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

Percentage Accurate: 84.2% → 95.3%

Time: 5.4s

Alternatives: 5

Speedup: 1.0×

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: 84.2% 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: 95.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.8 \cdot 10^{-176}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-y}{z - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 3.8e-176) (- x (* z (/ x y))) (/ x (/ (- y) (- z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.8e-176) {
		tmp = x - (z * (x / y));
	} else {
		tmp = x / (-y / (z - 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 <= 3.8d-176) then
        tmp = x - (z * (x / y))
    else
        tmp = x / (-y / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.8e-176) {
		tmp = x - (z * (x / y));
	} else {
		tmp = x / (-y / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 3.8e-176:
		tmp = x - (z * (x / y))
	else:
		tmp = x / (-y / (z - y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 3.8e-176)
		tmp = Float64(x - Float64(z * Float64(x / y)));
	else
		tmp = Float64(x / Float64(Float64(-y) / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 3.8e-176)
		tmp = x - (z * (x / y));
	else
		tmp = x / (-y / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 3.8e-176], N[(x - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[((-y) / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.80000000000000012e-176

   1. Initial program 78.3%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   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-- 79.8%

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

      3. associate-*r/ 77.0%

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

      4. associate-*l/ 96.6%

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

      5. *-inverses 96.6%

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

      6. *-lft-identity 96.6%

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

   3. Simplified 96.6%

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

   if 3.80000000000000012e-176 < x

   1. Initial program 84.9%

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

      1. frac-2neg 84.9%

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

      2. div-inv 84.8%

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

      3. distribute-rgt-neg-in 84.8%

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

   3. Applied egg-rr 84.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(-\left(y - z\right)\right)\right) \cdot \frac{1}{-y}} \]
   4. Step-by-step derivation

      1. associate-*r/ 84.9%

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

      2. *-rgt-identity 84.9%

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

      3. associate-/l* 99.8%

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

      4. neg-sub0 99.8%

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

      5. associate--r- 99.8%

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

      6. neg-sub0 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.8 \cdot 10^{-176}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-y}{z - y}}\\ \end{array} \]

Alternative 2: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+27} \lor \neg \left(z \leq 5.5 \cdot 10^{+25}\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8e+27) (not (<= z 5.5e+25))) (* z (/ (- x) y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8e+27) || !(z <= 5.5e+25)) {
		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 ((z <= (-8d+27)) .or. (.not. (z <= 5.5d+25))) 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 ((z <= -8e+27) || !(z <= 5.5e+25)) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8e+27) or not (z <= 5.5e+25):
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8e+27) || !(z <= 5.5e+25))
		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 ((z <= -8e+27) || ~((z <= 5.5e+25)))
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8e+27], N[Not[LessEqual[z, 5.5e+25]], $MachinePrecision]], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000001e27 or 5.50000000000000018e25 < z

   1. Initial program 87.8%

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

      1. associate-*l/ 87.8%

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

      2. distribute-rgt-out-- 85.2%

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

      3. associate-*r/ 85.3%

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

      4. associate-*l/ 96.0%

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

      5. *-inverses 96.0%

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

      6. *-lft-identity 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in z around inf 74.6%

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

      1. mul-1-neg 74.6%

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

      2. associate-*l/ 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

   6. Simplified 70.9%

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

   7. Taylor expanded in z around 0 74.6%

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

      1. associate-*r/ 77.5%

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

      2. neg-mul-1 77.5%

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

      3. distribute-rgt-neg-in 77.5%

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

      4. distribute-neg-frac 77.5%

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

   9. Simplified 77.5%

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

   if -8.0000000000000001e27 < z < 5.50000000000000018e25

   1. Initial program 75.1%

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

      1. associate-*l/ 82.7%

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

      2. distribute-rgt-out-- 77.6%

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

      3. associate-*r/ 74.0%

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

      4. associate-*l/ 95.9%

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

      5. *-inverses 95.9%

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

      6. *-lft-identity 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in z around 0 75.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+27} \lor \neg \left(z \leq 5.5 \cdot 10^{+25}\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.5e+28)
   (/ (* x (- z)) y)
   (if (<= z 3.3e+25) x (* z (/ (- x) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e+28) {
		tmp = (x * -z) / y;
	} else if (z <= 3.3e+25) {
		tmp = x;
	} else {
		tmp = 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 <= (-7.5d+28)) then
        tmp = (x * -z) / y
    else if (z <= 3.3d+25) then
        tmp = x
    else
        tmp = z * (-x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e+28) {
		tmp = (x * -z) / y;
	} else if (z <= 3.3e+25) {
		tmp = x;
	} else {
		tmp = z * (-x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.5e+28:
		tmp = (x * -z) / y
	elif z <= 3.3e+25:
		tmp = x
	else:
		tmp = z * (-x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.5e+28)
		tmp = Float64(Float64(x * Float64(-z)) / y);
	elseif (z <= 3.3e+25)
		tmp = x;
	else
		tmp = Float64(z * Float64(Float64(-x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.5e+28)
		tmp = (x * -z) / y;
	elseif (z <= 3.3e+25)
		tmp = x;
	else
		tmp = z * (-x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.5e+28], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 3.3e+25], x, N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.4999999999999998e28

   1. Initial program 94.1%

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

      1. associate-*l/ 79.6%

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

      2. distribute-rgt-out-- 77.6%

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

      3. associate-*r/ 89.2%

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

      4. associate-*l/ 94.9%

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

      5. *-inverses 94.9%

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

      6. *-lft-identity 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in z around inf 73.0%

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

      1. associate-*r/ 73.0%

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

      2. neg-mul-1 73.0%

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

      3. distribute-rgt-neg-in 73.0%

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

   6. Simplified 73.0%

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

   if -7.4999999999999998e28 < z < 3.3000000000000001e25

   1. Initial program 75.1%

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

      1. associate-*l/ 82.7%

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

      2. distribute-rgt-out-- 77.6%

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

      3. associate-*r/ 74.0%

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

      4. associate-*l/ 95.9%

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

      5. *-inverses 95.9%

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

      6. *-lft-identity 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in z around 0 75.7%

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

   if 3.3000000000000001e25 < z

   1. Initial program 83.0%

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

      1. associate-*l/ 93.9%

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

      2. distribute-rgt-out-- 90.9%

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

      3. associate-*r/ 82.4%

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

      4. associate-*l/ 96.8%

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

      5. *-inverses 96.8%

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

      6. *-lft-identity 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 75.8%

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

      1. mul-1-neg 75.8%

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

      2. associate-*l/ 79.1%

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

      3. distribute-rgt-neg-in 79.1%

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

   6. Simplified 79.1%

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

   7. Taylor expanded in z around 0 75.8%

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

      1. associate-*r/ 83.1%

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

      2. neg-mul-1 83.1%

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

      3. distribute-rgt-neg-in 83.1%

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

      4. distribute-neg-frac 83.1%

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

   9. Simplified 83.1%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \end{array} \]

Alternative 4: 94.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.9%

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

   1. associate-*l/ 85.1%

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

   2. distribute-rgt-out-- 81.1%

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

   3. associate-*r/ 79.2%

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

   4. associate-*l/ 95.9%

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

   5. *-inverses 95.9%

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

   6. *-lft-identity 95.9%

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

3. Simplified 95.9%

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

4. Final simplification 95.9%

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

Alternative 5: 50.2% 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 80.9%

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

   1. associate-*l/ 85.1%

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

   2. distribute-rgt-out-- 81.1%

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

   3. associate-*r/ 79.2%

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

   4. associate-*l/ 95.9%

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

   5. *-inverses 95.9%

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

   6. *-lft-identity 95.9%

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

3. Simplified 95.9%

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

4. Taylor expanded in z around 0 50.6%

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

5. Final simplification 50.6%

   \[\leadsto x \]

Developer target: 95.6% 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 2023230 
(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))