Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3

Percentage Accurate: 85.1% → 96.1%

Time: 7.3s

Alternatives: 9

Speedup: 0.8×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-115} \lor \neg \left(y \leq 7.4 \cdot 10^{-177}\right):\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.7e-115) (not (<= y 7.4e-177)))
   (- x (/ x (/ y z)))
   (- x (* z (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e-115) || !(y <= 7.4e-177)) {
		tmp = x - (x / (y / z));
	} else {
		tmp = x - (z * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.7d-115)) .or. (.not. (y <= 7.4d-177))) then
        tmp = x - (x / (y / z))
    else
        tmp = x - (z * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e-115) || !(y <= 7.4e-177)) {
		tmp = x - (x / (y / z));
	} else {
		tmp = x - (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.7e-115) or not (y <= 7.4e-177):
		tmp = x - (x / (y / z))
	else:
		tmp = x - (z * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.7e-115) || !(y <= 7.4e-177))
		tmp = Float64(x - Float64(x / Float64(y / z)));
	else
		tmp = Float64(x - Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.7e-115) || ~((y <= 7.4e-177)))
		tmp = x - (x / (y / z));
	else
		tmp = x - (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.7e-115], N[Not[LessEqual[y, 7.4e-177]], $MachinePrecision]], N[(x - N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e-115 or 7.39999999999999986e-177 < y

   1. Initial program 80.7%

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

      1. associate-*l/ 80.6%

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

      2. distribute-rgt-out-- 79.6%

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

      3. associate-*r/ 72.9%

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

      4. associate-*l/ 91.5%

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

      5. *-inverses 91.5%

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

      6. *-lft-identity 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in z around 0 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-/l* 99.4%

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

   6. Simplified 99.4%

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

   if -2.7e-115 < y < 7.39999999999999986e-177

   1. Initial program 88.9%

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

      1. associate-*l/ 98.1%

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

      2. distribute-rgt-out-- 88.3%

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

      3. associate-*r/ 90.9%

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

      4. associate-*l/ 98.2%

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

      5. *-inverses 98.2%

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

      6. *-lft-identity 98.2%

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

   3. Simplified 98.2%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-115} \lor \neg \left(y \leq 7.4 \cdot 10^{-177}\right):\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array} \]

Alternative 2: 69.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+61} \lor \neg \left(z \leq 3800000000000\right) \land \left(z \leq 3.5 \cdot 10^{+70} \lor \neg \left(z \leq 7.6 \cdot 10^{+117}\right)\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.15e+61)
         (and (not (<= z 3800000000000.0))
              (or (<= z 3.5e+70) (not (<= z 7.6e+117)))))
   (* x (/ (- z) y))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.15e+61) || (!(z <= 3800000000000.0) && ((z <= 3.5e+70) || !(z <= 7.6e+117)))) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.15d+61)) .or. (.not. (z <= 3800000000000.0d0)) .and. (z <= 3.5d+70) .or. (.not. (z <= 7.6d+117))) then
        tmp = x * (-z / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.15e+61) || (!(z <= 3800000000000.0) && ((z <= 3.5e+70) || !(z <= 7.6e+117)))) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.15e+61) or (not (z <= 3800000000000.0) and ((z <= 3.5e+70) or not (z <= 7.6e+117))):
		tmp = x * (-z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.15e+61) || (!(z <= 3800000000000.0) && ((z <= 3.5e+70) || !(z <= 7.6e+117))))
		tmp = Float64(x * Float64(Float64(-z) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.15e+61) || (~((z <= 3800000000000.0)) && ((z <= 3.5e+70) || ~((z <= 7.6e+117)))))
		tmp = x * (-z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.15e+61], And[N[Not[LessEqual[z, 3800000000000.0]], $MachinePrecision], Or[LessEqual[z, 3.5e+70], N[Not[LessEqual[z, 7.6e+117]], $MachinePrecision]]]], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e61 or 3.8e12 < z < 3.50000000000000002e70 or 7.6000000000000003e117 < z

   1. Initial program 88.9%

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

      1. associate-*l/ 83.6%

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

      2. distribute-rgt-out-- 80.1%

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

      3. associate-*r/ 78.4%

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

      4. associate-*l/ 89.4%

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

      5. *-inverses 89.4%

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

      6. *-lft-identity 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in z around inf 76.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 76.6%

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

      2. associate-*l/ 71.5%

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

      3. distribute-rgt-neg-in 71.5%

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

   6. Simplified 71.5%

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

   if -1.15e61 < z < 3.8e12 or 3.50000000000000002e70 < z < 7.6000000000000003e117

   1. Initial program 77.1%

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

      1. associate-*l/ 84.5%

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

      2. distribute-rgt-out-- 82.4%

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

      3. associate-*r/ 75.0%

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

      4. associate-*l/ 95.4%

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

      5. *-inverses 95.4%

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

      6. *-lft-identity 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in z around 0 77.1%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+61} \lor \neg \left(z \leq 3800000000000\right) \land \left(z \leq 3.5 \cdot 10^{+70} \lor \neg \left(z \leq 7.6 \cdot 10^{+117}\right)\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 70.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq 30000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+71} \lor \neg \left(z \leq 8 \cdot 10^{+117}\right):\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.9e+60)
   (* x (/ (- z) y))
   (if (<= z 30000000000.0)
     x
     (if (or (<= z 2.2e+71) (not (<= z 8e+117))) (/ x (/ (- y) z)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.9e+60) {
		tmp = x * (-z / y);
	} else if (z <= 30000000000.0) {
		tmp = x;
	} else if ((z <= 2.2e+71) || !(z <= 8e+117)) {
		tmp = x / (-y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.9d+60)) then
        tmp = x * (-z / y)
    else if (z <= 30000000000.0d0) then
        tmp = x
    else if ((z <= 2.2d+71) .or. (.not. (z <= 8d+117))) then
        tmp = x / (-y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.9e+60) {
		tmp = x * (-z / y);
	} else if (z <= 30000000000.0) {
		tmp = x;
	} else if ((z <= 2.2e+71) || !(z <= 8e+117)) {
		tmp = x / (-y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.9e+60:
		tmp = x * (-z / y)
	elif z <= 30000000000.0:
		tmp = x
	elif (z <= 2.2e+71) or not (z <= 8e+117):
		tmp = x / (-y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.9e+60)
		tmp = Float64(x * Float64(Float64(-z) / y));
	elseif (z <= 30000000000.0)
		tmp = x;
	elseif ((z <= 2.2e+71) || !(z <= 8e+117))
		tmp = Float64(x / Float64(Float64(-y) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.9e+60)
		tmp = x * (-z / y);
	elseif (z <= 30000000000.0)
		tmp = x;
	elseif ((z <= 2.2e+71) || ~((z <= 8e+117)))
		tmp = x / (-y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.9e+60], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 30000000000.0], x, If[Or[LessEqual[z, 2.2e+71], N[Not[LessEqual[z, 8e+117]], $MachinePrecision]], N[(x / N[((-y) / z), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e60

   1. Initial program 88.9%

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

      1. associate-*l/ 77.7%

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

      2. distribute-rgt-out-- 73.1%

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

      3. associate-*r/ 75.4%

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

      4. associate-*l/ 82.2%

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

      5. *-inverses 82.2%

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

      6. *-lft-identity 82.2%

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

   3. Simplified 82.2%

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

   4. Taylor expanded in z around inf 75.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 75.4%

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

      2. associate-*l/ 73.2%

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

      3. distribute-rgt-neg-in 73.2%

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

   6. Simplified 73.2%

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

   if -2.9e60 < z < 3e10 or 2.19999999999999995e71 < z < 8.0000000000000004e117

   1. Initial program 77.1%

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

      1. associate-*l/ 84.5%

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

      2. distribute-rgt-out-- 82.4%

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

      3. associate-*r/ 75.0%

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

      4. associate-*l/ 95.4%

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

      5. *-inverses 95.4%

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

      6. *-lft-identity 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in z around 0 77.1%

      \[\leadsto \color{blue}{x} \]

   if 3e10 < z < 2.19999999999999995e71 or 8.0000000000000004e117 < z

   1. Initial program 89.0%

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

      1. associate-*l/ 87.3%

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

      2. distribute-rgt-out-- 84.4%

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

      3. associate-*r/ 80.2%

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

      4. associate-*l/ 94.0%

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

      5. *-inverses 94.0%

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

      6. *-lft-identity 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in z around inf 77.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 77.3%

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

      2. associate-*l/ 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

   6. Simplified 70.5%

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

      1. add-sqr-sqrt 42.2%

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

      2. sqrt-unprod 34.2%

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

      3. sqr-neg 34.2%

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

      4. sqrt-unprod 0.4%

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

      5. clear-num 0.4%

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

      6. add-sqr-sqrt 1.9%

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

      7. associate-/r/ 1.9%

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

      8. frac-2neg 1.9%

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

      9. clear-num 1.9%

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

      10. add-sqr-sqrt 1.5%

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

      11. sqrt-unprod 26.8%

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

      12. sqr-neg 26.8%

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

      13. sqrt-unprod 29.6%

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

      14. add-sqr-sqrt 72.2%

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

      15. distribute-neg-frac 72.2%

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

   8. Applied egg-rr 72.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq 30000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+71} \lor \neg \left(z \leq 8 \cdot 10^{+117}\right):\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 70.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq 12500000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+84}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+117}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3e+60)
   (* x (/ (- z) y))
   (if (<= z 12500000000.0)
     x
     (if (<= z 2.9e+84)
       (/ (- z) (/ y x))
       (if (<= z 7.6e+117) (/ y (/ y x)) (/ x (/ (- y) z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e+60) {
		tmp = x * (-z / y);
	} else if (z <= 12500000000.0) {
		tmp = x;
	} else if (z <= 2.9e+84) {
		tmp = -z / (y / x);
	} else if (z <= 7.6e+117) {
		tmp = y / (y / x);
	} else {
		tmp = x / (-y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3d+60)) then
        tmp = x * (-z / y)
    else if (z <= 12500000000.0d0) then
        tmp = x
    else if (z <= 2.9d+84) then
        tmp = -z / (y / x)
    else if (z <= 7.6d+117) then
        tmp = y / (y / x)
    else
        tmp = x / (-y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e+60) {
		tmp = x * (-z / y);
	} else if (z <= 12500000000.0) {
		tmp = x;
	} else if (z <= 2.9e+84) {
		tmp = -z / (y / x);
	} else if (z <= 7.6e+117) {
		tmp = y / (y / x);
	} else {
		tmp = x / (-y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3e+60:
		tmp = x * (-z / y)
	elif z <= 12500000000.0:
		tmp = x
	elif z <= 2.9e+84:
		tmp = -z / (y / x)
	elif z <= 7.6e+117:
		tmp = y / (y / x)
	else:
		tmp = x / (-y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3e+60)
		tmp = Float64(x * Float64(Float64(-z) / y));
	elseif (z <= 12500000000.0)
		tmp = x;
	elseif (z <= 2.9e+84)
		tmp = Float64(Float64(-z) / Float64(y / x));
	elseif (z <= 7.6e+117)
		tmp = Float64(y / Float64(y / x));
	else
		tmp = Float64(x / Float64(Float64(-y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3e+60)
		tmp = x * (-z / y);
	elseif (z <= 12500000000.0)
		tmp = x;
	elseif (z <= 2.9e+84)
		tmp = -z / (y / x);
	elseif (z <= 7.6e+117)
		tmp = y / (y / x);
	else
		tmp = x / (-y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3e+60], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 12500000000.0], x, If[LessEqual[z, 2.9e+84], N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e+117], N[(y / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(x / N[((-y) / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.9999999999999998e60

   1. Initial program 88.9%

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

      1. associate-*l/ 77.7%

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

      2. distribute-rgt-out-- 73.1%

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

      3. associate-*r/ 75.4%

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

      4. associate-*l/ 82.2%

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

      5. *-inverses 82.2%

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

      6. *-lft-identity 82.2%

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

   3. Simplified 82.2%

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

   4. Taylor expanded in z around inf 75.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 75.4%

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

      2. associate-*l/ 73.2%

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

      3. distribute-rgt-neg-in 73.2%

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

   6. Simplified 73.2%

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

   if -2.9999999999999998e60 < z < 1.25e10

   1. Initial program 78.0%

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

      1. associate-*l/ 83.7%

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

      2. distribute-rgt-out-- 81.2%

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

      3. associate-*r/ 75.5%

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

      4. associate-*l/ 94.7%

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

      5. *-inverses 94.7%

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

      6. *-lft-identity 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around 0 79.6%

      \[\leadsto \color{blue}{x} \]

   if 1.25e10 < z < 2.89999999999999989e84

   1. Initial program 82.3%

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

      1. associate-*l/ 90.9%

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

      2. distribute-rgt-out-- 87.8%

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

      3. associate-*r/ 82.2%

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

      4. associate-*l/ 99.7%

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

      5. *-inverses 99.7%

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

      6. *-lft-identity 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 65.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 65.4%

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

      2. associate-*l/ 50.7%

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

      3. distribute-rgt-neg-in 50.7%

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

   6. Simplified 50.7%

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

      1. distribute-rgt-neg-out 50.7%

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

      2. associate-/r/ 65.5%

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

      3. distribute-neg-frac 65.5%

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

   8. Applied egg-rr 65.5%

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

   if 2.89999999999999989e84 < z < 7.6000000000000003e117

   1. Initial program 55.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]

   2. Taylor expanded in y around inf 27.8%

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

      1. associate-/l* 81.0%

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

      2. div-inv 80.7%

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

      3. clear-num 80.9%

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

   4. Applied egg-rr 80.9%

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

      1. clear-num 80.7%

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

      2. un-div-inv 81.0%

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

   6. Applied egg-rr 81.0%

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

   if 7.6000000000000003e117 < z

   1. Initial program 93.6%

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

      1. associate-*l/ 83.2%

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

      2. distribute-rgt-out-- 81.0%

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

      3. associate-*r/ 80.6%

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

      4. associate-*l/ 91.1%

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

      5. *-inverses 91.1%

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

      6. *-lft-identity 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in z around inf 81.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 81.8%

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

      2. associate-*l/ 77.7%

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

      3. distribute-rgt-neg-in 77.7%

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

   6. Simplified 77.7%

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

      1. add-sqr-sqrt 46.9%

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

      2. sqrt-unprod 38.2%

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

      3. sqr-neg 38.2%

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

      4. sqrt-unprod 0.3%

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

      5. clear-num 0.3%

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

      6. add-sqr-sqrt 1.8%

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

      7. associate-/r/ 1.8%

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

      8. frac-2neg 1.8%

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

      9. clear-num 1.8%

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

      10. add-sqr-sqrt 1.5%

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

      11. sqrt-unprod 28.4%

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

      12. sqr-neg 28.4%

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

      13. sqrt-unprod 30.6%

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

      14. add-sqr-sqrt 77.8%

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

      15. distribute-neg-frac 77.8%

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

   8. Applied egg-rr 77.8%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq 12500000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+84}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+117}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \end{array} \]

Alternative 5: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot \left(-z\right)}{y}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+61}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+84}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (- z)) y)))
   (if (<= z -1.2e+61)
     t_0
     (if (<= z 2.2e+16)
       x
       (if (<= z 4.8e+84)
         (/ (- z) (/ y x))
         (if (<= z 7.8e+117) (/ y (/ y x)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * -z) / y;
	double tmp;
	if (z <= -1.2e+61) {
		tmp = t_0;
	} else if (z <= 2.2e+16) {
		tmp = x;
	} else if (z <= 4.8e+84) {
		tmp = -z / (y / x);
	} else if (z <= 7.8e+117) {
		tmp = y / (y / x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * -z) / y
    if (z <= (-1.2d+61)) then
        tmp = t_0
    else if (z <= 2.2d+16) then
        tmp = x
    else if (z <= 4.8d+84) then
        tmp = -z / (y / x)
    else if (z <= 7.8d+117) then
        tmp = y / (y / x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * -z) / y;
	double tmp;
	if (z <= -1.2e+61) {
		tmp = t_0;
	} else if (z <= 2.2e+16) {
		tmp = x;
	} else if (z <= 4.8e+84) {
		tmp = -z / (y / x);
	} else if (z <= 7.8e+117) {
		tmp = y / (y / x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * -z) / y
	tmp = 0
	if z <= -1.2e+61:
		tmp = t_0
	elif z <= 2.2e+16:
		tmp = x
	elif z <= 4.8e+84:
		tmp = -z / (y / x)
	elif z <= 7.8e+117:
		tmp = y / (y / x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(-z)) / y)
	tmp = 0.0
	if (z <= -1.2e+61)
		tmp = t_0;
	elseif (z <= 2.2e+16)
		tmp = x;
	elseif (z <= 4.8e+84)
		tmp = Float64(Float64(-z) / Float64(y / x));
	elseif (z <= 7.8e+117)
		tmp = Float64(y / Float64(y / x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * -z) / y;
	tmp = 0.0;
	if (z <= -1.2e+61)
		tmp = t_0;
	elseif (z <= 2.2e+16)
		tmp = x;
	elseif (z <= 4.8e+84)
		tmp = -z / (y / x);
	elseif (z <= 7.8e+117)
		tmp = y / (y / x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -1.2e+61], t$95$0, If[LessEqual[z, 2.2e+16], x, If[LessEqual[z, 4.8e+84], N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+117], N[(y / N[(y / x), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1999999999999999e61 or 7.79999999999999981e117 < z

   1. Initial program 91.3%

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

      1. associate-*l/ 80.6%

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

      2. distribute-rgt-out-- 77.2%

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

      3. associate-*r/ 78.1%

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

      4. associate-*l/ 86.8%

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

      5. *-inverses 86.8%

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

      6. *-lft-identity 86.8%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in z around inf 78.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{y}} \]
   5. Step-by-step derivation

      1. associate-*r/ 78.7%

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

      2. neg-mul-1 78.7%

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

      3. distribute-rgt-neg-in 78.7%

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

   6. Simplified 78.7%

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

   if -1.1999999999999999e61 < z < 2.2e16

   1. Initial program 78.0%

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

      1. associate-*l/ 83.7%

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

      2. distribute-rgt-out-- 81.2%

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

      3. associate-*r/ 75.5%

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

      4. associate-*l/ 94.7%

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

      5. *-inverses 94.7%

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

      6. *-lft-identity 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around 0 79.6%

      \[\leadsto \color{blue}{x} \]

   if 2.2e16 < z < 4.7999999999999999e84

   1. Initial program 82.3%

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

      1. associate-*l/ 90.9%

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

      2. distribute-rgt-out-- 87.8%

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

      3. associate-*r/ 82.2%

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

      4. associate-*l/ 99.7%

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

      5. *-inverses 99.7%

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

      6. *-lft-identity 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 65.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 65.4%

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

      2. associate-*l/ 50.7%

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

      3. distribute-rgt-neg-in 50.7%

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

   6. Simplified 50.7%

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

      1. distribute-rgt-neg-out 50.7%

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

      2. associate-/r/ 65.5%

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

      3. distribute-neg-frac 65.5%

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

   8. Applied egg-rr 65.5%

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

   if 4.7999999999999999e84 < z < 7.79999999999999981e117

   1. Initial program 55.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]

   2. Taylor expanded in y around inf 27.8%

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

      1. associate-/l* 81.0%

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

      2. div-inv 80.7%

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

      3. clear-num 80.9%

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

   4. Applied egg-rr 80.9%

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

      1. clear-num 80.7%

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

      2. un-div-inv 81.0%

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

   6. Applied egg-rr 81.0%

      \[\leadsto \color{blue}{\frac{y}{\frac{y}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+84}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \]

Alternative 6: 93.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+212}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.8e+212) (/ (* x (- z)) y) (- x (* z (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+212) {
		tmp = (x * -z) / y;
	} else {
		tmp = x - (z * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.8d+212)) then
        tmp = (x * -z) / y
    else
        tmp = x - (z * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+212) {
		tmp = (x * -z) / y;
	} else {
		tmp = x - (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.8e+212:
		tmp = (x * -z) / y
	else:
		tmp = x - (z * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.8e+212)
		tmp = Float64(Float64(x * Float64(-z)) / y);
	else
		tmp = Float64(x - Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.8e+212)
		tmp = (x * -z) / y;
	else
		tmp = x - (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.8e+212], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], N[(x - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7999999999999997e212

   1. Initial program 94.9%

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

      1. associate-*l/ 64.5%

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

      2. distribute-rgt-out-- 59.3%

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

      3. associate-*r/ 64.8%

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

      4. associate-*l/ 64.8%

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

      5. *-inverses 64.8%

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

      6. *-lft-identity 64.8%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in z around inf 94.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot x}{y}} \]
   5. Step-by-step derivation

      1. associate-*r/ 94.1%

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

      2. neg-mul-1 94.1%

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

      3. distribute-rgt-neg-in 94.1%

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

   6. Simplified 94.1%

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

   if -5.7999999999999997e212 < z

   1. Initial program 81.3%

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

      1. associate-*l/ 85.7%

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

      2. distribute-rgt-out-- 83.1%

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

      3. associate-*r/ 77.4%

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

      4. associate-*l/ 95.0%

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

      5. *-inverses 95.0%

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

      6. *-lft-identity 95.0%

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

   3. Simplified 95.0%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+212}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array} \]

Alternative 7: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 2e-8) x (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2e-8) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Fortran

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

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 2e-8) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2e-8:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2e-8)
		tmp = x;
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2e-8)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2e-8], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2e-8

   1. Initial program 86.9%

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

      1. associate-*l/ 79.8%

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

      2. distribute-rgt-out-- 77.1%

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

      3. associate-*r/ 80.2%

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

      4. associate-*l/ 91.4%

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

      5. *-inverses 91.4%

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

      6. *-lft-identity 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in z around 0 53.2%

      \[\leadsto \color{blue}{x} \]

   if 2e-8 < x

   1. Initial program 68.7%

      \[\frac{x \cdot \left(y - z\right)}{y} \]

   2. Taylor expanded in y around inf 29.1%

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

      1. associate-/l* 62.4%

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

      2. div-inv 62.3%

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

      3. clear-num 62.4%

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

   4. Applied egg-rr 62.4%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]

Alternative 8: 51.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 1e+42) x (/ y (/ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e+42) {
		tmp = x;
	} else {
		tmp = y / (y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1d+42) then
        tmp = x
    else
        tmp = y / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1e+42) {
		tmp = x;
	} else {
		tmp = y / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1e+42:
		tmp = x
	else:
		tmp = y / (y / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1e+42)
		tmp = x;
	else
		tmp = Float64(y / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1e+42)
		tmp = x;
	else
		tmp = y / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1e+42], x, N[(y / N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.00000000000000004e42

   1. Initial program 87.3%

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

      1. associate-*l/ 80.4%

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

      2. distribute-rgt-out-- 77.8%

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

      3. associate-*r/ 80.8%

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

      4. associate-*l/ 91.6%

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

      5. *-inverses 91.6%

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

      6. *-lft-identity 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in z around 0 53.1%

      \[\leadsto \color{blue}{x} \]

   if 1.00000000000000004e42 < x

   1. Initial program 65.6%

      \[\frac{x \cdot \left(y - z\right)}{y} \]

   2. Taylor expanded in y around inf 26.8%

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

      1. associate-/l* 63.5%

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

      2. div-inv 63.4%

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

      3. clear-num 63.5%

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

   4. Applied egg-rr 63.5%

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

      1. clear-num 63.4%

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

      2. un-div-inv 63.5%

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

   6. Applied egg-rr 63.5%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \end{array} \]

Alternative 9: 50.4% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 82.3%

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

   1. associate-*l/ 84.1%

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

   2. distribute-rgt-out-- 81.3%

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

   3. associate-*r/ 76.5%

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

   4. associate-*l/ 92.8%

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

   5. *-inverses 92.8%

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

   6. *-lft-identity 92.8%

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

3. Simplified 92.8%

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

4. Taylor expanded in z around 0 53.4%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 53.4%

   \[\leadsto x \]

Developer target: 96.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z -2.060202331921739e+104)
   (- x (/ (* z x) y))
   (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z < (-2.060202331921739d+104)) then
        tmp = x - ((z * x) / y)
    else if (z < 1.6939766013828526d+213) then
        tmp = x / (y / (y - z))
    else
        tmp = (y - z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < -2.060202331921739e+104:
		tmp = x - ((z * x) / y)
	elif z < 1.6939766013828526e+213:
		tmp = x / (y / (y - z))
	else:
		tmp = (y - z) * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < -2.060202331921739e+104)
		tmp = Float64(x - Float64(Float64(z * x) / y));
	elseif (z < 1.6939766013828526e+213)
		tmp = Float64(x / Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < -2.060202331921739e+104)
		tmp = x - ((z * x) / y);
	elseif (z < 1.6939766013828526e+213)
		tmp = x / (y / (y - z));
	else
		tmp = (y - z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, -2.060202331921739e+104], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Less[z, 1.6939766013828526e+213], N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023228 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

  (/ (* x (- y z)) y))