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

Percentage Accurate: 84.5% → 95.9%

Time: 6.1s

Alternatives: 9

Speedup: 0.6×

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: 84.5% 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, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 8.1 \cdot 10^{+96}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 8.1e+96) (/ x (/ y (- y z))) (/ (* x (- y z)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 8.1e+96) {
		tmp = x / (y / (y - z));
	} 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 <= 8.1d+96) then
        tmp = x / (y / (y - z))
    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 <= 8.1e+96) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (x * (y - z)) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 8.1e+96:
		tmp = x / (y / (y - z))
	else:
		tmp = (x * (y - z)) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 8.1e+96)
		tmp = Float64(x / Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(x * Float64(y - z)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 8.1e+96)
		tmp = x / (y / (y - z));
	else
		tmp = (x * (y - z)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 8.1e+96], N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.1000000000000002e96

   1. Initial program 85.5%

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

      1. associate-*l/ 84.0%

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

   3. Simplified 84.0%

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

      1. associate-/r/ 99.3%

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

   6. Applied egg-rr 99.3%

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

   if 8.1000000000000002e96 < z

   1. Initial program 97.6%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8.1 \cdot 10^{+96}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-30} \lor \neg \left(z \leq 2.6 \cdot 10^{+103}\right):\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.2e-30) (not (<= z 2.6e+103))) (* (- x) (/ z y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.2e-30) || !(z <= 2.6e+103)) {
		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 <= (-4.2d-30)) .or. (.not. (z <= 2.6d+103))) 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 <= -4.2e-30) || !(z <= 2.6e+103)) {
		tmp = -x * (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.2e-30) or not (z <= 2.6e+103):
		tmp = -x * (z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.2e-30) || !(z <= 2.6e+103))
		tmp = Float64(Float64(-x) * Float64(z / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.2e-30) || ~((z <= 2.6e+103)))
		tmp = -x * (z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.2e-30], N[Not[LessEqual[z, 2.6e+103]], $MachinePrecision]], N[((-x) * N[(z / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000004e-30 or 2.6000000000000002e103 < z

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

      2. associate-*l/ 92.5%

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

      3. *-commutative 92.5%

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

      4. div-sub 92.5%

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

      5. *-inverses 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in z around inf 78.0%

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

      1. *-commutative 78.0%

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

      2. associate-/l* 75.0%

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

      3. associate-/r/ 74.3%

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

      4. associate-*l* 74.3%

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

      5. *-commutative 74.3%

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

      6. associate-*l* 74.3%

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

      7. neg-mul-1 74.3%

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

   7. Simplified 74.3%

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

   if -4.2000000000000004e-30 < z < 2.6000000000000002e103

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-*l/ 99.3%

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

      3. *-commutative 99.3%

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

      4. div-sub 99.3%

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

      5. *-inverses 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 75.2%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-30} \lor \neg \left(z \leq 2.6 \cdot 10^{+103}\right):\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-30} \lor \neg \left(z \leq 2.6 \cdot 10^{+103}\right):\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.4e-30) (not (<= z 2.6e+103))) (/ x (/ (- y) z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.4e-30) || !(z <= 2.6e+103)) {
		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 <= (-4.4d-30)) .or. (.not. (z <= 2.6d+103))) 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 <= -4.4e-30) || !(z <= 2.6e+103)) {
		tmp = x / (-y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.4e-30) or not (z <= 2.6e+103):
		tmp = x / (-y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.4e-30) || !(z <= 2.6e+103))
		tmp = Float64(x / Float64(Float64(-y) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.4e-30) || ~((z <= 2.6e+103)))
		tmp = x / (-y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.4e-30], N[Not[LessEqual[z, 2.6e+103]], $MachinePrecision]], N[(x / N[((-y) / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.39999999999999967e-30 or 2.6000000000000002e103 < z

   1. Initial program 90.8%

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

      1. associate-*l/ 86.7%

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

   3. Simplified 86.7%

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

      1. associate-/r/ 93.5%

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

   6. Applied egg-rr 93.5%

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

   7. Taylor expanded in y around 0 75.2%

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

      1. neg-mul-1 75.2%

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

      2. distribute-neg-frac 75.2%

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

   9. Simplified 75.2%

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

   if -4.39999999999999967e-30 < z < 2.6000000000000002e103

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-*l/ 99.3%

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

      3. *-commutative 99.3%

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

      4. div-sub 99.3%

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

      5. *-inverses 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 75.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-30} \lor \neg \left(z \leq 2.6 \cdot 10^{+103}\right):\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.1e-30)
   (/ x (/ (- y) z))
   (if (<= z 2.6e+103) x (/ (- z) (/ y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e-30) {
		tmp = x / (-y / z);
	} else if (z <= 2.6e+103) {
		tmp = x;
	} else {
		tmp = -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 (z <= (-4.1d-30)) then
        tmp = x / (-y / z)
    else if (z <= 2.6d+103) then
        tmp = x
    else
        tmp = -z / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e-30) {
		tmp = x / (-y / z);
	} else if (z <= 2.6e+103) {
		tmp = x;
	} else {
		tmp = -z / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.1e-30:
		tmp = x / (-y / z)
	elif z <= 2.6e+103:
		tmp = x
	else:
		tmp = -z / (y / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.1e-30)
		tmp = Float64(x / Float64(Float64(-y) / z));
	elseif (z <= 2.6e+103)
		tmp = x;
	else
		tmp = Float64(Float64(-z) / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.1e-30)
		tmp = x / (-y / z);
	elseif (z <= 2.6e+103)
		tmp = x;
	else
		tmp = -z / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.1e-30], N[(x / N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+103], x, N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1000000000000003e-30

   1. Initial program 86.7%

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

      1. associate-*l/ 86.3%

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

   3. Simplified 86.3%

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

      1. associate-/r/ 98.3%

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

   6. Applied egg-rr 98.3%

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

   7. Taylor expanded in y around 0 71.7%

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

      1. neg-mul-1 71.7%

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

      2. distribute-neg-frac 71.7%

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

   9. Simplified 71.7%

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

   if -4.1000000000000003e-30 < z < 2.6000000000000002e103

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-*l/ 99.3%

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

      3. *-commutative 99.3%

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

      4. div-sub 99.3%

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

      5. *-inverses 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 75.2%

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

   if 2.6000000000000002e103 < z

   1. Initial program 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-*l/ 83.1%

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

      3. *-commutative 83.1%

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

      4. div-sub 83.1%

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

      5. *-inverses 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in z around inf 95.1%

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

      1. *-commutative 95.1%

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

      2. associate-/l* 82.7%

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

      3. associate-/r/ 78.4%

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

      4. associate-*l* 78.4%

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

      5. *-commutative 78.4%

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

      6. associate-*l* 78.4%

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

      7. neg-mul-1 78.4%

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

   7. Simplified 78.4%

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

      1. associate-*l/ 95.1%

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

      2. *-un-lft-identity 95.1%

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

      3. times-frac 85.0%

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

      4. add-sqr-sqrt 51.2%

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

      5. sqrt-unprod 39.7%

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

      6. sqr-neg 39.7%

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

      7. sqrt-unprod 0.4%

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

      8. add-sqr-sqrt 1.1%

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

      9. *-un-lft-identity 1.1%

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

      10. *-commutative 1.1%

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

      11. metadata-eval 1.1%

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

      12. div-inv 1.1%

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

      13. associate-/r* 1.1%

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

      14. *-un-lft-identity 1.1%

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

      15. associate-/r/ 1.1%

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

      16. clear-num 1.1%

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

      17. frac-2neg 1.1%

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

      18. div-inv 1.1%

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

      19. distribute-lft-neg-in 1.1%

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

      20. *-inverses 1.1%

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

      21. associate-/r* 1.3%

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

      22. *-commutative 1.3%

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

      23. clear-num 1.3%

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

      24. *-commutative 1.3%

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

      25. associate-/l* 1.1%

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

      26. associate-/r/ 1.1%

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

      27. *-inverses 1.1%

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

      28. *-un-lft-identity 1.1%

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

      29. add-sqr-sqrt 0.4%

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

      30. sqrt-unprod 39.8%

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

      31. sqr-neg 39.8%

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

   9. Applied egg-rr 82.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.4e-30)
   (/ x (/ (- y) z))
   (if (<= z 3.25e+103) x (/ (* z (- x)) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.4e-30) {
		tmp = x / (-y / z);
	} else if (z <= 3.25e+103) {
		tmp = x;
	} else {
		tmp = (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 <= (-4.4d-30)) then
        tmp = x / (-y / z)
    else if (z <= 3.25d+103) then
        tmp = x
    else
        tmp = (z * -x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.4e-30) {
		tmp = x / (-y / z);
	} else if (z <= 3.25e+103) {
		tmp = x;
	} else {
		tmp = (z * -x) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.4e-30:
		tmp = x / (-y / z)
	elif z <= 3.25e+103:
		tmp = x
	else:
		tmp = (z * -x) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.4e-30)
		tmp = Float64(x / Float64(Float64(-y) / z));
	elseif (z <= 3.25e+103)
		tmp = x;
	else
		tmp = Float64(Float64(z * Float64(-x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.4e-30)
		tmp = x / (-y / z);
	elseif (z <= 3.25e+103)
		tmp = x;
	else
		tmp = (z * -x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.4e-30], N[(x / N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.25e+103], x, N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.39999999999999967e-30

   1. Initial program 86.7%

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

      1. associate-*l/ 86.3%

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

   3. Simplified 86.3%

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

      1. associate-/r/ 98.3%

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

   6. Applied egg-rr 98.3%

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

   7. Taylor expanded in y around 0 71.7%

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

      1. neg-mul-1 71.7%

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

      2. distribute-neg-frac 71.7%

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

   9. Simplified 71.7%

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

   if -4.39999999999999967e-30 < z < 3.25000000000000001e103

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-*l/ 99.3%

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

      3. *-commutative 99.3%

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

      4. div-sub 99.3%

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

      5. *-inverses 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 75.2%

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

   if 3.25000000000000001e103 < z

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0 95.1%

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

      1. associate-*r* 95.1%

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

      2. neg-mul-1 95.1%

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

   5. Simplified 95.1%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-30}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.6e-143) x (if (<= y 1.8e-74) (* y (/ x y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.6e-143) {
		tmp = x;
	} else if (y <= 1.8e-74) {
		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 <= (-2.6d-143)) then
        tmp = x
    else if (y <= 1.8d-74) 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 <= -2.6e-143) {
		tmp = x;
	} else if (y <= 1.8e-74) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.6e-143:
		tmp = x
	elif y <= 1.8e-74:
		tmp = y * (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.6e-143)
		tmp = x;
	elseif (y <= 1.8e-74)
		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 <= -2.6e-143)
		tmp = x;
	elseif (y <= 1.8e-74)
		tmp = y * (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.6e-143], x, If[LessEqual[y, 1.8e-74], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.59999999999999987e-143 or 1.8000000000000001e-74 < y

   1. Initial program 84.3%

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

      1. *-commutative 84.3%

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

      2. associate-*l/ 99.3%

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

      3. *-commutative 99.3%

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

      4. div-sub 99.3%

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

      5. *-inverses 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 71.7%

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

   if -2.59999999999999987e-143 < y < 1.8000000000000001e-74

   1. Initial program 93.5%

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

   3. Taylor expanded in y around inf 15.8%

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

      1. associate-/l* 19.8%

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

      2. associate-/r/ 29.8%

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

   5. Applied egg-rr 29.8%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 94.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 7.5e+106) (* x (- 1.0 (/ z y))) (/ (* z (- x)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 7.5e+106) {
		tmp = x * (1.0 - (z / y));
	} else {
		tmp = (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 <= 7.5d+106) then
        tmp = x * (1.0d0 - (z / y))
    else
        tmp = (z * -x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 7.5e+106) {
		tmp = x * (1.0 - (z / y));
	} else {
		tmp = (z * -x) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 7.5e+106:
		tmp = x * (1.0 - (z / y))
	else:
		tmp = (z * -x) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 7.5e+106)
		tmp = Float64(x * Float64(1.0 - Float64(z / y)));
	else
		tmp = Float64(Float64(z * Float64(-x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 7.5e+106)
		tmp = x * (1.0 - (z / y));
	else
		tmp = (z * -x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 7.5e+106], N[(x * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.50000000000000058e106

   1. Initial program 85.7%

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

      1. *-commutative 85.7%

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

      2. associate-*l/ 99.0%

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

      3. *-commutative 99.0%

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

      4. div-sub 99.0%

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

      5. *-inverses 99.0%

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

   3. Simplified 99.0%

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

   if 7.50000000000000058e106 < z

   1. Initial program 97.4%

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

   3. Taylor expanded in y around 0 95.1%

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

      1. associate-*r* 95.1%

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

      2. neg-mul-1 95.1%

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

   5. Simplified 95.1%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 6.8 \cdot 10^{+193}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 6.8e+193) (/ x (/ y (- y z))) (/ (* z (- x)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 6.8e+193) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (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 <= 6.8d+193) then
        tmp = x / (y / (y - z))
    else
        tmp = (z * -x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 6.8e+193) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (z * -x) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 6.8e+193:
		tmp = x / (y / (y - z))
	else:
		tmp = (z * -x) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 6.8e+193)
		tmp = Float64(x / Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(z * Float64(-x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 6.8e+193)
		tmp = x / (y / (y - z));
	else
		tmp = (z * -x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 6.8e+193], N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.79999999999999972e193

   1. Initial program 86.1%

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

      1. associate-*l/ 83.5%

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

   3. Simplified 83.5%

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

      1. associate-/r/ 98.9%

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

   6. Applied egg-rr 98.9%

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

   if 6.79999999999999972e193 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 99.8%

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

      1. associate-*r* 99.8%

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

      2. neg-mul-1 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6.8 \cdot 10^{+193}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.0% 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 87.5%

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

   1. *-commutative 87.5%

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

   2. associate-*l/ 96.6%

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

   3. *-commutative 96.6%

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

   4. div-sub 96.6%

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

   5. *-inverses 96.6%

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

3. Simplified 96.6%

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

5. Taylor expanded in z around 0 53.7%

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

6. Final simplification 53.7%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.1% 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 2024018 
(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))