Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 90.0% → 94.3%

Time: 9.1s

Alternatives: 13

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: 94.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq 2 \cdot 10^{+82}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* x 2.0) 2e+82)
   (* 2.0 (/ (/ x 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) <= 2e+82) {
		tmp = 2.0 * ((x / 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) <= 2d+82) then
        tmp = 2.0d0 * ((x / 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) <= 2e+82) {
		tmp = 2.0 * ((x / 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) <= 2e+82:
		tmp = 2.0 * ((x / 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(x * 2.0) <= 2e+82)
		tmp = Float64(2.0 * Float64(Float64(x / 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) <= 2e+82)
		tmp = 2.0 * ((x / 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[(x * 2.0), $MachinePrecision], 2e+82], N[(2.0 * N[(N[(x / z), $MachinePrecision] / 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 x 2) < 1.9999999999999999e82

   1. Initial program 86.9%

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

      1. associate-*l/ 86.9%

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

      2. *-commutative 86.9%

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

      3. distribute-rgt-out-- 90.2%

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

      4. associate-/r* 97.0%

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

   3. Simplified 97.0%

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

   if 1.9999999999999999e82 < (*.f64 x 2)

   1. Initial program 66.2%

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

      1. distribute-rgt-out-- 68.8%

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

   3. Simplified 68.8%

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

      1. *-commutative 68.8%

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

      2. times-frac 97.5%

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

   5. Applied egg-rr 97.5%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq 2 \cdot 10^{+82}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \end{array} \]

Alternative 2: 72.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+35} \lor \neg \left(y \leq 5.8 \cdot 10^{+38}\right):\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.4e+35) (not (<= y 5.8e+38)))
   (* 2.0 (/ x (* z y)))
   (* x (/ (/ -2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.4e+35) || !(y <= 5.8e+38)) {
		tmp = 2.0 * (x / (z * y));
	} 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 <= (-6.4d+35)) .or. (.not. (y <= 5.8d+38))) then
        tmp = 2.0d0 * (x / (z * y))
    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 <= -6.4e+35) || !(y <= 5.8e+38)) {
		tmp = 2.0 * (x / (z * y));
	} else {
		tmp = x * ((-2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.4e+35) or not (y <= 5.8e+38):
		tmp = 2.0 * (x / (z * y))
	else:
		tmp = x * ((-2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.4e+35) || !(y <= 5.8e+38))
		tmp = Float64(2.0 * Float64(x / Float64(z * y)));
	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 <= -6.4e+35) || ~((y <= 5.8e+38)))
		tmp = 2.0 * (x / (z * y));
	else
		tmp = x * ((-2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.4e+35], N[Not[LessEqual[y, 5.8e+38]], $MachinePrecision]], N[(2.0 * N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.39999999999999965e35 or 5.80000000000000013e38 < y

   1. Initial program 78.5%

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

      1. associate-*l/ 78.5%

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

      2. *-commutative 78.5%

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

      3. distribute-rgt-out-- 85.0%

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

      4. associate-/r* 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in y around inf 80.0%

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

   if -6.39999999999999965e35 < y < 5.80000000000000013e38

   1. Initial program 87.0%

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

      1. associate-*r/ 86.9%

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

      2. distribute-rgt-out-- 87.7%

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

      3. associate-/l/ 88.1%

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

      4. sub-neg 88.1%

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

      5. +-commutative 88.1%

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

      6. neg-sub0 88.1%

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

      7. associate-+l- 88.1%

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

      8. sub0-neg 88.1%

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

      9. neg-mul-1 88.1%

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

      10. associate-/r* 88.1%

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

      11. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in t around inf 75.7%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+35} \lor \neg \left(y \leq 5.8 \cdot 10^{+38}\right):\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \]

Alternative 3: 72.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+33} \lor \neg \left(y \leq 1.1 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.75e+33) (not (<= y 1.1e+39)))
   (* (/ x z) (/ 2.0 y))
   (* x (/ (/ -2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.75e+33) || !(y <= 1.1e+39)) {
		tmp = (x / z) * (2.0 / y);
	} 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 <= (-1.75d+33)) .or. (.not. (y <= 1.1d+39))) then
        tmp = (x / z) * (2.0d0 / y)
    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 <= -1.75e+33) || !(y <= 1.1e+39)) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = x * ((-2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.75e+33) or not (y <= 1.1e+39):
		tmp = (x / z) * (2.0 / y)
	else:
		tmp = x * ((-2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.75e+33) || !(y <= 1.1e+39))
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	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 <= -1.75e+33) || ~((y <= 1.1e+39)))
		tmp = (x / z) * (2.0 / y);
	else
		tmp = x * ((-2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.75e+33], N[Not[LessEqual[y, 1.1e+39]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.75000000000000005e33 or 1.1000000000000001e39 < y

   1. Initial program 78.5%

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

      1. associate-*r/ 78.5%

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

      2. distribute-rgt-out-- 85.0%

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

      3. associate-/l/ 86.5%

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

      4. sub-neg 86.5%

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

      5. +-commutative 86.5%

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

      6. neg-sub0 86.5%

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

      7. associate-+l- 86.5%

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

      8. sub0-neg 86.5%

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

      9. neg-mul-1 86.5%

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

      10. associate-/r* 86.5%

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

      11. metadata-eval 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in t around 0 80.0%

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

      1. associate-*r/ 80.0%

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

      2. times-frac 84.8%

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

   6. Simplified 84.8%

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

   if -1.75000000000000005e33 < y < 1.1000000000000001e39

   1. Initial program 87.0%

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

      1. associate-*r/ 86.9%

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

      2. distribute-rgt-out-- 87.7%

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

      3. associate-/l/ 88.1%

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

      4. sub-neg 88.1%

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

      5. +-commutative 88.1%

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

      6. neg-sub0 88.1%

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

      7. associate-+l- 88.1%

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

      8. sub0-neg 88.1%

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

      9. neg-mul-1 88.1%

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

      10. associate-/r* 88.1%

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

      11. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in t around inf 75.7%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+33} \lor \neg \left(y \leq 1.1 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \]

Alternative 4: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+35} \lor \neg \left(y \leq 2.15 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.5e+35) (not (<= y 2.15e+39)))
   (* (/ x z) (/ 2.0 y))
   (* (/ x z) (/ -2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.5e+35) || !(y <= 2.15e+39)) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = (x / z) * (-2.0 / 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 <= (-5.5d+35)) .or. (.not. (y <= 2.15d+39))) then
        tmp = (x / z) * (2.0d0 / y)
    else
        tmp = (x / z) * ((-2.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.5e+35) || !(y <= 2.15e+39)) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = (x / z) * (-2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.5e+35) or not (y <= 2.15e+39):
		tmp = (x / z) * (2.0 / y)
	else:
		tmp = (x / z) * (-2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.5e+35) || !(y <= 2.15e+39))
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	else
		tmp = Float64(Float64(x / z) * Float64(-2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.5e+35) || ~((y <= 2.15e+39)))
		tmp = (x / z) * (2.0 / y);
	else
		tmp = (x / z) * (-2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.5e+35], N[Not[LessEqual[y, 2.15e+39]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.50000000000000001e35 or 2.15e39 < y

   1. Initial program 78.5%

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

      1. associate-*r/ 78.5%

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

      2. distribute-rgt-out-- 85.0%

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

      3. associate-/l/ 86.5%

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

      4. sub-neg 86.5%

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

      5. +-commutative 86.5%

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

      6. neg-sub0 86.5%

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

      7. associate-+l- 86.5%

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

      8. sub0-neg 86.5%

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

      9. neg-mul-1 86.5%

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

      10. associate-/r* 86.5%

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

      11. metadata-eval 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in t around 0 80.0%

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

      1. associate-*r/ 80.0%

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

      2. times-frac 84.8%

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

   6. Simplified 84.8%

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

   if -5.50000000000000001e35 < y < 2.15e39

   1. Initial program 87.0%

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

      1. distribute-rgt-out-- 87.8%

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

      2. times-frac 94.3%

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

   3. Simplified 94.3%

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

      1. *-commutative 94.3%

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

      2. clear-num 94.2%

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

      3. un-div-inv 95.2%

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

   5. Applied egg-rr 95.2%

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

   6. Taylor expanded in y around 0 75.4%

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

      1. associate-*r/ 75.4%

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

      2. *-commutative 75.4%

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

      3. *-commutative 75.4%

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

      4. times-frac 80.1%

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

   8. Simplified 80.1%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+35} \lor \neg \left(y \leq 2.15 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \end{array} \]

Alternative 5: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+38} \lor \neg \left(y \leq 5.5 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.7e+38) (not (<= y 5.5e+40)))
   (* (/ x z) (/ 2.0 y))
   (* -2.0 (/ (/ x z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.7e+38) || !(y <= 5.5e+40)) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = -2.0 * ((x / 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 <= (-5.7d+38)) .or. (.not. (y <= 5.5d+40))) then
        tmp = (x / z) * (2.0d0 / y)
    else
        tmp = (-2.0d0) * ((x / 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 <= -5.7e+38) || !(y <= 5.5e+40)) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = -2.0 * ((x / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.7e+38) or not (y <= 5.5e+40):
		tmp = (x / z) * (2.0 / y)
	else:
		tmp = -2.0 * ((x / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.7e+38) || !(y <= 5.5e+40))
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	else
		tmp = Float64(-2.0 * Float64(Float64(x / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.7e+38) || ~((y <= 5.5e+40)))
		tmp = (x / z) * (2.0 / y);
	else
		tmp = -2.0 * ((x / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.7e+38], N[Not[LessEqual[y, 5.5e+40]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6999999999999997e38 or 5.49999999999999974e40 < y

   1. Initial program 78.5%

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

      1. associate-*r/ 78.5%

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

      2. distribute-rgt-out-- 85.0%

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

      3. associate-/l/ 86.5%

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

      4. sub-neg 86.5%

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

      5. +-commutative 86.5%

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

      6. neg-sub0 86.5%

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

      7. associate-+l- 86.5%

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

      8. sub0-neg 86.5%

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

      9. neg-mul-1 86.5%

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

      10. associate-/r* 86.5%

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

      11. metadata-eval 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in t around 0 80.0%

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

      1. associate-*r/ 80.0%

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

      2. times-frac 84.8%

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

   6. Simplified 84.8%

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

   if -5.6999999999999997e38 < y < 5.49999999999999974e40

   1. Initial program 87.0%

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

      1. associate-*r/ 86.9%

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

      2. distribute-rgt-out-- 87.7%

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

      3. associate-/l/ 88.1%

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

      4. sub-neg 88.1%

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

      5. +-commutative 88.1%

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

      6. neg-sub0 88.1%

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

      7. associate-+l- 88.1%

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

      8. sub0-neg 88.1%

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

      9. neg-mul-1 88.1%

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

      10. associate-/r* 88.1%

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

      11. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in t around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. *-commutative 75.4%

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

      3. associate-/r* 80.1%

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

   6. Simplified 80.1%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+38} \lor \neg \left(y \leq 5.5 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \end{array} \]

Alternative 6: 73.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.75e+34)
   (* x (/ (/ 2.0 y) z))
   (if (<= y 2.3e+39) (* x (/ (/ -2.0 t) z)) (* 2.0 (/ x (* z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e+34) {
		tmp = x * ((2.0 / y) / z);
	} else if (y <= 2.3e+39) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = 2.0 * (x / (z * 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 <= (-1.75d+34)) then
        tmp = x * ((2.0d0 / y) / z)
    else if (y <= 2.3d+39) then
        tmp = x * (((-2.0d0) / t) / z)
    else
        tmp = 2.0d0 * (x / (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e+34) {
		tmp = x * ((2.0 / y) / z);
	} else if (y <= 2.3e+39) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = 2.0 * (x / (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.75e+34:
		tmp = x * ((2.0 / y) / z)
	elif y <= 2.3e+39:
		tmp = x * ((-2.0 / t) / z)
	else:
		tmp = 2.0 * (x / (z * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.75e+34)
		tmp = Float64(x * Float64(Float64(2.0 / y) / z));
	elseif (y <= 2.3e+39)
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	else
		tmp = Float64(2.0 * Float64(x / Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.75e+34)
		tmp = x * ((2.0 / y) / z);
	elseif (y <= 2.3e+39)
		tmp = x * ((-2.0 / t) / z);
	else
		tmp = 2.0 * (x / (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.75e+34], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+39], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.74999999999999999e34

   1. Initial program 74.6%

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

      1. associate-*r/ 74.6%

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

      2. distribute-rgt-out-- 82.2%

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

      3. associate-/l/ 85.2%

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

      4. sub-neg 85.2%

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

      5. +-commutative 85.2%

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

      6. neg-sub0 85.2%

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

      7. associate-+l- 85.2%

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

      8. sub0-neg 85.2%

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

      9. neg-mul-1 85.2%

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

      10. associate-/r* 85.2%

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

      11. metadata-eval 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in t around 0 79.4%

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

   if -1.74999999999999999e34 < y < 2.30000000000000012e39

   1. Initial program 87.0%

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

      1. associate-*r/ 86.9%

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

      2. distribute-rgt-out-- 87.7%

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

      3. associate-/l/ 88.1%

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

      4. sub-neg 88.1%

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

      5. +-commutative 88.1%

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

      6. neg-sub0 88.1%

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

      7. associate-+l- 88.1%

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

      8. sub0-neg 88.1%

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

      9. neg-mul-1 88.1%

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

      10. associate-/r* 88.1%

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

      11. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in t around inf 75.7%

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

   if 2.30000000000000012e39 < y

   1. Initial program 82.4%

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

      1. associate-*l/ 82.4%

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

      2. *-commutative 82.4%

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

      3. distribute-rgt-out-- 87.9%

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

      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 inf 81.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{z \cdot y}\\ \end{array} \]

Alternative 7: 73.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+38}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.5e+39)
   (/ 2.0 (* z (/ y x)))
   (if (<= y 8.5e+38) (* -2.0 (/ (/ x z) t)) (* (/ x z) (/ 2.0 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.5e+39) {
		tmp = 2.0 / (z * (y / x));
	} else if (y <= 8.5e+38) {
		tmp = -2.0 * ((x / z) / t);
	} else {
		tmp = (x / z) * (2.0 / 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 <= (-3.5d+39)) then
        tmp = 2.0d0 / (z * (y / x))
    else if (y <= 8.5d+38) then
        tmp = (-2.0d0) * ((x / z) / t)
    else
        tmp = (x / z) * (2.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.5e+39) {
		tmp = 2.0 / (z * (y / x));
	} else if (y <= 8.5e+38) {
		tmp = -2.0 * ((x / z) / t);
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.5e+39:
		tmp = 2.0 / (z * (y / x))
	elif y <= 8.5e+38:
		tmp = -2.0 * ((x / z) / t)
	else:
		tmp = (x / z) * (2.0 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.5e+39)
		tmp = Float64(2.0 / Float64(z * Float64(y / x)));
	elseif (y <= 8.5e+38)
		tmp = Float64(-2.0 * Float64(Float64(x / z) / t));
	else
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.5e+39)
		tmp = 2.0 / (z * (y / x));
	elseif (y <= 8.5e+38)
		tmp = -2.0 * ((x / z) / t);
	else
		tmp = (x / z) * (2.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.5e+39], N[(2.0 / N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+38], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000002e39

   1. Initial program 74.6%

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

      1. distribute-rgt-out-- 82.2%

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

      2. times-frac 94.4%

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

   3. Simplified 94.4%

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

      1. clear-num 94.4%

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

      2. frac-times 94.5%

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

      3. metadata-eval 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in y around inf 78.3%

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

      1. associate-/l* 83.5%

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

      2. associate-/r/ 83.6%

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

   8. Simplified 83.6%

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

   if -3.5000000000000002e39 < y < 8.4999999999999997e38

   1. Initial program 87.0%

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

      1. associate-*r/ 86.9%

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

      2. distribute-rgt-out-- 87.7%

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

      3. associate-/l/ 88.1%

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

      4. sub-neg 88.1%

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

      5. +-commutative 88.1%

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

      6. neg-sub0 88.1%

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

      7. associate-+l- 88.1%

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

      8. sub0-neg 88.1%

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

      9. neg-mul-1 88.1%

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

      10. associate-/r* 88.1%

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

      11. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in t around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. *-commutative 75.4%

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

      3. associate-/r* 80.1%

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

   6. Simplified 80.1%

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

   if 8.4999999999999997e38 < y

   1. Initial program 82.4%

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

      1. associate-*r/ 82.3%

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

      2. distribute-rgt-out-- 87.8%

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

      3. associate-/l/ 87.8%

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

      4. sub-neg 87.8%

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

      5. +-commutative 87.8%

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

      6. neg-sub0 87.8%

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

      7. associate-+l- 87.8%

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

      8. sub0-neg 87.8%

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

      9. neg-mul-1 87.8%

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

      10. associate-/r* 87.8%

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

      11. metadata-eval 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in t around 0 81.8%

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

      1. associate-*r/ 81.8%

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

      2. times-frac 86.8%

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

   6. Simplified 86.8%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+38}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \]

Alternative 8: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+41}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+39}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{y}{\frac{x}{z}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.9e+41)
   (/ 2.0 (* z (/ y x)))
   (if (<= y 4e+39) (* -2.0 (/ (/ x z) t)) (/ 2.0 (/ y (/ x z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.9e+41) {
		tmp = 2.0 / (z * (y / x));
	} else if (y <= 4e+39) {
		tmp = -2.0 * ((x / z) / t);
	} else {
		tmp = 2.0 / (y / (x / 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 <= (-2.9d+41)) then
        tmp = 2.0d0 / (z * (y / x))
    else if (y <= 4d+39) then
        tmp = (-2.0d0) * ((x / z) / t)
    else
        tmp = 2.0d0 / (y / (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.9e+41) {
		tmp = 2.0 / (z * (y / x));
	} else if (y <= 4e+39) {
		tmp = -2.0 * ((x / z) / t);
	} else {
		tmp = 2.0 / (y / (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.9e+41:
		tmp = 2.0 / (z * (y / x))
	elif y <= 4e+39:
		tmp = -2.0 * ((x / z) / t)
	else:
		tmp = 2.0 / (y / (x / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.9e+41)
		tmp = Float64(2.0 / Float64(z * Float64(y / x)));
	elseif (y <= 4e+39)
		tmp = Float64(-2.0 * Float64(Float64(x / z) / t));
	else
		tmp = Float64(2.0 / Float64(y / Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.9e+41)
		tmp = 2.0 / (z * (y / x));
	elseif (y <= 4e+39)
		tmp = -2.0 * ((x / z) / t);
	else
		tmp = 2.0 / (y / (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.9e+41], N[(2.0 / N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+39], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.89999999999999988e41

   1. Initial program 74.6%

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

      1. distribute-rgt-out-- 82.2%

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

      2. times-frac 94.4%

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

   3. Simplified 94.4%

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

      1. clear-num 94.4%

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

      2. frac-times 94.5%

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

      3. metadata-eval 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in y around inf 78.3%

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

      1. associate-/l* 83.5%

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

      2. associate-/r/ 83.6%

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

   8. Simplified 83.6%

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

   if -2.89999999999999988e41 < y < 3.99999999999999976e39

   1. Initial program 87.0%

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

      1. associate-*r/ 86.9%

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

      2. distribute-rgt-out-- 87.7%

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

      3. associate-/l/ 88.1%

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

      4. sub-neg 88.1%

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

      5. +-commutative 88.1%

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

      6. neg-sub0 88.1%

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

      7. associate-+l- 88.1%

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

      8. sub0-neg 88.1%

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

      9. neg-mul-1 88.1%

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

      10. associate-/r* 88.1%

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

      11. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in t around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. *-commutative 75.4%

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

      3. associate-/r* 80.1%

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

   6. Simplified 80.1%

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

   if 3.99999999999999976e39 < y

   1. Initial program 82.4%

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

      1. associate-*l/ 82.4%

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

      2. *-commutative 82.4%

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

      3. distribute-rgt-out-- 87.9%

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

      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 inf 81.8%

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

      1. clear-num 81.7%

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

      2. un-div-inv 81.7%

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

      3. associate-/l* 86.8%

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

   6. Applied egg-rr 86.8%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+41}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+39}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{y}{\frac{x}{z}}}\\ \end{array} \]

Alternative 9: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+34}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+39}:\\ \;\;\;\;\frac{\frac{-2}{t}}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{y}{\frac{x}{z}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.4e+34)
   (/ 2.0 (* z (/ y x)))
   (if (<= y 1.25e+39) (/ (/ -2.0 t) (/ z x)) (/ 2.0 (/ y (/ x z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e+34) {
		tmp = 2.0 / (z * (y / x));
	} else if (y <= 1.25e+39) {
		tmp = (-2.0 / t) / (z / x);
	} else {
		tmp = 2.0 / (y / (x / 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 <= (-4.4d+34)) then
        tmp = 2.0d0 / (z * (y / x))
    else if (y <= 1.25d+39) then
        tmp = ((-2.0d0) / t) / (z / x)
    else
        tmp = 2.0d0 / (y / (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e+34) {
		tmp = 2.0 / (z * (y / x));
	} else if (y <= 1.25e+39) {
		tmp = (-2.0 / t) / (z / x);
	} else {
		tmp = 2.0 / (y / (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.4e+34:
		tmp = 2.0 / (z * (y / x))
	elif y <= 1.25e+39:
		tmp = (-2.0 / t) / (z / x)
	else:
		tmp = 2.0 / (y / (x / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.4e+34)
		tmp = Float64(2.0 / Float64(z * Float64(y / x)));
	elseif (y <= 1.25e+39)
		tmp = Float64(Float64(-2.0 / t) / Float64(z / x));
	else
		tmp = Float64(2.0 / Float64(y / Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.4e+34)
		tmp = 2.0 / (z * (y / x));
	elseif (y <= 1.25e+39)
		tmp = (-2.0 / t) / (z / x);
	else
		tmp = 2.0 / (y / (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.4e+34], N[(2.0 / N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+39], N[(N[(-2.0 / t), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4000000000000005e34

   1. Initial program 74.6%

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

      1. distribute-rgt-out-- 82.2%

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

      2. times-frac 94.4%

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

   3. Simplified 94.4%

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

      1. clear-num 94.4%

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

      2. frac-times 94.5%

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

      3. metadata-eval 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in y around inf 78.3%

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

      1. associate-/l* 83.5%

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

      2. associate-/r/ 83.6%

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

   8. Simplified 83.6%

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

   if -4.4000000000000005e34 < y < 1.25000000000000004e39

   1. Initial program 87.0%

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

      1. distribute-rgt-out-- 87.8%

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

      2. times-frac 94.3%

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

   3. Simplified 94.3%

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

      1. *-commutative 94.3%

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

      2. clear-num 94.2%

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

      3. un-div-inv 95.2%

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

   5. Applied egg-rr 95.2%

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

      1. flip-- 70.0%

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

      2. associate-/r/ 70.0%

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

   7. Applied egg-rr 70.0%

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

   8. Taylor expanded in y around 0 80.9%

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

   if 1.25000000000000004e39 < y

   1. Initial program 82.4%

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

      1. associate-*l/ 82.4%

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

      2. *-commutative 82.4%

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

      3. distribute-rgt-out-- 87.9%

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

      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 inf 81.8%

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

      1. clear-num 81.7%

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

      2. un-div-inv 81.7%

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

      3. associate-/l* 86.8%

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

   6. Applied egg-rr 86.8%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+34}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+39}:\\ \;\;\;\;\frac{\frac{-2}{t}}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{\frac{y}{\frac{x}{z}}}\\ \end{array} \]

Alternative 10: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+34}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{\frac{-2}{t}}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{y}}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.9e+34)
   (/ 2.0 (* z (/ y x)))
   (if (<= y 8.2e+40) (/ (/ -2.0 t) (/ z x)) (/ (/ 2.0 y) (/ z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.9e+34) {
		tmp = 2.0 / (z * (y / x));
	} else if (y <= 8.2e+40) {
		tmp = (-2.0 / t) / (z / x);
	} else {
		tmp = (2.0 / y) / (z / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.9d+34)) then
        tmp = 2.0d0 / (z * (y / x))
    else if (y <= 8.2d+40) then
        tmp = ((-2.0d0) / t) / (z / x)
    else
        tmp = (2.0d0 / y) / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.9e+34) {
		tmp = 2.0 / (z * (y / x));
	} else if (y <= 8.2e+40) {
		tmp = (-2.0 / t) / (z / x);
	} else {
		tmp = (2.0 / y) / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.9e+34:
		tmp = 2.0 / (z * (y / x))
	elif y <= 8.2e+40:
		tmp = (-2.0 / t) / (z / x)
	else:
		tmp = (2.0 / y) / (z / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.9e+34)
		tmp = Float64(2.0 / Float64(z * Float64(y / x)));
	elseif (y <= 8.2e+40)
		tmp = Float64(Float64(-2.0 / t) / Float64(z / x));
	else
		tmp = Float64(Float64(2.0 / y) / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.9e+34)
		tmp = 2.0 / (z * (y / x));
	elseif (y <= 8.2e+40)
		tmp = (-2.0 / t) / (z / x);
	else
		tmp = (2.0 / y) / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.9e+34], N[(2.0 / N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+40], N[(N[(-2.0 / t), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / y), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9000000000000001e34

   1. Initial program 74.6%

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

      1. distribute-rgt-out-- 82.2%

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

      2. times-frac 94.4%

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

   3. Simplified 94.4%

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

      1. clear-num 94.4%

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

      2. frac-times 94.5%

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

      3. metadata-eval 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in y around inf 78.3%

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

      1. associate-/l* 83.5%

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

      2. associate-/r/ 83.6%

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

   8. Simplified 83.6%

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

   if -2.9000000000000001e34 < y < 8.2000000000000003e40

   1. Initial program 87.0%

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

      1. distribute-rgt-out-- 87.8%

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

      2. times-frac 94.3%

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

   3. Simplified 94.3%

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

      1. *-commutative 94.3%

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

      2. clear-num 94.2%

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

      3. un-div-inv 95.2%

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

   5. Applied egg-rr 95.2%

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

      1. flip-- 70.0%

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

      2. associate-/r/ 70.0%

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

   7. Applied egg-rr 70.0%

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

   8. Taylor expanded in y around 0 80.9%

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

   if 8.2000000000000003e40 < y

   1. Initial program 82.4%

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

      1. distribute-rgt-out-- 87.9%

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

      2. times-frac 94.5%

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

   3. Simplified 94.5%

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

      1. *-commutative 94.5%

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

      2. clear-num 94.5%

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

      3. un-div-inv 94.6%

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

   5. Applied egg-rr 94.6%

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

      1. flip-- 50.6%

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

      2. associate-/r/ 50.7%

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

   7. Applied egg-rr 50.7%

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

   8. Taylor expanded in y around inf 86.9%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+34}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{\frac{-2}{t}}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{y}}{\frac{z}{x}}\\ \end{array} \]

Alternative 11: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+39}:\\ \;\;\;\;\frac{\frac{-2}{t}}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.4e+37)
   (/ 2.0 (* z (/ y x)))
   (if (<= y 4.3e+39) (/ (/ -2.0 t) (/ z x)) (/ (/ (* x 2.0) z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.4e+37) {
		tmp = 2.0 / (z * (y / x));
	} else if (y <= 4.3e+39) {
		tmp = (-2.0 / t) / (z / x);
	} else {
		tmp = ((x * 2.0) / z) / 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 <= (-6.4d+37)) then
        tmp = 2.0d0 / (z * (y / x))
    else if (y <= 4.3d+39) then
        tmp = ((-2.0d0) / t) / (z / x)
    else
        tmp = ((x * 2.0d0) / z) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.4e+37) {
		tmp = 2.0 / (z * (y / x));
	} else if (y <= 4.3e+39) {
		tmp = (-2.0 / t) / (z / x);
	} else {
		tmp = ((x * 2.0) / z) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.4e+37:
		tmp = 2.0 / (z * (y / x))
	elif y <= 4.3e+39:
		tmp = (-2.0 / t) / (z / x)
	else:
		tmp = ((x * 2.0) / z) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.4e+37)
		tmp = Float64(2.0 / Float64(z * Float64(y / x)));
	elseif (y <= 4.3e+39)
		tmp = Float64(Float64(-2.0 / t) / Float64(z / x));
	else
		tmp = Float64(Float64(Float64(x * 2.0) / z) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.4e+37)
		tmp = 2.0 / (z * (y / x));
	elseif (y <= 4.3e+39)
		tmp = (-2.0 / t) / (z / x);
	else
		tmp = ((x * 2.0) / z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.4e+37], N[(2.0 / N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+39], N[(N[(-2.0 / t), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * 2.0), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.40000000000000027e37

   1. Initial program 74.6%

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

      1. distribute-rgt-out-- 82.2%

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

      2. times-frac 94.4%

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

   3. Simplified 94.4%

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

      1. clear-num 94.4%

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

      2. frac-times 94.5%

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

      3. metadata-eval 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in y around inf 78.3%

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

      1. associate-/l* 83.5%

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

      2. associate-/r/ 83.6%

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

   8. Simplified 83.6%

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

   if -6.40000000000000027e37 < y < 4.3e39

   1. Initial program 87.0%

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

      1. distribute-rgt-out-- 87.8%

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

      2. times-frac 94.3%

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

   3. Simplified 94.3%

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

      1. *-commutative 94.3%

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

      2. clear-num 94.2%

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

      3. un-div-inv 95.2%

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

   5. Applied egg-rr 95.2%

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

      1. flip-- 70.0%

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

      2. associate-/r/ 70.0%

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

   7. Applied egg-rr 70.0%

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

   8. Taylor expanded in y around 0 80.9%

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

   if 4.3e39 < y

   1. Initial program 82.4%

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

      1. distribute-rgt-out-- 87.9%

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

      2. times-frac 94.5%

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

   3. Simplified 94.5%

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

      1. clear-num 94.5%

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

      2. frac-times 94.5%

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

      3. metadata-eval 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in y around inf 81.8%

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

      1. associate-*r/ 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-/l/ 86.9%

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

   8. Simplified 86.9%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+39}:\\ \;\;\;\;\frac{\frac{-2}{t}}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{z}}{y}\\ \end{array} \]

Alternative 12: 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 83.4%

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

   1. associate-*l/ 83.4%

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

   2. *-commutative 83.4%

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

   3. distribute-rgt-out-- 86.6%

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

   4. associate-/r* 94.5%

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

3. Simplified 94.5%

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

4. Final simplification 94.5%

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

Alternative 13: 54.4% accurate, 1.6× speedup

Math

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

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(x / Float64(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[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.4%

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

   1. associate-*l/ 83.4%

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

   2. *-commutative 83.4%

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

   3. distribute-rgt-out-- 86.6%

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

   4. associate-/r* 94.5%

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

3. Simplified 94.5%

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

4. Taylor expanded in y around inf 48.8%

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

5. Final simplification 48.8%

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

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 2023240 
(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))))