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

Percentage Accurate: 84.8% → 95.8%

Time: 4.8s

Alternatives: 7

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: 84.8% 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: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - (x / (y / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.5%

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

   1. --rgt-identity 86.5%

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

   2. associate-*l/ 81.8%

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

   3. sub-neg 81.8%

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

   4. distribute-rgt-in 77.4%

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

   5. *-commutative 77.4%

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

   6. distribute-lft-neg-out 77.4%

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

   7. unsub-neg 77.4%

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

   8. associate--r+ 77.4%

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

   9. associate-*l/ 81.8%

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

   10. associate-/l* 93.0%

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

   11. *-inverses 93.0%

       \[\leadsto \frac{x}{\color{blue}{1}} - \left(z \cdot \frac{x}{y} + 0\right) \]

   12. /-rgt-identity 93.0%

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

   13. +-rgt-identity 93.0%

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

   14. *-commutative 93.0%

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

   15. associate-/r/ 96.9%

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

3. Simplified 96.9%

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

4. Final simplification 96.9%

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

Alternative 2: 70.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-32}:\\ \;\;\;\;-x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e+61) x (if (<= y 2.9e-32) (- (* x (/ z y))) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+61) {
		tmp = x;
	} else if (y <= 2.9e-32) {
		tmp = -(x * (z / y));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.9d+61)) then
        tmp = x
    else if (y <= 2.9d-32) then
        tmp = -(x * (z / y))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e+61) {
		tmp = x;
	} else if (y <= 2.9e-32) {
		tmp = -(x * (z / y));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e+61:
		tmp = x
	elif y <= 2.9e-32:
		tmp = -(x * (z / y))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e+61)
		tmp = x;
	elseif (y <= 2.9e-32)
		tmp = Float64(-Float64(x * Float64(z / y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.9e+61)
		tmp = x;
	elseif (y <= 2.9e-32)
		tmp = -(x * (z / y));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e+61], x, If[LessEqual[y, 2.9e-32], (-N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.89999999999999998e61 or 2.89999999999999996e-32 < y

   1. Initial program 79.3%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 82.0%

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

   if -1.89999999999999998e61 < y < 2.89999999999999996e-32

   1. Initial program 92.7%

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

      1. associate-*r/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around 0 69.0%

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

      1. neg-mul-1 69.0%

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

      2. distribute-neg-frac 69.0%

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

   6. Simplified 69.0%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-32}:\\ \;\;\;\;-x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 73.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{-29}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.85e+61) x (if (<= y 1e-29) (* z (/ (- x) y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.85e+61) {
		tmp = x;
	} else if (y <= 1e-29) {
		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 <= (-1.85d+61)) then
        tmp = x
    else if (y <= 1d-29) 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 <= -1.85e+61) {
		tmp = x;
	} else if (y <= 1e-29) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.85e+61:
		tmp = x
	elif y <= 1e-29:
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.85e+61)
		tmp = x;
	elseif (y <= 1e-29)
		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 <= -1.85e+61)
		tmp = x;
	elseif (y <= 1e-29)
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.85e+61], x, If[LessEqual[y, 1e-29], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85000000000000001e61 or 9.99999999999999943e-30 < y

   1. Initial program 79.3%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 82.0%

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

   if -1.85000000000000001e61 < y < 9.99999999999999943e-30

   1. Initial program 92.7%

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

      1. associate-*r/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around 0 72.6%

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

      1. mul-1-neg 72.6%

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

      2. associate-*l/ 71.8%

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

      3. distribute-lft-neg-in 71.8%

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

      4. *-commutative 71.8%

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

      5. distribute-neg-frac 71.8%

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

   6. Simplified 71.8%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{-29}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 73.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-31}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+61) x (if (<= y 2.95e-31) (/ (* x (- z)) y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+61) {
		tmp = x;
	} else if (y <= 2.95e-31) {
		tmp = (x * -z) / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2d+61)) then
        tmp = x
    else if (y <= 2.95d-31) then
        tmp = (x * -z) / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+61) {
		tmp = x;
	} else if (y <= 2.95e-31) {
		tmp = (x * -z) / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+61:
		tmp = x
	elif y <= 2.95e-31:
		tmp = (x * -z) / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+61)
		tmp = x;
	elseif (y <= 2.95e-31)
		tmp = Float64(Float64(x * Float64(-z)) / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e+61)
		tmp = x;
	elseif (y <= 2.95e-31)
		tmp = (x * -z) / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+61], x, If[LessEqual[y, 2.95e-31], N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9999999999999999e61 or 2.95000000000000016e-31 < y

   1. Initial program 79.3%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 82.0%

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

   if -1.9999999999999999e61 < y < 2.95000000000000016e-31

   1. Initial program 92.7%

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

      1. associate-*r/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around 0 72.6%

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

      1. associate-*r/ 72.6%

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

      2. mul-1-neg 72.6%

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

      3. distribute-rgt-neg-out 72.6%

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

   6. Simplified 72.6%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-31}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 52.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8e-97) x (if (<= y 3.05e-151) (* y (/ x y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e-97) {
		tmp = x;
	} else if (y <= 3.05e-151) {
		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 (y <= (-8d-97)) then
        tmp = x
    else if (y <= 3.05d-151) 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 (y <= -8e-97) {
		tmp = x;
	} else if (y <= 3.05e-151) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8e-97:
		tmp = x
	elif y <= 3.05e-151:
		tmp = y * (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8e-97)
		tmp = x;
	elseif (y <= 3.05e-151)
		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 (y <= -8e-97)
		tmp = x;
	elseif (y <= 3.05e-151)
		tmp = y * (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8e-97], x, If[LessEqual[y, 3.05e-151], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -8.00000000000000029e-97 or 3.05e-151 < y

   1. Initial program 85.6%

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

      1. associate-*r/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in y around inf 66.3%

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

   if -8.00000000000000029e-97 < y < 3.05e-151

   1. Initial program 88.7%

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

   2. Taylor expanded in y around inf 12.1%

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

      1. associate-/l* 18.1%

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

      2. associate-/r/ 29.6%

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

   4. Applied egg-rr 29.6%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-97}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 95.5% accurate, 1.0× speedup

Math

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

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(x * Float64(Float64(y - z) / y))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.5%

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

   1. associate-*r/ 96.5%

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

3. Simplified 96.5%

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

4. Final simplification 96.5%

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

Alternative 7: 50.1% 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 86.5%

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

   1. associate-*r/ 96.5%

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

3. Simplified 96.5%

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

4. Taylor expanded in y around inf 52.4%

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

5. Final simplification 52.4%

   \[\leadsto x \]

Developer target: 96.1% 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 2023271 
(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))