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

Percentage Accurate: 85.0% → 96.3%

Time: 7.7s

Alternatives: 8

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: 85.0% 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: 96.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.2%

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

   1. associate-*l/ 83.2%

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

3. Simplified 83.2%

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

   1. associate-/r/ 97.0%

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

6. Applied egg-rr 97.0%

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

7. Final simplification 97.0%

   \[\leadsto \frac{x}{\frac{y}{y - z}} \]
8. Add Preprocessing

Alternative 2: 68.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{-z}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+124}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ (- z) y))))
   (if (<= y -9e+124)
     x
     (if (<= y -2.3e+29)
       t_0
       (if (<= y -7e-94) (* y (/ x y)) (if (<= y 7.2e-20) t_0 x))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-z / y);
	double tmp;
	if (y <= -9e+124) {
		tmp = x;
	} else if (y <= -2.3e+29) {
		tmp = t_0;
	} else if (y <= -7e-94) {
		tmp = y * (x / y);
	} else if (y <= 7.2e-20) {
		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 <= (-9d+124)) then
        tmp = x
    else if (y <= (-2.3d+29)) then
        tmp = t_0
    else if (y <= (-7d-94)) then
        tmp = y * (x / y)
    else if (y <= 7.2d-20) 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 <= -9e+124) {
		tmp = x;
	} else if (y <= -2.3e+29) {
		tmp = t_0;
	} else if (y <= -7e-94) {
		tmp = y * (x / y);
	} else if (y <= 7.2e-20) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-z / y)
	tmp = 0
	if y <= -9e+124:
		tmp = x
	elif y <= -2.3e+29:
		tmp = t_0
	elif y <= -7e-94:
		tmp = y * (x / y)
	elif y <= 7.2e-20:
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(-z) / y))
	tmp = 0.0
	if (y <= -9e+124)
		tmp = x;
	elseif (y <= -2.3e+29)
		tmp = t_0;
	elseif (y <= -7e-94)
		tmp = Float64(y * Float64(x / y));
	elseif (y <= 7.2e-20)
		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 <= -9e+124)
		tmp = x;
	elseif (y <= -2.3e+29)
		tmp = t_0;
	elseif (y <= -7e-94)
		tmp = y * (x / y);
	elseif (y <= 7.2e-20)
		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, -9e+124], x, If[LessEqual[y, -2.3e+29], t$95$0, If[LessEqual[y, -7e-94], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-20], t$95$0, x]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.0000000000000008e124 or 7.19999999999999948e-20 < y

   1. Initial program 75.9%

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

      1. *-commutative 75.9%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. div-sub 99.9%

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

      5. *-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 82.1%

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

   if -9.0000000000000008e124 < y < -2.3000000000000001e29 or -6.99999999999999996e-94 < y < 7.19999999999999948e-20

   1. Initial program 94.8%

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

      1. associate-*l/ 91.7%

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

   3. Simplified 91.7%

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

      1. associate-/r/ 94.1%

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

   6. Applied egg-rr 94.1%

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

   7. Taylor expanded in y around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. associate-*r/ 72.2%

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

      3. distribute-rgt-neg-in 72.2%

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

      4. distribute-neg-frac 72.2%

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

   9. Simplified 72.2%

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

   if -2.3000000000000001e29 < y < -6.99999999999999996e-94

   1. Initial program 83.3%

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

   3. Taylor expanded in y around inf 62.2%

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

      1. associate-/l* 77.5%

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

      2. associate-/r/ 80.9%

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

   5. Applied egg-rr 80.9%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+124}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+124}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-77}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-20}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9e+124)
   x
   (if (<= y -1.6e+29)
     (* x (/ (- z) y))
     (if (<= y -2.35e-77)
       (* y (/ x y))
       (if (<= y 6.6e-20) (* z (/ (- x) y)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+124) {
		tmp = x;
	} else if (y <= -1.6e+29) {
		tmp = x * (-z / y);
	} else if (y <= -2.35e-77) {
		tmp = y * (x / y);
	} else if (y <= 6.6e-20) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-9d+124)) then
        tmp = x
    else if (y <= (-1.6d+29)) then
        tmp = x * (-z / y)
    else if (y <= (-2.35d-77)) then
        tmp = y * (x / y)
    else if (y <= 6.6d-20) then
        tmp = z * (-x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+124) {
		tmp = x;
	} else if (y <= -1.6e+29) {
		tmp = x * (-z / y);
	} else if (y <= -2.35e-77) {
		tmp = y * (x / y);
	} else if (y <= 6.6e-20) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9e+124:
		tmp = x
	elif y <= -1.6e+29:
		tmp = x * (-z / y)
	elif y <= -2.35e-77:
		tmp = y * (x / y)
	elif y <= 6.6e-20:
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9e+124)
		tmp = x;
	elseif (y <= -1.6e+29)
		tmp = Float64(x * Float64(Float64(-z) / y));
	elseif (y <= -2.35e-77)
		tmp = Float64(y * Float64(x / y));
	elseif (y <= 6.6e-20)
		tmp = Float64(z * Float64(Float64(-x) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9e+124)
		tmp = x;
	elseif (y <= -1.6e+29)
		tmp = x * (-z / y);
	elseif (y <= -2.35e-77)
		tmp = y * (x / y);
	elseif (y <= 6.6e-20)
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9e+124], x, If[LessEqual[y, -1.6e+29], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.35e-77], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e-20], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.0000000000000008e124 or 6.6e-20 < y

   1. Initial program 75.9%

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

      1. *-commutative 75.9%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. div-sub 99.9%

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

      5. *-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 82.1%

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

   if -9.0000000000000008e124 < y < -1.59999999999999993e29

   1. Initial program 94.0%

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

      1. associate-*l/ 80.5%

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

   3. Simplified 80.5%

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

      1. associate-/r/ 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around 0 62.2%

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

      1. mul-1-neg 62.2%

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

      2. associate-*r/ 67.8%

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

      3. distribute-rgt-neg-in 67.8%

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

      4. distribute-neg-frac 67.8%

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

   9. Simplified 67.8%

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

   if -1.59999999999999993e29 < y < -2.3499999999999999e-77

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf 74.6%

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

      1. associate-/l* 85.2%

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

      2. associate-/r/ 89.8%

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

   5. Applied egg-rr 89.8%

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

   if -2.3499999999999999e-77 < y < 6.6e-20

   1. Initial program 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*l/ 92.9%

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

      3. *-commutative 92.9%

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

      4. div-sub 92.9%

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

      5. *-inverses 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. associate-*l/ 74.4%

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

      3. distribute-rgt-neg-out 74.4%

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

      4. *-commutative 74.4%

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

   7. Simplified 74.4%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+124}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-77}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-20}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+124}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-19}:\\ \;\;\;\;\frac{z}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9e+124)
   x
   (if (<= y -1.4e+29)
     (* x (/ (- z) y))
     (if (<= y -3.3e-76)
       (* y (/ x y))
       (if (<= y 4.4e-19) (/ z (/ (- y) x)) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9e+124) {
		tmp = x;
	} else if (y <= -1.4e+29) {
		tmp = x * (-z / y);
	} else if (y <= -3.3e-76) {
		tmp = y * (x / y);
	} else if (y <= 4.4e-19) {
		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 <= (-9d+124)) then
        tmp = x
    else if (y <= (-1.4d+29)) then
        tmp = x * (-z / y)
    else if (y <= (-3.3d-76)) then
        tmp = y * (x / y)
    else if (y <= 4.4d-19) 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 <= -9e+124) {
		tmp = x;
	} else if (y <= -1.4e+29) {
		tmp = x * (-z / y);
	} else if (y <= -3.3e-76) {
		tmp = y * (x / y);
	} else if (y <= 4.4e-19) {
		tmp = z / (-y / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9e+124:
		tmp = x
	elif y <= -1.4e+29:
		tmp = x * (-z / y)
	elif y <= -3.3e-76:
		tmp = y * (x / y)
	elif y <= 4.4e-19:
		tmp = z / (-y / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9e+124)
		tmp = x;
	elseif (y <= -1.4e+29)
		tmp = Float64(x * Float64(Float64(-z) / y));
	elseif (y <= -3.3e-76)
		tmp = Float64(y * Float64(x / y));
	elseif (y <= 4.4e-19)
		tmp = Float64(z / Float64(Float64(-y) / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9e+124)
		tmp = x;
	elseif (y <= -1.4e+29)
		tmp = x * (-z / y);
	elseif (y <= -3.3e-76)
		tmp = y * (x / y);
	elseif (y <= 4.4e-19)
		tmp = z / (-y / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9e+124], x, If[LessEqual[y, -1.4e+29], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.3e-76], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e-19], N[(z / N[((-y) / x), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.0000000000000008e124 or 4.3999999999999997e-19 < y

   1. Initial program 75.9%

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

      1. *-commutative 75.9%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. div-sub 99.9%

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

      5. *-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 82.1%

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

   if -9.0000000000000008e124 < y < -1.4e29

   1. Initial program 94.0%

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

      1. associate-*l/ 80.5%

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

   3. Simplified 80.5%

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

      1. associate-/r/ 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around 0 62.2%

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

      1. mul-1-neg 62.2%

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

      2. associate-*r/ 67.8%

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

      3. distribute-rgt-neg-in 67.8%

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

      4. distribute-neg-frac 67.8%

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

   9. Simplified 67.8%

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

   if -1.4e29 < y < -3.29999999999999984e-76

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf 74.6%

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

      1. associate-/l* 85.2%

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

      2. associate-/r/ 89.8%

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

   5. Applied egg-rr 89.8%

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

   if -3.29999999999999984e-76 < y < 4.3999999999999997e-19

   1. Initial program 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*l/ 92.9%

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

      3. *-commutative 92.9%

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

      4. div-sub 92.9%

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

      5. *-inverses 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around inf 74.9%

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

      1. mul-1-neg 74.9%

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

      2. associate-*l/ 74.4%

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

      3. distribute-rgt-neg-out 74.4%

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

      4. *-commutative 74.4%

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

   7. Simplified 74.4%

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

      1. associate-*r/ 74.9%

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

      2. distribute-lft-neg-in 74.9%

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

      3. distribute-rgt-neg-out 74.9%

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

      4. associate-/l* 74.4%

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

      5. frac-2neg 74.4%

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

      6. add-sqr-sqrt 40.3%

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

      7. sqrt-unprod 32.5%

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

      8. sqr-neg 32.5%

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

      9. sqrt-unprod 0.7%

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

      10. add-sqr-sqrt 1.5%

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

      11. add-sqr-sqrt 0.5%

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

      12. sqrt-unprod 27.7%

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

      13. sqr-neg 27.7%

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

      14. sqrt-unprod 35.0%

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

      15. add-sqr-sqrt 74.4%

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

   9. Applied egg-rr 74.4%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+124}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-19}:\\ \;\;\;\;\frac{z}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-19}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.1e+125)
   x
   (if (<= y -1.4e+28)
     (* x (/ (- z) y))
     (if (<= y -5.1e-76)
       (* y (/ x y))
       (if (<= y 6e-19) (/ (* z (- x)) y) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.1e+125) {
		tmp = x;
	} else if (y <= -1.4e+28) {
		tmp = x * (-z / y);
	} else if (y <= -5.1e-76) {
		tmp = y * (x / y);
	} else if (y <= 6e-19) {
		tmp = (z * -x) / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.1d+125)) then
        tmp = x
    else if (y <= (-1.4d+28)) then
        tmp = x * (-z / y)
    else if (y <= (-5.1d-76)) then
        tmp = y * (x / y)
    else if (y <= 6d-19) then
        tmp = (z * -x) / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.1e+125) {
		tmp = x;
	} else if (y <= -1.4e+28) {
		tmp = x * (-z / y);
	} else if (y <= -5.1e-76) {
		tmp = y * (x / y);
	} else if (y <= 6e-19) {
		tmp = (z * -x) / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.1e+125:
		tmp = x
	elif y <= -1.4e+28:
		tmp = x * (-z / y)
	elif y <= -5.1e-76:
		tmp = y * (x / y)
	elif y <= 6e-19:
		tmp = (z * -x) / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.1e+125)
		tmp = x;
	elseif (y <= -1.4e+28)
		tmp = Float64(x * Float64(Float64(-z) / y));
	elseif (y <= -5.1e-76)
		tmp = Float64(y * Float64(x / y));
	elseif (y <= 6e-19)
		tmp = Float64(Float64(z * Float64(-x)) / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.1e+125)
		tmp = x;
	elseif (y <= -1.4e+28)
		tmp = x * (-z / y);
	elseif (y <= -5.1e-76)
		tmp = y * (x / y);
	elseif (y <= 6e-19)
		tmp = (z * -x) / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.1e+125], x, If[LessEqual[y, -1.4e+28], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.1e-76], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-19], N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.09999999999999995e125 or 5.99999999999999985e-19 < y

   1. Initial program 75.9%

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

      1. *-commutative 75.9%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. div-sub 99.9%

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

      5. *-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 82.1%

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

   if -1.09999999999999995e125 < y < -1.4000000000000001e28

   1. Initial program 94.0%

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

      1. associate-*l/ 80.5%

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

   3. Simplified 80.5%

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

      1. associate-/r/ 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around 0 62.2%

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

      1. mul-1-neg 62.2%

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

      2. associate-*r/ 67.8%

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

      3. distribute-rgt-neg-in 67.8%

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

      4. distribute-neg-frac 67.8%

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

   9. Simplified 67.8%

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

   if -1.4000000000000001e28 < y < -5.09999999999999986e-76

   1. Initial program 87.5%

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

   3. Taylor expanded in y around inf 74.6%

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

      1. associate-/l* 85.2%

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

      2. associate-/r/ 89.8%

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

   5. Applied egg-rr 89.8%

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

   if -5.09999999999999986e-76 < y < 5.99999999999999985e-19

   1. Initial program 93.5%

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

   3. Taylor expanded in y around 0 74.9%

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

      1. associate-*r* 74.9%

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

      2. neg-mul-1 74.9%

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

      3. *-commutative 74.9%

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

   5. Simplified 74.9%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-76}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-19}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.3e+94) x (if (<= y 6.5e-151) (* y (/ x y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.3e+94) {
		tmp = x;
	} else if (y <= 6.5e-151) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.3d+94)) then
        tmp = x
    else if (y <= 6.5d-151) then
        tmp = y * (x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.3e+94) {
		tmp = x;
	} else if (y <= 6.5e-151) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.3e+94:
		tmp = x
	elif y <= 6.5e-151:
		tmp = y * (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.3e+94)
		tmp = x;
	elseif (y <= 6.5e-151)
		tmp = Float64(y * Float64(x / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.3e+94)
		tmp = x;
	elseif (y <= 6.5e-151)
		tmp = y * (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.3e+94], x, If[LessEqual[y, 6.5e-151], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e94 or 6.4999999999999994e-151 < y

   1. Initial program 82.5%

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

      1. *-commutative 82.5%

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

      2. associate-*l/ 98.1%

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

      3. *-commutative 98.1%

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

      4. div-sub 98.1%

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

      5. *-inverses 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in z around 0 69.9%

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

   if -3.3e94 < y < 6.4999999999999994e-151

   1. Initial program 89.6%

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

   3. Taylor expanded in y around inf 26.3%

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

      1. associate-/l* 31.5%

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

      2. associate-/r/ 40.8%

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

   5. Applied egg-rr 40.8%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 96.1% 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 85.2%

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

   1. *-commutative 85.2%

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

   2. associate-*l/ 97.0%

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

   3. *-commutative 97.0%

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

   4. div-sub 97.0%

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

   5. *-inverses 97.0%

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

3. Simplified 97.0%

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

5. Final simplification 97.0%

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

Alternative 8: 50.3% 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 85.2%

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

   1. *-commutative 85.2%

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

   2. associate-*l/ 97.0%

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

   3. *-commutative 97.0%

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

   4. div-sub 97.0%

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

   5. *-inverses 97.0%

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

3. Simplified 97.0%

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

5. Taylor expanded in z around 0 55.2%

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

6. Final simplification 55.2%

   \[\leadsto x \]
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 2024024 
(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))