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

Percentage Accurate: 84.3% → 95.9%

Time: 7.4s

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: 84.3% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-140}:\\ \;\;\;\;x - \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{-1}{\frac{y}{z \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.6e-140)
   (- x (/ z (/ y x)))
   (if (<= z 9.5e-74) (+ x (/ -1.0 (/ y (* z x)))) (- x (* z (/ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.6e-140) {
		tmp = x - (z / (y / x));
	} else if (z <= 9.5e-74) {
		tmp = x + (-1.0 / (y / (z * x)));
	} else {
		tmp = x - (z * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-7.6d-140)) then
        tmp = x - (z / (y / x))
    else if (z <= 9.5d-74) then
        tmp = x + ((-1.0d0) / (y / (z * x)))
    else
        tmp = x - (z * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.6e-140) {
		tmp = x - (z / (y / x));
	} else if (z <= 9.5e-74) {
		tmp = x + (-1.0 / (y / (z * x)));
	} else {
		tmp = x - (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.6e-140:
		tmp = x - (z / (y / x))
	elif z <= 9.5e-74:
		tmp = x + (-1.0 / (y / (z * x)))
	else:
		tmp = x - (z * (x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.6e-140)
		tmp = Float64(x - Float64(z / Float64(y / x)));
	elseif (z <= 9.5e-74)
		tmp = Float64(x + Float64(-1.0 / Float64(y / Float64(z * x))));
	else
		tmp = Float64(x - Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.6e-140)
		tmp = x - (z / (y / x));
	elseif (z <= 9.5e-74)
		tmp = x + (-1.0 / (y / (z * x)));
	else
		tmp = x - (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.6e-140], N[(x - N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-74], N[(x + N[(-1.0 / N[(y / N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.59999999999999997e-140

   1. Initial program 80.0%

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

      1. associate-*l/ 89.0%

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

      2. distribute-rgt-out-- 86.4%

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

      3. associate-*r/ 85.1%

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

      4. associate-*l/ 97.5%

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

      5. *-inverses 97.5%

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

      6. *-lft-identity 97.5%

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

   3. Simplified 97.5%

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

      1. clear-num 97.5%

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

      2. un-div-inv 97.9%

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

   5. Applied egg-rr 97.9%

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

   if -7.59999999999999997e-140 < z < 9.5000000000000007e-74

   1. Initial program 84.4%

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

      1. associate-*l/ 75.6%

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

      2. distribute-rgt-out-- 72.9%

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

      3. associate-*r/ 72.0%

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

      4. associate-*l/ 86.6%

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

      5. *-inverses 86.6%

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

      6. *-lft-identity 86.6%

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

   3. Simplified 86.6%

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

      1. associate-*r/ 99.1%

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

      2. clear-num 99.1%

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

   5. Applied egg-rr 99.1%

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

   if 9.5000000000000007e-74 < z

   1. Initial program 82.2%

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

      1. associate-*l/ 91.7%

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

      2. distribute-rgt-out-- 85.4%

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

      3. associate-*r/ 82.6%

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

      4. associate-*l/ 99.3%

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

      5. *-inverses 99.3%

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

      6. *-lft-identity 99.3%

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

   3. Simplified 99.3%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-140}:\\ \;\;\;\;x - \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{-1}{\frac{y}{z \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{x}{y}\\ \end{array} \]

Alternative 2: 70.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+57} \lor \neg \left(z \leq -3.1\right) \land \left(z \leq -1.05 \cdot 10^{-50} \lor \neg \left(z \leq 1.7 \cdot 10^{+64}\right)\right):\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.95e+57)
         (and (not (<= z -3.1)) (or (<= z -1.05e-50) (not (<= z 1.7e+64)))))
   (/ (- x) (/ y z))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.95e+57) || (!(z <= -3.1) && ((z <= -1.05e-50) || !(z <= 1.7e+64)))) {
		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 <= (-2.95d+57)) .or. (.not. (z <= (-3.1d0))) .and. (z <= (-1.05d-50)) .or. (.not. (z <= 1.7d+64))) 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 <= -2.95e+57) || (!(z <= -3.1) && ((z <= -1.05e-50) || !(z <= 1.7e+64)))) {
		tmp = -x / (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.95e+57) or (not (z <= -3.1) and ((z <= -1.05e-50) or not (z <= 1.7e+64))):
		tmp = -x / (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.95e+57) || (!(z <= -3.1) && ((z <= -1.05e-50) || !(z <= 1.7e+64))))
		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 <= -2.95e+57) || (~((z <= -3.1)) && ((z <= -1.05e-50) || ~((z <= 1.7e+64)))))
		tmp = -x / (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.95e+57], And[N[Not[LessEqual[z, -3.1]], $MachinePrecision], Or[LessEqual[z, -1.05e-50], N[Not[LessEqual[z, 1.7e+64]], $MachinePrecision]]]], N[((-x) / N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.95000000000000006e57 or -3.10000000000000009 < z < -1.05e-50 or 1.7000000000000001e64 < z

   1. Initial program 83.4%

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

   2. Taylor expanded in y around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. associate-*l/ 73.7%

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

      3. *-commutative 73.7%

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

      4. distribute-rgt-neg-in 73.7%

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

      5. distribute-frac-neg 73.7%

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

   4. Simplified 73.7%

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

      1. associate-*r/ 75.2%

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

      2. associate-*l/ 79.5%

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

      3. add-sqr-sqrt 36.5%

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

      4. sqrt-unprod 22.1%

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

      5. sqr-neg 22.1%

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

      6. sqrt-unprod 0.4%

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

      7. add-sqr-sqrt 1.5%

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

      8. clear-num 1.5%

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

      9. associate-/r/ 1.5%

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

      10. frac-2neg 1.5%

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

      11. clear-num 1.5%

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

      12. neg-mul-1 1.5%

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

      13. associate-/l* 1.5%

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

      14. add-sqr-sqrt 0.4%

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

      15. sqrt-unprod 22.4%

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

      16. sqr-neg 22.4%

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

      17. sqrt-unprod 36.8%

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

      18. add-sqr-sqrt 79.3%

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

      19. frac-2neg 79.3%

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

      20. associate-/l/ 75.1%

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

   6. Applied egg-rr 75.1%

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

      1. div-inv 75.1%

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

      2. clear-num 75.2%

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

      3. mul-1-neg 75.2%

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

      4. *-commutative 75.2%

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

      5. associate-/l* 73.7%

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

   8. Applied egg-rr 73.7%

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

   if -2.95000000000000006e57 < z < -3.10000000000000009 or -1.05e-50 < z < 1.7000000000000001e64

   1. Initial program 81.7%

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

   2. Taylor expanded in y around inf 82.6%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+57} \lor \neg \left(z \leq -3.1\right) \land \left(z \leq -1.05 \cdot 10^{-50} \lor \neg \left(z \leq 1.7 \cdot 10^{+64}\right)\right):\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 70.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+57}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq -60:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-51} \lor \neg \left(z \leq 1.45 \cdot 10^{+60}\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7e+57)
   (/ (- x) (/ y z))
   (if (<= z -60.0)
     x
     (if (or (<= z -3e-51) (not (<= z 1.45e+60))) (* x (/ (- z) y)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7e+57) {
		tmp = -x / (y / z);
	} else if (z <= -60.0) {
		tmp = x;
	} else if ((z <= -3e-51) || !(z <= 1.45e+60)) {
		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 <= (-7d+57)) then
        tmp = -x / (y / z)
    else if (z <= (-60.0d0)) then
        tmp = x
    else if ((z <= (-3d-51)) .or. (.not. (z <= 1.45d+60))) 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 <= -7e+57) {
		tmp = -x / (y / z);
	} else if (z <= -60.0) {
		tmp = x;
	} else if ((z <= -3e-51) || !(z <= 1.45e+60)) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7e+57:
		tmp = -x / (y / z)
	elif z <= -60.0:
		tmp = x
	elif (z <= -3e-51) or not (z <= 1.45e+60):
		tmp = x * (-z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7e+57)
		tmp = Float64(Float64(-x) / Float64(y / z));
	elseif (z <= -60.0)
		tmp = x;
	elseif ((z <= -3e-51) || !(z <= 1.45e+60))
		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 <= -7e+57)
		tmp = -x / (y / z);
	elseif (z <= -60.0)
		tmp = x;
	elseif ((z <= -3e-51) || ~((z <= 1.45e+60)))
		tmp = x * (-z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7e+57], N[((-x) / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -60.0], x, If[Or[LessEqual[z, -3e-51], N[Not[LessEqual[z, 1.45e+60]], $MachinePrecision]], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.9999999999999995e57

   1. Initial program 85.4%

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

   2. Taylor expanded in y around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. associate-*l/ 68.6%

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

      3. *-commutative 68.6%

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

      4. distribute-rgt-neg-in 68.6%

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

      5. distribute-frac-neg 68.6%

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

   4. Simplified 68.6%

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

      1. associate-*r/ 75.8%

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

      2. associate-*l/ 78.1%

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

      3. add-sqr-sqrt 77.8%

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

      4. sqrt-unprod 39.1%

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

      5. sqr-neg 39.1%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 2.0%

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

      8. clear-num 2.0%

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

      9. associate-/r/ 2.0%

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

      10. frac-2neg 2.0%

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

      11. clear-num 2.0%

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

      12. neg-mul-1 2.0%

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

      13. associate-/l* 2.0%

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

      14. add-sqr-sqrt 0.0%

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

      15. sqrt-unprod 39.0%

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

      16. sqr-neg 39.0%

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

      17. sqrt-unprod 77.9%

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

      18. add-sqr-sqrt 78.1%

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

      19. frac-2neg 78.1%

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

      20. associate-/l/ 75.8%

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

   6. Applied egg-rr 75.8%

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

      1. div-inv 75.8%

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

      2. clear-num 75.8%

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

      3. mul-1-neg 75.8%

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

      4. *-commutative 75.8%

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

      5. associate-/l* 68.7%

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

   8. Applied egg-rr 68.7%

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

   if -6.9999999999999995e57 < z < -60 or -3.00000000000000002e-51 < z < 1.45e60

   1. Initial program 81.7%

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

   2. Taylor expanded in y around inf 82.6%

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

   if -60 < z < -3.00000000000000002e-51 or 1.45e60 < z

   1. Initial program 82.3%

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

   2. Taylor expanded in y around 0 74.9%

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

      1. mul-1-neg 74.9%

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

      2. associate-*l/ 76.8%

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

      3. *-commutative 76.8%

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

      4. distribute-rgt-neg-in 76.8%

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

      5. distribute-frac-neg 76.8%

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

   4. Simplified 76.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+57}:\\ \;\;\;\;\frac{-x}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq -60:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-51} \lor \neg \left(z \leq 1.45 \cdot 10^{+60}\right):\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 70.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{-x}{y}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -0.052:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ (- x) y))))
   (if (<= z -2.5e+135)
     t_0
     (if (<= z -0.052)
       x
       (if (<= z -9e-52) (* x (/ (- z) y)) (if (<= z 8.2e+58) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (-x / y);
	double tmp;
	if (z <= -2.5e+135) {
		tmp = t_0;
	} else if (z <= -0.052) {
		tmp = x;
	} else if (z <= -9e-52) {
		tmp = x * (-z / y);
	} else if (z <= 8.2e+58) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	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 = z * (-x / y)
    if (z <= (-2.5d+135)) then
        tmp = t_0
    else if (z <= (-0.052d0)) then
        tmp = x
    else if (z <= (-9d-52)) then
        tmp = x * (-z / y)
    else if (z <= 8.2d+58) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (-x / y);
	double tmp;
	if (z <= -2.5e+135) {
		tmp = t_0;
	} else if (z <= -0.052) {
		tmp = x;
	} else if (z <= -9e-52) {
		tmp = x * (-z / y);
	} else if (z <= 8.2e+58) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (-x / y)
	tmp = 0
	if z <= -2.5e+135:
		tmp = t_0
	elif z <= -0.052:
		tmp = x
	elif z <= -9e-52:
		tmp = x * (-z / y)
	elif z <= 8.2e+58:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(-x) / y))
	tmp = 0.0
	if (z <= -2.5e+135)
		tmp = t_0;
	elseif (z <= -0.052)
		tmp = x;
	elseif (z <= -9e-52)
		tmp = Float64(x * Float64(Float64(-z) / y));
	elseif (z <= 8.2e+58)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (-x / y);
	tmp = 0.0;
	if (z <= -2.5e+135)
		tmp = t_0;
	elseif (z <= -0.052)
		tmp = x;
	elseif (z <= -9e-52)
		tmp = x * (-z / y);
	elseif (z <= 8.2e+58)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+135], t$95$0, If[LessEqual[z, -0.052], x, If[LessEqual[z, -9e-52], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+58], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000015e135 or 8.2e58 < z

   1. Initial program 83.3%

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

   2. Taylor expanded in y around 0 79.9%

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

      1. mul-1-neg 79.9%

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

      2. associate-*r/ 84.9%

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

      3. *-commutative 84.9%

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

      4. distribute-rgt-neg-in 84.9%

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

   4. Simplified 84.9%

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

   if -2.50000000000000015e135 < z < -0.0519999999999999976 or -9.0000000000000001e-52 < z < 8.2e58

   1. Initial program 82.0%

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

   2. Taylor expanded in y around inf 80.9%

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

   if -0.0519999999999999976 < z < -9.0000000000000001e-52

   1. Initial program 81.5%

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

   2. Taylor expanded in y around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. associate-*l/ 74.3%

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

      3. *-commutative 74.3%

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

      4. distribute-rgt-neg-in 74.3%

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

      5. distribute-frac-neg 74.3%

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

   4. Simplified 74.3%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+135}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{elif}\;z \leq -0.052:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \end{array} \]

Alternative 5: 94.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.4%

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

   1. associate-*l/ 84.6%

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

   2. distribute-rgt-out-- 80.8%

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

   3. associate-*r/ 79.2%

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

   4. associate-*l/ 93.8%

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

   5. *-inverses 93.8%

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

   6. *-lft-identity 93.8%

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

3. Simplified 93.8%

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

4. Final simplification 93.8%

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

Alternative 6: 94.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.4%

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

   1. associate-*l/ 84.6%

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

   2. distribute-rgt-out-- 80.8%

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

   3. associate-*r/ 79.2%

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

   4. associate-*l/ 93.8%

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

   5. *-inverses 93.8%

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

   6. *-lft-identity 93.8%

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

3. Simplified 93.8%

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

   1. clear-num 93.6%

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

   2. un-div-inv 94.1%

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

5. Applied egg-rr 94.1%

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

6. Final simplification 94.1%

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

Alternative 7: 50.4% 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 82.4%

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

2. Taylor expanded in y around inf 57.6%

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

3. Final simplification 57.6%

   \[\leadsto x \]

Developer target: 95.7% 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 2023174 
(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))