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

Percentage Accurate: 85.1% → 95.5%

Time: 6.0s

Alternatives: 6

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: 85.1% 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: 95.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+58}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.18e+58) (/ (* x (- y z)) y) (* x (/ (- y z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.18e+58) {
		tmp = (x * (y - z)) / 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 (z <= (-1.18d+58)) then
        tmp = (x * (y - z)) / 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 (z <= -1.18e+58) {
		tmp = (x * (y - z)) / y;
	} else {
		tmp = x * ((y - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.18e+58:
		tmp = (x * (y - z)) / y
	else:
		tmp = x * ((y - z) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.18e+58)
		tmp = Float64(Float64(x * Float64(y - z)) / y);
	else
		tmp = Float64(x * Float64(Float64(y - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.18e+58)
		tmp = (x * (y - z)) / y;
	else
		tmp = x * ((y - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.18e+58], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.18000000000000003e58

   1. Initial program 97.5%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   if -1.18000000000000003e58 < z

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

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

      2. associate-*l/ 99.0%

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

      3. *-commutative 99.0%

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

   3. Simplified 99.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+58}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.08e-20) x (if (<= y 1.4e-17) (* z (/ (- x) y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.08e-20) {
		tmp = x;
	} else if (y <= 1.4e-17) {
		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 <= (-1.08d-20)) then
        tmp = x
    else if (y <= 1.4d-17) 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 <= -1.08e-20) {
		tmp = x;
	} else if (y <= 1.4e-17) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.08e-20:
		tmp = x
	elif y <= 1.4e-17:
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.08e-20)
		tmp = x;
	elseif (y <= 1.4e-17)
		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 <= -1.08e-20)
		tmp = x;
	elseif (y <= 1.4e-17)
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.08e-20], x, If[LessEqual[y, 1.4e-17], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.08e-20 or 1.3999999999999999e-17 < y

   1. Initial program 80.4%

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

      1. *-commutative 80.4%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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. Add Preprocessing

   5. Taylor expanded in y around inf 79.8%

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

   if -1.08e-20 < y < 1.3999999999999999e-17

   1. Initial program 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-*l/ 92.6%

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

      3. *-commutative 92.6%

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

   3. Simplified 92.6%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. associate-*l/ 75.4%

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

      3. distribute-rgt-neg-out 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-17}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-17}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.5e-59) x (if (<= y 2.7e-17) (/ (- z) (/ y x)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e-59) {
		tmp = x;
	} else if (y <= 2.7e-17) {
		tmp = -z / (y / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-8.5d-59)) then
        tmp = x
    else if (y <= 2.7d-17) then
        tmp = -z / (y / x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e-59) {
		tmp = x;
	} else if (y <= 2.7e-17) {
		tmp = -z / (y / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.5e-59:
		tmp = x
	elif y <= 2.7e-17:
		tmp = -z / (y / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.5e-59)
		tmp = x;
	elseif (y <= 2.7e-17)
		tmp = Float64(Float64(-z) / Float64(y / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.5e-59)
		tmp = x;
	elseif (y <= 2.7e-17)
		tmp = -z / (y / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.5e-59], x, If[LessEqual[y, 2.7e-17], N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -8.49999999999999933e-59 or 2.7000000000000001e-17 < y

   1. Initial program 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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. Add Preprocessing

   5. Taylor expanded in y around inf 76.9%

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

   if -8.49999999999999933e-59 < y < 2.7000000000000001e-17

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

      2. associate-*l/ 91.6%

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

      3. *-commutative 91.6%

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

   3. Simplified 91.6%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. *-commutative 82.3%

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

      3. associate-/l* 79.2%

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

      4. associate-/r/ 76.3%

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

      5. distribute-lft-neg-in 76.3%

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

      6. distribute-neg-frac 76.3%

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

      7. neg-mul-1 76.3%

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

      8. remove-double-neg 76.3%

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

      9. neg-mul-1 76.3%

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

      10. times-frac 76.3%

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

      11. metadata-eval 76.3%

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

      12. *-lft-identity 76.3%

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

   7. Simplified 76.3%

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

      1. associate-*l/ 82.3%

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

      2. add-sqr-sqrt 35.6%

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

      3. sqrt-unprod 24.9%

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

      4. sqr-neg 24.9%

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

      5. sqrt-unprod 0.8%

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

      6. add-sqr-sqrt 1.5%

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

      7. associate-*l/ 1.5%

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

      8. associate-/r/ 1.6%

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

      9. frac-2neg 1.6%

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

      10. distribute-neg-frac 1.6%

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

      11. add-sqr-sqrt 0.7%

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

      12. sqrt-unprod 34.0%

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

      13. sqr-neg 34.0%

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

      14. sqrt-unprod 45.0%

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

      15. add-sqr-sqrt 79.2%

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

   9. Applied egg-rr 79.2%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-17}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8e-59) x (if (<= y 7.5e-17) (/ (* z (- x)) y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e-59) {
		tmp = x;
	} else if (y <= 7.5e-17) {
		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 <= (-8d-59)) then
        tmp = x
    else if (y <= 7.5d-17) 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 <= -8e-59) {
		tmp = x;
	} else if (y <= 7.5e-17) {
		tmp = (z * -x) / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8e-59:
		tmp = x
	elif y <= 7.5e-17:
		tmp = (z * -x) / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8e-59)
		tmp = x;
	elseif (y <= 7.5e-17)
		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 <= -8e-59)
		tmp = x;
	elseif (y <= 7.5e-17)
		tmp = (z * -x) / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8e-59], x, If[LessEqual[y, 7.5e-17], N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -8.0000000000000002e-59 or 7.49999999999999984e-17 < y

   1. Initial program 81.7%

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

      1. *-commutative 81.7%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 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. Add Preprocessing

   5. Taylor expanded in y around inf 76.9%

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

   if -8.0000000000000002e-59 < y < 7.49999999999999984e-17

   1. Initial program 94.4%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. distribute-rgt-neg-out 82.3%

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

   5. Simplified 82.3%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-17}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.8% 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 86.8%

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

   1. *-commutative 86.8%

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

   2. associate-*l/ 96.6%

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

   3. *-commutative 96.6%

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

3. Simplified 96.6%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
4. Add Preprocessing

5. Final simplification 96.6%

   \[\leadsto x \cdot \frac{y - z}{y} \]
6. Add Preprocessing

Alternative 6: 50.3% 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 86.8%

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

   1. *-commutative 86.8%

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

   2. associate-*l/ 96.6%

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

   3. *-commutative 96.6%

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

3. Simplified 96.6%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{y}} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 52.6%

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

6. Final simplification 52.6%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.4% accurate, 0.4× 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 2024026 
(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))