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

Percentage Accurate: 84.3% → 95.9%

Time: 6.1s

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: 84.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y - z)) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.3%

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

   1. associate-*r/ 98.0%

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

   2. div-sub 98.1%

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

   3. *-inverses 98.1%

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

3. Simplified 98.1%

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

   1. sub-neg 98.1%

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

   2. distribute-rgt-in 98.1%

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

   3. *-un-lft-identity 98.1%

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

   4. distribute-neg-frac 98.1%

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

5. Applied egg-rr 98.1%

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

6. Final simplification 98.1%

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

Alternative 2: 70.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-30} \lor \neg \left(z \leq 7.4 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.1e-30) (not (<= z 7.4e+33))) (* x (/ (- z) y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.1e-30) || !(z <= 7.4e+33)) {
		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 ((z <= (-3.1d-30)) .or. (.not. (z <= 7.4d+33))) 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 ((z <= -3.1e-30) || !(z <= 7.4e+33)) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.1e-30) or not (z <= 7.4e+33):
		tmp = x * (-z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.1e-30) || !(z <= 7.4e+33))
		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 ((z <= -3.1e-30) || ~((z <= 7.4e+33)))
		tmp = x * (-z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.1e-30], N[Not[LessEqual[z, 7.4e+33]], $MachinePrecision]], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.09999999999999991e-30 or 7.3999999999999997e33 < z

   1. Initial program 87.4%

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

      1. associate-*r/ 96.4%

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

      2. div-sub 96.4%

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

      3. *-inverses 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around inf 69.0%

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

      1. associate-*r/ 69.0%

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

      2. mul-1-neg 69.0%

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

      3. distribute-rgt-neg-out 69.0%

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

      4. associate-*r/ 69.2%

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

   6. Simplified 69.2%

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

   if -3.09999999999999991e-30 < z < 7.3999999999999997e33

   1. Initial program 78.6%

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

      1. associate-*r/ 99.9%

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

      2. div-sub 99.9%

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

      3. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 80.5%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-30} \lor \neg \left(z \leq 7.4 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 71.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-30} \lor \neg \left(z \leq 2.9 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.1e-30) (not (<= z 2.9e+31))) (/ (- x) (/ y z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.1e-30) || !(z <= 2.9e+31)) {
		tmp = -x / (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.1d-30)) .or. (.not. (z <= 2.9d+31))) then
        tmp = -x / (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.1e-30) || !(z <= 2.9e+31)) {
		tmp = -x / (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.1e-30) or not (z <= 2.9e+31):
		tmp = -x / (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.1e-30) || !(z <= 2.9e+31))
		tmp = Float64(Float64(-x) / Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.1e-30) || ~((z <= 2.9e+31)))
		tmp = -x / (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.1e-30], N[Not[LessEqual[z, 2.9e+31]], $MachinePrecision]], N[((-x) / N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.09999999999999991e-30 or 2.9e31 < z

   1. Initial program 87.4%

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

      1. associate-*r/ 96.4%

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

      2. div-sub 96.4%

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

      3. *-inverses 96.4%

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

   3. Simplified 96.4%

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

      1. sub-neg 96.4%

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

      2. distribute-rgt-in 96.4%

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

      3. *-un-lft-identity 96.4%

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

      4. distribute-neg-frac 96.4%

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

   5. Applied egg-rr 96.4%

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

      1. distribute-frac-neg 96.4%

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

      2. distribute-lft-neg-out 96.4%

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

      3. associate-/r/ 93.5%

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

      4. unsub-neg 93.5%

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

      5. div-inv 93.5%

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

      6. clear-num 94.7%

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

   7. Applied egg-rr 94.7%

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

      1. associate-*r/ 88.6%

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

      2. clear-num 88.7%

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

   9. Applied egg-rr 88.7%

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

   10. Taylor expanded in y around 0 69.0%

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

       1. mul-1-neg 69.0%

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

       2. associate-/l* 69.3%

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

       3. distribute-neg-frac 69.3%

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

   12. Simplified 69.3%

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

   if -3.09999999999999991e-30 < z < 2.9e31

   1. Initial program 78.6%

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

      1. associate-*r/ 99.9%

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

      2. div-sub 99.9%

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

      3. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 80.5%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-30} \lor \neg \left(z \leq 2.9 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 71.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-30}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.9e-30)
   (/ (- x) (/ y z))
   (if (<= z 2.05e+31) x (/ (* x (- z)) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.9e-30) {
		tmp = -x / (y / z);
	} else if (z <= 2.05e+31) {
		tmp = x;
	} else {
		tmp = (x * -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 <= (-2.9d-30)) then
        tmp = -x / (y / z)
    else if (z <= 2.05d+31) then
        tmp = x
    else
        tmp = (x * -z) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.9e-30) {
		tmp = -x / (y / z);
	} else if (z <= 2.05e+31) {
		tmp = x;
	} else {
		tmp = (x * -z) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.9e-30:
		tmp = -x / (y / z)
	elif z <= 2.05e+31:
		tmp = x
	else:
		tmp = (x * -z) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.9e-30)
		tmp = Float64(Float64(-x) / Float64(y / z));
	elseif (z <= 2.05e+31)
		tmp = x;
	else
		tmp = Float64(Float64(x * Float64(-z)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.9e-30)
		tmp = -x / (y / z);
	elseif (z <= 2.05e+31)
		tmp = x;
	else
		tmp = (x * -z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.9e-30], N[((-x) / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+31], x, N[(N[(x * (-z)), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.89999999999999989e-30

   1. Initial program 85.5%

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

      1. associate-*r/ 98.8%

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

      2. div-sub 98.8%

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

      3. *-inverses 98.8%

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

   3. Simplified 98.8%

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

      1. sub-neg 98.8%

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

      2. distribute-rgt-in 98.8%

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

      3. *-un-lft-identity 98.8%

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

      4. distribute-neg-frac 98.8%

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

   5. Applied egg-rr 98.8%

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

      1. distribute-frac-neg 98.8%

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

      2. distribute-lft-neg-out 98.8%

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

      3. associate-/r/ 94.3%

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

      4. unsub-neg 94.3%

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

      5. div-inv 94.3%

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

      6. clear-num 96.1%

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

   7. Applied egg-rr 96.1%

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

      1. associate-*r/ 86.4%

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

      2. clear-num 86.5%

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

   9. Applied egg-rr 86.5%

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

   10. Taylor expanded in y around 0 63.9%

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

       1. mul-1-neg 63.9%

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

       2. associate-/l* 67.4%

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

       3. distribute-neg-frac 67.4%

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

   12. Simplified 67.4%

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

   if -2.89999999999999989e-30 < z < 2.0500000000000001e31

   1. Initial program 78.6%

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

      1. associate-*r/ 99.9%

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

      2. div-sub 99.9%

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

      3. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 80.5%

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

   if 2.0500000000000001e31 < z

   1. Initial program 90.6%

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

   2. Taylor expanded in y around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. distribute-rgt-neg-out 77.6%

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

   4. Simplified 77.6%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-30}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{y}\\ \end{array} \]

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 83.3%

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

   1. associate-*r/ 98.0%

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

   2. div-sub 98.1%

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

   3. *-inverses 98.1%

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

3. Simplified 98.1%

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

4. Final simplification 98.1%

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

Alternative 6: 50.6% 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 83.3%

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

   1. associate-*r/ 98.0%

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

   2. div-sub 98.1%

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

   3. *-inverses 98.1%

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

3. Simplified 98.1%

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

4. Taylor expanded in z around 0 53.6%

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

5. Final simplification 53.6%

   \[\leadsto x \]

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 2023308 
(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))