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

Percentage Accurate: 84.1% → 95.6%

Time: 6.1s

Alternatives: 4

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: 84.1% 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: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - (z / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.2%

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

   1. remove-double-neg 83.2%

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

   2. distribute-frac-neg2 83.2%

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

   3. distribute-frac-neg 83.2%

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

   4. distribute-rgt-neg-in 83.2%

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

   5. associate-/l* 95.1%

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

   6. distribute-frac-neg 95.1%

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

   7. distribute-frac-neg2 95.1%

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

   8. remove-double-neg 95.1%

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

   9. div-sub 95.1%

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

   10. *-inverses 95.1%

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

3. Simplified 95.1%

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

5. Final simplification 95.1%

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

Alternative 2: 71.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-139} \lor \neg \left(y \leq -2 \cdot 10^{-170}\right) \land y \leq 3.1 \cdot 10^{+112}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e-19)
   x
   (if (or (<= y -4.4e-139) (and (not (<= y -2e-170)) (<= y 3.1e+112)))
     (/ (- z) (/ y x))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e-19) {
		tmp = x;
	} else if ((y <= -4.4e-139) || (!(y <= -2e-170) && (y <= 3.1e+112))) {
		tmp = -z / (y / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.4d-19)) then
        tmp = x
    else if ((y <= (-4.4d-139)) .or. (.not. (y <= (-2d-170))) .and. (y <= 3.1d+112)) then
        tmp = -z / (y / x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e-19) {
		tmp = x;
	} else if ((y <= -4.4e-139) || (!(y <= -2e-170) && (y <= 3.1e+112))) {
		tmp = -z / (y / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e-19:
		tmp = x
	elif (y <= -4.4e-139) or (not (y <= -2e-170) and (y <= 3.1e+112)):
		tmp = -z / (y / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e-19)
		tmp = x;
	elseif ((y <= -4.4e-139) || (!(y <= -2e-170) && (y <= 3.1e+112)))
		tmp = Float64(Float64(-z) / Float64(y / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.4e-19)
		tmp = x;
	elseif ((y <= -4.4e-139) || (~((y <= -2e-170)) && (y <= 3.1e+112)))
		tmp = -z / (y / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e-19], x, If[Or[LessEqual[y, -4.4e-139], And[N[Not[LessEqual[y, -2e-170]], $MachinePrecision], LessEqual[y, 3.1e+112]]], N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.40000000000000001e-19 or -4.40000000000000021e-139 < y < -1.99999999999999997e-170 or 3.09999999999999983e112 < y

   1. Initial program 76.6%

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

      1. remove-double-neg 76.6%

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

      2. distribute-frac-neg2 76.6%

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

      3. distribute-frac-neg 76.6%

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

      4. distribute-rgt-neg-in 76.6%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 81.0%

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

   if -1.40000000000000001e-19 < y < -4.40000000000000021e-139 or -1.99999999999999997e-170 < y < 3.09999999999999983e112

   1. Initial program 89.1%

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

      1. remove-double-neg 89.1%

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

      2. distribute-frac-neg2 89.1%

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

      3. distribute-frac-neg 89.1%

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

      4. distribute-rgt-neg-in 89.1%

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

      5. associate-/l* 90.7%

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

      6. distribute-frac-neg 90.7%

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

      7. distribute-frac-neg2 90.7%

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

      8. remove-double-neg 90.7%

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

      9. div-sub 90.8%

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

      10. *-inverses 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in z around inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. distribute-frac-neg2 66.9%

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

   7. Simplified 66.9%

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

      1. distribute-frac-neg2 66.9%

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

      2. distribute-rgt-neg-out 66.9%

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

      3. add-sqr-sqrt 37.3%

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

      4. sqrt-unprod 28.6%

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

      5. sqr-neg 28.6%

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

      6. sqrt-unprod 0.7%

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

      7. add-sqr-sqrt 1.9%

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

      8. associate-*r/ 2.0%

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

      9. frac-2neg 2.0%

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

      10. *-commutative 2.0%

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

      11. distribute-rgt-neg-out 2.0%

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

      12. remove-double-neg 2.0%

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

      13. associate-*r/ 1.9%

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

      14. clear-num 1.9%

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

      15. un-div-inv 1.9%

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

      16. frac-2neg 1.9%

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

      17. add-sqr-sqrt 0.8%

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

      18. sqrt-unprod 30.8%

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

      19. sqr-neg 30.8%

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

      20. sqrt-unprod 40.4%

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

      21. add-sqr-sqrt 72.3%

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

      22. remove-double-neg 72.3%

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

   9. Applied egg-rr 72.3%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-139} \lor \neg \left(y \leq -2 \cdot 10^{-170}\right) \land y \leq 3.1 \cdot 10^{+112}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-139}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+111}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e-21)
   x
   (if (<= y -4.4e-139)
     (/ (* z (- x)) y)
     (if (<= y -2e-170) x (if (<= y 7.4e+111) (/ (- z) (/ y x)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e-21) {
		tmp = x;
	} else if (y <= -4.4e-139) {
		tmp = (z * -x) / y;
	} else if (y <= -2e-170) {
		tmp = x;
	} else if (y <= 7.4e+111) {
		tmp = -z / (y / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.8d-21)) then
        tmp = x
    else if (y <= (-4.4d-139)) then
        tmp = (z * -x) / y
    else if (y <= (-2d-170)) then
        tmp = x
    else if (y <= 7.4d+111) then
        tmp = -z / (y / x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e-21) {
		tmp = x;
	} else if (y <= -4.4e-139) {
		tmp = (z * -x) / y;
	} else if (y <= -2e-170) {
		tmp = x;
	} else if (y <= 7.4e+111) {
		tmp = -z / (y / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e-21:
		tmp = x
	elif y <= -4.4e-139:
		tmp = (z * -x) / y
	elif y <= -2e-170:
		tmp = x
	elif y <= 7.4e+111:
		tmp = -z / (y / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e-21)
		tmp = x;
	elseif (y <= -4.4e-139)
		tmp = Float64(Float64(z * Float64(-x)) / y);
	elseif (y <= -2e-170)
		tmp = x;
	elseif (y <= 7.4e+111)
		tmp = Float64(Float64(-z) / Float64(y / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e-21)
		tmp = x;
	elseif (y <= -4.4e-139)
		tmp = (z * -x) / y;
	elseif (y <= -2e-170)
		tmp = x;
	elseif (y <= 7.4e+111)
		tmp = -z / (y / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e-21], x, If[LessEqual[y, -4.4e-139], N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -2e-170], x, If[LessEqual[y, 7.4e+111], N[((-z) / N[(y / x), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999998e-21 or -4.40000000000000021e-139 < y < -1.99999999999999997e-170 or 7.4000000000000005e111 < y

   1. Initial program 76.6%

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

      1. remove-double-neg 76.6%

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

      2. distribute-frac-neg2 76.6%

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

      3. distribute-frac-neg 76.6%

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

      4. distribute-rgt-neg-in 76.6%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 81.0%

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

   if -3.7999999999999998e-21 < y < -4.40000000000000021e-139

   1. Initial program 96.4%

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

   3. Taylor expanded in y around 0 63.8%

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

      1. associate-*r* 63.8%

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

      2. mul-1-neg 63.8%

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

   5. Simplified 63.8%

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

   if -1.99999999999999997e-170 < y < 7.4000000000000005e111

   1. Initial program 87.3%

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

      1. remove-double-neg 87.3%

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

      2. distribute-frac-neg2 87.3%

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

      3. distribute-frac-neg 87.3%

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

      4. distribute-rgt-neg-in 87.3%

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

      5. associate-/l* 88.6%

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

      6. distribute-frac-neg 88.6%

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

      7. distribute-frac-neg2 88.6%

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

      8. remove-double-neg 88.6%

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

      9. div-sub 88.6%

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

      10. *-inverses 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in z around inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. distribute-frac-neg2 67.7%

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

   7. Simplified 67.7%

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

      1. distribute-frac-neg2 67.7%

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

      2. distribute-rgt-neg-out 67.7%

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

      3. add-sqr-sqrt 46.2%

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

      4. sqrt-unprod 35.0%

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

      5. sqr-neg 35.0%

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

      6. sqrt-unprod 0.5%

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

      7. add-sqr-sqrt 1.9%

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

      8. associate-*r/ 2.0%

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

      9. frac-2neg 2.0%

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

      10. *-commutative 2.0%

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

      11. distribute-rgt-neg-out 2.0%

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

      12. remove-double-neg 2.0%

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

      13. associate-*r/ 1.9%

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

      14. clear-num 1.9%

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

      15. un-div-inv 1.9%

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

      16. frac-2neg 1.9%

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

      17. add-sqr-sqrt 0.5%

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

      18. sqrt-unprod 37.7%

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

      19. sqr-neg 37.7%

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

      20. sqrt-unprod 50.1%

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

      21. add-sqr-sqrt 74.3%

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

      22. remove-double-neg 74.3%

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

   9. Applied egg-rr 74.3%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-139}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+111}:\\ \;\;\;\;\frac{-z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.2% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 83.2%

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

   1. remove-double-neg 83.2%

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

   2. distribute-frac-neg2 83.2%

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

   3. distribute-frac-neg 83.2%

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

   4. distribute-rgt-neg-in 83.2%

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

   5. associate-/l* 95.1%

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

   6. distribute-frac-neg 95.1%

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

   7. distribute-frac-neg2 95.1%

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

   8. remove-double-neg 95.1%

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

   9. div-sub 95.1%

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

   10. *-inverses 95.1%

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

3. Simplified 95.1%

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

5. Taylor expanded in z around 0 51.8%

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

6. Final simplification 51.8%

   \[\leadsto x \]
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 2024071 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :alt
  (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))