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

Percentage Accurate: 84.2% → 94.5%

Time: 5.2s

Alternatives: 8

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: 94.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.2 \cdot 10^{-254}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.2e-254) (- x (/ (* x z) y)) (- x (/ z (/ y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.2e-254) {
		tmp = x - ((x * z) / y);
	} else {
		tmp = x - (z / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.2d-254) then
        tmp = x - ((x * z) / y)
    else
        tmp = x - (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.2e-254) {
		tmp = x - ((x * z) / y);
	} else {
		tmp = x - (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.2e-254:
		tmp = x - ((x * z) / y)
	else:
		tmp = x - (z / (y / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.2e-254)
		tmp = Float64(x - Float64(Float64(x * z) / y));
	else
		tmp = Float64(x - Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.2e-254)
		tmp = x - ((x * z) / y);
	else
		tmp = x - (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.2e-254], N[(x - N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.20000000000000001e-254

   1. Initial program 91.1%

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

      1. associate-*l/ 81.4%

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

      2. distribute-rgt-out-- 76.1%

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

      3. associate-*r/ 82.9%

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

      4. associate-*l/ 92.4%

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

      5. *-inverses 92.4%

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

      6. *-lft-identity 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around 0 97.6%

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

   if 1.20000000000000001e-254 < x

   1. Initial program 88.4%

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

      1. associate-*l/ 92.5%

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

      2. distribute-rgt-out-- 87.6%

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

      3. associate-*r/ 88.0%

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

      4. associate-*l/ 97.7%

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

      5. *-inverses 97.7%

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

      6. *-lft-identity 97.7%

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

   3. Simplified 97.7%

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

      1. clear-num 97.6%

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

      2. un-div-inv 98.4%

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

   5. Applied egg-rr 98.4%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.2 \cdot 10^{-254}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 2: 70.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.2e-7) x (if (<= y 4.5e+53) (* x (/ (- z) y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.2e-7) {
		tmp = x;
	} else if (y <= 4.5e+53) {
		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 <= (-5.2d-7)) then
        tmp = x
    else if (y <= 4.5d+53) 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 <= -5.2e-7) {
		tmp = x;
	} else if (y <= 4.5e+53) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.2e-7:
		tmp = x
	elif y <= 4.5e+53:
		tmp = x * (-z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.2e-7)
		tmp = x;
	elseif (y <= 4.5e+53)
		tmp = Float64(x * Float64(Float64(-z) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.2e-7)
		tmp = x;
	elseif (y <= 4.5e+53)
		tmp = x * (-z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.2e-7], x, If[LessEqual[y, 4.5e+53], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -5.19999999999999998e-7 or 4.5000000000000002e53 < y

   1. Initial program 81.5%

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

   2. Taylor expanded in y around inf 79.2%

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

   if -5.19999999999999998e-7 < y < 4.5000000000000002e53

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. associate-*l/ 69.5%

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

      3. *-commutative 69.5%

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

      4. distribute-rgt-neg-in 69.5%

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

      5. distribute-frac-neg 69.5%

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

   4. Simplified 69.5%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-7) x (if (<= y 5.5e+49) (* z (/ (- x) y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-7) {
		tmp = x;
	} else if (y <= 5.5e+49) {
		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 <= (-5d-7)) then
        tmp = x
    else if (y <= 5.5d+49) 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 <= -5e-7) {
		tmp = x;
	} else if (y <= 5.5e+49) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e-7:
		tmp = x
	elif y <= 5.5e+49:
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-7)
		tmp = x;
	elseif (y <= 5.5e+49)
		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 <= -5e-7)
		tmp = x;
	elseif (y <= 5.5e+49)
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-7], x, If[LessEqual[y, 5.5e+49], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999977e-7 or 5.50000000000000042e49 < y

   1. Initial program 81.5%

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

   2. Taylor expanded in y around inf 79.2%

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

   if -4.99999999999999977e-7 < y < 5.50000000000000042e49

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. associate-*r/ 74.8%

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

      3. *-commutative 74.8%

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

      4. distribute-rgt-neg-in 74.8%

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

   4. Simplified 74.8%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 72.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.6e-7) x (if (<= y 6.5e+49) (/ (* z (- x)) y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.6e-7) {
		tmp = x;
	} else if (y <= 6.5e+49) {
		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 <= (-3.6d-7)) then
        tmp = x
    else if (y <= 6.5d+49) 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 <= -3.6e-7) {
		tmp = x;
	} else if (y <= 6.5e+49) {
		tmp = (z * -x) / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.6e-7:
		tmp = x
	elif y <= 6.5e+49:
		tmp = (z * -x) / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.6e-7)
		tmp = x;
	elseif (y <= 6.5e+49)
		tmp = Float64(Float64(z * Float64(-x)) / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.6e-7)
		tmp = x;
	elseif (y <= 6.5e+49)
		tmp = (z * -x) / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.6e-7], x, If[LessEqual[y, 6.5e+49], N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.59999999999999994e-7 or 6.5000000000000005e49 < y

   1. Initial program 81.5%

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

   2. Taylor expanded in y around inf 79.2%

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

   if -3.59999999999999994e-7 < y < 6.5000000000000005e49

   1. Initial program 96.3%

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

   2. Taylor expanded in y around 0 77.1%

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

      1. associate-*r/ 77.1%

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

      2. neg-mul-1 77.1%

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

      3. distribute-rgt-neg-in 77.1%

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

   4. Simplified 77.1%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 53.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e-92) x (if (<= y 1.08e-75) (* y (/ x y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e-92) {
		tmp = x;
	} else if (y <= 1.08e-75) {
		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 <= (-2d-92)) then
        tmp = x
    else if (y <= 1.08d-75) 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 <= -2e-92) {
		tmp = x;
	} else if (y <= 1.08e-75) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e-92:
		tmp = x
	elif y <= 1.08e-75:
		tmp = y * (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e-92)
		tmp = x;
	elseif (y <= 1.08e-75)
		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 <= -2e-92)
		tmp = x;
	elseif (y <= 1.08e-75)
		tmp = y * (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e-92], x, If[LessEqual[y, 1.08e-75], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.99999999999999998e-92 or 1.08e-75 < y

   1. Initial program 86.2%

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

   2. Taylor expanded in y around inf 65.3%

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

   if -1.99999999999999998e-92 < y < 1.08e-75

   1. Initial program 95.2%

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

   2. Taylor expanded in y around inf 18.5%

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

      1. associate-/l* 29.7%

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

      2. div-inv 30.3%

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

      3. clear-num 30.4%

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

   4. Applied egg-rr 30.4%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 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 89.8%

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

   1. associate-*l/ 86.8%

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

   2. distribute-rgt-out-- 81.7%

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

   3. associate-*r/ 85.3%

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

   4. associate-*l/ 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. Final simplification 95.0%

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

Alternative 7: 94.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.8%

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

   1. associate-*l/ 86.8%

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

   2. distribute-rgt-out-- 81.7%

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

   3. associate-*r/ 85.3%

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

   4. associate-*l/ 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. Step-by-step derivation

   1. clear-num 94.9%

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

   2. un-div-inv 95.9%

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

5. Applied egg-rr 95.9%

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

6. Final simplification 95.9%

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

Alternative 8: 51.1% 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 89.8%

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

2. Taylor expanded in y around inf 47.6%

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

3. Final simplification 47.6%

   \[\leadsto x \]

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 2023221 
(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))