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

Percentage Accurate: 84.3% → 97.1%

Time: 4.6s

Alternatives: 5

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: 84.3% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-50}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 2e-50) (- x (/ x (/ y z))) (- x (* z (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2e-50) {
		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 (z <= 2d-50) 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 (z <= 2e-50) {
		tmp = x - (x / (y / z));
	} else {
		tmp = x - (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2e-50:
		tmp = x - (x / (y / z))
	else:
		tmp = x - (z * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2e-50)
		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 (z <= 2e-50)
		tmp = x - (x / (y / z));
	else
		tmp = x - (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2e-50], 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 z < 2.00000000000000002e-50

   1. Initial program 84.5%

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

      1. associate-*l/ 79.4%

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

      2. distribute-rgt-out-- 75.4%

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

      3. associate-*r/ 75.4%

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

      4. associate-*l/ 88.5%

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

      5. *-inverses 88.5%

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

      6. *-lft-identity 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in z around 0 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-/l* 98.1%

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

   6. Simplified 98.1%

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

   if 2.00000000000000002e-50 < z

   1. Initial program 81.3%

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

      1. associate-*l/ 93.6%

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

      2. distribute-rgt-out-- 90.3%

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

      3. associate-*r/ 84.5%

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

      4. associate-*l/ 98.4%

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

      5. *-inverses 98.4%

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

      6. *-lft-identity 98.4%

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

   3. Simplified 98.4%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{-50}:\\ \;\;\;\;x - \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array} \]

Alternative 2: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -170000000 \lor \neg \left(z \leq 8\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -170000000.0) (not (<= z 8.0))) (* z (/ (- x) y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -170000000.0) || !(z <= 8.0)) {
		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 <= (-170000000.0d0)) .or. (.not. (z <= 8.0d0))) 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 <= -170000000.0) || !(z <= 8.0)) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -170000000.0) or not (z <= 8.0):
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -170000000.0) || !(z <= 8.0))
		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 <= -170000000.0) || ~((z <= 8.0)))
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -170000000.0], N[Not[LessEqual[z, 8.0]], $MachinePrecision]], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e8 or 8 < z

   1. Initial program 85.8%

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

      1. associate-*l/ 91.2%

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

      2. distribute-rgt-out-- 85.2%

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

      3. associate-*r/ 85.4%

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

      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 0 89.2%

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

      1. *-commutative 89.2%

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

      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 73.1%

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

      1. mul-1-neg 73.1%

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

      2. associate-*r/ 76.5%

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

      3. distribute-rgt-neg-in 76.5%

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

      4. distribute-frac-neg 76.5%

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

   9. Simplified 76.5%

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

   if -1.7e8 < z < 8

   1. Initial program 81.4%

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

      1. associate-*l/ 73.6%

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

      2. distribute-rgt-out-- 72.1%

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

      3. associate-*r/ 69.1%

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

      4. associate-*l/ 84.4%

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

      5. *-inverses 84.4%

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

      6. *-lft-identity 84.4%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in z around 0 80.9%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -170000000 \lor \neg \left(z \leq 8\right):\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 95.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{+169}:\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 7.5e+169) (- x (* x (/ z y))) (* z (/ (- x) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 7.5e+169) {
		tmp = x - (x * (z / y));
	} 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+169) then
        tmp = x - (x * (z / y))
    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+169) {
		tmp = x - (x * (z / y));
	} else {
		tmp = z * (-x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 7.5e+169:
		tmp = x - (x * (z / y))
	else:
		tmp = z * (-x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 7.5e+169)
		tmp = Float64(x - Float64(x * Float64(z / y)));
	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+169)
		tmp = x - (x * (z / y));
	else
		tmp = z * (-x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 7.5e+169], N[(x - N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.49999999999999992e169

   1. Initial program 83.8%

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

      1. associate-*l/ 81.5%

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

      2. distribute-rgt-out-- 77.3%

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

      3. associate-*r/ 75.7%

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

      4. associate-*l/ 90.1%

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

      5. *-inverses 90.1%

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

      6. *-lft-identity 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in z around 0 93.8%

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

      1. associate-*l/ 97.8%

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

      2. *-commutative 97.8%

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

   6. Simplified 97.8%

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

   if 7.49999999999999992e169 < z

   1. Initial program 82.9%

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

      1. associate-*l/ 92.9%

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

      2. distribute-rgt-out-- 92.9%

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

      3. associate-*r/ 93.4%

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

      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 0 83.0%

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

      1. *-commutative 83.0%

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

      2. associate-/l* 79.0%

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

   6. Simplified 79.0%

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

   7. Taylor expanded in y around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. associate-*r/ 91.2%

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

      3. distribute-rgt-neg-in 91.2%

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

      4. distribute-frac-neg 91.2%

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

   9. Simplified 91.2%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{+169}:\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \end{array} \]

Alternative 4: 96.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1e+61)
		tmp = Float64(x - 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 <= 1e+61)
		tmp = x - (x * (z / y));
	else
		tmp = x - (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < 9.99999999999999949e60

   1. Initial program 84.1%

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

      1. associate-*l/ 80.2%

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

      2. distribute-rgt-out-- 75.6%

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

      3. associate-*r/ 75.6%

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

      4. associate-*l/ 89.2%

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

      5. *-inverses 89.2%

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

      6. *-lft-identity 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in z around 0 94.6%

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

      1. associate-*l/ 98.1%

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

      2. *-commutative 98.1%

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

   6. Simplified 98.1%

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

   if 9.99999999999999949e60 < z

   1. Initial program 82.1%

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

      1. associate-*l/ 93.8%

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

      2. distribute-rgt-out-- 93.8%

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

      3. associate-*r/ 86.2%

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

      4. associate-*l/ 98.1%

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

      5. *-inverses 98.1%

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

      6. *-lft-identity 98.1%

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

   3. Simplified 98.1%

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

4. Final simplification 98.1%

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

Alternative 5: 50.5% 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 83.7%

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

   1. associate-*l/ 82.8%

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

   2. distribute-rgt-out-- 79.0%

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

   3. associate-*r/ 77.6%

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

   4. associate-*l/ 90.9%

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

   5. *-inverses 90.9%

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

   6. *-lft-identity 90.9%

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

3. Simplified 90.9%

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

4. Taylor expanded in z around 0 49.9%

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

5. Final simplification 49.9%

   \[\leadsto x \]

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 2023199 
(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))