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

Percentage Accurate: 84.7% → 96.2%

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: 84.7% 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: 96.2% 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 86.0%

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

   1. remove-double-neg 86.0%

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

   2. distribute-frac-neg2 86.0%

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

   3. distribute-frac-neg 86.0%

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

   4. distribute-rgt-neg-in 86.0%

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

   5. associate-/l* 97.7%

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

   6. distribute-frac-neg 97.7%

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

   7. distribute-frac-neg2 97.7%

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

   8. remove-double-neg 97.7%

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

   9. div-sub 97.7%

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

   10. *-inverses 97.7%

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

3. Simplified 97.7%

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

5. Final simplification 97.7%

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

Alternative 2: 69.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{z}{-y}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-27}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 0.105:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ z (- y)))))
   (if (<= y -1.55e+65)
     x
     (if (<= y -2.85e-27)
       t_0
       (if (<= y -1.65e-112) (* y (/ x y)) (if (<= y 0.105) t_0 x))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z / -y);
	double tmp;
	if (y <= -1.55e+65) {
		tmp = x;
	} else if (y <= -2.85e-27) {
		tmp = t_0;
	} else if (y <= -1.65e-112) {
		tmp = y * (x / y);
	} else if (y <= 0.105) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * (z / -y)
    if (y <= (-1.55d+65)) then
        tmp = x
    else if (y <= (-2.85d-27)) then
        tmp = t_0
    else if (y <= (-1.65d-112)) then
        tmp = y * (x / y)
    else if (y <= 0.105d0) then
        tmp = t_0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z / -y);
	double tmp;
	if (y <= -1.55e+65) {
		tmp = x;
	} else if (y <= -2.85e-27) {
		tmp = t_0;
	} else if (y <= -1.65e-112) {
		tmp = y * (x / y);
	} else if (y <= 0.105) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z / -y)
	tmp = 0
	if y <= -1.55e+65:
		tmp = x
	elif y <= -2.85e-27:
		tmp = t_0
	elif y <= -1.65e-112:
		tmp = y * (x / y)
	elif y <= 0.105:
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z / Float64(-y)))
	tmp = 0.0
	if (y <= -1.55e+65)
		tmp = x;
	elseif (y <= -2.85e-27)
		tmp = t_0;
	elseif (y <= -1.65e-112)
		tmp = Float64(y * Float64(x / y));
	elseif (y <= 0.105)
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z / -y);
	tmp = 0.0;
	if (y <= -1.55e+65)
		tmp = x;
	elseif (y <= -2.85e-27)
		tmp = t_0;
	elseif (y <= -1.65e-112)
		tmp = y * (x / y);
	elseif (y <= 0.105)
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+65], x, If[LessEqual[y, -2.85e-27], t$95$0, If[LessEqual[y, -1.65e-112], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.105], t$95$0, x]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.54999999999999995e65 or 0.104999999999999996 < y

   1. Initial program 77.2%

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

      1. remove-double-neg 77.2%

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

      2. distribute-frac-neg2 77.2%

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

      3. distribute-frac-neg 77.2%

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

      4. distribute-rgt-neg-in 77.2%

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

      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 83.9%

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

   if -1.54999999999999995e65 < y < -2.8499999999999998e-27 or -1.65e-112 < y < 0.104999999999999996

   1. Initial program 91.6%

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

      1. associate-/l* 95.3%

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

      2. add-sqr-sqrt 41.4%

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

      3. associate-*l* 41.4%

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

   4. Applied egg-rr 41.4%

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

   5. Taylor expanded in y around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. distribute-frac-neg2 76.4%

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

      3. associate-/l* 78.4%

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

   7. Simplified 78.4%

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

   if -2.8499999999999998e-27 < y < -1.65e-112

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-/l* 77.1%

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

   5. Applied egg-rr 77.1%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 0.105:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 1750:\\ \;\;\;\;\frac{z}{\frac{y}{-x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.95e+65)
   x
   (if (<= y -2.15e-32)
     (* x (/ z (- y)))
     (if (<= y -1.6e-112)
       (* y (/ x y))
       (if (<= y 1750.0) (/ z (/ y (- x))) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.95e+65) {
		tmp = x;
	} else if (y <= -2.15e-32) {
		tmp = x * (z / -y);
	} else if (y <= -1.6e-112) {
		tmp = y * (x / y);
	} else if (y <= 1750.0) {
		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 <= (-1.95d+65)) then
        tmp = x
    else if (y <= (-2.15d-32)) then
        tmp = x * (z / -y)
    else if (y <= (-1.6d-112)) then
        tmp = y * (x / y)
    else if (y <= 1750.0d0) 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 <= -1.95e+65) {
		tmp = x;
	} else if (y <= -2.15e-32) {
		tmp = x * (z / -y);
	} else if (y <= -1.6e-112) {
		tmp = y * (x / y);
	} else if (y <= 1750.0) {
		tmp = z / (y / -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.95e+65:
		tmp = x
	elif y <= -2.15e-32:
		tmp = x * (z / -y)
	elif y <= -1.6e-112:
		tmp = y * (x / y)
	elif y <= 1750.0:
		tmp = z / (y / -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.95e+65)
		tmp = x;
	elseif (y <= -2.15e-32)
		tmp = Float64(x * Float64(z / Float64(-y)));
	elseif (y <= -1.6e-112)
		tmp = Float64(y * Float64(x / y));
	elseif (y <= 1750.0)
		tmp = Float64(z / Float64(y / Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.95e+65)
		tmp = x;
	elseif (y <= -2.15e-32)
		tmp = x * (z / -y);
	elseif (y <= -1.6e-112)
		tmp = y * (x / y);
	elseif (y <= 1750.0)
		tmp = z / (y / -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.95e+65], x, If[LessEqual[y, -2.15e-32], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e-112], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1750.0], N[(z / N[(y / (-x)), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.9499999999999999e65 or 1750 < y

   1. Initial program 77.2%

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

      1. remove-double-neg 77.2%

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

      2. distribute-frac-neg2 77.2%

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

      3. distribute-frac-neg 77.2%

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

      4. distribute-rgt-neg-in 77.2%

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

      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 83.9%

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

   if -1.9499999999999999e65 < y < -2.14999999999999995e-32

   1. Initial program 93.0%

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

      1. associate-/l* 99.9%

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

      2. add-sqr-sqrt 53.6%

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

      3. associate-*l* 53.6%

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

   4. Applied egg-rr 53.6%

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

   5. Taylor expanded in y around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. distribute-frac-neg2 63.9%

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

      3. associate-/l* 70.7%

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

   7. Simplified 70.7%

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

   if -2.14999999999999995e-32 < y < -1.59999999999999997e-112

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-/l* 77.1%

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

   5. Applied egg-rr 77.1%

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

   if -1.59999999999999997e-112 < y < 1750

   1. Initial program 91.4%

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

      1. associate-/l* 94.8%

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

      2. add-sqr-sqrt 39.9%

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

      3. associate-*l* 40.0%

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

   4. Applied egg-rr 40.0%

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

   5. Taylor expanded in y around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. distribute-frac-neg2 77.8%

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

      3. associate-/l* 79.3%

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

   7. Simplified 79.3%

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

      1. associate-*r/ 77.8%

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

      2. add-sqr-sqrt 26.8%

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

      3. sqrt-unprod 17.1%

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

      4. sqr-neg 17.1%

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

      5. sqrt-unprod 0.9%

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

      6. add-sqr-sqrt 1.5%

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

      7. *-commutative 1.5%

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

      8. associate-*l/ 1.4%

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

      9. associate-/r/ 1.4%

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

      10. frac-2neg 1.4%

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

      11. distribute-neg-frac 1.4%

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

      12. add-sqr-sqrt 0.6%

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

      13. sqrt-unprod 38.4%

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

      14. sqr-neg 38.4%

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

      15. sqrt-unprod 51.9%

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

      16. add-sqr-sqrt 80.7%

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

   9. Applied egg-rr 80.7%

      \[\leadsto \color{blue}{\frac{-z}{\frac{y}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+65}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 1750:\\ \;\;\;\;\frac{z}{\frac{y}{-x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.3% 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 86.0%

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

   1. remove-double-neg 86.0%

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

   2. distribute-frac-neg2 86.0%

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

   3. distribute-frac-neg 86.0%

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

   4. distribute-rgt-neg-in 86.0%

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

   5. associate-/l* 97.7%

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

   6. distribute-frac-neg 97.7%

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

   7. distribute-frac-neg2 97.7%

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

   8. remove-double-neg 97.7%

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

   9. div-sub 97.7%

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

   10. *-inverses 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in z around 0 51.0%

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

6. Final simplification 51.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.2% 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 2024067 
(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))