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

Percentage Accurate: 84.8% → 96.5%

Time: 6.2s

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: 84.8% 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: 96.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / (y / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.3%

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

   1. associate-*l/ 82.4%

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

   2. distribute-rgt-out-- 77.2%

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

   3. associate-*r/ 81.9%

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

   4. associate-*l/ 93.3%

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

   5. *-inverses 93.3%

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

   6. *-lft-identity 93.3%

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

3. Simplified 93.3%

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

4. Taylor expanded in z around 0 96.2%

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

   1. *-commutative 96.2%

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

   2. associate-/l* 96.6%

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

6. Simplified 96.6%

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

7. Final simplification 96.6%

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

Alternative 2: 70.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -58000 \lor \neg \left(z \leq 4 \cdot 10^{-98} \lor \neg \left(z \leq 6 \cdot 10^{-80}\right) \land z \leq 1.4 \cdot 10^{+67}\right):\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -58000.0)
         (not (or (<= z 4e-98) (and (not (<= z 6e-80)) (<= z 1.4e+67)))))
   (* (- x) (/ z y))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -58000.0) || !((z <= 4e-98) || (!(z <= 6e-80) && (z <= 1.4e+67)))) {
		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 <= (-58000.0d0)) .or. (.not. (z <= 4d-98) .or. (.not. (z <= 6d-80)) .and. (z <= 1.4d+67))) 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 <= -58000.0) || !((z <= 4e-98) || (!(z <= 6e-80) && (z <= 1.4e+67)))) {
		tmp = -x * (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -58000.0) or not ((z <= 4e-98) or (not (z <= 6e-80) and (z <= 1.4e+67))):
		tmp = -x * (z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -58000.0) || !((z <= 4e-98) || (!(z <= 6e-80) && (z <= 1.4e+67))))
		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 <= -58000.0) || ~(((z <= 4e-98) || (~((z <= 6e-80)) && (z <= 1.4e+67)))))
		tmp = -x * (z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -58000.0], N[Not[Or[LessEqual[z, 4e-98], And[N[Not[LessEqual[z, 6e-80]], $MachinePrecision], LessEqual[z, 1.4e+67]]]], $MachinePrecision]], N[((-x) * N[(z / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -58000 or 3.99999999999999976e-98 < z < 6.00000000000000014e-80 or 1.3999999999999999e67 < z

   1. Initial program 91.8%

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

      1. associate-*l/ 87.6%

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

      2. distribute-rgt-out-- 77.5%

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

      3. associate-*r/ 87.1%

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

      4. associate-*l/ 91.9%

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

      5. *-inverses 91.9%

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

      6. *-lft-identity 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in z around inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. associate-*l/ 76.8%

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

      3. distribute-rgt-neg-in 76.8%

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

   6. Simplified 76.8%

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

   if -58000 < z < 3.99999999999999976e-98 or 6.00000000000000014e-80 < z < 1.3999999999999999e67

   1. Initial program 81.5%

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

      1. associate-*l/ 77.9%

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

      2. distribute-rgt-out-- 76.9%

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

      3. associate-*r/ 77.5%

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

      4. associate-*l/ 94.4%

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

      5. *-inverses 94.4%

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

      6. *-lft-identity 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around 0 79.8%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -58000 \lor \neg \left(z \leq 4 \cdot 10^{-98} \lor \neg \left(z \leq 6 \cdot 10^{-80}\right) \land z \leq 1.4 \cdot 10^{+67}\right):\\ \;\;\;\;\left(-x\right) \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -78000 \lor \neg \left(z \leq 3.4 \cdot 10^{-98}\right) \land \left(z \leq 3.6 \cdot 10^{-80} \lor \neg \left(z \leq 1.02 \cdot 10^{+68}\right)\right):\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -78000.0)
         (and (not (<= z 3.4e-98)) (or (<= z 3.6e-80) (not (<= z 1.02e+68)))))
   (/ x (/ (- y) z))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -78000.0) || (!(z <= 3.4e-98) && ((z <= 3.6e-80) || !(z <= 1.02e+68)))) {
		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 <= (-78000.0d0)) .or. (.not. (z <= 3.4d-98)) .and. (z <= 3.6d-80) .or. (.not. (z <= 1.02d+68))) 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 <= -78000.0) || (!(z <= 3.4e-98) && ((z <= 3.6e-80) || !(z <= 1.02e+68)))) {
		tmp = x / (-y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -78000.0) or (not (z <= 3.4e-98) and ((z <= 3.6e-80) or not (z <= 1.02e+68))):
		tmp = x / (-y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -78000.0) || (!(z <= 3.4e-98) && ((z <= 3.6e-80) || !(z <= 1.02e+68))))
		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 <= -78000.0) || (~((z <= 3.4e-98)) && ((z <= 3.6e-80) || ~((z <= 1.02e+68)))))
		tmp = x / (-y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -78000.0], And[N[Not[LessEqual[z, 3.4e-98]], $MachinePrecision], Or[LessEqual[z, 3.6e-80], N[Not[LessEqual[z, 1.02e+68]], $MachinePrecision]]]], N[(x / N[((-y) / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -78000 or 3.4000000000000001e-98 < z < 3.6e-80 or 1.02e68 < z

   1. Initial program 91.8%

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

      1. associate-*l/ 87.6%

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

      2. distribute-rgt-out-- 77.5%

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

      3. associate-*r/ 87.1%

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

      4. associate-*l/ 91.9%

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

      5. *-inverses 91.9%

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

      6. *-lft-identity 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in z around inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. associate-*l/ 76.8%

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

      3. distribute-rgt-neg-in 76.8%

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

   6. Simplified 76.8%

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

      1. clear-num 76.7%

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

      2. add-sqr-sqrt 44.0%

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

      3. sqrt-unprod 35.9%

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

      4. sqr-neg 35.9%

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

      5. sqrt-unprod 0.8%

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

      6. add-sqr-sqrt 1.3%

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

      7. associate-/r/ 1.3%

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

      8. frac-2neg 1.3%

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

      9. clear-num 1.3%

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

      10. add-sqr-sqrt 0.6%

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

      11. sqrt-unprod 28.7%

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

      12. sqr-neg 28.7%

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

      13. sqrt-unprod 33.3%

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

      14. add-sqr-sqrt 77.7%

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

   8. Applied egg-rr 77.7%

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

   if -78000 < z < 3.4000000000000001e-98 or 3.6e-80 < z < 1.02e68

   1. Initial program 81.5%

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

      1. associate-*l/ 77.9%

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

      2. distribute-rgt-out-- 76.9%

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

      3. associate-*r/ 77.5%

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

      4. associate-*l/ 94.4%

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

      5. *-inverses 94.4%

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

      6. *-lft-identity 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around 0 79.8%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -78000 \lor \neg \left(z \leq 3.4 \cdot 10^{-98}\right) \land \left(z \leq 3.6 \cdot 10^{-80} \lor \neg \left(z \leq 1.02 \cdot 10^{+68}\right)\right):\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 71.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\frac{-y}{z}}\\ \mathbf{if}\;z \leq -112000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-79}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (/ (- y) z))))
   (if (<= z -112000.0)
     t_0
     (if (<= z 5.6e-98)
       x
       (if (<= z 2.1e-79) t_0 (if (<= z 1.55e+65) x (/ (* z (- x)) y)))))))

C

double code(double x, double y, double z) {
	double t_0 = x / (-y / z);
	double tmp;
	if (z <= -112000.0) {
		tmp = t_0;
	} else if (z <= 5.6e-98) {
		tmp = x;
	} else if (z <= 2.1e-79) {
		tmp = t_0;
	} else if (z <= 1.55e+65) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x / (-y / z)
    if (z <= (-112000.0d0)) then
        tmp = t_0
    else if (z <= 5.6d-98) then
        tmp = x
    else if (z <= 2.1d-79) then
        tmp = t_0
    else if (z <= 1.55d+65) 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 t_0 = x / (-y / z);
	double tmp;
	if (z <= -112000.0) {
		tmp = t_0;
	} else if (z <= 5.6e-98) {
		tmp = x;
	} else if (z <= 2.1e-79) {
		tmp = t_0;
	} else if (z <= 1.55e+65) {
		tmp = x;
	} else {
		tmp = (z * -x) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / (-y / z)
	tmp = 0
	if z <= -112000.0:
		tmp = t_0
	elif z <= 5.6e-98:
		tmp = x
	elif z <= 2.1e-79:
		tmp = t_0
	elif z <= 1.55e+65:
		tmp = x
	else:
		tmp = (z * -x) / y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(Float64(-y) / z))
	tmp = 0.0
	if (z <= -112000.0)
		tmp = t_0;
	elseif (z <= 5.6e-98)
		tmp = x;
	elseif (z <= 2.1e-79)
		tmp = t_0;
	elseif (z <= 1.55e+65)
		tmp = x;
	else
		tmp = Float64(Float64(z * Float64(-x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / (-y / z);
	tmp = 0.0;
	if (z <= -112000.0)
		tmp = t_0;
	elseif (z <= 5.6e-98)
		tmp = x;
	elseif (z <= 2.1e-79)
		tmp = t_0;
	elseif (z <= 1.55e+65)
		tmp = x;
	else
		tmp = (z * -x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / N[((-y) / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -112000.0], t$95$0, If[LessEqual[z, 5.6e-98], x, If[LessEqual[z, 2.1e-79], t$95$0, If[LessEqual[z, 1.55e+65], x, N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -112000 or 5.5999999999999998e-98 < z < 2.0999999999999999e-79

   1. Initial program 94.3%

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

      1. associate-*l/ 89.6%

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

      2. distribute-rgt-out-- 80.6%

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

      3. associate-*r/ 94.3%

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

      4. associate-*l/ 94.3%

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

      5. *-inverses 94.3%

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

      6. *-lft-identity 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in z around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. associate-*l/ 77.6%

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

      3. distribute-rgt-neg-in 77.6%

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

   6. Simplified 77.6%

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

      1. clear-num 77.5%

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

      2. add-sqr-sqrt 43.1%

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

      3. sqrt-unprod 38.2%

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

      4. sqr-neg 38.2%

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

      5. sqrt-unprod 0.8%

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

      6. add-sqr-sqrt 1.3%

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

      7. associate-/r/ 1.3%

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

      8. frac-2neg 1.3%

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

      9. clear-num 1.3%

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

      10. add-sqr-sqrt 0.6%

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

      11. sqrt-unprod 29.9%

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

      12. sqr-neg 29.9%

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

      13. sqrt-unprod 34.2%

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

      14. add-sqr-sqrt 77.9%

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

   8. Applied egg-rr 77.9%

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

   if -112000 < z < 5.5999999999999998e-98 or 2.0999999999999999e-79 < z < 1.54999999999999995e65

   1. Initial program 81.5%

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

      1. associate-*l/ 77.9%

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

      2. distribute-rgt-out-- 76.9%

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

      3. associate-*r/ 77.5%

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

      4. associate-*l/ 94.4%

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

      5. *-inverses 94.4%

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

      6. *-lft-identity 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around 0 79.8%

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

   if 1.54999999999999995e65 < z

   1. Initial program 88.6%

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

      1. associate-*l/ 85.0%

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

      2. distribute-rgt-out-- 73.3%

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

      3. associate-*r/ 77.4%

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

      4. associate-*l/ 88.7%

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

      5. *-inverses 88.7%

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

      6. *-lft-identity 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in z around inf 85.0%

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

      1. associate-*r/ 85.0%

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

      2. neg-mul-1 85.0%

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

      3. distribute-rgt-neg-in 85.0%

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

   6. Simplified 85.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -112000:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-98}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{\frac{-y}{z}}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \]

Alternative 5: 92.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.9 \cdot 10^{+166}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.9e+166) (- x (* z (/ x y))) (/ (* z (- x)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.9e+166) {
		tmp = x - (z * (x / 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 <= 1.9d+166) then
        tmp = x - (z * (x / 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 <= 1.9e+166) {
		tmp = x - (z * (x / y));
	} else {
		tmp = (z * -x) / y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.9e+166:
		tmp = x - (z * (x / y))
	else:
		tmp = (z * -x) / y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.9e+166)
		tmp = Float64(x - Float64(z * Float64(x / 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 <= 1.9e+166)
		tmp = x - (z * (x / y));
	else
		tmp = (z * -x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.9e+166], N[(x - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.90000000000000003e166

   1. Initial program 84.9%

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

      1. associate-*l/ 82.6%

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

      2. distribute-rgt-out-- 77.5%

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

      3. associate-*r/ 82.4%

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

      4. associate-*l/ 94.9%

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

      5. *-inverses 94.9%

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

      6. *-lft-identity 94.9%

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

   3. Simplified 94.9%

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

   if 1.90000000000000003e166 < z

   1. Initial program 96.6%

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

      1. associate-*l/ 81.3%

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

      2. distribute-rgt-out-- 74.9%

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

      3. associate-*r/ 78.2%

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

      4. associate-*l/ 81.4%

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

      5. *-inverses 81.4%

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

      6. *-lft-identity 81.4%

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

   3. Simplified 81.4%

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

   4. Taylor expanded in z around inf 96.6%

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

      1. associate-*r/ 96.6%

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

      2. neg-mul-1 96.6%

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

      3. distribute-rgt-neg-in 96.6%

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

   6. Simplified 96.6%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.9 \cdot 10^{+166}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \end{array} \]

Alternative 6: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -9.2e+93) (* y (/ x y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.2e+93) {
		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 (x <= (-9.2d+93)) 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 (x <= -9.2e+93) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.2e+93:
		tmp = y * (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.2e+93)
		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 (x <= -9.2e+93)
		tmp = y * (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.2e+93], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if x < -9.2000000000000006e93

   1. Initial program 70.6%

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

   2. Taylor expanded in y around inf 19.9%

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

      1. associate-/l* 57.9%

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

      2. div-inv 59.8%

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

      3. clear-num 59.9%

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

   4. Applied egg-rr 59.9%

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

   if -9.2000000000000006e93 < x

   1. Initial program 89.5%

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

      1. associate-*l/ 80.1%

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

      2. distribute-rgt-out-- 76.7%

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

      3. associate-*r/ 85.6%

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

      4. associate-*l/ 93.2%

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

      5. *-inverses 93.2%

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

      6. *-lft-identity 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 51.6%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 50.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 86.3%

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

   1. associate-*l/ 82.4%

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

   2. distribute-rgt-out-- 77.2%

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

   3. associate-*r/ 81.9%

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

   4. associate-*l/ 93.3%

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

   5. *-inverses 93.3%

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

   6. *-lft-identity 93.3%

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

3. Simplified 93.3%

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

4. Taylor expanded in z around 0 50.4%

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

5. Final simplification 50.4%

   \[\leadsto x \]

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 2023181 
(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))