Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 90.0% → 98.0%

Time: 9.3s

Alternatives: 13

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 90.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - z \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+296}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t_1 \leq 10^{+151}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{y - t}}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) (* z t))))
   (if (<= t_1 -5e+296)
     (* 2.0 (/ (/ x z) (- y t)))
     (if (<= t_1 1e+151)
       (/ (* 2.0 x) (* z (- y t)))
       (/ (/ 2.0 (- y t)) (/ z x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if (t_1 <= -5e+296) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else if (t_1 <= 1e+151) {
		tmp = (2.0 * x) / (z * (y - t));
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (y * z) - (z * t)
    if (t_1 <= (-5d+296)) then
        tmp = 2.0d0 * ((x / z) / (y - t))
    else if (t_1 <= 1d+151) then
        tmp = (2.0d0 * x) / (z * (y - t))
    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 t_1 = (y * z) - (z * t);
	double tmp;
	if (t_1 <= -5e+296) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else if (t_1 <= 1e+151) {
		tmp = (2.0 * x) / (z * (y - t));
	} else {
		tmp = (2.0 / (y - t)) / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - (z * t)
	tmp = 0
	if t_1 <= -5e+296:
		tmp = 2.0 * ((x / z) / (y - t))
	elif t_1 <= 1e+151:
		tmp = (2.0 * x) / (z * (y - t))
	else:
		tmp = (2.0 / (y - t)) / (z / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= -5e+296)
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	elseif (t_1 <= 1e+151)
		tmp = Float64(Float64(2.0 * x) / Float64(z * Float64(y - t)));
	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)
	t_1 = (y * z) - (z * t);
	tmp = 0.0;
	if (t_1 <= -5e+296)
		tmp = 2.0 * ((x / z) / (y - t));
	elseif (t_1 <= 1e+151)
		tmp = (2.0 * x) / (z * (y - t));
	else
		tmp = (2.0 / (y - t)) / (z / x);
	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, -5e+296], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+151], N[(N[(2.0 * x), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 y z) (*.f64 t z)) < -5.0000000000000001e296

   1. Initial program 69.5%

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

      1. associate-*l/ 69.5%

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

      2. *-commutative 69.5%

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

      3. distribute-rgt-out-- 69.5%

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

      4. associate-/r* 100.0%

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

   3. Simplified 100.0%

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

   if -5.0000000000000001e296 < (-.f64 (*.f64 y z) (*.f64 t z)) < 1.00000000000000002e151

   1. Initial program 98.7%

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

      1. distribute-rgt-out-- 98.7%

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

   3. Simplified 98.7%

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

   if 1.00000000000000002e151 < (-.f64 (*.f64 y z) (*.f64 t z))

   1. Initial program 78.7%

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

      1. associate-*l/ 78.7%

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

      2. *-commutative 78.7%

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

      3. distribute-rgt-out-- 84.1%

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

      4. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-*r/ 99.8%

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

      2. associate-*l/ 99.8%

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

      3. clear-num 99.7%

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

      4. un-div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - z \cdot t \leq -5 \cdot 10^{+296}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;y \cdot z - z \cdot t \leq 10^{+151}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{y - t}}{\frac{z}{x}}\\ \end{array} \]

Alternative 2: 96.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+22} \lor \neg \left(z \leq 6.8 \cdot 10^{+133}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4e+22) (not (<= z 6.8e+133)))
   (* 2.0 (/ (/ x z) (- y t)))
   (* x (/ 2.0 (* z (- y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e+22) || !(z <= 6.8e+133)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = x * (2.0 / (z * (y - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4d+22)) .or. (.not. (z <= 6.8d+133))) then
        tmp = 2.0d0 * ((x / z) / (y - t))
    else
        tmp = x * (2.0d0 / (z * (y - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e+22) || !(z <= 6.8e+133)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = x * (2.0 / (z * (y - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4e+22) or not (z <= 6.8e+133):
		tmp = 2.0 * ((x / z) / (y - t))
	else:
		tmp = x * (2.0 / (z * (y - t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4e+22) || !(z <= 6.8e+133))
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(x * Float64(2.0 / Float64(z * Float64(y - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4e+22) || ~((z <= 6.8e+133)))
		tmp = 2.0 * ((x / z) / (y - t));
	else
		tmp = x * (2.0 / (z * (y - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4e+22], N[Not[LessEqual[z, 6.8e+133]], $MachinePrecision]], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e22 or 6.79999999999999975e133 < z

   1. Initial program 80.4%

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

      1. associate-*l/ 80.4%

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

      2. *-commutative 80.4%

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

      3. distribute-rgt-out-- 83.9%

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

      4. associate-/r* 96.6%

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

   3. Simplified 96.6%

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

   if -4e22 < z < 6.79999999999999975e133

   1. Initial program 98.0%

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

      1. associate-*r/ 97.9%

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

      2. distribute-rgt-out-- 98.0%

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

   3. Simplified 98.0%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+22} \lor \neg \left(z \leq 6.8 \cdot 10^{+133}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 3: 96.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+22} \lor \neg \left(z \leq 6.8 \cdot 10^{+133}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t - y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.5e+22) (not (<= z 6.8e+133)))
   (* 2.0 (/ (/ x z) (- y t)))
   (* x (/ (/ -2.0 (- t y)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.5e+22) || !(z <= 6.8e+133)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = x * ((-2.0 / (t - y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.5d+22)) .or. (.not. (z <= 6.8d+133))) then
        tmp = 2.0d0 * ((x / z) / (y - t))
    else
        tmp = x * (((-2.0d0) / (t - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.5e+22) || !(z <= 6.8e+133)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = x * ((-2.0 / (t - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.5e+22) or not (z <= 6.8e+133):
		tmp = 2.0 * ((x / z) / (y - t))
	else:
		tmp = x * ((-2.0 / (t - y)) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.5e+22) || !(z <= 6.8e+133))
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(x * Float64(Float64(-2.0 / Float64(t - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.5e+22) || ~((z <= 6.8e+133)))
		tmp = 2.0 * ((x / z) / (y - t));
	else
		tmp = x * ((-2.0 / (t - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.5e+22], N[Not[LessEqual[z, 6.8e+133]], $MachinePrecision]], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(-2.0 / N[(t - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999998e22 or 6.79999999999999975e133 < z

   1. Initial program 80.4%

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

      1. associate-*l/ 80.4%

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

      2. *-commutative 80.4%

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

      3. distribute-rgt-out-- 83.9%

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

      4. associate-/r* 96.6%

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

   3. Simplified 96.6%

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

   if -4.4999999999999998e22 < z < 6.79999999999999975e133

   1. Initial program 98.0%

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

      1. associate-*r/ 97.9%

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

      2. distribute-rgt-out-- 98.0%

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

      3. associate-/l/ 98.4%

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

      4. sub-neg 98.4%

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

      5. +-commutative 98.4%

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

      6. neg-sub0 98.4%

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

      7. associate-+l- 98.4%

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

      8. sub0-neg 98.4%

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

      9. neg-mul-1 98.4%

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

      10. associate-/r* 98.4%

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

      11. metadata-eval 98.4%

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

   3. Simplified 98.4%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+22} \lor \neg \left(z \leq 6.8 \cdot 10^{+133}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t - y}}{z}\\ \end{array} \]

Alternative 4: 96.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t - y}}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.6e+24)
   (* (/ x z) (/ 2.0 (- y t)))
   (if (<= z 6.8e+133)
     (* x (/ (/ -2.0 (- t y)) z))
     (* 2.0 (/ (/ x z) (- y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.6e+24) {
		tmp = (x / z) * (2.0 / (y - t));
	} else if (z <= 6.8e+133) {
		tmp = x * ((-2.0 / (t - y)) / z);
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6.6d+24)) then
        tmp = (x / z) * (2.0d0 / (y - t))
    else if (z <= 6.8d+133) then
        tmp = x * (((-2.0d0) / (t - y)) / z)
    else
        tmp = 2.0d0 * ((x / z) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.6e+24) {
		tmp = (x / z) * (2.0 / (y - t));
	} else if (z <= 6.8e+133) {
		tmp = x * ((-2.0 / (t - y)) / z);
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.6e+24:
		tmp = (x / z) * (2.0 / (y - t))
	elif z <= 6.8e+133:
		tmp = x * ((-2.0 / (t - y)) / z)
	else:
		tmp = 2.0 * ((x / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.6e+24)
		tmp = Float64(Float64(x / z) * Float64(2.0 / Float64(y - t)));
	elseif (z <= 6.8e+133)
		tmp = Float64(x * Float64(Float64(-2.0 / Float64(t - y)) / z));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.6e+24)
		tmp = (x / z) * (2.0 / (y - t));
	elseif (z <= 6.8e+133)
		tmp = x * ((-2.0 / (t - y)) / z);
	else
		tmp = 2.0 * ((x / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.6e+24], N[(N[(x / z), $MachinePrecision] * N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+133], N[(x * N[(N[(-2.0 / N[(t - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5999999999999998e24

   1. Initial program 81.4%

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

      1. distribute-rgt-out-- 84.9%

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

      2. times-frac 96.7%

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

   3. Simplified 96.7%

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

   if -6.5999999999999998e24 < z < 6.79999999999999975e133

   1. Initial program 98.0%

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

      1. associate-*r/ 97.9%

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

      2. distribute-rgt-out-- 98.0%

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

      3. associate-/l/ 98.4%

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

      4. sub-neg 98.4%

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

      5. +-commutative 98.4%

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

      6. neg-sub0 98.4%

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

      7. associate-+l- 98.4%

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

      8. sub0-neg 98.4%

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

      9. neg-mul-1 98.4%

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

      10. associate-/r* 98.4%

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

      11. metadata-eval 98.4%

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

   3. Simplified 98.4%

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

   if 6.79999999999999975e133 < z

   1. Initial program 78.7%

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

      1. associate-*l/ 78.7%

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

      2. *-commutative 78.7%

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

      3. distribute-rgt-out-- 82.1%

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

      4. associate-/r* 96.5%

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

   3. Simplified 96.5%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t - y}}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 5: 94.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot x \leq 2 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t - y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{2}{y - t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* 2.0 x) 2e-81)
   (* x (/ (/ -2.0 (- t y)) z))
   (/ (* x (/ 2.0 (- y t))) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((2.0 * x) <= 2e-81) {
		tmp = x * ((-2.0 / (t - y)) / z);
	} else {
		tmp = (x * (2.0 / (y - t))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((2.0d0 * x) <= 2d-81) then
        tmp = x * (((-2.0d0) / (t - y)) / z)
    else
        tmp = (x * (2.0d0 / (y - t))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((2.0 * x) <= 2e-81) {
		tmp = x * ((-2.0 / (t - y)) / z);
	} else {
		tmp = (x * (2.0 / (y - t))) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (2.0 * x) <= 2e-81:
		tmp = x * ((-2.0 / (t - y)) / z)
	else:
		tmp = (x * (2.0 / (y - t))) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(2.0 * x) <= 2e-81)
		tmp = Float64(x * Float64(Float64(-2.0 / Float64(t - y)) / z));
	else
		tmp = Float64(Float64(x * Float64(2.0 / Float64(y - t))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((2.0 * x) <= 2e-81)
		tmp = x * ((-2.0 / (t - y)) / z);
	else
		tmp = (x * (2.0 / (y - t))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(2.0 * x), $MachinePrecision], 2e-81], N[(x * N[(N[(-2.0 / N[(t - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 2) < 1.9999999999999999e-81

   1. Initial program 95.2%

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

      1. associate-*r/ 95.1%

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

      2. distribute-rgt-out-- 95.7%

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

      3. associate-/l/ 96.1%

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

      4. sub-neg 96.1%

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

      5. +-commutative 96.1%

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

      6. neg-sub0 96.1%

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

      7. associate-+l- 96.1%

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

      8. sub0-neg 96.1%

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

      9. neg-mul-1 96.1%

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

      10. associate-/r* 96.1%

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

      11. metadata-eval 96.1%

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

   3. Simplified 96.1%

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

   if 1.9999999999999999e-81 < (*.f64 x 2)

   1. Initial program 82.8%

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

      1. associate-*l/ 82.8%

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

      2. *-commutative 82.8%

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

      3. distribute-rgt-out-- 85.7%

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

      4. associate-/r* 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. Step-by-step derivation

      1. associate-*r/ 93.1%

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

      2. associate-*l/ 93.1%

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

      3. *-commutative 93.1%

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

      4. associate-*l/ 98.5%

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

   5. Applied egg-rr 98.5%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x \leq 2 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t - y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{2}{y - t}}{z}\\ \end{array} \]

Alternative 6: 72.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+22}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.4e+22)
   (* -2.0 (/ (/ x t) z))
   (if (<= t 1.5e-107) (* x (/ 2.0 (* y z))) (* -2.0 (/ x (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.4e+22) {
		tmp = -2.0 * ((x / t) / z);
	} else if (t <= 1.5e-107) {
		tmp = x * (2.0 / (y * z));
	} else {
		tmp = -2.0 * (x / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.4d+22)) then
        tmp = (-2.0d0) * ((x / t) / z)
    else if (t <= 1.5d-107) then
        tmp = x * (2.0d0 / (y * z))
    else
        tmp = (-2.0d0) * (x / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.4e+22) {
		tmp = -2.0 * ((x / t) / z);
	} else if (t <= 1.5e-107) {
		tmp = x * (2.0 / (y * z));
	} else {
		tmp = -2.0 * (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.4e+22:
		tmp = -2.0 * ((x / t) / z)
	elif t <= 1.5e-107:
		tmp = x * (2.0 / (y * z))
	else:
		tmp = -2.0 * (x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.4e+22)
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	elseif (t <= 1.5e-107)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	else
		tmp = Float64(-2.0 * Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.4e+22)
		tmp = -2.0 * ((x / t) / z);
	elseif (t <= 1.5e-107)
		tmp = x * (2.0 / (y * z));
	else
		tmp = -2.0 * (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.4e+22], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-107], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4e22

   1. Initial program 83.8%

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

      1. associate-*l/ 83.8%

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

      2. *-commutative 83.8%

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

      3. distribute-rgt-out-- 87.2%

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

      4. associate-/r* 95.3%

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

   3. Simplified 95.3%

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

      1. associate-/r* 87.2%

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

      2. associate-*r/ 87.2%

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

      3. associate-/l* 86.4%

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

   5. Applied egg-rr 86.4%

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

   6. Taylor expanded in y around 0 72.4%

      \[\leadsto \frac{2}{\color{blue}{-1 \cdot \frac{t \cdot z}{x}}} \]
   7. Step-by-step derivation

      1. mul-1-neg 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-/l* 76.6%

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

      4. distribute-neg-frac 76.6%

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

   8. Simplified 76.6%

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

      1. frac-2neg 76.6%

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

      2. metadata-eval 76.6%

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

      3. div-inv 76.6%

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

      4. distribute-neg-frac 76.6%

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

      5. add-sqr-sqrt 37.7%

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

      6. sqrt-unprod 52.4%

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

      7. sqr-neg 52.4%

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

      8. sqrt-unprod 18.0%

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

      9. add-sqr-sqrt 40.4%

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

      10. clear-num 39.8%

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

      11. add-sqr-sqrt 21.8%

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

      12. sqrt-unprod 53.0%

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

      13. sqr-neg 53.0%

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

      14. sqrt-unprod 38.8%

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

      15. add-sqr-sqrt 76.8%

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

   10. Applied egg-rr 76.8%

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

   if -2.4e22 < t < 1.4999999999999999e-107

   1. Initial program 96.2%

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

      1. associate-*r/ 96.1%

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

      2. distribute-rgt-out-- 96.1%

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

      3. associate-/l/ 96.1%

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

      4. sub-neg 96.1%

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

      5. +-commutative 96.1%

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

      6. neg-sub0 96.1%

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

      7. associate-+l- 96.1%

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

      8. sub0-neg 96.1%

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

      9. neg-mul-1 96.1%

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

      10. associate-/r* 96.1%

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

      11. metadata-eval 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in t around 0 79.3%

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

   if 1.4999999999999999e-107 < t

   1. Initial program 92.1%

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

      1. associate-*r/ 91.9%

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

      2. distribute-rgt-out-- 93.1%

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

      3. associate-/l/ 94.7%

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

      4. sub-neg 94.7%

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

      5. +-commutative 94.7%

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

      6. neg-sub0 94.7%

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

      7. associate-+l- 94.7%

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

      8. sub0-neg 94.7%

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

      9. neg-mul-1 94.7%

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

      10. associate-/r* 94.7%

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

      11. metadata-eval 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around inf 82.4%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+22}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 7: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+19}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2e+19)
   (* -2.0 (/ (/ x t) z))
   (if (<= t 1.5e-107) (* x (/ 2.0 (* y z))) (* x (/ (/ -2.0 t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2e+19) {
		tmp = -2.0 * ((x / t) / z);
	} else if (t <= 1.5e-107) {
		tmp = x * (2.0 / (y * z));
	} else {
		tmp = x * ((-2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2d+19)) then
        tmp = (-2.0d0) * ((x / t) / z)
    else if (t <= 1.5d-107) then
        tmp = x * (2.0d0 / (y * z))
    else
        tmp = x * (((-2.0d0) / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2e+19) {
		tmp = -2.0 * ((x / t) / z);
	} else if (t <= 1.5e-107) {
		tmp = x * (2.0 / (y * z));
	} else {
		tmp = x * ((-2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2e+19:
		tmp = -2.0 * ((x / t) / z)
	elif t <= 1.5e-107:
		tmp = x * (2.0 / (y * z))
	else:
		tmp = x * ((-2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2e+19)
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	elseif (t <= 1.5e-107)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	else
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2e+19)
		tmp = -2.0 * ((x / t) / z);
	elseif (t <= 1.5e-107)
		tmp = x * (2.0 / (y * z));
	else
		tmp = x * ((-2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2e+19], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-107], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e19

   1. Initial program 83.8%

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

      1. associate-*l/ 83.8%

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

      2. *-commutative 83.8%

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

      3. distribute-rgt-out-- 87.2%

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

      4. associate-/r* 95.3%

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

   3. Simplified 95.3%

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

      1. associate-/r* 87.2%

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

      2. associate-*r/ 87.2%

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

      3. associate-/l* 86.4%

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

   5. Applied egg-rr 86.4%

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

   6. Taylor expanded in y around 0 72.4%

      \[\leadsto \frac{2}{\color{blue}{-1 \cdot \frac{t \cdot z}{x}}} \]
   7. Step-by-step derivation

      1. mul-1-neg 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-/l* 76.6%

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

      4. distribute-neg-frac 76.6%

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

   8. Simplified 76.6%

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

      1. frac-2neg 76.6%

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

      2. metadata-eval 76.6%

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

      3. div-inv 76.6%

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

      4. distribute-neg-frac 76.6%

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

      5. add-sqr-sqrt 37.7%

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

      6. sqrt-unprod 52.4%

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

      7. sqr-neg 52.4%

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

      8. sqrt-unprod 18.0%

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

      9. add-sqr-sqrt 40.4%

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

      10. clear-num 39.8%

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

      11. add-sqr-sqrt 21.8%

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

      12. sqrt-unprod 53.0%

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

      13. sqr-neg 53.0%

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

      14. sqrt-unprod 38.8%

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

      15. add-sqr-sqrt 76.8%

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

   10. Applied egg-rr 76.8%

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

   if -2e19 < t < 1.4999999999999999e-107

   1. Initial program 96.2%

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

      1. associate-*r/ 96.1%

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

      2. distribute-rgt-out-- 96.1%

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

      3. associate-/l/ 96.1%

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

      4. sub-neg 96.1%

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

      5. +-commutative 96.1%

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

      6. neg-sub0 96.1%

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

      7. associate-+l- 96.1%

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

      8. sub0-neg 96.1%

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

      9. neg-mul-1 96.1%

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

      10. associate-/r* 96.1%

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

      11. metadata-eval 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in t around 0 79.3%

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

   if 1.4999999999999999e-107 < t

   1. Initial program 92.1%

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

      1. associate-*r/ 91.9%

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

      2. distribute-rgt-out-- 93.1%

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

      3. associate-/l/ 94.7%

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

      4. sub-neg 94.7%

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

      5. +-commutative 94.7%

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

      6. neg-sub0 94.7%

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

      7. associate-+l- 94.7%

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

      8. sub0-neg 94.7%

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

      9. neg-mul-1 94.7%

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

      10. associate-/r* 94.7%

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

      11. metadata-eval 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around inf 82.8%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+19}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \]

Alternative 8: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.4e-9)
   (/ -2.0 (* t (/ z x)))
   (if (<= t 1.3e-107) (* x (/ 2.0 (* y z))) (* x (/ (/ -2.0 t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.4e-9) {
		tmp = -2.0 / (t * (z / x));
	} else if (t <= 1.3e-107) {
		tmp = x * (2.0 / (y * z));
	} else {
		tmp = x * ((-2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.4d-9)) then
        tmp = (-2.0d0) / (t * (z / x))
    else if (t <= 1.3d-107) then
        tmp = x * (2.0d0 / (y * z))
    else
        tmp = x * (((-2.0d0) / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.4e-9) {
		tmp = -2.0 / (t * (z / x));
	} else if (t <= 1.3e-107) {
		tmp = x * (2.0 / (y * z));
	} else {
		tmp = x * ((-2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.4e-9:
		tmp = -2.0 / (t * (z / x))
	elif t <= 1.3e-107:
		tmp = x * (2.0 / (y * z))
	else:
		tmp = x * ((-2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.4e-9)
		tmp = Float64(-2.0 / Float64(t * Float64(z / x)));
	elseif (t <= 1.3e-107)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	else
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.4e-9)
		tmp = -2.0 / (t * (z / x));
	elseif (t <= 1.3e-107)
		tmp = x * (2.0 / (y * z));
	else
		tmp = x * ((-2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.4e-9], N[(-2.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-107], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.39999999999999992e-9

   1. Initial program 84.3%

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

      1. associate-*r/ 84.2%

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

      2. distribute-rgt-out-- 87.5%

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

      3. associate-/l/ 88.6%

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

      4. sub-neg 88.6%

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

      5. +-commutative 88.6%

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

      6. neg-sub0 88.6%

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

      7. associate-+l- 88.6%

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

      8. sub0-neg 88.6%

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

      9. neg-mul-1 88.6%

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

      10. associate-/r* 88.6%

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

      11. metadata-eval 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in t around inf 72.0%

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

      1. clear-num 71.7%

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

      2. un-div-inv 71.7%

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

      3. *-commutative 71.7%

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

   6. Applied egg-rr 71.7%

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

      1. associate-/l* 75.9%

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

      2. associate-/r/ 76.0%

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

   8. Applied egg-rr 76.0%

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

   if -1.39999999999999992e-9 < t < 1.3e-107

   1. Initial program 96.1%

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

      1. associate-*r/ 96.0%

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

      2. distribute-rgt-out-- 96.0%

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

      3. associate-/l/ 96.0%

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

      4. sub-neg 96.0%

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

      5. +-commutative 96.0%

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

      6. neg-sub0 96.0%

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

      7. associate-+l- 96.0%

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

      8. sub0-neg 96.0%

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

      9. neg-mul-1 96.0%

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

      10. associate-/r* 96.0%

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

      11. metadata-eval 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in t around 0 79.9%

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

   if 1.3e-107 < t

   1. Initial program 92.1%

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

      1. associate-*r/ 91.9%

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

      2. distribute-rgt-out-- 93.1%

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

      3. associate-/l/ 94.7%

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

      4. sub-neg 94.7%

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

      5. +-commutative 94.7%

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

      6. neg-sub0 94.7%

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

      7. associate-+l- 94.7%

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

      8. sub0-neg 94.7%

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

      9. neg-mul-1 94.7%

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

      10. associate-/r* 94.7%

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

      11. metadata-eval 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around inf 82.8%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \]

Alternative 9: 72.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-107}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.8e-7)
   (/ -2.0 (* t (/ z x)))
   (if (<= t 1.5e-107) (/ (* 2.0 x) (* y z)) (* x (/ (/ -2.0 t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.8e-7) {
		tmp = -2.0 / (t * (z / x));
	} else if (t <= 1.5e-107) {
		tmp = (2.0 * x) / (y * z);
	} else {
		tmp = x * ((-2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5.8d-7)) then
        tmp = (-2.0d0) / (t * (z / x))
    else if (t <= 1.5d-107) then
        tmp = (2.0d0 * x) / (y * z)
    else
        tmp = x * (((-2.0d0) / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.8e-7) {
		tmp = -2.0 / (t * (z / x));
	} else if (t <= 1.5e-107) {
		tmp = (2.0 * x) / (y * z);
	} else {
		tmp = x * ((-2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.8e-7:
		tmp = -2.0 / (t * (z / x))
	elif t <= 1.5e-107:
		tmp = (2.0 * x) / (y * z)
	else:
		tmp = x * ((-2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.8e-7)
		tmp = Float64(-2.0 / Float64(t * Float64(z / x)));
	elseif (t <= 1.5e-107)
		tmp = Float64(Float64(2.0 * x) / Float64(y * z));
	else
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.8e-7)
		tmp = -2.0 / (t * (z / x));
	elseif (t <= 1.5e-107)
		tmp = (2.0 * x) / (y * z);
	else
		tmp = x * ((-2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.8e-7], N[(-2.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e-107], N[(N[(2.0 * x), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.7999999999999995e-7

   1. Initial program 84.3%

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

      1. associate-*r/ 84.2%

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

      2. distribute-rgt-out-- 87.5%

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

      3. associate-/l/ 88.6%

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

      4. sub-neg 88.6%

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

      5. +-commutative 88.6%

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

      6. neg-sub0 88.6%

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

      7. associate-+l- 88.6%

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

      8. sub0-neg 88.6%

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

      9. neg-mul-1 88.6%

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

      10. associate-/r* 88.6%

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

      11. metadata-eval 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in t around inf 72.0%

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

      1. clear-num 71.7%

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

      2. un-div-inv 71.7%

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

      3. *-commutative 71.7%

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

   6. Applied egg-rr 71.7%

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

      1. associate-/l* 75.9%

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

      2. associate-/r/ 76.0%

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

   8. Applied egg-rr 76.0%

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

   if -5.7999999999999995e-7 < t < 1.4999999999999999e-107

   1. Initial program 96.1%

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

      1. distribute-rgt-out-- 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in y around inf 79.9%

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

   if 1.4999999999999999e-107 < t

   1. Initial program 92.1%

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

      1. associate-*r/ 91.9%

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

      2. distribute-rgt-out-- 93.1%

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

      3. associate-/l/ 94.7%

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

      4. sub-neg 94.7%

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

      5. +-commutative 94.7%

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

      6. neg-sub0 94.7%

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

      7. associate-+l- 94.7%

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

      8. sub0-neg 94.7%

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

      9. neg-mul-1 94.7%

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

      10. associate-/r* 94.7%

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

      11. metadata-eval 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around inf 82.8%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-107}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \]

Alternative 10: 72.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{z}}{t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.35e-11)
   (/ (/ (* x -2.0) z) t)
   (if (<= t 6.5e-108) (/ (* 2.0 x) (* y z)) (* x (/ (/ -2.0 t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.35e-11) {
		tmp = ((x * -2.0) / z) / t;
	} else if (t <= 6.5e-108) {
		tmp = (2.0 * x) / (y * z);
	} else {
		tmp = x * ((-2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.35d-11)) then
        tmp = ((x * (-2.0d0)) / z) / t
    else if (t <= 6.5d-108) then
        tmp = (2.0d0 * x) / (y * z)
    else
        tmp = x * (((-2.0d0) / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.35e-11) {
		tmp = ((x * -2.0) / z) / t;
	} else if (t <= 6.5e-108) {
		tmp = (2.0 * x) / (y * z);
	} else {
		tmp = x * ((-2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.35e-11:
		tmp = ((x * -2.0) / z) / t
	elif t <= 6.5e-108:
		tmp = (2.0 * x) / (y * z)
	else:
		tmp = x * ((-2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.35e-11)
		tmp = Float64(Float64(Float64(x * -2.0) / z) / t);
	elseif (t <= 6.5e-108)
		tmp = Float64(Float64(2.0 * x) / Float64(y * z));
	else
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.35e-11)
		tmp = ((x * -2.0) / z) / t;
	elseif (t <= 6.5e-108)
		tmp = (2.0 * x) / (y * z);
	else
		tmp = x * ((-2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.35e-11], N[(N[(N[(x * -2.0), $MachinePrecision] / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 6.5e-108], N[(N[(2.0 * x), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35000000000000002e-11

   1. Initial program 84.3%

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

      1. associate-*l/ 84.3%

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

      2. *-commutative 84.3%

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

      3. distribute-rgt-out-- 87.6%

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

      4. associate-/r* 93.9%

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

   3. Simplified 93.9%

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

      1. associate-/r* 87.6%

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

      2. associate-*r/ 87.6%

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

      3. associate-/l* 86.8%

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

   5. Applied egg-rr 86.8%

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

   6. Taylor expanded in y around 0 72.0%

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

      1. associate-*r/ 72.0%

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

      2. *-commutative 72.0%

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

      3. associate-/l/ 76.9%

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

   8. Simplified 76.9%

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

   if -1.35000000000000002e-11 < t < 6.5000000000000002e-108

   1. Initial program 96.1%

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

      1. distribute-rgt-out-- 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in y around inf 79.9%

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

   if 6.5000000000000002e-108 < t

   1. Initial program 92.1%

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

      1. associate-*r/ 91.9%

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

      2. distribute-rgt-out-- 93.1%

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

      3. associate-/l/ 94.7%

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

      4. sub-neg 94.7%

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

      5. +-commutative 94.7%

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

      6. neg-sub0 94.7%

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

      7. associate-+l- 94.7%

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

      8. sub0-neg 94.7%

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

      9. neg-mul-1 94.7%

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

      10. associate-/r* 94.7%

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

      11. metadata-eval 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around inf 82.8%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{z}}{t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \end{array} \]

Alternative 11: 52.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-30}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4e-30) (* -2.0 (/ (/ x t) z)) (* -2.0 (/ x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e-30) {
		tmp = -2.0 * ((x / t) / z);
	} else {
		tmp = -2.0 * (x / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4d-30)) then
        tmp = (-2.0d0) * ((x / t) / z)
    else
        tmp = (-2.0d0) * (x / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e-30) {
		tmp = -2.0 * ((x / t) / z);
	} else {
		tmp = -2.0 * (x / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4e-30:
		tmp = -2.0 * ((x / t) / z)
	else:
		tmp = -2.0 * (x / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4e-30)
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	else
		tmp = Float64(-2.0 * Float64(x / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4e-30)
		tmp = -2.0 * ((x / t) / z);
	else
		tmp = -2.0 * (x / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4e-30], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e-30

   1. Initial program 84.5%

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

      1. associate-*l/ 84.5%

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

      2. *-commutative 84.5%

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

      3. distribute-rgt-out-- 87.4%

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

      4. associate-/r* 97.2%

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

   3. Simplified 97.2%

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

      1. associate-/r* 87.4%

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

      2. associate-*r/ 87.4%

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

      3. associate-/l* 86.7%

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

   5. Applied egg-rr 86.7%

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

   6. Taylor expanded in y around 0 59.2%

      \[\leadsto \frac{2}{\color{blue}{-1 \cdot \frac{t \cdot z}{x}}} \]
   7. Step-by-step derivation

      1. mul-1-neg 59.2%

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

      2. *-commutative 59.2%

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

      3. associate-/l* 69.5%

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

      4. distribute-neg-frac 69.5%

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

   8. Simplified 69.5%

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

      1. frac-2neg 69.5%

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

      2. metadata-eval 69.5%

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

      3. div-inv 69.5%

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

      4. distribute-neg-frac 69.5%

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

      5. add-sqr-sqrt 69.4%

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

      6. sqrt-unprod 60.2%

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

      7. sqr-neg 60.2%

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

      8. sqrt-unprod 0.0%

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

      9. add-sqr-sqrt 35.7%

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

      10. clear-num 35.2%

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

      11. add-sqr-sqrt 35.2%

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

      12. sqrt-unprod 39.3%

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

      13. sqr-neg 39.3%

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

      14. sqrt-unprod 0.0%

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

      15. add-sqr-sqrt 69.6%

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

   10. Applied egg-rr 69.6%

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

   if -4e-30 < z

   1. Initial program 94.5%

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

      1. associate-*r/ 94.4%

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

      2. distribute-rgt-out-- 95.0%

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

      3. associate-/l/ 95.5%

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

      4. sub-neg 95.5%

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

      5. +-commutative 95.5%

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

      6. neg-sub0 95.5%

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

      7. associate-+l- 95.5%

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

      8. sub0-neg 95.5%

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

      9. neg-mul-1 95.5%

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

      10. associate-/r* 95.5%

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

      11. metadata-eval 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in t around inf 57.2%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-30}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 12: 91.7% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.7%

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

   1. associate-*l/ 91.7%

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

   2. *-commutative 91.7%

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

   3. distribute-rgt-out-- 92.9%

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

   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. Final simplification 91.1%

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

Alternative 13: 51.9% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.7%

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

   1. associate-*r/ 91.6%

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

   2. distribute-rgt-out-- 92.8%

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

   3. associate-/l/ 93.7%

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

   4. sub-neg 93.7%

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

   5. +-commutative 93.7%

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

   6. neg-sub0 93.7%

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

   7. associate-+l- 93.7%

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

   8. sub0-neg 93.7%

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

   9. neg-mul-1 93.7%

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

   10. associate-/r* 93.7%

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

   11. metadata-eval 93.7%

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

3. Simplified 93.7%

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

4. Taylor expanded in t around inf 57.6%

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

5. Final simplification 57.6%

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

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 2023192 
(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))))