Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.5% → 95.7%

Time: 9.2s

Alternatives: 15

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: 89.5% 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: 95.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - z \cdot t\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+208}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{y - t}}{z}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-253}:\\ \;\;\;\;\frac{x \cdot 2}{t_1}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) (* z t))))
   (if (<= t_1 -4e+208)
     (/ (/ (* x 2.0) (- y t)) z)
     (if (<= t_1 -1e-253) (/ (* x 2.0) t_1) (* 2.0 (/ (/ x z) (- y t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if (t_1 <= -4e+208) {
		tmp = ((x * 2.0) / (y - t)) / z;
	} else if (t_1 <= -1e-253) {
		tmp = (x * 2.0) / t_1;
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * z) - (z * t)
    if (t_1 <= (-4d+208)) then
        tmp = ((x * 2.0d0) / (y - t)) / z
    else if (t_1 <= (-1d-253)) then
        tmp = (x * 2.0d0) / t_1
    else
        tmp = 2.0d0 * ((x / z) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if (t_1 <= -4e+208) {
		tmp = ((x * 2.0) / (y - t)) / z;
	} else if (t_1 <= -1e-253) {
		tmp = (x * 2.0) / t_1;
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - (z * t)
	tmp = 0
	if t_1 <= -4e+208:
		tmp = ((x * 2.0) / (y - t)) / z
	elif t_1 <= -1e-253:
		tmp = (x * 2.0) / t_1
	else:
		tmp = 2.0 * ((x / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= -4e+208)
		tmp = Float64(Float64(Float64(x * 2.0) / Float64(y - t)) / z);
	elseif (t_1 <= -1e-253)
		tmp = Float64(Float64(x * 2.0) / t_1);
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) - (z * t);
	tmp = 0.0;
	if (t_1 <= -4e+208)
		tmp = ((x * 2.0) / (y - t)) / z;
	elseif (t_1 <= -1e-253)
		tmp = (x * 2.0) / t_1;
	else
		tmp = 2.0 * ((x / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+208], N[(N[(N[(x * 2.0), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -1e-253], N[(N[(x * 2.0), $MachinePrecision] / t$95$1), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 y z) (*.f64 t z)) < -3.9999999999999999e208

   1. Initial program 78.4%

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

      1. associate-*l/ 78.4%

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

      2. *-commutative 78.4%

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

      3. distribute-rgt-out-- 78.4%

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

      4. associate-/r* 97.4%

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

   3. Simplified 97.4%

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

      1. associate-/l/ 78.4%

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

      2. *-un-lft-identity 78.4%

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

      3. times-frac 97.3%

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

      4. associate-*l* 97.3%

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

      5. div-inv 97.3%

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

      6. *-commutative 97.3%

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

      7. associate-*l/ 99.8%

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

      8. associate-*r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   if -3.9999999999999999e208 < (-.f64 (*.f64 y z) (*.f64 t z)) < -1.0000000000000001e-253

   1. Initial program 99.7%

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

   if -1.0000000000000001e-253 < (-.f64 (*.f64 y z) (*.f64 t z))

   1. Initial program 83.6%

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

      1. associate-*l/ 83.6%

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

      2. *-commutative 83.6%

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

      3. distribute-rgt-out-- 85.8%

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

      4. associate-/r* 97.7%

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

   3. Simplified 97.7%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - z \cdot t \leq -4 \cdot 10^{+208}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{y - t}}{z}\\ \mathbf{elif}\;y \cdot z - z \cdot t \leq -1 \cdot 10^{-253}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 2: 96.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -4 \cdot 10^{+86} \lor \neg \left(x \cdot 2 \leq 5 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{\frac{x \cdot 2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{y - t}}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* x 2.0) -4e+86) (not (<= (* x 2.0) 5e-31)))
   (/ (/ (* x 2.0) (- y t)) z)
   (/ (/ 2.0 (- y t)) (/ z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * 2.0) <= -4e+86) || !((x * 2.0) <= 5e-31)) {
		tmp = ((x * 2.0) / (y - t)) / z;
	} else {
		tmp = (2.0 / (y - t)) / (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 (((x * 2.0d0) <= (-4d+86)) .or. (.not. ((x * 2.0d0) <= 5d-31))) then
        tmp = ((x * 2.0d0) / (y - t)) / z
    else
        tmp = (2.0d0 / (y - t)) / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * 2.0) <= -4e+86) || !((x * 2.0) <= 5e-31)) {
		tmp = ((x * 2.0) / (y - t)) / z;
	} else {
		tmp = (2.0 / (y - t)) / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * 2.0) <= -4e+86) or not ((x * 2.0) <= 5e-31):
		tmp = ((x * 2.0) / (y - t)) / z
	else:
		tmp = (2.0 / (y - t)) / (z / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x * 2.0) <= -4e+86) || !(Float64(x * 2.0) <= 5e-31))
		tmp = Float64(Float64(Float64(x * 2.0) / Float64(y - t)) / z);
	else
		tmp = Float64(Float64(2.0 / Float64(y - t)) / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * 2.0) <= -4e+86) || ~(((x * 2.0) <= 5e-31)))
		tmp = ((x * 2.0) / (y - t)) / z;
	else
		tmp = (2.0 / (y - t)) / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x * 2.0), $MachinePrecision], -4e+86], N[Not[LessEqual[N[(x * 2.0), $MachinePrecision], 5e-31]], $MachinePrecision]], N[(N[(N[(x * 2.0), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 2) < -4.0000000000000001e86 or 5e-31 < (*.f64 x 2)

   1. Initial program 80.3%

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

      1. associate-*l/ 80.3%

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

      2. *-commutative 80.3%

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

      3. distribute-rgt-out-- 81.3%

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

      4. associate-/r* 88.9%

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

   3. Simplified 88.9%

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

      1. associate-/l/ 81.3%

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

      2. *-un-lft-identity 81.3%

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

      3. times-frac 88.8%

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

      4. associate-*l* 88.8%

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

      5. div-inv 88.8%

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

      6. *-commutative 88.8%

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

      7. associate-*l/ 98.0%

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

      8. associate-*r/ 98.2%

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

   5. Applied egg-rr 98.2%

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

   if -4.0000000000000001e86 < (*.f64 x 2) < 5e-31

   1. Initial program 93.6%

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

      1. associate-*l/ 93.6%

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

      2. *-commutative 93.6%

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

      3. distribute-rgt-out-- 95.0%

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

      4. associate-/r* 97.1%

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

   3. Simplified 97.1%

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

      1. clear-num 96.1%

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

      2. associate-*r/ 96.1%

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

      3. div-inv 96.1%

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

      4. clear-num 96.2%

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

      5. frac-times 97.1%

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

      6. un-div-inv 97.2%

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

   5. Applied egg-rr 97.2%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -4 \cdot 10^{+86} \lor \neg \left(x \cdot 2 \leq 5 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{\frac{x \cdot 2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{y - t}}{\frac{z}{x}}\\ \end{array} \]

Alternative 3: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-21}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-79}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.8e-21)
   (* -2.0 (/ (/ x z) t))
   (if (<= t -1.05e-72)
     (* (/ x z) (/ 2.0 y))
     (if (<= t -2.15e-79)
       (* -2.0 (/ x (* z t)))
       (if (<= t 6.5e-36) (/ 2.0 (* z (/ y x))) (* -2.0 (/ (/ x t) z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.8e-21) {
		tmp = -2.0 * ((x / z) / t);
	} else if (t <= -1.05e-72) {
		tmp = (x / z) * (2.0 / y);
	} else if (t <= -2.15e-79) {
		tmp = -2.0 * (x / (z * t));
	} else if (t <= 6.5e-36) {
		tmp = 2.0 / (z * (y / x));
	} else {
		tmp = -2.0 * ((x / 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 (t <= (-5.8d-21)) then
        tmp = (-2.0d0) * ((x / z) / t)
    else if (t <= (-1.05d-72)) then
        tmp = (x / z) * (2.0d0 / y)
    else if (t <= (-2.15d-79)) then
        tmp = (-2.0d0) * (x / (z * t))
    else if (t <= 6.5d-36) then
        tmp = 2.0d0 / (z * (y / x))
    else
        tmp = (-2.0d0) * ((x / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.8e-21) {
		tmp = -2.0 * ((x / z) / t);
	} else if (t <= -1.05e-72) {
		tmp = (x / z) * (2.0 / y);
	} else if (t <= -2.15e-79) {
		tmp = -2.0 * (x / (z * t));
	} else if (t <= 6.5e-36) {
		tmp = 2.0 / (z * (y / x));
	} else {
		tmp = -2.0 * ((x / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.8e-21:
		tmp = -2.0 * ((x / z) / t)
	elif t <= -1.05e-72:
		tmp = (x / z) * (2.0 / y)
	elif t <= -2.15e-79:
		tmp = -2.0 * (x / (z * t))
	elif t <= 6.5e-36:
		tmp = 2.0 / (z * (y / x))
	else:
		tmp = -2.0 * ((x / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.8e-21)
		tmp = Float64(-2.0 * Float64(Float64(x / z) / t));
	elseif (t <= -1.05e-72)
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	elseif (t <= -2.15e-79)
		tmp = Float64(-2.0 * Float64(x / Float64(z * t)));
	elseif (t <= 6.5e-36)
		tmp = Float64(2.0 / Float64(z * Float64(y / x)));
	else
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.8e-21)
		tmp = -2.0 * ((x / z) / t);
	elseif (t <= -1.05e-72)
		tmp = (x / z) * (2.0 / y);
	elseif (t <= -2.15e-79)
		tmp = -2.0 * (x / (z * t));
	elseif (t <= 6.5e-36)
		tmp = 2.0 / (z * (y / x));
	else
		tmp = -2.0 * ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.8e-21], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.05e-72], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.15e-79], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e-36], N[(2.0 / N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.8e-21

   1. Initial program 86.4%

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

      1. associate-*l/ 86.3%

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

      2. *-commutative 86.3%

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

      3. distribute-rgt-out-- 88.0%

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

      4. associate-/r* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. *-commutative 71.8%

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

      3. associate-/r* 79.3%

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

   6. Simplified 79.3%

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

   if -5.8e-21 < t < -1.05e-72

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. distribute-rgt-out-- 99.7%

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

      4. associate-/r* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in y around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. *-commutative 86.1%

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

      3. *-commutative 86.1%

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

      4. associate-/r* 86.1%

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

      5. associate-*l/ 86.1%

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

      6. *-commutative 86.1%

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

   6. Simplified 86.1%

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

      1. clear-num 86.1%

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

      2. un-div-inv 86.1%

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

   8. Applied egg-rr 86.1%

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

      1. associate-/r/ 86.1%

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

      2. clear-num 86.1%

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

      3. associate-*l/ 86.1%

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

      4. *-un-lft-identity 86.1%

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

      5. un-div-inv 86.1%

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

      6. clear-num 86.1%

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

      7. associate-*r/ 86.1%

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

      8. associate-/r* 86.1%

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

      9. times-frac 86.1%

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

   10. Applied egg-rr 86.1%

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

   if -1.05e-72 < t < -2.14999999999999991e-79

   1. Initial program 75.0%

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

      1. associate-*l/ 75.0%

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

      2. *-commutative 75.0%

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

      3. distribute-rgt-out-- 100.0%

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

      4. associate-/r* 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around 0 100.0%

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

   if -2.14999999999999991e-79 < t < 6.50000000000000012e-36

   1. Initial program 85.7%

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

      1. associate-*l/ 85.7%

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

      2. *-commutative 85.7%

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

      3. distribute-rgt-out-- 85.7%

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

      4. associate-/r* 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in y around inf 74.5%

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

      1. associate-*r/ 74.5%

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

      2. *-commutative 74.5%

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

      3. *-commutative 74.5%

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

      4. associate-/r* 80.8%

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

      5. associate-*l/ 80.8%

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

      6. *-commutative 80.8%

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

   6. Simplified 80.8%

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

      1. clear-num 80.7%

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

      2. un-div-inv 80.7%

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

   8. Applied egg-rr 80.7%

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

      1. associate-/r/ 80.7%

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

      2. clear-num 80.7%

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

      3. associate-*l/ 80.8%

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

      4. *-un-lft-identity 80.8%

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

      5. un-div-inv 80.7%

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

      6. clear-num 80.7%

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

      7. associate-*r/ 80.8%

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

      8. associate-/r* 74.5%

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

      9. times-frac 80.7%

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

   10. Applied egg-rr 80.7%

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

       1. frac-times 74.5%

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

       2. *-commutative 74.5%

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

       3. associate-/l* 74.0%

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

       4. *-commutative 74.0%

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

       5. associate-*l/ 81.8%

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

       6. *-commutative 81.8%

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

   12. Applied egg-rr 81.8%

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

   if 6.50000000000000012e-36 < t

   1. Initial program 90.9%

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

      1. associate-*l/ 90.9%

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

      2. *-commutative 90.9%

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

      3. distribute-rgt-out-- 92.4%

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

      4. associate-/r* 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in y around 0 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-/r* 76.5%

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

   6. Simplified 76.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{z} \cdot -2} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-21}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-79}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \]

Alternative 4: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-19}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-79}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-33}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.5e-19)
   (* -2.0 (/ (/ x z) t))
   (if (<= t -3.2e-72)
     (* (/ x z) (/ 2.0 y))
     (if (<= t -1.35e-79)
       (* -2.0 (/ x (* z t)))
       (if (<= t 2.4e-33) (/ (* 2.0 (/ x y)) z) (* -2.0 (/ (/ x t) z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.5e-19) {
		tmp = -2.0 * ((x / z) / t);
	} else if (t <= -3.2e-72) {
		tmp = (x / z) * (2.0 / y);
	} else if (t <= -1.35e-79) {
		tmp = -2.0 * (x / (z * t));
	} else if (t <= 2.4e-33) {
		tmp = (2.0 * (x / y)) / z;
	} else {
		tmp = -2.0 * ((x / 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 (t <= (-3.5d-19)) then
        tmp = (-2.0d0) * ((x / z) / t)
    else if (t <= (-3.2d-72)) then
        tmp = (x / z) * (2.0d0 / y)
    else if (t <= (-1.35d-79)) then
        tmp = (-2.0d0) * (x / (z * t))
    else if (t <= 2.4d-33) then
        tmp = (2.0d0 * (x / y)) / z
    else
        tmp = (-2.0d0) * ((x / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.5e-19) {
		tmp = -2.0 * ((x / z) / t);
	} else if (t <= -3.2e-72) {
		tmp = (x / z) * (2.0 / y);
	} else if (t <= -1.35e-79) {
		tmp = -2.0 * (x / (z * t));
	} else if (t <= 2.4e-33) {
		tmp = (2.0 * (x / y)) / z;
	} else {
		tmp = -2.0 * ((x / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.5e-19:
		tmp = -2.0 * ((x / z) / t)
	elif t <= -3.2e-72:
		tmp = (x / z) * (2.0 / y)
	elif t <= -1.35e-79:
		tmp = -2.0 * (x / (z * t))
	elif t <= 2.4e-33:
		tmp = (2.0 * (x / y)) / z
	else:
		tmp = -2.0 * ((x / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.5e-19)
		tmp = Float64(-2.0 * Float64(Float64(x / z) / t));
	elseif (t <= -3.2e-72)
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	elseif (t <= -1.35e-79)
		tmp = Float64(-2.0 * Float64(x / Float64(z * t)));
	elseif (t <= 2.4e-33)
		tmp = Float64(Float64(2.0 * Float64(x / y)) / z);
	else
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.5e-19)
		tmp = -2.0 * ((x / z) / t);
	elseif (t <= -3.2e-72)
		tmp = (x / z) * (2.0 / y);
	elseif (t <= -1.35e-79)
		tmp = -2.0 * (x / (z * t));
	elseif (t <= 2.4e-33)
		tmp = (2.0 * (x / y)) / z;
	else
		tmp = -2.0 * ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.5e-19], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.2e-72], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.35e-79], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-33], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.50000000000000015e-19

   1. Initial program 86.4%

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

      1. associate-*l/ 86.3%

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

      2. *-commutative 86.3%

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

      3. distribute-rgt-out-- 88.0%

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

      4. associate-/r* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. *-commutative 71.8%

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

      3. associate-/r* 79.3%

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

   6. Simplified 79.3%

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

   if -3.50000000000000015e-19 < t < -3.19999999999999999e-72

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. distribute-rgt-out-- 99.7%

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

      4. associate-/r* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in y around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. *-commutative 86.1%

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

      3. *-commutative 86.1%

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

      4. associate-/r* 86.1%

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

      5. associate-*l/ 86.1%

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

      6. *-commutative 86.1%

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

   6. Simplified 86.1%

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

      1. clear-num 86.1%

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

      2. un-div-inv 86.1%

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

   8. Applied egg-rr 86.1%

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

      1. associate-/r/ 86.1%

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

      2. clear-num 86.1%

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

      3. associate-*l/ 86.1%

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

      4. *-un-lft-identity 86.1%

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

      5. un-div-inv 86.1%

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

      6. clear-num 86.1%

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

      7. associate-*r/ 86.1%

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

      8. associate-/r* 86.1%

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

      9. times-frac 86.1%

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

   10. Applied egg-rr 86.1%

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

   if -3.19999999999999999e-72 < t < -1.3500000000000001e-79

   1. Initial program 75.0%

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

      1. associate-*l/ 75.0%

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

      2. *-commutative 75.0%

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

      3. distribute-rgt-out-- 100.0%

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

      4. associate-/r* 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around 0 100.0%

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

   if -1.3500000000000001e-79 < t < 2.4e-33

   1. Initial program 85.7%

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

      1. associate-*l/ 85.7%

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

      2. *-commutative 85.7%

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

      3. distribute-rgt-out-- 85.7%

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

      4. associate-/r* 92.0%

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

   3. Simplified 92.0%

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

      1. associate-/l/ 85.7%

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

      2. *-un-lft-identity 85.7%

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

      3. times-frac 91.9%

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

      4. associate-*l* 91.9%

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

      5. div-inv 91.9%

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

      6. *-commutative 91.9%

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

      7. associate-*l/ 95.8%

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

      8. associate-*r/ 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in y around inf 83.1%

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

   if 2.4e-33 < t

   1. Initial program 90.9%

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

      1. associate-*l/ 90.9%

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

      2. *-commutative 90.9%

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

      3. distribute-rgt-out-- 92.4%

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

      4. associate-/r* 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in y around 0 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-/r* 76.5%

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

   6. Simplified 76.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{z} \cdot -2} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-19}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-79}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-33}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \]

Alternative 5: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-21}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{z}}{t}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;t \leq -1.36 \cdot 10^{-80}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-34}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.4e-21)
   (/ (/ (* x -2.0) z) t)
   (if (<= t -1.15e-72)
     (* (/ x z) (/ 2.0 y))
     (if (<= t -1.36e-80)
       (* -2.0 (/ x (* z t)))
       (if (<= t 4.8e-34) (/ (* 2.0 (/ x y)) z) (* -2.0 (/ (/ x t) z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.4e-21) {
		tmp = ((x * -2.0) / z) / t;
	} else if (t <= -1.15e-72) {
		tmp = (x / z) * (2.0 / y);
	} else if (t <= -1.36e-80) {
		tmp = -2.0 * (x / (z * t));
	} else if (t <= 4.8e-34) {
		tmp = (2.0 * (x / y)) / z;
	} else {
		tmp = -2.0 * ((x / 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 (t <= (-3.4d-21)) then
        tmp = ((x * (-2.0d0)) / z) / t
    else if (t <= (-1.15d-72)) then
        tmp = (x / z) * (2.0d0 / y)
    else if (t <= (-1.36d-80)) then
        tmp = (-2.0d0) * (x / (z * t))
    else if (t <= 4.8d-34) then
        tmp = (2.0d0 * (x / y)) / z
    else
        tmp = (-2.0d0) * ((x / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.4e-21) {
		tmp = ((x * -2.0) / z) / t;
	} else if (t <= -1.15e-72) {
		tmp = (x / z) * (2.0 / y);
	} else if (t <= -1.36e-80) {
		tmp = -2.0 * (x / (z * t));
	} else if (t <= 4.8e-34) {
		tmp = (2.0 * (x / y)) / z;
	} else {
		tmp = -2.0 * ((x / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.4e-21:
		tmp = ((x * -2.0) / z) / t
	elif t <= -1.15e-72:
		tmp = (x / z) * (2.0 / y)
	elif t <= -1.36e-80:
		tmp = -2.0 * (x / (z * t))
	elif t <= 4.8e-34:
		tmp = (2.0 * (x / y)) / z
	else:
		tmp = -2.0 * ((x / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.4e-21)
		tmp = Float64(Float64(Float64(x * -2.0) / z) / t);
	elseif (t <= -1.15e-72)
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	elseif (t <= -1.36e-80)
		tmp = Float64(-2.0 * Float64(x / Float64(z * t)));
	elseif (t <= 4.8e-34)
		tmp = Float64(Float64(2.0 * Float64(x / y)) / z);
	else
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.4e-21)
		tmp = ((x * -2.0) / z) / t;
	elseif (t <= -1.15e-72)
		tmp = (x / z) * (2.0 / y);
	elseif (t <= -1.36e-80)
		tmp = -2.0 * (x / (z * t));
	elseif (t <= 4.8e-34)
		tmp = (2.0 * (x / y)) / z;
	else
		tmp = -2.0 * ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.4e-21], N[(N[(N[(x * -2.0), $MachinePrecision] / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -1.15e-72], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.36e-80], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-34], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.4e-21

   1. Initial program 86.4%

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

      1. associate-*l/ 86.3%

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

      2. *-commutative 86.3%

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

      3. distribute-rgt-out-- 88.0%

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

      4. associate-/r* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around 0 71.8%

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

      1. associate-*r/ 71.8%

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

      2. metadata-eval 71.8%

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

      3. distribute-lft-neg-in 71.8%

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

      4. *-commutative 71.8%

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

      5. *-commutative 71.8%

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

      6. associate-/r* 79.3%

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

      7. distribute-rgt-neg-in 79.3%

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

      8. metadata-eval 79.3%

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

   6. Applied egg-rr 79.3%

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

   if -3.4e-21 < t < -1.14999999999999997e-72

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. distribute-rgt-out-- 99.7%

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

      4. associate-/r* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in y around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. *-commutative 86.1%

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

      3. *-commutative 86.1%

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

      4. associate-/r* 86.1%

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

      5. associate-*l/ 86.1%

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

      6. *-commutative 86.1%

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

   6. Simplified 86.1%

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

      1. clear-num 86.1%

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

      2. un-div-inv 86.1%

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

   8. Applied egg-rr 86.1%

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

      1. associate-/r/ 86.1%

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

      2. clear-num 86.1%

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

      3. associate-*l/ 86.1%

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

      4. *-un-lft-identity 86.1%

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

      5. un-div-inv 86.1%

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

      6. clear-num 86.1%

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

      7. associate-*r/ 86.1%

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

      8. associate-/r* 86.1%

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

      9. times-frac 86.1%

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

   10. Applied egg-rr 86.1%

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

   if -1.14999999999999997e-72 < t < -1.3599999999999999e-80

   1. Initial program 75.0%

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

      1. associate-*l/ 75.0%

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

      2. *-commutative 75.0%

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

      3. distribute-rgt-out-- 100.0%

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

      4. associate-/r* 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around 0 100.0%

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

   if -1.3599999999999999e-80 < t < 4.79999999999999982e-34

   1. Initial program 85.7%

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

      1. associate-*l/ 85.7%

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

      2. *-commutative 85.7%

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

      3. distribute-rgt-out-- 85.7%

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

      4. associate-/r* 92.0%

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

   3. Simplified 92.0%

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

      1. associate-/l/ 85.7%

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

      2. *-un-lft-identity 85.7%

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

      3. times-frac 91.9%

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

      4. associate-*l* 91.9%

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

      5. div-inv 91.9%

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

      6. *-commutative 91.9%

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

      7. associate-*l/ 95.8%

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

      8. associate-*r/ 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in y around inf 83.1%

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

   if 4.79999999999999982e-34 < t

   1. Initial program 90.9%

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

      1. associate-*l/ 90.9%

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

      2. *-commutative 90.9%

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

      3. distribute-rgt-out-- 92.4%

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

      4. associate-/r* 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in y around 0 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-/r* 76.5%

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

   6. Simplified 76.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{z} \cdot -2} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-21}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{z}}{t}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;t \leq -1.36 \cdot 10^{-80}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-34}:\\ \;\;\;\;\frac{2 \cdot \frac{x}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \]

Alternative 6: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-21}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{z}}{t}\\ \mathbf{elif}\;t \leq -1.26 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-80}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-34}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4e-21)
   (/ (/ (* x -2.0) z) t)
   (if (<= t -1.26e-73)
     (* (/ x z) (/ 2.0 y))
     (if (<= t -7.2e-80)
       (* -2.0 (/ x (* z t)))
       (if (<= t 1.8e-34) (/ (/ (* x 2.0) y) z) (* -2.0 (/ (/ x t) z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4e-21) {
		tmp = ((x * -2.0) / z) / t;
	} else if (t <= -1.26e-73) {
		tmp = (x / z) * (2.0 / y);
	} else if (t <= -7.2e-80) {
		tmp = -2.0 * (x / (z * t));
	} else if (t <= 1.8e-34) {
		tmp = ((x * 2.0) / y) / z;
	} else {
		tmp = -2.0 * ((x / 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 (t <= (-4d-21)) then
        tmp = ((x * (-2.0d0)) / z) / t
    else if (t <= (-1.26d-73)) then
        tmp = (x / z) * (2.0d0 / y)
    else if (t <= (-7.2d-80)) then
        tmp = (-2.0d0) * (x / (z * t))
    else if (t <= 1.8d-34) then
        tmp = ((x * 2.0d0) / y) / z
    else
        tmp = (-2.0d0) * ((x / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4e-21) {
		tmp = ((x * -2.0) / z) / t;
	} else if (t <= -1.26e-73) {
		tmp = (x / z) * (2.0 / y);
	} else if (t <= -7.2e-80) {
		tmp = -2.0 * (x / (z * t));
	} else if (t <= 1.8e-34) {
		tmp = ((x * 2.0) / y) / z;
	} else {
		tmp = -2.0 * ((x / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4e-21:
		tmp = ((x * -2.0) / z) / t
	elif t <= -1.26e-73:
		tmp = (x / z) * (2.0 / y)
	elif t <= -7.2e-80:
		tmp = -2.0 * (x / (z * t))
	elif t <= 1.8e-34:
		tmp = ((x * 2.0) / y) / z
	else:
		tmp = -2.0 * ((x / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4e-21)
		tmp = Float64(Float64(Float64(x * -2.0) / z) / t);
	elseif (t <= -1.26e-73)
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	elseif (t <= -7.2e-80)
		tmp = Float64(-2.0 * Float64(x / Float64(z * t)));
	elseif (t <= 1.8e-34)
		tmp = Float64(Float64(Float64(x * 2.0) / y) / z);
	else
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4e-21)
		tmp = ((x * -2.0) / z) / t;
	elseif (t <= -1.26e-73)
		tmp = (x / z) * (2.0 / y);
	elseif (t <= -7.2e-80)
		tmp = -2.0 * (x / (z * t));
	elseif (t <= 1.8e-34)
		tmp = ((x * 2.0) / y) / z;
	else
		tmp = -2.0 * ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4e-21], N[(N[(N[(x * -2.0), $MachinePrecision] / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, -1.26e-73], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.2e-80], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-34], N[(N[(N[(x * 2.0), $MachinePrecision] / y), $MachinePrecision] / z), $MachinePrecision], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.99999999999999963e-21

   1. Initial program 86.4%

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

      1. associate-*l/ 86.3%

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

      2. *-commutative 86.3%

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

      3. distribute-rgt-out-- 88.0%

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

      4. associate-/r* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around 0 71.8%

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

      1. associate-*r/ 71.8%

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

      2. metadata-eval 71.8%

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

      3. distribute-lft-neg-in 71.8%

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

      4. *-commutative 71.8%

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

      5. *-commutative 71.8%

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

      6. associate-/r* 79.3%

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

      7. distribute-rgt-neg-in 79.3%

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

      8. metadata-eval 79.3%

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

   6. Applied egg-rr 79.3%

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

   if -3.99999999999999963e-21 < t < -1.26000000000000001e-73

   1. Initial program 99.7%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. distribute-rgt-out-- 99.7%

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

      4. associate-/r* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in y around inf 86.1%

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

      1. associate-*r/ 86.1%

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

      2. *-commutative 86.1%

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

      3. *-commutative 86.1%

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

      4. associate-/r* 86.1%

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

      5. associate-*l/ 86.1%

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

      6. *-commutative 86.1%

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

   6. Simplified 86.1%

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

      1. clear-num 86.1%

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

      2. un-div-inv 86.1%

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

   8. Applied egg-rr 86.1%

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

      1. associate-/r/ 86.1%

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

      2. clear-num 86.1%

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

      3. associate-*l/ 86.1%

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

      4. *-un-lft-identity 86.1%

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

      5. un-div-inv 86.1%

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

      6. clear-num 86.1%

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

      7. associate-*r/ 86.1%

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

      8. associate-/r* 86.1%

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

      9. times-frac 86.1%

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

   10. Applied egg-rr 86.1%

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

   if -1.26000000000000001e-73 < t < -7.2e-80

   1. Initial program 75.0%

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

      1. associate-*l/ 75.0%

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

      2. *-commutative 75.0%

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

      3. distribute-rgt-out-- 100.0%

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

      4. associate-/r* 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in y around 0 100.0%

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

   if -7.2e-80 < t < 1.80000000000000004e-34

   1. Initial program 85.7%

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

      1. associate-*r/ 85.5%

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

      2. distribute-rgt-out-- 85.5%

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

      3. associate-/l/ 85.7%

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

      4. sub-neg 85.7%

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

      5. +-commutative 85.7%

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

      6. neg-sub0 85.7%

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

      7. associate-+l- 85.7%

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

      8. sub0-neg 85.7%

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

      9. neg-mul-1 85.7%

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

      10. associate-/r* 85.7%

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

      11. metadata-eval 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in t around 0 74.4%

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

      1. associate-*r/ 74.5%

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

      2. associate-/r* 83.1%

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

   6. Applied egg-rr 83.1%

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

   if 1.80000000000000004e-34 < t

   1. Initial program 90.9%

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

      1. associate-*l/ 90.9%

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

      2. *-commutative 90.9%

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

      3. distribute-rgt-out-- 92.4%

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

      4. associate-/r* 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in y around 0 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-/r* 76.5%

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

   6. Simplified 76.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{t}}{z} \cdot -2} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-21}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{z}}{t}\\ \mathbf{elif}\;t \leq -1.26 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-80}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-34}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \]

Alternative 7: 72.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-22} \lor \neg \left(t \leq 2.2 \cdot 10^{+41}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7e-22) (not (<= t 2.2e+41)))
   (* -2.0 (/ x (* z t)))
   (* x (/ 2.0 (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7e-22) || !(t <= 2.2e+41)) {
		tmp = -2.0 * (x / (z * t));
	} else {
		tmp = x * (2.0 / (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-7d-22)) .or. (.not. (t <= 2.2d+41))) then
        tmp = (-2.0d0) * (x / (z * t))
    else
        tmp = x * (2.0d0 / (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7e-22) || !(t <= 2.2e+41)) {
		tmp = -2.0 * (x / (z * t));
	} else {
		tmp = x * (2.0 / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7e-22) or not (t <= 2.2e+41):
		tmp = -2.0 * (x / (z * t))
	else:
		tmp = x * (2.0 / (y * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7e-22) || !(t <= 2.2e+41))
		tmp = Float64(-2.0 * Float64(x / Float64(z * t)));
	else
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -7e-22) || ~((t <= 2.2e+41)))
		tmp = -2.0 * (x / (z * t));
	else
		tmp = x * (2.0 / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7e-22], N[Not[LessEqual[t, 2.2e+41]], $MachinePrecision]], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.00000000000000011e-22 or 2.1999999999999999e41 < t

   1. Initial program 88.7%

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

      1. associate-*l/ 88.6%

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

      2. *-commutative 88.6%

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

      3. distribute-rgt-out-- 90.3%

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

      4. associate-/r* 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in y around 0 75.4%

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

   if -7.00000000000000011e-22 < t < 2.1999999999999999e41

   1. Initial program 87.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   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-- 87.6%

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

      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 72.3%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{-22} \lor \neg \left(t \leq 2.2 \cdot 10^{+41}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \end{array} \]

Alternative 8: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-20} \lor \neg \left(t \leq 2.8 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.2e-20) (not (<= t 2.8e+41)))
   (* x (/ (/ -2.0 t) z))
   (* x (/ 2.0 (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.2e-20) || !(t <= 2.8e+41)) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = x * (2.0 / (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.2d-20)) .or. (.not. (t <= 2.8d+41))) then
        tmp = x * (((-2.0d0) / t) / z)
    else
        tmp = x * (2.0d0 / (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.2e-20) || !(t <= 2.8e+41)) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = x * (2.0 / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.2e-20) or not (t <= 2.8e+41):
		tmp = x * ((-2.0 / t) / z)
	else:
		tmp = x * (2.0 / (y * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.2e-20) || !(t <= 2.8e+41))
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	else
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.2e-20) || ~((t <= 2.8e+41)))
		tmp = x * ((-2.0 / t) / z);
	else
		tmp = x * (2.0 / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.2e-20], N[Not[LessEqual[t, 2.8e+41]], $MachinePrecision]], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.19999999999999991e-20 or 2.7999999999999999e41 < t

   1. Initial program 88.7%

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

      1. associate-*r/ 88.6%

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

      2. distribute-rgt-out-- 90.2%

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

      3. associate-/l/ 90.8%

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

      4. sub-neg 90.8%

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

      5. +-commutative 90.8%

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

      6. neg-sub0 90.8%

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

      7. associate-+l- 90.8%

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

      8. sub0-neg 90.8%

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

      9. neg-mul-1 90.8%

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

      10. associate-/r* 90.8%

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

      11. metadata-eval 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around inf 75.4%

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

   if -2.19999999999999991e-20 < t < 2.7999999999999999e41

   1. Initial program 87.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   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-- 87.6%

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

      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 72.3%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-20} \lor \neg \left(t \leq 2.8 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \end{array} \]

Alternative 9: 73.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-22} \lor \neg \left(t \leq 2.3 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9.5e-22) (not (<= t 2.3e+42)))
   (* x (/ (/ -2.0 t) z))
   (* x (/ (/ 2.0 y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.5e-22) || !(t <= 2.3e+42)) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = x * ((2.0 / y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-9.5d-22)) .or. (.not. (t <= 2.3d+42))) then
        tmp = x * (((-2.0d0) / t) / z)
    else
        tmp = x * ((2.0d0 / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.5e-22) || !(t <= 2.3e+42)) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = x * ((2.0 / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9.5e-22) or not (t <= 2.3e+42):
		tmp = x * ((-2.0 / t) / z)
	else:
		tmp = x * ((2.0 / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9.5e-22) || !(t <= 2.3e+42))
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	else
		tmp = Float64(x * Float64(Float64(2.0 / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9.5e-22) || ~((t <= 2.3e+42)))
		tmp = x * ((-2.0 / t) / z);
	else
		tmp = x * ((2.0 / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9.5e-22], N[Not[LessEqual[t, 2.3e+42]], $MachinePrecision]], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.4999999999999994e-22 or 2.3e42 < t

   1. Initial program 88.7%

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

      1. associate-*r/ 88.6%

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

      2. distribute-rgt-out-- 90.2%

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

      3. associate-/l/ 90.8%

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

      4. sub-neg 90.8%

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

      5. +-commutative 90.8%

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

      6. neg-sub0 90.8%

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

      7. associate-+l- 90.8%

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

      8. sub0-neg 90.8%

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

      9. neg-mul-1 90.8%

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

      10. associate-/r* 90.8%

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

      11. metadata-eval 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around inf 75.4%

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

   if -9.4999999999999994e-22 < t < 2.3e42

   1. Initial program 87.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   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-- 87.6%

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

      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 72.5%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-22} \lor \neg \left(t \leq 2.3 \cdot 10^{+42}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \]

Alternative 10: 72.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-20} \lor \neg \left(t \leq 9.2 \cdot 10^{+106}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.1e-20) (not (<= t 9.2e+106)))
   (* x (/ (/ -2.0 t) z))
   (* (/ x z) (/ 2.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.1e-20) || !(t <= 9.2e+106)) {
		tmp = x * ((-2.0 / t) / z);
	} 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 ((t <= (-3.1d-20)) .or. (.not. (t <= 9.2d+106))) then
        tmp = x * (((-2.0d0) / t) / z)
    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 ((t <= -3.1e-20) || !(t <= 9.2e+106)) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.1e-20) or not (t <= 9.2e+106):
		tmp = x * ((-2.0 / t) / z)
	else:
		tmp = (x / z) * (2.0 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.1e-20) || !(t <= 9.2e+106))
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	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 ((t <= -3.1e-20) || ~((t <= 9.2e+106)))
		tmp = x * ((-2.0 / t) / z);
	else
		tmp = (x / z) * (2.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.1e-20], N[Not[LessEqual[t, 9.2e+106]], $MachinePrecision]], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1e-20 or 9.2000000000000008e106 < t

   1. Initial program 88.8%

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

      1. associate-*r/ 88.7%

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

      2. distribute-rgt-out-- 89.7%

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

      3. associate-/l/ 90.3%

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

      4. sub-neg 90.3%

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

      5. +-commutative 90.3%

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

      6. neg-sub0 90.3%

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

      7. associate-+l- 90.3%

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

      8. sub0-neg 90.3%

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

      9. neg-mul-1 90.3%

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

      10. associate-/r* 90.3%

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

      11. metadata-eval 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in t around inf 75.3%

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

   if -3.1e-20 < t < 9.2000000000000008e106

   1. Initial program 87.1%

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

      1. associate-*l/ 87.1%

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

      2. *-commutative 87.1%

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

      3. distribute-rgt-out-- 88.4%

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

      4. associate-/r* 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around inf 70.9%

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

      1. associate-*r/ 70.9%

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

      2. *-commutative 70.9%

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

      3. *-commutative 70.9%

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

      4. associate-/r* 76.7%

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

      5. associate-*l/ 77.3%

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

      6. *-commutative 77.3%

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

   6. Simplified 77.3%

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

      1. clear-num 77.2%

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

      2. un-div-inv 77.2%

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

   8. Applied egg-rr 77.2%

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

      1. associate-/r/ 76.6%

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

      2. clear-num 76.6%

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

      3. associate-*l/ 76.7%

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

      4. *-un-lft-identity 76.7%

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

      5. un-div-inv 76.6%

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

      6. clear-num 76.6%

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

      7. associate-*r/ 76.7%

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

      8. associate-/r* 70.9%

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

      9. times-frac 77.2%

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

   10. Applied egg-rr 77.2%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-20} \lor \neg \left(t \leq 9.2 \cdot 10^{+106}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \]

Alternative 11: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-21} \lor \neg \left(t \leq 1.4 \cdot 10^{-34}\right):\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.7e-21) (not (<= t 1.4e-34)))
   (* -2.0 (/ (/ x t) z))
   (* (/ x z) (/ 2.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.7e-21) || !(t <= 1.4e-34)) {
		tmp = -2.0 * ((x / t) / z);
	} 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 ((t <= (-3.7d-21)) .or. (.not. (t <= 1.4d-34))) then
        tmp = (-2.0d0) * ((x / t) / z)
    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 ((t <= -3.7e-21) || !(t <= 1.4e-34)) {
		tmp = -2.0 * ((x / t) / z);
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.7e-21) or not (t <= 1.4e-34):
		tmp = -2.0 * ((x / t) / z)
	else:
		tmp = (x / z) * (2.0 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.7e-21) || !(t <= 1.4e-34))
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	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 ((t <= -3.7e-21) || ~((t <= 1.4e-34)))
		tmp = -2.0 * ((x / t) / z);
	else
		tmp = (x / z) * (2.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.7e-21], N[Not[LessEqual[t, 1.4e-34]], $MachinePrecision]], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.7000000000000002e-21 or 1.39999999999999998e-34 < t

   1. Initial program 88.7%

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

      1. associate-*l/ 88.6%

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

      2. *-commutative 88.6%

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

      3. distribute-rgt-out-- 90.2%

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

      4. associate-/r* 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 73.3%

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

      1. *-commutative 73.3%

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

      2. associate-/r* 75.9%

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

   6. Simplified 75.9%

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

   if -3.7000000000000002e-21 < t < 1.39999999999999998e-34

   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-- 87.7%

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

      4. associate-/r* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around inf 73.6%

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

      1. associate-*r/ 73.6%

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

      2. *-commutative 73.6%

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

      3. *-commutative 73.6%

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

      4. associate-/r* 78.9%

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

      5. associate-*l/ 78.9%

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

      6. *-commutative 78.9%

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

   6. Simplified 78.9%

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

      1. clear-num 78.9%

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

      2. un-div-inv 78.9%

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

   8. Applied egg-rr 78.9%

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

      1. associate-/r/ 78.9%

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

      2. clear-num 78.9%

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

      3. associate-*l/ 78.9%

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

      4. *-un-lft-identity 78.9%

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

      5. un-div-inv 78.9%

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

      6. clear-num 78.9%

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

      7. associate-*r/ 78.9%

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

      8. associate-/r* 73.6%

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

      9. times-frac 78.8%

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

   10. Applied egg-rr 78.8%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-21} \lor \neg \left(t \leq 1.4 \cdot 10^{-34}\right):\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \]

Alternative 12: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-19}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9.5e-19)
   (* -2.0 (/ (/ x z) t))
   (if (<= t 1.2e-35) (* (/ x z) (/ 2.0 y)) (* -2.0 (/ (/ x t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.5e-19) {
		tmp = -2.0 * ((x / z) / t);
	} else if (t <= 1.2e-35) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = -2.0 * ((x / 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 (t <= (-9.5d-19)) then
        tmp = (-2.0d0) * ((x / z) / t)
    else if (t <= 1.2d-35) then
        tmp = (x / z) * (2.0d0 / y)
    else
        tmp = (-2.0d0) * ((x / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.5e-19) {
		tmp = -2.0 * ((x / z) / t);
	} else if (t <= 1.2e-35) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = -2.0 * ((x / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -9.5e-19:
		tmp = -2.0 * ((x / z) / t)
	elif t <= 1.2e-35:
		tmp = (x / z) * (2.0 / y)
	else:
		tmp = -2.0 * ((x / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9.5e-19)
		tmp = Float64(-2.0 * Float64(Float64(x / z) / t));
	elseif (t <= 1.2e-35)
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	else
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -9.5e-19)
		tmp = -2.0 * ((x / z) / t);
	elseif (t <= 1.2e-35)
		tmp = (x / z) * (2.0 / y);
	else
		tmp = -2.0 * ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -9.5e-19], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-35], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.4999999999999995e-19

   1. Initial program 86.4%

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

      1. associate-*l/ 86.3%

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

      2. *-commutative 86.3%

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

      3. distribute-rgt-out-- 88.0%

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

      4. associate-/r* 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around 0 71.8%

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

      1. *-commutative 71.8%

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

      2. *-commutative 71.8%

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

      3. associate-/r* 79.3%

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

   6. Simplified 79.3%

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

   if -9.4999999999999995e-19 < t < 1.2000000000000001e-35

   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-- 87.7%

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

      4. associate-/r* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around inf 73.6%

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

      1. associate-*r/ 73.6%

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

      2. *-commutative 73.6%

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

      3. *-commutative 73.6%

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

      4. associate-/r* 78.9%

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

      5. associate-*l/ 78.9%

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

      6. *-commutative 78.9%

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

   6. Simplified 78.9%

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

      1. clear-num 78.9%

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

      2. un-div-inv 78.9%

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

   8. Applied egg-rr 78.9%

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

      1. associate-/r/ 78.9%

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

      2. clear-num 78.9%

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

      3. associate-*l/ 78.9%

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

      4. *-un-lft-identity 78.9%

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

      5. un-div-inv 78.9%

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

      6. clear-num 78.9%

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

      7. associate-*r/ 78.9%

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

      8. associate-/r* 73.6%

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

      9. times-frac 78.8%

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

   10. Applied egg-rr 78.8%

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

   if 1.2000000000000001e-35 < t

   1. Initial program 90.9%

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

      1. associate-*l/ 90.9%

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

      2. *-commutative 90.9%

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

      3. distribute-rgt-out-- 92.4%

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

      4. associate-/r* 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in y around 0 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-/r* 76.5%

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

   6. Simplified 76.5%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-19}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \]

Alternative 13: 91.6% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.8%

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

   1. associate-*l/ 87.8%

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

   2. *-commutative 87.8%

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

   3. distribute-rgt-out-- 89.0%

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

   4. associate-/r* 93.5%

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

3. Simplified 93.5%

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

4. Final simplification 93.5%

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

Alternative 14: 92.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 / (y - t)) / (z / x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.8%

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

   1. associate-*l/ 87.8%

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

   2. *-commutative 87.8%

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

   3. distribute-rgt-out-- 89.0%

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

   4. associate-/r* 93.5%

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

3. Simplified 93.5%

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

   1. clear-num 92.8%

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

   2. associate-*r/ 92.8%

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

   3. div-inv 92.7%

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

   4. clear-num 92.9%

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

   5. frac-times 93.4%

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

   6. un-div-inv 93.6%

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

5. Applied egg-rr 93.6%

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

6. Final simplification 93.6%

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

Alternative 15: 52.5% 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 87.8%

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

   1. associate-*l/ 87.8%

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

   2. *-commutative 87.8%

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

   3. distribute-rgt-out-- 89.0%

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

   4. associate-/r* 93.5%

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

3. Simplified 93.5%

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

4. Taylor expanded in y around 0 49.7%

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

5. Final simplification 49.7%

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

Developer target: 97.0% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023195 
(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))))