Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.9% → 94.5%

Time: 7.3s

Alternatives: 11

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.9% 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: 94.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - z \cdot t} \leq -5 \cdot 10^{-277}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x 2.0) (- (* y z) (* z t))) -5e-277)
   (/ (* x 2.0) (* z (- y t)))
   (* (/ x (- y t)) (/ 2.0 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * 2.0) / ((y * z) - (z * t))) <= -5e-277) {
		tmp = (x * 2.0) / (z * (y - t));
	} else {
		tmp = (x / (y - t)) * (2.0 / 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 (((x * 2.0d0) / ((y * z) - (z * t))) <= (-5d-277)) then
        tmp = (x * 2.0d0) / (z * (y - t))
    else
        tmp = (x / (y - t)) * (2.0d0 / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * 2.0) / ((y * z) - (z * t))) <= -5e-277) {
		tmp = (x * 2.0) / (z * (y - t));
	} else {
		tmp = (x / (y - t)) * (2.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * 2.0) / ((y * z) - (z * t))) <= -5e-277:
		tmp = (x * 2.0) / (z * (y - t))
	else:
		tmp = (x / (y - t)) * (2.0 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(z * t))) <= -5e-277)
		tmp = Float64(Float64(x * 2.0) / Float64(z * Float64(y - t)));
	else
		tmp = Float64(Float64(x / Float64(y - t)) * Float64(2.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * 2.0) / ((y * z) - (z * t))) <= -5e-277)
		tmp = (x * 2.0) / (z * (y - t));
	else
		tmp = (x / (y - t)) * (2.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e-277], N[(N[(x * 2.0), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x 2) (-.f64 (*.f64 y z) (*.f64 t z))) < -5e-277

   1. Initial program 99.5%

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

      1. distribute-rgt-out-- 99.5%

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

   3. Simplified 99.5%

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

   if -5e-277 < (/.f64 (*.f64 x 2) (-.f64 (*.f64 y z) (*.f64 t z)))

   1. Initial program 86.8%

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

      1. distribute-rgt-out-- 90.9%

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

   3. Simplified 90.9%

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

      1. *-commutative 90.9%

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

      2. times-frac 98.8%

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

   5. Applied egg-rr 98.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - z \cdot t} \leq -5 \cdot 10^{-277}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \end{array} \]

Alternative 2: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-84} \lor \neg \left(y \leq 2.7 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.5e-84) (not (<= y 2.7e-8)))
   (* 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 <= -4.5e-84) || !(y <= 2.7e-8)) {
		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 <= (-4.5d-84)) .or. (.not. (y <= 2.7d-8))) 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 <= -4.5e-84) || !(y <= 2.7e-8)) {
		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 <= -4.5e-84) or not (y <= 2.7e-8):
		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 <= -4.5e-84) || !(y <= 2.7e-8))
		tmp = Float64(x * Float64(Float64(2.0 / 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 <= -4.5e-84) || ~((y <= 2.7e-8)))
		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, -4.5e-84], N[Not[LessEqual[y, 2.7e-8]], $MachinePrecision]], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.50000000000000016e-84 or 2.70000000000000002e-8 < y

   1. Initial program 89.7%

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

      1. associate-*r/ 89.6%

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

      2. distribute-rgt-out-- 94.7%

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

      3. associate-/l/ 95.6%

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

      4. sub-neg 95.6%

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

      5. +-commutative 95.6%

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

      6. neg-sub0 95.6%

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

      7. associate-+l- 95.6%

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

      8. sub0-neg 95.6%

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

      9. neg-mul-1 95.6%

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

      10. associate-/r* 95.6%

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

      11. metadata-eval 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in t around 0 82.7%

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

   if -4.50000000000000016e-84 < y < 2.70000000000000002e-8

   1. Initial program 92.5%

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

      1. associate-*r/ 92.5%

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

      2. distribute-rgt-out-- 92.6%

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

      3. associate-/l/ 92.8%

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

      4. sub-neg 92.8%

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

      5. +-commutative 92.8%

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

      6. neg-sub0 92.8%

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

      7. associate-+l- 92.8%

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

      8. sub0-neg 92.8%

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

      9. neg-mul-1 92.8%

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

      10. associate-/r* 92.8%

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

      11. metadata-eval 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in t around inf 82.3%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-84} \lor \neg \left(y \leq 2.7 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \]

Alternative 3: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.5e-84)
   (* x (/ (/ 2.0 y) z))
   (if (<= y 9e-5) (* 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 <= -4.5e-84) {
		tmp = x * ((2.0 / y) / z);
	} else if (y <= 9e-5) {
		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 <= (-4.5d-84)) then
        tmp = x * ((2.0d0 / y) / z)
    else if (y <= 9d-5) 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 <= -4.5e-84) {
		tmp = x * ((2.0 / y) / z);
	} else if (y <= 9e-5) {
		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 <= -4.5e-84:
		tmp = x * ((2.0 / y) / z)
	elif y <= 9e-5:
		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 <= -4.5e-84)
		tmp = Float64(x * Float64(Float64(2.0 / y) / z));
	elseif (y <= 9e-5)
		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 <= -4.5e-84)
		tmp = x * ((2.0 / y) / z);
	elseif (y <= 9e-5)
		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, -4.5e-84], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-5], 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 < -4.50000000000000016e-84

   1. Initial program 89.5%

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

      1. associate-*r/ 89.5%

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

      2. distribute-rgt-out-- 96.0%

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

      3. associate-/l/ 97.1%

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

      4. sub-neg 97.1%

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

      5. +-commutative 97.1%

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

      6. neg-sub0 97.1%

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

      7. associate-+l- 97.1%

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

      8. sub0-neg 97.1%

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

      9. neg-mul-1 97.1%

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

      10. associate-/r* 97.1%

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

      11. metadata-eval 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in t around 0 85.1%

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

   if -4.50000000000000016e-84 < y < 9.00000000000000057e-5

   1. Initial program 92.5%

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

      1. associate-*r/ 92.5%

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

      2. distribute-rgt-out-- 92.6%

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

      3. associate-/l/ 92.8%

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

      4. sub-neg 92.8%

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

      5. +-commutative 92.8%

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

      6. neg-sub0 92.8%

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

      7. associate-+l- 92.8%

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

      8. sub0-neg 92.8%

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

      9. neg-mul-1 92.8%

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

      10. associate-/r* 92.8%

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

      11. metadata-eval 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in t around inf 82.3%

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

   if 9.00000000000000057e-5 < y

   1. Initial program 89.9%

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

      1. distribute-rgt-out-- 93.2%

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

   3. Simplified 93.2%

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

      1. *-commutative 93.2%

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

      2. times-frac 96.7%

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

   5. Applied egg-rr 96.7%

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

   6. Taylor expanded in y around inf 81.0%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 4: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-7}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.5e-84)
   (* x (/ (/ 2.0 y) z))
   (if (<= y 4e-7) (* -2.0 (/ (/ x t) z)) (* (/ 2.0 z) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.5e-84) {
		tmp = x * ((2.0 / y) / z);
	} else if (y <= 4e-7) {
		tmp = -2.0 * ((x / 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 <= (-4.5d-84)) then
        tmp = x * ((2.0d0 / y) / z)
    else if (y <= 4d-7) then
        tmp = (-2.0d0) * ((x / 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 <= -4.5e-84) {
		tmp = x * ((2.0 / y) / z);
	} else if (y <= 4e-7) {
		tmp = -2.0 * ((x / t) / z);
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.5e-84:
		tmp = x * ((2.0 / y) / z)
	elif y <= 4e-7:
		tmp = -2.0 * ((x / t) / z)
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.5e-84)
		tmp = Float64(x * Float64(Float64(2.0 / y) / z));
	elseif (y <= 4e-7)
		tmp = Float64(-2.0 * Float64(Float64(x / 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 <= -4.5e-84)
		tmp = x * ((2.0 / y) / z);
	elseif (y <= 4e-7)
		tmp = -2.0 * ((x / t) / z);
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.5e-84], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-7], N[(-2.0 * N[(N[(x / 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 < -4.50000000000000016e-84

   1. Initial program 89.5%

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

      1. associate-*r/ 89.5%

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

      2. distribute-rgt-out-- 96.0%

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

      3. associate-/l/ 97.1%

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

      4. sub-neg 97.1%

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

      5. +-commutative 97.1%

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

      6. neg-sub0 97.1%

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

      7. associate-+l- 97.1%

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

      8. sub0-neg 97.1%

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

      9. neg-mul-1 97.1%

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

      10. associate-/r* 97.1%

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

      11. metadata-eval 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in t around 0 85.1%

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

   if -4.50000000000000016e-84 < y < 3.9999999999999998e-7

   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-- 92.6%

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

      4. associate-/r* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around 0 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-/r* 86.9%

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

   6. Simplified 86.9%

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

   if 3.9999999999999998e-7 < y

   1. Initial program 89.9%

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

      1. distribute-rgt-out-- 93.2%

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

   3. Simplified 93.2%

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

      1. *-commutative 93.2%

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

      2. times-frac 96.7%

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

   5. Applied egg-rr 96.7%

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

   6. Taylor expanded in y around inf 81.0%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-7}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-9}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.2e-84)
   (* x (/ (/ 2.0 y) z))
   (if (<= y 1.3e-9) (* -2.0 (/ (/ x t) z)) (/ (/ x y) (* z 0.5)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e-84) {
		tmp = x * ((2.0 / y) / z);
	} else if (y <= 1.3e-9) {
		tmp = -2.0 * ((x / t) / z);
	} else {
		tmp = (x / y) / (z * 0.5);
	}
	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 <= (-4.2d-84)) then
        tmp = x * ((2.0d0 / y) / z)
    else if (y <= 1.3d-9) then
        tmp = (-2.0d0) * ((x / t) / z)
    else
        tmp = (x / y) / (z * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e-84) {
		tmp = x * ((2.0 / y) / z);
	} else if (y <= 1.3e-9) {
		tmp = -2.0 * ((x / t) / z);
	} else {
		tmp = (x / y) / (z * 0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.2e-84:
		tmp = x * ((2.0 / y) / z)
	elif y <= 1.3e-9:
		tmp = -2.0 * ((x / t) / z)
	else:
		tmp = (x / y) / (z * 0.5)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.2e-84)
		tmp = Float64(x * Float64(Float64(2.0 / y) / z));
	elseif (y <= 1.3e-9)
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	else
		tmp = Float64(Float64(x / y) / Float64(z * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.2e-84)
		tmp = x * ((2.0 / y) / z);
	elseif (y <= 1.3e-9)
		tmp = -2.0 * ((x / t) / z);
	else
		tmp = (x / y) / (z * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.2e-84], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-9], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / N[(z * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.19999999999999996e-84

   1. Initial program 89.5%

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

      1. associate-*r/ 89.5%

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

      2. distribute-rgt-out-- 96.0%

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

      3. associate-/l/ 97.1%

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

      4. sub-neg 97.1%

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

      5. +-commutative 97.1%

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

      6. neg-sub0 97.1%

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

      7. associate-+l- 97.1%

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

      8. sub0-neg 97.1%

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

      9. neg-mul-1 97.1%

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

      10. associate-/r* 97.1%

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

      11. metadata-eval 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in t around 0 85.1%

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

   if -4.19999999999999996e-84 < y < 1.3000000000000001e-9

   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-- 92.6%

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

      4. associate-/r* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around 0 82.1%

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

      1. *-commutative 82.1%

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

      2. associate-/r* 86.9%

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

   6. Simplified 86.9%

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

   if 1.3000000000000001e-9 < y

   1. Initial program 89.9%

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

      1. associate-*r/ 89.8%

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

      2. distribute-rgt-out-- 93.1%

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

      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 0 79.6%

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

      1. associate-/r* 79.0%

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

      2. associate-*r/ 79.1%

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

      3. times-frac 81.0%

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

      4. clear-num 81.0%

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

      5. un-div-inv 81.1%

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

      6. div-inv 81.1%

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

      7. metadata-eval 81.1%

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

   6. Applied egg-rr 81.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{z \cdot 0.5}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-9}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \end{array} \]

Alternative 6: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.5e-84)
   (* x (/ (/ 2.0 y) z))
   (if (<= y 4.5e-11) (/ (/ (* x -2.0) t) z) (/ (/ x y) (* z 0.5)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.5e-84) {
		tmp = x * ((2.0 / y) / z);
	} else if (y <= 4.5e-11) {
		tmp = ((x * -2.0) / t) / z;
	} else {
		tmp = (x / y) / (z * 0.5);
	}
	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 <= (-4.5d-84)) then
        tmp = x * ((2.0d0 / y) / z)
    else if (y <= 4.5d-11) then
        tmp = ((x * (-2.0d0)) / t) / z
    else
        tmp = (x / y) / (z * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.5e-84) {
		tmp = x * ((2.0 / y) / z);
	} else if (y <= 4.5e-11) {
		tmp = ((x * -2.0) / t) / z;
	} else {
		tmp = (x / y) / (z * 0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.5e-84:
		tmp = x * ((2.0 / y) / z)
	elif y <= 4.5e-11:
		tmp = ((x * -2.0) / t) / z
	else:
		tmp = (x / y) / (z * 0.5)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.5e-84)
		tmp = Float64(x * Float64(Float64(2.0 / y) / z));
	elseif (y <= 4.5e-11)
		tmp = Float64(Float64(Float64(x * -2.0) / t) / z);
	else
		tmp = Float64(Float64(x / y) / Float64(z * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.5e-84)
		tmp = x * ((2.0 / y) / z);
	elseif (y <= 4.5e-11)
		tmp = ((x * -2.0) / t) / z;
	else
		tmp = (x / y) / (z * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.5e-84], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-11], N[(N[(N[(x * -2.0), $MachinePrecision] / t), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / N[(z * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.50000000000000016e-84

   1. Initial program 89.5%

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

      1. associate-*r/ 89.5%

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

      2. distribute-rgt-out-- 96.0%

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

      3. associate-/l/ 97.1%

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

      4. sub-neg 97.1%

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

      5. +-commutative 97.1%

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

      6. neg-sub0 97.1%

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

      7. associate-+l- 97.1%

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

      8. sub0-neg 97.1%

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

      9. neg-mul-1 97.1%

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

      10. associate-/r* 97.1%

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

      11. metadata-eval 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in t around 0 85.1%

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

   if -4.50000000000000016e-84 < y < 4.5e-11

   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-- 92.6%

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

      4. associate-/r* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around 0 82.1%

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

      1. associate-*r/ 82.1%

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

      2. metadata-eval 82.1%

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

      3. distribute-lft-neg-in 82.1%

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

      4. *-commutative 82.1%

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

      5. associate-/r* 86.9%

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

      6. distribute-rgt-neg-in 86.9%

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

      7. metadata-eval 86.9%

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

   6. Applied egg-rr 86.9%

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

   if 4.5e-11 < y

   1. Initial program 89.9%

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

      1. associate-*r/ 89.8%

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

      2. distribute-rgt-out-- 93.1%

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

      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 0 79.6%

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

      1. associate-/r* 79.0%

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

      2. associate-*r/ 79.1%

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

      3. times-frac 81.0%

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

      4. clear-num 81.0%

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

      5. un-div-inv 81.1%

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

      6. div-inv 81.1%

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

      7. metadata-eval 81.1%

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

   6. Applied egg-rr 81.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{z \cdot 0.5}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \end{array} \]

Alternative 7: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.4 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t - y}}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 1.4e-211) (* x (/ (/ -2.0 (- t y)) z)) (* 2.0 (/ (/ x z) (- y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.4e-211) {
		tmp = x * ((-2.0 / (t - y)) / z);
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 1.4d-211) then
        tmp = x * (((-2.0d0) / (t - y)) / z)
    else
        tmp = 2.0d0 * ((x / z) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.4e-211) {
		tmp = x * ((-2.0 / (t - y)) / z);
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 1.4e-211:
		tmp = x * ((-2.0 / (t - y)) / z)
	else:
		tmp = 2.0 * ((x / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 1.4e-211)
		tmp = Float64(x * Float64(Float64(-2.0 / Float64(t - y)) / z));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 1.4e-211)
		tmp = x * ((-2.0 / (t - y)) / z);
	else
		tmp = 2.0 * ((x / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 1.4e-211], N[(x * N[(N[(-2.0 / N[(t - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.3999999999999999e-211

   1. Initial program 93.2%

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

      1. associate-*r/ 93.2%

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

      2. distribute-rgt-out-- 94.0%

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

      3. associate-/l/ 95.0%

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

      4. sub-neg 95.0%

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

      5. +-commutative 95.0%

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

      6. neg-sub0 95.0%

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

      7. associate-+l- 95.0%

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

      8. sub0-neg 95.0%

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

      9. neg-mul-1 95.0%

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

      10. associate-/r* 95.0%

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

      11. metadata-eval 95.0%

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

   3. Simplified 95.0%

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

   if 1.3999999999999999e-211 < z

   1. Initial program 88.0%

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

      1. associate-*l/ 88.0%

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

      2. *-commutative 88.0%

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

      3. distribute-rgt-out-- 93.5%

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

      4. associate-/r* 98.9%

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

   3. Simplified 98.9%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.4 \cdot 10^{-211}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t - y}}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 8: 91.7% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.0%

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

   1. associate-*l/ 91.0%

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

   2. *-commutative 91.0%

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

   3. distribute-rgt-out-- 93.8%

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

   4. associate-/r* 94.7%

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

3. Simplified 94.7%

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

4. Final simplification 94.7%

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

Alternative 9: 91.7% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.0%

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

   1. distribute-rgt-out-- 93.8%

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

3. Simplified 93.8%

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

   1. *-commutative 93.8%

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

   2. times-frac 97.3%

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

5. Applied egg-rr 97.3%

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

6. Final simplification 97.3%

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

Alternative 10: 54.1% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.0%

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

   1. associate-*l/ 91.0%

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

   2. *-commutative 91.0%

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

   3. distribute-rgt-out-- 93.8%

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

   4. associate-/r* 94.7%

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

3. Simplified 94.7%

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

4. Taylor expanded in y around 0 55.6%

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

5. Final simplification 55.6%

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

Alternative 11: 54.2% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.0%

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

   1. associate-*r/ 90.9%

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

   2. distribute-rgt-out-- 93.7%

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

   3. associate-/l/ 94.3%

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

   4. sub-neg 94.3%

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

   5. +-commutative 94.3%

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

   6. neg-sub0 94.3%

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

   7. associate-+l- 94.3%

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

   8. sub0-neg 94.3%

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

   9. neg-mul-1 94.3%

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

   10. associate-/r* 94.3%

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

   11. metadata-eval 94.3%

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

3. Simplified 94.3%

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

4. Taylor expanded in t around inf 55.7%

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

5. Final simplification 55.7%

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

Developer target: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ t_2 := \frac{x \cdot 2}{y \cdot z - t \cdot z}\\ \mathbf{if}\;t_2 < -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 1.045027827330126 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x (* (- y t) z)) 2.0))
        (t_2 (/ (* x 2.0) (- (* y z) (* t z)))))
   (if (< t_2 -2.559141628295061e-13)
     t_1
     (if (< t_2 1.045027827330126e-269) (/ (* (/ x z) 2.0) (- y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / ((y - t) * z)) * 2.0;
	double t_2 = (x * 2.0) / ((y * z) - (t * z));
	double tmp;
	if (t_2 < -2.559141628295061e-13) {
		tmp = t_1;
	} else if (t_2 < 1.045027827330126e-269) {
		tmp = ((x / z) * 2.0) / (y - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / ((y - t) * z)) * 2.0d0
    t_2 = (x * 2.0d0) / ((y * z) - (t * z))
    if (t_2 < (-2.559141628295061d-13)) then
        tmp = t_1
    else if (t_2 < 1.045027827330126d-269) then
        tmp = ((x / z) * 2.0d0) / (y - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / ((y - t) * z)) * 2.0;
	double t_2 = (x * 2.0) / ((y * z) - (t * z));
	double tmp;
	if (t_2 < -2.559141628295061e-13) {
		tmp = t_1;
	} else if (t_2 < 1.045027827330126e-269) {
		tmp = ((x / z) * 2.0) / (y - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / ((y - t) * z)) * 2.0
	t_2 = (x * 2.0) / ((y * z) - (t * z))
	tmp = 0
	if t_2 < -2.559141628295061e-13:
		tmp = t_1
	elif t_2 < 1.045027827330126e-269:
		tmp = ((x / z) * 2.0) / (y - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(Float64(y - t) * z)) * 2.0)
	t_2 = Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
	tmp = 0.0
	if (t_2 < -2.559141628295061e-13)
		tmp = t_1;
	elseif (t_2 < 1.045027827330126e-269)
		tmp = Float64(Float64(Float64(x / z) * 2.0) / Float64(y - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / ((y - t) * z)) * 2.0;
	t_2 = (x * 2.0) / ((y * z) - (t * z));
	tmp = 0.0;
	if (t_2 < -2.559141628295061e-13)
		tmp = t_1;
	elseif (t_2 < 1.045027827330126e-269)
		tmp = ((x / z) * 2.0) / (y - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -2.559141628295061e-13], t$95$1, If[Less[t$95$2, 1.045027827330126e-269], N[(N[(N[(x / z), $MachinePrecision] * 2.0), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023242 
(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))))