.3%

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

      11. metadata-eval 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around 0 76.8%

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

   if -1.9999999999999999e-112 < y < 1900

   1. Initial program 94.6%

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

      1. associate-*r/ 93.9%

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

      2. distribute-rgt-out-- 93.9%

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

      3. associate-/l/ 94.0%

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

      4. sub-neg 94.0%

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

      5. +-commutative 94.0%

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

      6. neg-sub0 94.0%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 94.0%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 94.0%

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

      9. neg-mul-1 94.0%

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

      10. associate-/r* 94.0%

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

      11. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in t around inf 76.6%

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

      1. associate-/r* 76.7%

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

   6. Simplified 76.7%

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

   if 1900 < y

   1. Initial program 88.1%

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

      1. associate-*r/ 87.9%

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

      2. distribute-rgt-out-- 91.3%

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

      3. associate-/l/ 91.9%

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

      4. sub-neg 91.9%

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

      5. +-commutative 91.9%

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

      6. neg-sub0 91.9%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 91.9%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 91.9%

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

      9. neg-mul-1 91.9%

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

      10. associate-/r* 91.9%

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

      11. metadata-eval 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in t around 0 79.6%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 1900:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \]

Alternative 6: 72.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.45:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2e-112)
   (* x (/ 2.0 (* y z)))
   (if (<= y 3.45) (* x (/ (/ -2.0 t) z)) (* (/ 2.0 z) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e-112) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 3.45) {
		tmp = x * ((-2.0 / t) / z);
	} 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 (y <= (-2d-112)) then
        tmp = x * (2.0d0 / (y * z))
    else if (y <= 3.45d0) then
        tmp = x * (((-2.0d0) / t) / z)
    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 (y <= -2e-112) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 3.45) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2e-112:
		tmp = x * (2.0 / (y * z))
	elif y <= 3.45:
		tmp = x * ((-2.0 / t) / z)
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2e-112)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	elseif (y <= 3.45)
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	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 (y <= -2e-112)
		tmp = x * (2.0 / (y * z));
	elseif (y <= 3.45)
		tmp = x * ((-2.0 / t) / z);
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2e-112], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.45], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9999999999999999e-112

   1. Initial program 92.8%

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

      1. associate-*r/ 92.7%

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

      2. distribute-rgt-out-- 96.3%

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

      3. associate-/l/ 96.3%

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

      4. sub-neg 96.3%

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

      5. +-commutative 96.3%

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

      6. neg-sub0 96.3%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 96.3%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 96.3%

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

      9. neg-mul-1 96.3%

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

      10. associate-/r* 96.3%

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

      11. metadata-eval 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around 0 76.8%

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

   if -1.9999999999999999e-112 < y < 3.4500000000000002

   1. Initial program 94.6%

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

      1. associate-*r/ 93.9%

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

      2. distribute-rgt-out-- 93.9%

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

      3. associate-/l/ 94.0%

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

      4. sub-neg 94.0%

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

      5. +-commutative 94.0%

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

      6. neg-sub0 94.0%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 94.0%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 94.0%

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

      9. neg-mul-1 94.0%

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

      10. associate-/r* 94.0%

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

      11. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in t around inf 76.6%

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

      1. associate-/r* 76.7%

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

   6. Simplified 76.7%

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

   if 3.4500000000000002 < y

   1. Initial program 88.1%

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

      1. associate-*l/ 88.1%

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

      2. *-commutative 88.1%

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

      3. distribute-rgt-out-- 91.5%

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

      4. associate-/r* 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in y around inf 79.2%

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

      1. associate-*r/ 79.2%

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

      2. *-commutative 79.2%

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

   6. Simplified 79.2%

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

      1. times-frac 85.5%

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

   8. Applied egg-rr 85.5%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.45:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 7: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-51}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e-113)
   (* x (/ 2.0 (* y z)))
   (if (<= y 8.2e-51) (* -2.0 (/ (/ x z) t)) (* (/ 2.0 z) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e-113) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 8.2e-51) {
		tmp = -2.0 * ((x / 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 (y <= (-9d-113)) then
        tmp = x * (2.0d0 / (y * z))
    else if (y <= 8.2d-51) then
        tmp = (-2.0d0) * ((x / 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 (y <= -9e-113) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 8.2e-51) {
		tmp = -2.0 * ((x / z) / t);
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9e-113:
		tmp = x * (2.0 / (y * z))
	elif y <= 8.2e-51:
		tmp = -2.0 * ((x / z) / t)
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9e-113)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	elseif (y <= 8.2e-51)
		tmp = Float64(-2.0 * Float64(Float64(x / 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 (y <= -9e-113)
		tmp = x * (2.0 / (y * z));
	elseif (y <= 8.2e-51)
		tmp = -2.0 * ((x / z) / t);
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9e-113], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-51], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.0000000000000002e-113

   1. Initial program 92.8%

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

      1. associate-*r/ 92.7%

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

      2. distribute-rgt-out-- 96.3%

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

      3. associate-/l/ 96.3%

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

      4. sub-neg 96.3%

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

      5. +-commutative 96.3%

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

      6. neg-sub0 96.3%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 96.3%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 96.3%

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

      9. neg-mul-1 96.3%

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

      10. associate-/r* 96.3%

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

      11. metadata-eval 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around 0 76.8%

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

   if -9.0000000000000002e-113 < y < 8.19999999999999947e-51

   1. Initial program 94.5%

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

      1. associate-*l/ 94.5%

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

      2. *-commutative 94.5%

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

      3. distribute-rgt-out-- 94.5%

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

      4. associate-/r* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around 0 81.0%

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

      1. *-commutative 81.0%

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

      2. *-commutative 81.0%

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

      3. associate-/r* 84.9%

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

   6. Simplified 84.9%

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

   if 8.19999999999999947e-51 < y

   1. Initial program 90.0%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

      3. distribute-rgt-out-- 92.5%

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

      4. associate-/r* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in y around inf 72.5%

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

      1. associate-*r/ 72.5%

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

      2. *-commutative 72.5%

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

   6. Simplified 72.5%

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

      1. times-frac 77.1%

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

   8. Applied egg-rr 77.1%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-51}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 8: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-50}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e-114)
   (/ (* x 2.0) (* y z))
   (if (<= y 1.6e-50) (* -2.0 (/ (/ x z) t)) (* (/ 2.0 z) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e-114) {
		tmp = (x * 2.0) / (y * z);
	} else if (y <= 1.6e-50) {
		tmp = -2.0 * ((x / 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 (y <= (-7.5d-114)) then
        tmp = (x * 2.0d0) / (y * z)
    else if (y <= 1.6d-50) then
        tmp = (-2.0d0) * ((x / 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 (y <= -7.5e-114) {
		tmp = (x * 2.0) / (y * z);
	} else if (y <= 1.6e-50) {
		tmp = -2.0 * ((x / z) / t);
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e-114:
		tmp = (x * 2.0) / (y * z)
	elif y <= 1.6e-50:
		tmp = -2.0 * ((x / z) / t)
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e-114)
		tmp = Float64(Float64(x * 2.0) / Float64(y * z));
	elseif (y <= 1.6e-50)
		tmp = Float64(-2.0 * Float64(Float64(x / 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 (y <= -7.5e-114)
		tmp = (x * 2.0) / (y * z);
	elseif (y <= 1.6e-50)
		tmp = -2.0 * ((x / z) / t);
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e-114], N[(N[(x * 2.0), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-50], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5000000000000002e-114

   1. Initial program 92.8%

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

      1. associate-*l/ 92.8%

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

      2. *-commutative 92.8%

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

      3. distribute-rgt-out-- 96.4%

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

      4. associate-/r* 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in y around inf 77.0%

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

      1. associate-*r/ 77.0%

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

      2. *-commutative 77.0%

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

   6. Simplified 77.0%

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

   if -7.5000000000000002e-114 < y < 1.6e-50

   1. Initial program 94.5%

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

      1. associate-*l/ 94.5%

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

      2. *-commutative 94.5%

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

      3. distribute-rgt-out-- 94.5%

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

      4. associate-/r* 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around 0 81.0%

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

      1. *-commutative 81.0%

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

      2. *-commutative 81.0%

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

      3. associate-/r* 84.9%

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

   6. Simplified 84.9%

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

   if 1.6e-50 < y

   1. Initial program 90.0%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

      3. distribute-rgt-out-- 92.5%

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

      4. associate-/r* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in y around inf 72.5%

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

      1. associate-*r/ 72.5%

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

      2. *-commutative 72.5%

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

   6. Simplified 72.5%

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

      1. times-frac 77.1%

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

   8. Applied egg-rr 77.1%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-50}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 9: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-112}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-51}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e-112)
   (/ (* x 2.0) (* y z))
   (if (<= y 1.55e-51) (/ (/ (* x -2.0) z) t) (* (/ 2.0 z) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e-112) {
		tmp = (x * 2.0) / (y * z);
	} else if (y <= 1.55e-51) {
		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 (y <= (-1.7d-112)) then
        tmp = (x * 2.0d0) / (y * z)
    else if (y <= 1.55d-51) 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 (y <= -1.7e-112) {
		tmp = (x * 2.0) / (y * z);
	} else if (y <= 1.55e-51) {
		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 y <= -1.7e-112:
		tmp = (x * 2.0) / (y * z)
	elif y <= 1.55e-51:
		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 (y <= -1.7e-112)
		tmp = Float64(Float64(x * 2.0) / Float64(y * z));
	elseif (y <= 1.55e-51)
		tmp = Float64(Float64(Float64(x * -2.0) / z) / t);
	else
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e-112)
		tmp = (x * 2.0) / (y * z);
	elseif (y <= 1.55e-51)
		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[LessEqual[y, -1.7e-112], N[(N[(x * 2.0), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-51], N[(N[(N[(x * -2.0), $MachinePrecision] / z), $MachinePrecision] / t), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6999999999999999e-112

   1. Initial program 92.8%

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

      1. associate-*l/ 92.8%

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

      2. *-commutative 92.8%

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

      3. distribute-rgt-out-- 96.4%

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

      4. associate-/r* 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in y around inf 77.0%

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

      1. associate-*r/ 77.0%

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

      2. *-commutative 77.0%

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

   6. Simplified 77.0%

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

   if -1.6999999999999999e-112 < y < 1.5499999999999999e-51

   1. Initial program 94.5%

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

      1. associate-*r/ 93.5%

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

      2. distribute-rgt-out-- 93.6%

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

      3. associate-/l/ 93.7%

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

      4. sub-neg 93.7%

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

      5. +-commutative 93.7%

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

      6. neg-sub0 93.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 93.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 93.7%

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

      9. neg-mul-1 93.7%

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

      10. associate-/r* 93.7%

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

      11. metadata-eval 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in t around inf 81.0%

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

      1. associate-*r/ 81.0%

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

      2. metadata-eval 81.0%

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

      3. distribute-rgt-neg-in 81.0%

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

      4. *-commutative 81.0%

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

      5. associate-/r* 84.9%

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

      6. distribute-rgt-neg-in 84.9%

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

      7. metadata-eval 84.9%

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

   6. Applied egg-rr 84.9%

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

   if 1.5499999999999999e-51 < y

   1. Initial program 90.0%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

      3. distribute-rgt-out-- 92.5%

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

      4. associate-/r* 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in y around inf 72.5%

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

      1. associate-*r/ 72.5%

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

      2. *-commutative 72.5%

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

   6. Simplified 72.5%

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

      1. times-frac 77.1%

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

   8. Applied egg-rr 77.1%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-112}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-51}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 10: 92.2% 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 92.5%

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

   1. associate-*l/ 92.5%

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

   2. *-commutative 92.5%

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

   3. distribute-rgt-out-- 94.5%

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

   4. associate-/r* 91.6%

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

3. Simplified 91.6%

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

4. Final simplification 91.6%

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

Alternative 11: 92.4% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.5%

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

   1. associate-*r/ 92.1%

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

   2. distribute-rgt-out-- 94.1%

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

   3. associate-/l/ 94.2%

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

   4. sub-neg 94.2%

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

   5. +-commutative 94.2%

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

   6. neg-sub0 94.2%

      \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

   7. associate-+l- 94.2%

      \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

   8. sub0-neg 94.2%

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

   9. neg-mul-1 94.2%

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

   10. associate-/r* 94.2%

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

   11. metadata-eval 94.2%

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

3. Simplified 94.2%

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

4. Final simplification 94.2%

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

Alternative 12: 92.4% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.5%

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

   1. associate-*l/ 92.5%

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

   2. *-commutative 92.5%

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

   3. distribute-rgt-out-- 94.5%

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

   4. associate-/r* 91.6%

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

3. Simplified 91.6%

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

4. Taylor expanded in x around 0 94.5%

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

   1. associate-*r/ 94.5%

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

   2. *-commutative 94.5%

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

   3. times-frac 92.3%

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

   4. associate-*l/ 91.5%

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

   5. associate-*r/ 94.2%

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

6. Simplified 94.2%

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

7. Final simplification 94.2%

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

Alternative 13: 92.2% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.5%

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

   1. distribute-rgt-out-- 94.5%

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

3. Simplified 94.5%

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

4. Final simplification 94.5%

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

Alternative 14: 55.1% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

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)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.5%

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

   1. associate-*l/ 92.5%

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

   2. *-commutative 92.5%

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

   3. distribute-rgt-out-- 94.5%

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

   4. associate-/r* 91.6%

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

3. Simplified 91.6%

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

4. Taylor expanded in x around 0 94.5%

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

   1. associate-*r/ 94.5%

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

   2. *-commutative 94.5%

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

   3. times-frac 92.3%

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

   4. associate-*l/ 91.5%

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

   5. associate-*r/ 94.2%

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

6. Simplified 94.2%

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

7. Taylor expanded in y around inf 57.2%

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

   1. associate-/l/ 56.8%

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

9. Simplified 56.8%

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

10. Final simplification 56.8%

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

Developer target: 96.9% 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 2023199 
(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))))