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

Percentage Accurate: 84.8% → 97.1%

Time: 8.8s

Alternatives: 8

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: 84.8% 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: 97.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+24}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5e+24) (- x (* z (/ x y))) (- x (/ x (/ y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+24) {
		tmp = x - (z * (x / y));
	} else {
		tmp = x - (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 <= (-5d+24)) then
        tmp = x - (z * (x / y))
    else
        tmp = x - (x / (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+24) {
		tmp = x - (z * (x / y));
	} else {
		tmp = x - (x / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5e+24:
		tmp = x - (z * (x / y))
	else:
		tmp = x - (x / (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5e+24)
		tmp = Float64(x - Float64(z * Float64(x / y)));
	else
		tmp = Float64(x - Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5e+24)
		tmp = x - (z * (x / y));
	else
		tmp = x - (x / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5e+24], N[(x - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000045e24

   1. Initial program 90.9%

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

      1. associate-*l/ 92.3%

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

      2. distribute-rgt-out-- 82.7%

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

      3. associate-*r/ 90.3%

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

      4. associate-*l/ 97.8%

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

      5. *-inverses 97.8%

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

      6. *-lft-identity 97.8%

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

   3. Simplified 97.8%

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

   if -5.00000000000000045e24 < z

   1. Initial program 86.2%

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

      1. associate-*l/ 85.5%

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

      2. distribute-rgt-out-- 81.8%

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

      3. associate-*r/ 82.0%

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

      4. associate-*l/ 94.1%

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

      5. *-inverses 94.1%

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

      6. *-lft-identity 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in z around 0 96.9%

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

      1. *-commutative 96.9%

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

      2. associate-/l* 98.9%

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

   6. Simplified 98.9%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+24}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \end{array} \]

Alternative 2: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+61} \lor \neg \left(y \leq 8.5 \cdot 10^{+92}\right) \land y \leq 7 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.5e-43)
   x
   (if (or (<= y 1.35e+61) (and (not (<= y 8.5e+92)) (<= y 7e+108)))
     (* z (/ (- x) y))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e-43) {
		tmp = x;
	} else if ((y <= 1.35e+61) || (!(y <= 8.5e+92) && (y <= 7e+108))) {
		tmp = z * (-x / 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 (y <= (-3.5d-43)) then
        tmp = x
    else if ((y <= 1.35d+61) .or. (.not. (y <= 8.5d+92)) .and. (y <= 7d+108)) then
        tmp = z * (-x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e-43) {
		tmp = x;
	} else if ((y <= 1.35e+61) || (!(y <= 8.5e+92) && (y <= 7e+108))) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.5e-43:
		tmp = x
	elif (y <= 1.35e+61) or (not (y <= 8.5e+92) and (y <= 7e+108)):
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.5e-43)
		tmp = x;
	elseif ((y <= 1.35e+61) || (!(y <= 8.5e+92) && (y <= 7e+108)))
		tmp = Float64(z * Float64(Float64(-x) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.5e-43)
		tmp = x;
	elseif ((y <= 1.35e+61) || (~((y <= 8.5e+92)) && (y <= 7e+108)))
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.5e-43], x, If[Or[LessEqual[y, 1.35e+61], And[N[Not[LessEqual[y, 8.5e+92]], $MachinePrecision], LessEqual[y, 7e+108]]], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.49999999999999997e-43 or 1.3500000000000001e61 < y < 8.5000000000000001e92 or 7.0000000000000005e108 < y

   1. Initial program 77.9%

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

      1. associate-*l/ 76.8%

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

      2. distribute-rgt-out-- 76.7%

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

      3. associate-*r/ 73.5%

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

      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 80.3%

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

   if -3.49999999999999997e-43 < y < 1.3500000000000001e61 or 8.5000000000000001e92 < y < 7.0000000000000005e108

   1. Initial program 94.6%

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

      1. associate-*l/ 95.1%

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

      2. distribute-rgt-out-- 86.1%

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

      3. associate-*r/ 92.0%

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

      4. associate-*l/ 95.1%

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

      5. *-inverses 95.1%

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

      6. *-lft-identity 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in z around 0 97.2%

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

      1. *-commutative 97.2%

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

      2. associate-/l* 92.1%

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

   6. Simplified 92.1%

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

   7. Taylor expanded in y around 0 81.3%

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

      1. mul-1-neg 81.3%

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

      2. associate-*r/ 80.2%

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

      3. distribute-rgt-neg-in 80.2%

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

      4. distribute-frac-neg 80.2%

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

   9. Simplified 80.2%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+61} \lor \neg \left(y \leq 8.5 \cdot 10^{+92}\right) \land y \leq 7 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+62}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.9e-44)
   x
   (if (<= y 2.65e+62)
     (/ (- z) (/ y x))
     (if (<= y 1.2e+93) x (if (<= y 7e+108) (* z (/ (- x) y)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.9e-44) {
		tmp = x;
	} else if (y <= 2.65e+62) {
		tmp = -z / (y / x);
	} else if (y <= 1.2e+93) {
		tmp = x;
	} else if (y <= 7e+108) {
		tmp = z * (-x / 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 (y <= (-3.9d-44)) then
        tmp = x
    else if (y <= 2.65d+62) then
        tmp = -z / (y / x)
    else if (y <= 1.2d+93) then
        tmp = x
    else if (y <= 7d+108) then
        tmp = z * (-x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.9e-44) {
		tmp = x;
	} else if (y <= 2.65e+62) {
		tmp = -z / (y / x);
	} else if (y <= 1.2e+93) {
		tmp = x;
	} else if (y <= 7e+108) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.9e-44:
		tmp = x
	elif y <= 2.65e+62:
		tmp = -z / (y / x)
	elif y <= 1.2e+93:
		tmp = x
	elif y <= 7e+108:
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.9e-44)
		tmp = x;
	elseif (y <= 2.65e+62)
		tmp = Float64(Float64(-z) / Float64(y / x));
	elseif (y <= 1.2e+93)
		tmp = x;
	elseif (y <= 7e+108)
		tmp = Float64(z * Float64(Float64(-x) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.9e-44)
		tmp = x;
	elseif (y <= 2.65e+62)
		tmp = -z / (y / x);
	elseif (y <= 1.2e+93)
		tmp = x;
	elseif (y <= 7e+108)
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.9e-44], x, If[LessEqual[y, 2.65e+62], N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+93], x, If[LessEqual[y, 7e+108], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9000000000000002e-44 or 2.6500000000000001e62 < y < 1.20000000000000005e93 or 7.0000000000000005e108 < y

   1. Initial program 77.9%

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

      1. associate-*l/ 76.8%

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

      2. distribute-rgt-out-- 76.7%

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

      3. associate-*r/ 73.5%

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

      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 80.3%

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

   if -3.9000000000000002e-44 < y < 2.6500000000000001e62

   1. Initial program 94.4%

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

      1. associate-*l/ 94.9%

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

      2. distribute-rgt-out-- 85.6%

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

      3. associate-*r/ 91.8%

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

      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%

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

   4. Taylor expanded in z around inf 80.7%

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

      1. mul-1-neg 80.7%

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

      2. associate-*l/ 74.8%

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

      3. distribute-rgt-neg-in 74.8%

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

   6. Simplified 74.8%

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

      1. distribute-rgt-neg-out 74.8%

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

      2. associate-/r/ 79.5%

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

      3. distribute-neg-frac 79.5%

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

   8. Applied egg-rr 79.5%

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

   if 1.20000000000000005e93 < y < 7.0000000000000005e108

   1. Initial program 99.7%

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

      1. associate-*l/ 100.0%

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

      2. distribute-rgt-out-- 100.0%

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

      3. associate-*r/ 100.0%

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

      4. associate-*l/ 100.0%

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

      5. *-inverses 100.0%

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

      6. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in y around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. associate-*r/ 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. distribute-frac-neg 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+62}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 72.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.15e-40)
   x
   (if (<= y 5.5e+60)
     (/ (* z (- x)) y)
     (if (<= y 1.22e+93) x (if (<= y 7e+108) (* z (/ (- x) y)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.15e-40) {
		tmp = x;
	} else if (y <= 5.5e+60) {
		tmp = (z * -x) / y;
	} else if (y <= 1.22e+93) {
		tmp = x;
	} else if (y <= 7e+108) {
		tmp = z * (-x / 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 (y <= (-1.15d-40)) then
        tmp = x
    else if (y <= 5.5d+60) then
        tmp = (z * -x) / y
    else if (y <= 1.22d+93) then
        tmp = x
    else if (y <= 7d+108) then
        tmp = z * (-x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.15e-40) {
		tmp = x;
	} else if (y <= 5.5e+60) {
		tmp = (z * -x) / y;
	} else if (y <= 1.22e+93) {
		tmp = x;
	} else if (y <= 7e+108) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.15e-40:
		tmp = x
	elif y <= 5.5e+60:
		tmp = (z * -x) / y
	elif y <= 1.22e+93:
		tmp = x
	elif y <= 7e+108:
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.15e-40)
		tmp = x;
	elseif (y <= 5.5e+60)
		tmp = Float64(Float64(z * Float64(-x)) / y);
	elseif (y <= 1.22e+93)
		tmp = x;
	elseif (y <= 7e+108)
		tmp = Float64(z * Float64(Float64(-x) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.15e-40)
		tmp = x;
	elseif (y <= 5.5e+60)
		tmp = (z * -x) / y;
	elseif (y <= 1.22e+93)
		tmp = x;
	elseif (y <= 7e+108)
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.15e-40], x, If[LessEqual[y, 5.5e+60], N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.22e+93], x, If[LessEqual[y, 7e+108], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15e-40 or 5.5000000000000001e60 < y < 1.21999999999999995e93 or 7.0000000000000005e108 < y

   1. Initial program 77.9%

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

      1. associate-*l/ 76.8%

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

      2. distribute-rgt-out-- 76.7%

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

      3. associate-*r/ 73.5%

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

      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 80.3%

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

   if -1.15e-40 < y < 5.5000000000000001e60

   1. Initial program 94.4%

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

      1. associate-*l/ 94.9%

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

      2. distribute-rgt-out-- 85.6%

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

      3. associate-*r/ 91.8%

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

      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%

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

   4. Taylor expanded in z around inf 80.7%

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

      1. associate-*r/ 80.7%

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

      2. neg-mul-1 80.7%

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

      3. distribute-rgt-neg-in 80.7%

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

   6. Simplified 80.7%

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

   if 1.21999999999999995e93 < y < 7.0000000000000005e108

   1. Initial program 99.7%

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

      1. associate-*l/ 100.0%

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

      2. distribute-rgt-out-- 100.0%

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

      3. associate-*r/ 100.0%

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

      4. associate-*l/ 100.0%

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

      5. *-inverses 100.0%

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

      6. *-lft-identity 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in y around 0 99.7%

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

      1. mul-1-neg 99.7%

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

      2. associate-*r/ 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. distribute-frac-neg 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 51.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+189} \lor \neg \left(x \leq 1.05 \cdot 10^{+52}\right):\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.75e+189) (not (<= x 1.05e+52))) (* y (/ x y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.75e+189) || !(x <= 1.05e+52)) {
		tmp = y * (x / 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 ((x <= (-1.75d+189)) .or. (.not. (x <= 1.05d+52))) then
        tmp = y * (x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.75e+189) || !(x <= 1.05e+52)) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.75e+189) or not (x <= 1.05e+52):
		tmp = y * (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.75e+189) || !(x <= 1.05e+52))
		tmp = Float64(y * Float64(x / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.75e+189) || ~((x <= 1.05e+52)))
		tmp = y * (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.75e+189], N[Not[LessEqual[x, 1.05e+52]], $MachinePrecision]], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if x < -1.74999999999999998e189 or 1.05e52 < x

   1. Initial program 74.7%

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

   2. Taylor expanded in y around inf 19.5%

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

      1. associate-/l* 56.8%

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

      2. div-inv 56.6%

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

      3. clear-num 56.7%

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

   4. Applied egg-rr 56.7%

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

   if -1.74999999999999998e189 < x < 1.05e52

   1. Initial program 92.1%

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

      1. associate-*l/ 85.4%

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

      2. distribute-rgt-out-- 84.8%

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

      3. associate-*r/ 90.1%

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

      4. associate-*l/ 96.1%

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

      5. *-inverses 96.1%

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

      6. *-lft-identity 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in z around 0 46.1%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+189} \lor \neg \left(x \leq 1.05 \cdot 10^{+52}\right):\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 51.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+61}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.8e-114) x (if (<= y 1e+61) (/ y (/ y x)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.8e-114) {
		tmp = x;
	} else if (y <= 1e+61) {
		tmp = y / (y / x);
	} 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 (y <= (-9.8d-114)) then
        tmp = x
    else if (y <= 1d+61) then
        tmp = y / (y / x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.8e-114) {
		tmp = x;
	} else if (y <= 1e+61) {
		tmp = y / (y / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.8e-114:
		tmp = x
	elif y <= 1e+61:
		tmp = y / (y / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.8e-114)
		tmp = x;
	elseif (y <= 1e+61)
		tmp = Float64(y / Float64(y / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.8e-114)
		tmp = x;
	elseif (y <= 1e+61)
		tmp = y / (y / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.8e-114], x, If[LessEqual[y, 1e+61], N[(y / N[(y / x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -9.7999999999999994e-114 or 9.99999999999999949e60 < y

   1. Initial program 81.0%

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

      1. associate-*l/ 80.0%

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

      2. distribute-rgt-out-- 79.9%

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

      3. associate-*r/ 77.2%

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

      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 72.6%

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

   if -9.7999999999999994e-114 < y < 9.99999999999999949e60

   1. Initial program 93.8%

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

   2. Taylor expanded in y around inf 13.3%

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

      1. associate-/l* 25.4%

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

      2. div-inv 25.0%

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

      3. clear-num 25.1%

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

   4. Applied egg-rr 25.1%

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

      1. clear-num 25.0%

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

      2. un-div-inv 25.4%

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

   6. Applied egg-rr 25.4%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+61}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 92.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5.5 \cdot 10^{+170}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 5.5e+170) (- x (* z (/ x y))) (/ x (/ (- y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 5.5e+170) {
		tmp = x - (z * (x / y));
	} 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 <= 5.5d+170) then
        tmp = x - (z * (x / y))
    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 <= 5.5e+170) {
		tmp = x - (z * (x / y));
	} else {
		tmp = x / (-y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 5.5e+170:
		tmp = x - (z * (x / y))
	else:
		tmp = x / (-y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 5.5e+170)
		tmp = Float64(x - Float64(z * Float64(x / y)));
	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 <= 5.5e+170)
		tmp = x - (z * (x / y));
	else
		tmp = x / (-y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 5.5e+170], N[(x - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[((-y) / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.4999999999999999e170

   1. Initial program 86.2%

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

      1. associate-*l/ 87.5%

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

      2. distribute-rgt-out-- 83.0%

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

      3. associate-*r/ 84.4%

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

      4. associate-*l/ 96.3%

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

      5. *-inverses 96.3%

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

      6. *-lft-identity 96.3%

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

   3. Simplified 96.3%

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

   if 5.4999999999999999e170 < z

   1. Initial program 96.6%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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-- 74.2%

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

      3. associate-*r/ 81.1%

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

      4. associate-*l/ 84.5%

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

      5. *-inverses 84.5%

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

      6. *-lft-identity 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in z around inf 95.6%

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

      1. mul-1-neg 95.6%

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

      2. associate-*l/ 98.7%

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

      3. distribute-rgt-neg-in 98.7%

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

   6. Simplified 98.7%

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

      1. add-sqr-sqrt 48.0%

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

      2. sqrt-unprod 32.2%

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

      3. sqr-neg 32.2%

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

      4. sqrt-unprod 0.5%

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

      5. clear-num 0.5%

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

      6. add-sqr-sqrt 0.9%

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

      7. associate-/r/ 0.9%

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

      8. frac-2neg 0.9%

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

      9. clear-num 0.9%

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

      10. add-sqr-sqrt 0.4%

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

      11. sqrt-unprod 35.9%

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

      12. sqr-neg 35.9%

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

      13. sqrt-unprod 50.4%

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

      14. add-sqr-sqrt 98.8%

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

      15. distribute-neg-frac 98.8%

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

   8. Applied egg-rr 98.8%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5.5 \cdot 10^{+170}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \end{array} \]

Alternative 8: 49.9% 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 87.4%

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

   1. associate-*l/ 87.2%

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

   2. distribute-rgt-out-- 82.0%

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

   3. associate-*r/ 84.0%

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

   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%

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

4. Taylor expanded in z around 0 44.7%

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

5. Final simplification 44.7%

   \[\leadsto x \]

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 2023229 
(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))