Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.2% → 97.3%

Time: 8.4s

Alternatives: 10

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: 89.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - z \cdot t\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+197}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+84}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{y - t}}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) (* z t))))
   (if (<= t_1 -2e+197)
     (* (/ 2.0 z) (/ x (- y t)))
     (if (<= t_1 4e+84)
       (/ (* 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 <= -2e+197) {
		tmp = (2.0 / z) * (x / (y - t));
	} else if (t_1 <= 4e+84) {
		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 <= (-2d+197)) then
        tmp = (2.0d0 / z) * (x / (y - t))
    else if (t_1 <= 4d+84) 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 <= -2e+197) {
		tmp = (2.0 / z) * (x / (y - t));
	} else if (t_1 <= 4e+84) {
		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 <= -2e+197:
		tmp = (2.0 / z) * (x / (y - t))
	elif t_1 <= 4e+84:
		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 <= -2e+197)
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	elseif (t_1 <= 4e+84)
		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 <= -2e+197)
		tmp = (2.0 / z) * (x / (y - t));
	elseif (t_1 <= 4e+84)
		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, -2e+197], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+84], 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)) < -1.9999999999999999e197

   1. Initial program 79.1%

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

      1. *-commutative 79.1%

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

      2. distribute-rgt-out-- 79.1%

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

      3. times-frac 99.8%

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

   3. Simplified 99.8%

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

   if -1.9999999999999999e197 < (-.f64 (*.f64 y z) (*.f64 t z)) < 4.00000000000000023e84

   1. Initial program 97.6%

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

      1. distribute-rgt-out-- 98.4%

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

   3. Simplified 98.4%

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

   if 4.00000000000000023e84 < (-.f64 (*.f64 y z) (*.f64 t z))

   1. Initial program 78.8%

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

      1. *-commutative 78.8%

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

      2. associate-*r/ 78.8%

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

      3. distribute-rgt-out-- 85.7%

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

      4. associate-/r* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-*r/ 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r/ 99.7%

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

      4. clear-num 99.7%

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

      5. associate-*l/ 99.8%

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

      6. *-un-lft-identity 99.8%

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

   5. Applied egg-rr 99.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - z \cdot t \leq -2 \cdot 10^{+197}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{elif}\;y \cdot z - z \cdot t \leq 4 \cdot 10^{+84}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{y - t}}{\frac{z}{x}}\\ \end{array} \]

Alternative 2: 96.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+40} \lor \neg \left(z \leq 1.28 \cdot 10^{+104}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.2e+40) (not (<= z 1.28e+104)))
   (* 2.0 (/ (/ x z) (- y t)))
   (* x (/ (/ 2.0 (- y t)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e+40) || !(z <= 1.28e+104)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} 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 ((z <= (-5.2d+40)) .or. (.not. (z <= 1.28d+104))) then
        tmp = 2.0d0 * ((x / z) / (y - t))
    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 ((z <= -5.2e+40) || !(z <= 1.28e+104)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = x * ((2.0 / (y - t)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.2e+40) or not (z <= 1.28e+104):
		tmp = 2.0 * ((x / z) / (y - t))
	else:
		tmp = x * ((2.0 / (y - t)) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.2e+40) || !(z <= 1.28e+104))
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(x * Float64(Float64(2.0 / Float64(y - t)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.2e+40) || ~((z <= 1.28e+104)))
		tmp = 2.0 * ((x / z) / (y - t));
	else
		tmp = x * ((2.0 / (y - t)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.2e+40], N[Not[LessEqual[z, 1.28e+104]], $MachinePrecision]], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2000000000000001e40 or 1.27999999999999997e104 < z

   1. Initial program 77.6%

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

      1. *-commutative 77.6%

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

      2. associate-*r/ 77.6%

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

      3. distribute-rgt-out-- 83.0%

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

      4. associate-/r* 98.7%

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

   3. Simplified 98.7%

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

   if -5.2000000000000001e40 < z < 1.27999999999999997e104

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

      2. associate-*r/ 97.2%

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

      3. distribute-rgt-out-- 97.9%

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

      4. associate-/r* 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in x around 0 97.9%

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

      1. *-commutative 97.9%

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

      2. associate-*l/ 97.3%

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

      3. times-frac 86.3%

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

      4. associate-*l/ 89.7%

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

      5. associate-*r/ 97.9%

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

   6. Simplified 97.9%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+40} \lor \neg \left(z \leq 1.28 \cdot 10^{+104}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \end{array} \]

Alternative 3: 95.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-192}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.22e-192)
   (* (/ 2.0 z) (/ x (- y t)))
   (if (<= z 2e+104) (* x (/ (/ 2.0 (- y t)) z)) (* 2.0 (/ (/ x z) (- y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.22e-192) {
		tmp = (2.0 / z) * (x / (y - t));
	} else if (z <= 2e+104) {
		tmp = x * ((2.0 / (y - t)) / z);
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.22d-192)) then
        tmp = (2.0d0 / z) * (x / (y - t))
    else if (z <= 2d+104) then
        tmp = x * ((2.0d0 / (y - t)) / z)
    else
        tmp = 2.0d0 * ((x / z) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.22e-192) {
		tmp = (2.0 / z) * (x / (y - t));
	} else if (z <= 2e+104) {
		tmp = x * ((2.0 / (y - t)) / z);
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.22e-192:
		tmp = (2.0 / z) * (x / (y - t))
	elif z <= 2e+104:
		tmp = x * ((2.0 / (y - t)) / z)
	else:
		tmp = 2.0 * ((x / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.22e-192)
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	elseif (z <= 2e+104)
		tmp = Float64(x * Float64(Float64(2.0 / Float64(y - t)) / z));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.22e-192)
		tmp = (2.0 / z) * (x / (y - t));
	elseif (z <= 2e+104)
		tmp = x * ((2.0 / (y - t)) / z);
	else
		tmp = 2.0 * ((x / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.22e-192], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+104], N[(x * N[(N[(2.0 / N[(y - t), $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 < -1.22000000000000002e-192

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

      2. distribute-rgt-out-- 90.1%

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

      3. times-frac 99.0%

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

   3. Simplified 99.0%

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

   if -1.22000000000000002e-192 < z < 2e104

   1. Initial program 96.5%

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

      1. *-commutative 96.5%

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

      2. associate-*r/ 97.3%

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

      3. distribute-rgt-out-- 98.1%

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

      4. associate-/r* 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in x around 0 98.1%

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

      1. *-commutative 98.1%

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

      2. associate-*l/ 97.4%

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

      3. times-frac 86.6%

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

      4. associate-*l/ 87.2%

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

      5. associate-*r/ 98.0%

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

   6. Simplified 98.0%

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

   if 2e104 < z

   1. Initial program 73.2%

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

      1. *-commutative 73.2%

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

      2. associate-*r/ 73.2%

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

      3. distribute-rgt-out-- 79.0%

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

      4. associate-/r* 97.2%

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

   3. Simplified 97.2%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-192}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 4: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-38} \lor \neg \left(t \leq 2 \cdot 10^{-83}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7.8e-38) (not (<= t 2e-83)))
   (* -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 <= -7.8e-38) || !(t <= 2e-83)) {
		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 <= (-7.8d-38)) .or. (.not. (t <= 2d-83))) 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 <= -7.8e-38) || !(t <= 2e-83)) {
		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 <= -7.8e-38) or not (t <= 2e-83):
		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 <= -7.8e-38) || !(t <= 2e-83))
		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 <= -7.8e-38) || ~((t <= 2e-83)))
		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, -7.8e-38], N[Not[LessEqual[t, 2e-83]], $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 < -7.7999999999999998e-38 or 2.0000000000000001e-83 < t

   1. Initial program 85.8%

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

      1. *-commutative 85.8%

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

      2. associate-*r/ 86.4%

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

      3. distribute-rgt-out-- 89.6%

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

      4. associate-/r* 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in y around 0 76.7%

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

   if -7.7999999999999998e-38 < t < 2.0000000000000001e-83

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. associate-*r/ 95.7%

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

      3. distribute-rgt-out-- 96.8%

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

      4. associate-/r* 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*l/ 96.8%

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

      3. times-frac 90.1%

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

      4. associate-*l/ 92.7%

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

      5. associate-*r/ 96.7%

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

   6. Simplified 96.7%

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

   7. Taylor expanded in y around inf 85.1%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{-38} \lor \neg \left(t \leq 2 \cdot 10^{-83}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \end{array} \]

Alternative 5: 72.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-35} \lor \neg \left(t \leq 4.1 \cdot 10^{-83}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.8e-35) (not (<= t 4.1e-83)))
   (* -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 <= -2.8e-35) || !(t <= 4.1e-83)) {
		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 <= (-2.8d-35)) .or. (.not. (t <= 4.1d-83))) 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 <= -2.8e-35) || !(t <= 4.1e-83)) {
		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 <= -2.8e-35) or not (t <= 4.1e-83):
		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 <= -2.8e-35) || !(t <= 4.1e-83))
		tmp = Float64(-2.0 * Float64(x / Float64(z * t)));
	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 <= -2.8e-35) || ~((t <= 4.1e-83)))
		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, -2.8e-35], N[Not[LessEqual[t, 4.1e-83]], $MachinePrecision]], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8e-35 or 4.1e-83 < t

   1. Initial program 85.8%

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

      1. *-commutative 85.8%

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

      2. associate-*r/ 86.4%

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

      3. distribute-rgt-out-- 89.6%

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

      4. associate-/r* 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in y around 0 76.7%

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

   if -2.8e-35 < t < 4.1e-83

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. associate-*r/ 95.7%

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

      3. distribute-rgt-out-- 96.8%

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

      4. associate-/r* 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*l/ 96.8%

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

      3. times-frac 90.1%

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

      4. associate-*l/ 92.7%

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

      5. associate-*r/ 96.7%

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

   6. Simplified 96.7%

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

   7. Taylor expanded in y around inf 85.1%

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

      1. associate-/r* 85.1%

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

   9. Simplified 85.1%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-35} \lor \neg \left(t \leq 4.1 \cdot 10^{-83}\right):\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \]

Alternative 6: 73.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-39} \lor \neg \left(t \leq 4.1 \cdot 10^{-83}\right):\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.6e-39) (not (<= t 4.1e-83)))
   (/ -2.0 (* z (/ t x)))
   (* x (/ (/ 2.0 y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.6e-39) || !(t <= 4.1e-83)) {
		tmp = -2.0 / (z * (t / x));
	} 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 <= (-5.6d-39)) .or. (.not. (t <= 4.1d-83))) then
        tmp = (-2.0d0) / (z * (t / x))
    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 <= -5.6e-39) || !(t <= 4.1e-83)) {
		tmp = -2.0 / (z * (t / x));
	} else {
		tmp = x * ((2.0 / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.6e-39) or not (t <= 4.1e-83):
		tmp = -2.0 / (z * (t / x))
	else:
		tmp = x * ((2.0 / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.6e-39) || !(t <= 4.1e-83))
		tmp = Float64(-2.0 / Float64(z * Float64(t / x)));
	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 <= -5.6e-39) || ~((t <= 4.1e-83)))
		tmp = -2.0 / (z * (t / x));
	else
		tmp = x * ((2.0 / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.6e-39], N[Not[LessEqual[t, 4.1e-83]], $MachinePrecision]], N[(-2.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.6000000000000003e-39 or 4.1e-83 < t

   1. Initial program 85.8%

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

      1. *-commutative 85.8%

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

      2. associate-*r/ 86.4%

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

      3. distribute-rgt-out-- 89.6%

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

      4. associate-/r* 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in y around 0 76.7%

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

      1. clear-num 75.4%

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

      2. un-div-inv 75.4%

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

      3. *-un-lft-identity 75.4%

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

      4. *-commutative 75.4%

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

      5. times-frac 78.8%

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

      6. add-sqr-sqrt 39.0%

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

      7. sqrt-unprod 44.7%

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

      8. sqr-neg 44.7%

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

      9. sqrt-unprod 16.5%

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

      10. add-sqr-sqrt 27.5%

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

      11. associate-/r/ 27.5%

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

      12. clear-num 27.4%

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

      13. div-inv 27.5%

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

      14. clear-num 27.5%

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

      15. add-sqr-sqrt 16.5%

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

      16. sqrt-unprod 44.7%

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

      17. sqr-neg 44.7%

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

      18. sqrt-unprod 39.0%

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

      19. add-sqr-sqrt 78.8%

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

   6. Applied egg-rr 78.8%

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

   if -5.6000000000000003e-39 < t < 4.1e-83

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. associate-*r/ 95.7%

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

      3. distribute-rgt-out-- 96.8%

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

      4. associate-/r* 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*l/ 96.8%

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

      3. times-frac 90.1%

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

      4. associate-*l/ 92.7%

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

      5. associate-*r/ 96.7%

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

   6. Simplified 96.7%

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

   7. Taylor expanded in y around inf 85.1%

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

      1. associate-/r* 85.1%

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

   9. Simplified 85.1%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-39} \lor \neg \left(t \leq 4.1 \cdot 10^{-83}\right):\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \]

Alternative 7: 73.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-33} \lor \neg \left(t \leq 3.7 \cdot 10^{-83}\right):\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.2e-33) (not (<= t 3.7e-83)))
   (/ -2.0 (* z (/ t x)))
   (/ (* 2.0 x) (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.2e-33) || !(t <= 3.7e-83)) {
		tmp = -2.0 / (z * (t / x));
	} else {
		tmp = (2.0 * x) / (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-33)) .or. (.not. (t <= 3.7d-83))) then
        tmp = (-2.0d0) / (z * (t / x))
    else
        tmp = (2.0d0 * x) / (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-33) || !(t <= 3.7e-83)) {
		tmp = -2.0 / (z * (t / x));
	} else {
		tmp = (2.0 * x) / (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.2e-33) or not (t <= 3.7e-83):
		tmp = -2.0 / (z * (t / x))
	else:
		tmp = (2.0 * x) / (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.2e-33) || !(t <= 3.7e-83))
		tmp = Float64(-2.0 / Float64(z * Float64(t / x)));
	else
		tmp = Float64(Float64(2.0 * x) / Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.2e-33) || ~((t <= 3.7e-83)))
		tmp = -2.0 / (z * (t / x));
	else
		tmp = (2.0 * x) / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.2e-33], N[Not[LessEqual[t, 3.7e-83]], $MachinePrecision]], N[(-2.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.20000000000000005e-33 or 3.69999999999999995e-83 < t

   1. Initial program 85.8%

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

      1. *-commutative 85.8%

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

      2. associate-*r/ 86.4%

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

      3. distribute-rgt-out-- 89.6%

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

      4. associate-/r* 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in y around 0 76.7%

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

      1. clear-num 75.4%

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

      2. un-div-inv 75.4%

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

      3. *-un-lft-identity 75.4%

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

      4. *-commutative 75.4%

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

      5. times-frac 78.8%

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

      6. add-sqr-sqrt 39.0%

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

      7. sqrt-unprod 44.7%

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

      8. sqr-neg 44.7%

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

      9. sqrt-unprod 16.5%

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

      10. add-sqr-sqrt 27.5%

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

      11. associate-/r/ 27.5%

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

      12. clear-num 27.4%

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

      13. div-inv 27.5%

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

      14. clear-num 27.5%

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

      15. add-sqr-sqrt 16.5%

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

      16. sqrt-unprod 44.7%

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

      17. sqr-neg 44.7%

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

      18. sqrt-unprod 39.0%

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

      19. add-sqr-sqrt 78.8%

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

   6. Applied egg-rr 78.8%

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

   if -2.20000000000000005e-33 < t < 3.69999999999999995e-83

   1. Initial program 95.7%

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

      1. distribute-rgt-out-- 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in y around inf 85.1%

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

      1. *-commutative 85.1%

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

   6. Simplified 85.1%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-33} \lor \neg \left(t \leq 3.7 \cdot 10^{-83}\right):\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z}\\ \end{array} \]

Alternative 8: 72.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9.8e-26)
   (* (/ x z) (/ -2.0 t))
   (if (<= t 3.3e-83) (* 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 <= -9.8e-26) {
		tmp = (x / z) * (-2.0 / t);
	} else if (t <= 3.3e-83) {
		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 <= (-9.8d-26)) then
        tmp = (x / z) * ((-2.0d0) / t)
    else if (t <= 3.3d-83) 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 <= -9.8e-26) {
		tmp = (x / z) * (-2.0 / t);
	} else if (t <= 3.3e-83) {
		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 <= -9.8e-26:
		tmp = (x / z) * (-2.0 / t)
	elif t <= 3.3e-83:
		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 <= -9.8e-26)
		tmp = Float64(Float64(x / z) * Float64(-2.0 / t));
	elseif (t <= 3.3e-83)
		tmp = Float64(x * Float64(Float64(2.0 / 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 <= -9.8e-26)
		tmp = (x / z) * (-2.0 / t);
	elseif (t <= 3.3e-83)
		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, -9.8e-26], N[(N[(x / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e-83], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.7999999999999998e-26

   1. Initial program 84.3%

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

      1. *-commutative 84.3%

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

      2. associate-*r/ 84.3%

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

      3. distribute-rgt-out-- 88.8%

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

      4. associate-/r* 94.2%

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

   3. Simplified 94.2%

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

   4. Taylor expanded in y around 0 76.4%

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

      1. associate-*r/ 76.5%

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

      2. *-commutative 76.5%

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

      3. *-commutative 76.5%

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

      4. times-frac 77.6%

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

   6. Simplified 77.6%

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

   if -9.7999999999999998e-26 < t < 3.2999999999999999e-83

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. associate-*r/ 95.7%

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

      3. distribute-rgt-out-- 96.8%

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

      4. associate-/r* 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*l/ 96.8%

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

      3. times-frac 90.1%

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

      4. associate-*l/ 92.7%

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

      5. associate-*r/ 96.7%

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

   6. Simplified 96.7%

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

   7. Taylor expanded in y around inf 85.1%

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

      1. associate-/r* 85.1%

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

   9. Simplified 85.1%

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

   if 3.2999999999999999e-83 < t

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

      2. associate-*r/ 88.0%

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

      3. distribute-rgt-out-- 90.2%

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

      4. associate-/r* 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in y around 0 76.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{x}{z \cdot t}\\ \end{array} \]

Alternative 9: 91.8% 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 89.6%

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

   1. *-commutative 89.6%

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

   2. associate-*r/ 89.9%

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

   3. distribute-rgt-out-- 92.4%

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

   4. associate-/r* 90.9%

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

3. Simplified 90.9%

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

4. Final simplification 90.9%

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

Alternative 10: 53.3% 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 89.6%

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

   1. *-commutative 89.6%

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

   2. associate-*r/ 89.9%

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

   3. distribute-rgt-out-- 92.4%

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

   4. associate-/r* 90.9%

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

3. Simplified 90.9%

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

4. Taylor expanded in y around 0 54.5%

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

5. Final simplification 54.5%

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

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 2023320 
(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))))