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

Percentage Accurate: 84.7% → 95.8%

Time: 4.9s

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: 84.7% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 10^{+161}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* x (- y z)) y) 1e+161) (/ x (/ y (- y z))) (- x (* z (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * (y - z)) / y) <= 1e+161) {
		tmp = x / (y / (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 (((x * (y - z)) / y) <= 1d+161) then
        tmp = x / (y / (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 (((x * (y - z)) / y) <= 1e+161) {
		tmp = x / (y / (y - z));
	} else {
		tmp = x - (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * (y - z)) / y) <= 1e+161:
		tmp = x / (y / (y - z))
	else:
		tmp = x - (z * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(x * Float64(y - z)) / y) <= 1e+161)
		tmp = Float64(x / Float64(y / 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 (((x * (y - z)) / y) <= 1e+161)
		tmp = x / (y / (y - z));
	else
		tmp = x - (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], 1e+161], N[(x / N[(y / 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 (/.f64 (*.f64 x (-.f64 y z)) y) < 1e161

   1. Initial program 84.5%

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

      1. associate-*l/ 80.4%

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

   3. Simplified 80.4%

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

      1. associate-/r/ 98.3%

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

   5. Applied egg-rr 98.3%

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

   if 1e161 < (/.f64 (*.f64 x (-.f64 y z)) y)

   1. Initial program 77.1%

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

      1. associate-*l/ 97.9%

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

      2. distribute-rgt-out-- 91.8%

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

      3. associate-*r/ 75.1%

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

      4. associate-*l/ 98.0%

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

      5. *-inverses 98.0%

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

      6. *-lft-identity 98.0%

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

   3. Simplified 98.0%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 10^{+161}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array} \]

Alternative 2: 70.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.014:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.9e-53) x (if (<= y 0.014) (* (/ z y) (- x)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.9e-53) {
		tmp = x;
	} else if (y <= 0.014) {
		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 <= (-2.9d-53)) then
        tmp = x
    else if (y <= 0.014d0) 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 <= -2.9e-53) {
		tmp = x;
	} else if (y <= 0.014) {
		tmp = (z / y) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.9e-53:
		tmp = x
	elif y <= 0.014:
		tmp = (z / y) * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.9e-53)
		tmp = x;
	elseif (y <= 0.014)
		tmp = Float64(Float64(z / y) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.9e-53)
		tmp = x;
	elseif (y <= 0.014)
		tmp = (z / y) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.9e-53], x, If[LessEqual[y, 0.014], N[(N[(z / y), $MachinePrecision] * (-x)), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8999999999999998e-53 or 0.0140000000000000003 < y

   1. Initial program 78.9%

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

      1. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in y around inf 77.6%

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

   if -2.8999999999999998e-53 < y < 0.0140000000000000003

   1. Initial program 87.7%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

      1. associate-/r/ 93.1%

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

   5. Applied egg-rr 93.1%

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

   6. Taylor expanded in y around 0 75.8%

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

      1. associate-*r/ 75.8%

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

      2. neg-mul-1 75.8%

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

   8. Simplified 75.8%

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

      1. frac-2neg 75.8%

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

      2. div-inv 74.5%

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

      3. distribute-neg-frac 74.5%

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

      4. remove-double-neg 74.5%

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

      5. add-sqr-sqrt 41.5%

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

      6. sqrt-prod 29.1%

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

      7. sqr-neg 29.1%

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

      8. sqrt-unprod 0.8%

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

      9. add-sqr-sqrt 1.7%

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

      10. clear-num 1.7%

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

      11. add-sqr-sqrt 0.8%

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

      12. sqrt-unprod 29.1%

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

      13. sqr-neg 29.1%

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

      14. sqrt-prod 41.5%

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

      15. add-sqr-sqrt 74.6%

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

   10. Applied egg-rr 74.6%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.014:\\ \;\;\;\;\frac{z}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 72.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.044:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.8e-56) x (if (<= y 0.044) (* z (/ (- x) y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.8e-56) {
		tmp = x;
	} else if (y <= 0.044) {
		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 <= (-4.8d-56)) then
        tmp = x
    else if (y <= 0.044d0) 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 <= -4.8e-56) {
		tmp = x;
	} else if (y <= 0.044) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.8e-56:
		tmp = x
	elif y <= 0.044:
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.8e-56)
		tmp = x;
	elseif (y <= 0.044)
		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 <= -4.8e-56)
		tmp = x;
	elseif (y <= 0.044)
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.8e-56], x, If[LessEqual[y, 0.044], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -4.80000000000000001e-56 or 0.043999999999999997 < y

   1. Initial program 78.9%

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

      1. associate-*l/ 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in y around inf 77.6%

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

   if -4.80000000000000001e-56 < y < 0.043999999999999997

   1. Initial program 87.7%

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

      1. associate-*l/ 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in y around 0 74.7%

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

      1. *-commutative 74.7%

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

      2. associate-*r/ 74.7%

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

      3. neg-mul-1 74.7%

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

      4. distribute-rgt-neg-in 74.7%

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

      5. associate-*l/ 80.4%

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

   6. Simplified 80.4%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.044:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 72.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-35}:\\ \;\;\;\;\frac{z}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.9e-55) x (if (<= y 5e-35) (/ z (/ (- y) x)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.9e-55) {
		tmp = x;
	} else if (y <= 5e-35) {
		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 <= (-1.9d-55)) then
        tmp = x
    else if (y <= 5d-35) 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 <= -1.9e-55) {
		tmp = x;
	} else if (y <= 5e-35) {
		tmp = z / (-y / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.9e-55:
		tmp = x
	elif y <= 5e-35:
		tmp = z / (-y / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.9e-55)
		tmp = x;
	elseif (y <= 5e-35)
		tmp = Float64(z / Float64(Float64(-y) / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.9e-55)
		tmp = x;
	elseif (y <= 5e-35)
		tmp = z / (-y / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.9e-55], x, If[LessEqual[y, 5e-35], N[(z / N[((-y) / x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8999999999999998e-55 or 4.99999999999999964e-35 < y

   1. Initial program 79.8%

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

      1. associate-*l/ 74.6%

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

   3. Simplified 74.6%

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

   4. Taylor expanded in y around inf 76.5%

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

   if -1.8999999999999998e-55 < y < 4.99999999999999964e-35

   1. Initial program 87.1%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in y around 0 76.0%

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

      1. *-commutative 76.0%

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

      2. associate-*r/ 76.0%

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

      3. neg-mul-1 76.0%

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

      4. distribute-rgt-neg-in 76.0%

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

      5. associate-*l/ 81.9%

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

   6. Simplified 81.9%

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

      1. associate-*l/ 76.0%

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

      2. distribute-rgt-neg-out 76.0%

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

      3. distribute-lft-neg-out 76.0%

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

      4. *-commutative 76.0%

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

      5. associate-/l* 82.3%

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

      6. frac-2neg 82.3%

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

      7. add-sqr-sqrt 37.5%

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

      8. sqrt-unprod 26.9%

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

      9. sqr-neg 26.9%

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

      10. sqrt-unprod 0.8%

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

      11. add-sqr-sqrt 1.6%

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

      12. add-sqr-sqrt 1.0%

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

      13. sqrt-unprod 34.2%

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

      14. sqr-neg 34.2%

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

      15. sqrt-unprod 44.5%

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

      16. add-sqr-sqrt 82.3%

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

   8. Applied egg-rr 82.3%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-35}:\\ \;\;\;\;\frac{z}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{z}{y}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (/ z y))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (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 * (1.0d0 - (z / y))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (z / y));
}

Python

def code(x, y, z):
	return x * (1.0 - (z / y))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(z / y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (z / y));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.1%

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

   1. associate-*l/ 83.7%

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

   2. distribute-rgt-out-- 79.8%

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

   3. associate-*r/ 83.9%

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

   4. associate-*l/ 96.3%

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

   5. *-inverses 96.3%

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

   6. *-lft-identity 96.3%

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

3. Simplified 96.3%

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

4. Taylor expanded in x around 0 95.8%

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

5. Final simplification 95.8%

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

Alternative 6: 94.1% 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 83.1%

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

   1. associate-*l/ 83.7%

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

   2. distribute-rgt-out-- 79.8%

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

   3. associate-*r/ 83.9%

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

   4. associate-*l/ 96.3%

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

   5. *-inverses 96.3%

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

   6. *-lft-identity 96.3%

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

3. Simplified 96.3%

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

4. Final simplification 96.3%

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

Alternative 7: 50.9% 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 83.1%

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

   1. associate-*l/ 83.7%

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

3. Simplified 83.7%

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

4. Taylor expanded in y around inf 49.5%

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

5. Final simplification 49.5%

   \[\leadsto x \]

Developer target: 96.0% 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 2023240 
(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))