Data.Colour.RGB:hslsv from colour-2.3.3, C

Percentage Accurate: 100.0% → 100.0%

Time: 8.8s

Alternatives: 10

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{2 - \left(x + y\right)} \]

2. Final simplification 100.0%

   \[\leadsto \frac{x - y}{2 - \left(x + y\right)} \]

Alternative 2: 71.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+142} \lor \neg \left(x \leq 3.6 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{1}{\frac{x}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.95e+142) (not (<= x 3.6e+26)))
   (/ 1.0 (/ x (- y x)))
   (/ y (+ y -2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.95e+142) || !(x <= 3.6e+26)) {
		tmp = 1.0 / (x / (y - x));
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.95d+142)) .or. (.not. (x <= 3.6d+26))) then
        tmp = 1.0d0 / (x / (y - x))
    else
        tmp = y / (y + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.95e+142) || !(x <= 3.6e+26)) {
		tmp = 1.0 / (x / (y - x));
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.95e+142) or not (x <= 3.6e+26):
		tmp = 1.0 / (x / (y - x))
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.95e+142) || !(x <= 3.6e+26))
		tmp = Float64(1.0 / Float64(x / Float64(y - x)));
	else
		tmp = Float64(y / Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.95e+142) || ~((x <= 3.6e+26)))
		tmp = 1.0 / (x / (y - x));
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.95e+142], N[Not[LessEqual[x, 3.6e+26]], $MachinePrecision]], N[(1.0 / N[(x / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.95e142 or 3.60000000000000024e26 < x

   1. Initial program 100.0%

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

      1. clear-num 100.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{2 - \left(x + y\right)}{x - y}}} \]

      2. associate-/r/ 99.7%

         \[\leadsto \color{blue}{\frac{1}{2 - \left(x + y\right)} \cdot \left(x - y\right)} \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{2 - \left(x + y\right)} \cdot \left(x - y\right)} \]

   4. Taylor expanded in x around inf 89.6%

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

      1. associate-*l/ 89.9%

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

      2. clear-num 89.9%

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

      3. neg-mul-1 89.9%

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

      4. sub-neg 89.9%

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

      5. distribute-neg-in 89.9%

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

      6. remove-double-neg 89.9%

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

   6. Applied egg-rr 89.9%

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

   if -1.95e142 < x < 3.60000000000000024e26

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in x around 0 69.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   3. Step-by-step derivation

      1. mul-1-neg 69.6%

         \[\leadsto \color{blue}{-\frac{y}{2 - y}} \]

      2. distribute-neg-frac 69.6%

         \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   4. Simplified 69.6%

      \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]
   5. Step-by-step derivation

      1. frac-2neg 69.6%

         \[\leadsto \color{blue}{\frac{-\left(-y\right)}{-\left(2 - y\right)}} \]

      2. div-inv 69.5%

         \[\leadsto \color{blue}{\left(-\left(-y\right)\right) \cdot \frac{1}{-\left(2 - y\right)}} \]

      3. remove-double-neg 69.5%

         \[\leadsto \color{blue}{y} \cdot \frac{1}{-\left(2 - y\right)} \]

      4. sub-neg 69.5%

         \[\leadsto y \cdot \frac{1}{-\color{blue}{\left(2 + \left(-y\right)\right)}} \]

      5. distribute-neg-in 69.5%

         \[\leadsto y \cdot \frac{1}{\color{blue}{\left(-2\right) + \left(-\left(-y\right)\right)}} \]

      6. metadata-eval 69.5%

         \[\leadsto y \cdot \frac{1}{\color{blue}{-2} + \left(-\left(-y\right)\right)} \]

      7. remove-double-neg 69.5%

         \[\leadsto y \cdot \frac{1}{-2 + \color{blue}{y}} \]

   6. Applied egg-rr 69.5%

      \[\leadsto \color{blue}{y \cdot \frac{1}{-2 + y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 69.6%

         \[\leadsto \color{blue}{\frac{y \cdot 1}{-2 + y}} \]

      2. *-rgt-identity 69.6%

         \[\leadsto \frac{\color{blue}{y}}{-2 + y} \]

      3. +-commutative 69.6%

         \[\leadsto \frac{y}{\color{blue}{y + -2}} \]

   8. Simplified 69.6%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+142} \lor \neg \left(x \leq 3.6 \cdot 10^{+26}\right):\\ \;\;\;\;\frac{1}{\frac{x}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]

Alternative 3: 56.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+142}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-225}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-6}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+22}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.7e+142)
   -1.0
   (if (<= x 1.05e-225)
     1.0
     (if (<= x 1.1e-6) (* x 0.5) (if (<= x 1.65e+22) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.7e+142) {
		tmp = -1.0;
	} else if (x <= 1.05e-225) {
		tmp = 1.0;
	} else if (x <= 1.1e-6) {
		tmp = x * 0.5;
	} else if (x <= 1.65e+22) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.7d+142)) then
        tmp = -1.0d0
    else if (x <= 1.05d-225) then
        tmp = 1.0d0
    else if (x <= 1.1d-6) then
        tmp = x * 0.5d0
    else if (x <= 1.65d+22) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.7e+142) {
		tmp = -1.0;
	} else if (x <= 1.05e-225) {
		tmp = 1.0;
	} else if (x <= 1.1e-6) {
		tmp = x * 0.5;
	} else if (x <= 1.65e+22) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.7e+142:
		tmp = -1.0
	elif x <= 1.05e-225:
		tmp = 1.0
	elif x <= 1.1e-6:
		tmp = x * 0.5
	elif x <= 1.65e+22:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.7e+142)
		tmp = -1.0;
	elseif (x <= 1.05e-225)
		tmp = 1.0;
	elseif (x <= 1.1e-6)
		tmp = Float64(x * 0.5);
	elseif (x <= 1.65e+22)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.7e+142)
		tmp = -1.0;
	elseif (x <= 1.05e-225)
		tmp = 1.0;
	elseif (x <= 1.1e-6)
		tmp = x * 0.5;
	elseif (x <= 1.65e+22)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.7e+142], -1.0, If[LessEqual[x, 1.05e-225], 1.0, If[LessEqual[x, 1.1e-6], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 1.65e+22], 1.0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6999999999999999e142 or 1.6499999999999999e22 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in x around inf 89.8%

      \[\leadsto \color{blue}{-1} \]

   if -1.6999999999999999e142 < x < 1.05e-225 or 1.1000000000000001e-6 < x < 1.6499999999999999e22

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in y around inf 56.1%

      \[\leadsto \color{blue}{1} \]

   if 1.05e-225 < x < 1.1000000000000001e-6

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in y around 0 51.0%

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]

   3. Taylor expanded in x around 0 49.8%

      \[\leadsto \color{blue}{0.5 \cdot x} \]
   4. Step-by-step derivation

      1. *-commutative 49.8%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   5. Simplified 49.8%

      \[\leadsto \color{blue}{x \cdot 0.5} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+142}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-225}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-6}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+22}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4: 58.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+142}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-264}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-176}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.7e+142)
   -1.0
   (if (<= x -1.8e-264)
     1.0
     (if (<= x 1.25e-176) (* y -0.5) (if (<= x 8.8e+17) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.7e+142) {
		tmp = -1.0;
	} else if (x <= -1.8e-264) {
		tmp = 1.0;
	} else if (x <= 1.25e-176) {
		tmp = y * -0.5;
	} else if (x <= 8.8e+17) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.7d+142)) then
        tmp = -1.0d0
    else if (x <= (-1.8d-264)) then
        tmp = 1.0d0
    else if (x <= 1.25d-176) then
        tmp = y * (-0.5d0)
    else if (x <= 8.8d+17) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.7e+142) {
		tmp = -1.0;
	} else if (x <= -1.8e-264) {
		tmp = 1.0;
	} else if (x <= 1.25e-176) {
		tmp = y * -0.5;
	} else if (x <= 8.8e+17) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.7e+142:
		tmp = -1.0
	elif x <= -1.8e-264:
		tmp = 1.0
	elif x <= 1.25e-176:
		tmp = y * -0.5
	elif x <= 8.8e+17:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.7e+142)
		tmp = -1.0;
	elseif (x <= -1.8e-264)
		tmp = 1.0;
	elseif (x <= 1.25e-176)
		tmp = Float64(y * -0.5);
	elseif (x <= 8.8e+17)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.7e+142)
		tmp = -1.0;
	elseif (x <= -1.8e-264)
		tmp = 1.0;
	elseif (x <= 1.25e-176)
		tmp = y * -0.5;
	elseif (x <= 8.8e+17)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.7e+142], -1.0, If[LessEqual[x, -1.8e-264], 1.0, If[LessEqual[x, 1.25e-176], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 8.8e+17], 1.0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6999999999999999e142 or 8.8e17 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in x around inf 89.8%

      \[\leadsto \color{blue}{-1} \]

   if -1.6999999999999999e142 < x < -1.8000000000000001e-264 or 1.25e-176 < x < 8.8e17

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in y around inf 57.2%

      \[\leadsto \color{blue}{1} \]

   if -1.8000000000000001e-264 < x < 1.25e-176

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in x around 0 85.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   3. Step-by-step derivation

      1. mul-1-neg 85.6%

         \[\leadsto \color{blue}{-\frac{y}{2 - y}} \]

      2. distribute-neg-frac 85.6%

         \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   4. Simplified 85.6%

      \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   5. Taylor expanded in y around 0 56.5%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 56.5%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   7. Simplified 56.5%

      \[\leadsto \color{blue}{y \cdot -0.5} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+142}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-264}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-176}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5: 58.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+141}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-256}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-176}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.55e+141)
   -1.0
   (if (<= x -1.8e-256)
     (- 1.0 (/ x y))
     (if (<= x 1.3e-176) (* y -0.5) (if (<= x 4e+35) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.55e+141) {
		tmp = -1.0;
	} else if (x <= -1.8e-256) {
		tmp = 1.0 - (x / y);
	} else if (x <= 1.3e-176) {
		tmp = y * -0.5;
	} else if (x <= 4e+35) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.55d+141)) then
        tmp = -1.0d0
    else if (x <= (-1.8d-256)) then
        tmp = 1.0d0 - (x / y)
    else if (x <= 1.3d-176) then
        tmp = y * (-0.5d0)
    else if (x <= 4d+35) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.55e+141) {
		tmp = -1.0;
	} else if (x <= -1.8e-256) {
		tmp = 1.0 - (x / y);
	} else if (x <= 1.3e-176) {
		tmp = y * -0.5;
	} else if (x <= 4e+35) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.55e+141:
		tmp = -1.0
	elif x <= -1.8e-256:
		tmp = 1.0 - (x / y)
	elif x <= 1.3e-176:
		tmp = y * -0.5
	elif x <= 4e+35:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.55e+141)
		tmp = -1.0;
	elseif (x <= -1.8e-256)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= 1.3e-176)
		tmp = Float64(y * -0.5);
	elseif (x <= 4e+35)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.55e+141)
		tmp = -1.0;
	elseif (x <= -1.8e-256)
		tmp = 1.0 - (x / y);
	elseif (x <= 1.3e-176)
		tmp = y * -0.5;
	elseif (x <= 4e+35)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.55e+141], -1.0, If[LessEqual[x, -1.8e-256], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e-176], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 4e+35], 1.0, -1.0]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.55000000000000002e141 or 3.9999999999999999e35 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in x around inf 89.1%

      \[\leadsto \color{blue}{-1} \]

   if -1.55000000000000002e141 < x < -1.8000000000000001e-256

   1. Initial program 100.0%

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

      1. clear-num 99.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{2 - \left(x + y\right)}{x - y}}} \]

      2. associate-/r/ 99.8%

         \[\leadsto \color{blue}{\frac{1}{2 - \left(x + y\right)} \cdot \left(x - y\right)} \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{1}{2 - \left(x + y\right)} \cdot \left(x - y\right)} \]

   4. Taylor expanded in y around inf 61.3%

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

   5. Taylor expanded in y around 0 61.4%

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

      1. mul-1-neg 61.4%

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

      2. unsub-neg 61.4%

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

   7. Simplified 61.4%

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

   if -1.8000000000000001e-256 < x < 1.29999999999999996e-176

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in x around 0 85.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   3. Step-by-step derivation

      1. mul-1-neg 85.6%

         \[\leadsto \color{blue}{-\frac{y}{2 - y}} \]

      2. distribute-neg-frac 85.6%

         \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   4. Simplified 85.6%

      \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   5. Taylor expanded in y around 0 56.5%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 56.5%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   7. Simplified 56.5%

      \[\leadsto \color{blue}{y \cdot -0.5} \]

   if 1.29999999999999996e-176 < x < 3.9999999999999999e35

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in y around inf 51.8%

      \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+141}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-256}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-176}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6: 74.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+14} \lor \neg \left(y \leq 5.2 \cdot 10^{+82}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6.5e+14) (not (<= y 5.2e+82)))
   (- 1.0 (/ x y))
   (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6.5e+14) || !(y <= 5.2e+82)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-6.5d+14)) .or. (.not. (y <= 5.2d+82))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -6.5e+14) || !(y <= 5.2e+82)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6.5e+14) or not (y <= 5.2e+82):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6.5e+14) || !(y <= 5.2e+82))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -6.5e+14) || ~((y <= 5.2e+82)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6.5e+14], N[Not[LessEqual[y, 5.2e+82]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e14 or 5.1999999999999997e82 < y

   1. Initial program 100.0%

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

      1. clear-num 100.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{2 - \left(x + y\right)}{x - y}}} \]

      2. associate-/r/ 99.7%

         \[\leadsto \color{blue}{\frac{1}{2 - \left(x + y\right)} \cdot \left(x - y\right)} \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{2 - \left(x + y\right)} \cdot \left(x - y\right)} \]

   4. Taylor expanded in y around inf 75.3%

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

   5. Taylor expanded in y around 0 75.4%

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

      1. mul-1-neg 75.4%

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

      2. unsub-neg 75.4%

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

   7. Simplified 75.4%

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

   if -6.5e14 < y < 5.1999999999999997e82

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in y around 0 78.2%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+14} \lor \neg \left(y \leq 5.2 \cdot 10^{+82}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 7: 71.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+142} \lor \neg \left(x \leq 1.8 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.7e+142) (not (<= x 1.8e+22)))
   (/ (- y x) x)
   (/ y (+ y -2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.7e+142) || !(x <= 1.8e+22)) {
		tmp = (y - x) / x;
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.7d+142)) .or. (.not. (x <= 1.8d+22))) then
        tmp = (y - x) / x
    else
        tmp = y / (y + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.7e+142) || !(x <= 1.8e+22)) {
		tmp = (y - x) / x;
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.7e+142) or not (x <= 1.8e+22):
		tmp = (y - x) / x
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.7e+142) || !(x <= 1.8e+22))
		tmp = Float64(Float64(y - x) / x);
	else
		tmp = Float64(y / Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.7e+142) || ~((x <= 1.8e+22)))
		tmp = (y - x) / x;
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.7e+142], N[Not[LessEqual[x, 1.8e+22]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] / x), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6999999999999999e142 or 1.8e22 < x

   1. Initial program 100.0%

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

      1. clear-num 100.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{2 - \left(x + y\right)}{x - y}}} \]

      2. associate-/r/ 99.7%

         \[\leadsto \color{blue}{\frac{1}{2 - \left(x + y\right)} \cdot \left(x - y\right)} \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{2 - \left(x + y\right)} \cdot \left(x - y\right)} \]

   4. Taylor expanded in x around inf 89.6%

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

      1. associate-*l/ 89.9%

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

      2. neg-mul-1 89.9%

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

      3. sub-neg 89.9%

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

      4. distribute-neg-in 89.9%

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

      5. remove-double-neg 89.9%

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

   6. Applied egg-rr 89.9%

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

      1. +-commutative 89.9%

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

      2. unsub-neg 89.9%

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

   8. Simplified 89.9%

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

   if -1.6999999999999999e142 < x < 1.8e22

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in x around 0 69.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   3. Step-by-step derivation

      1. mul-1-neg 69.6%

         \[\leadsto \color{blue}{-\frac{y}{2 - y}} \]

      2. distribute-neg-frac 69.6%

         \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   4. Simplified 69.6%

      \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]
   5. Step-by-step derivation

      1. frac-2neg 69.6%

         \[\leadsto \color{blue}{\frac{-\left(-y\right)}{-\left(2 - y\right)}} \]

      2. div-inv 69.5%

         \[\leadsto \color{blue}{\left(-\left(-y\right)\right) \cdot \frac{1}{-\left(2 - y\right)}} \]

      3. remove-double-neg 69.5%

         \[\leadsto \color{blue}{y} \cdot \frac{1}{-\left(2 - y\right)} \]

      4. sub-neg 69.5%

         \[\leadsto y \cdot \frac{1}{-\color{blue}{\left(2 + \left(-y\right)\right)}} \]

      5. distribute-neg-in 69.5%

         \[\leadsto y \cdot \frac{1}{\color{blue}{\left(-2\right) + \left(-\left(-y\right)\right)}} \]

      6. metadata-eval 69.5%

         \[\leadsto y \cdot \frac{1}{\color{blue}{-2} + \left(-\left(-y\right)\right)} \]

      7. remove-double-neg 69.5%

         \[\leadsto y \cdot \frac{1}{-2 + \color{blue}{y}} \]

   6. Applied egg-rr 69.5%

      \[\leadsto \color{blue}{y \cdot \frac{1}{-2 + y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 69.6%

         \[\leadsto \color{blue}{\frac{y \cdot 1}{-2 + y}} \]

      2. *-rgt-identity 69.6%

         \[\leadsto \frac{\color{blue}{y}}{-2 + y} \]

      3. +-commutative 69.6%

         \[\leadsto \frac{y}{\color{blue}{y + -2}} \]

   8. Simplified 69.6%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+142} \lor \neg \left(x \leq 1.8 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{y - x}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]

Alternative 8: 71.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+142}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+19}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.7e+142) -1.0 (if (<= x 3.9e+19) (/ y (+ y -2.0)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.7e+142) {
		tmp = -1.0;
	} else if (x <= 3.9e+19) {
		tmp = y / (y + -2.0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.7d+142)) then
        tmp = -1.0d0
    else if (x <= 3.9d+19) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.7e+142) {
		tmp = -1.0;
	} else if (x <= 3.9e+19) {
		tmp = y / (y + -2.0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.7e+142:
		tmp = -1.0
	elif x <= 3.9e+19:
		tmp = y / (y + -2.0)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.7e+142)
		tmp = -1.0;
	elseif (x <= 3.9e+19)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.7e+142)
		tmp = -1.0;
	elseif (x <= 3.9e+19)
		tmp = y / (y + -2.0);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.7e+142], -1.0, If[LessEqual[x, 3.9e+19], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6999999999999999e142 or 3.9e19 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in x around inf 89.8%

      \[\leadsto \color{blue}{-1} \]

   if -1.6999999999999999e142 < x < 3.9e19

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in x around 0 69.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   3. Step-by-step derivation

      1. mul-1-neg 69.6%

         \[\leadsto \color{blue}{-\frac{y}{2 - y}} \]

      2. distribute-neg-frac 69.6%

         \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   4. Simplified 69.6%

      \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]
   5. Step-by-step derivation

      1. frac-2neg 69.6%

         \[\leadsto \color{blue}{\frac{-\left(-y\right)}{-\left(2 - y\right)}} \]

      2. div-inv 69.5%

         \[\leadsto \color{blue}{\left(-\left(-y\right)\right) \cdot \frac{1}{-\left(2 - y\right)}} \]

      3. remove-double-neg 69.5%

         \[\leadsto \color{blue}{y} \cdot \frac{1}{-\left(2 - y\right)} \]

      4. sub-neg 69.5%

         \[\leadsto y \cdot \frac{1}{-\color{blue}{\left(2 + \left(-y\right)\right)}} \]

      5. distribute-neg-in 69.5%

         \[\leadsto y \cdot \frac{1}{\color{blue}{\left(-2\right) + \left(-\left(-y\right)\right)}} \]

      6. metadata-eval 69.5%

         \[\leadsto y \cdot \frac{1}{\color{blue}{-2} + \left(-\left(-y\right)\right)} \]

      7. remove-double-neg 69.5%

         \[\leadsto y \cdot \frac{1}{-2 + \color{blue}{y}} \]

   6. Applied egg-rr 69.5%

      \[\leadsto \color{blue}{y \cdot \frac{1}{-2 + y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 69.6%

         \[\leadsto \color{blue}{\frac{y \cdot 1}{-2 + y}} \]

      2. *-rgt-identity 69.6%

         \[\leadsto \frac{\color{blue}{y}}{-2 + y} \]

      3. +-commutative 69.6%

         \[\leadsto \frac{y}{\color{blue}{y + -2}} \]

   8. Simplified 69.6%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+142}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+19}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 9: 59.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+141}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.65e+141) -1.0 (if (<= x 6e+18) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.65e+141) {
		tmp = -1.0;
	} else if (x <= 6e+18) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.65d+141)) then
        tmp = -1.0d0
    else if (x <= 6d+18) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.65e+141) {
		tmp = -1.0;
	} else if (x <= 6e+18) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.65e+141:
		tmp = -1.0
	elif x <= 6e+18:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.65e+141)
		tmp = -1.0;
	elseif (x <= 6e+18)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.65e+141)
		tmp = -1.0;
	elseif (x <= 6e+18)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.65e+141], -1.0, If[LessEqual[x, 6e+18], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6499999999999998e141 or 6e18 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in x around inf 89.1%

      \[\leadsto \color{blue}{-1} \]

   if -1.6499999999999998e141 < x < 6e18

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]

   2. Taylor expanded in y around inf 51.4%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+141}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 10: 38.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

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

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{2 - \left(x + y\right)} \]

2. Taylor expanded in x around inf 41.8%

   \[\leadsto \color{blue}{-1} \]

3. Final simplification 41.8%

   \[\leadsto -1 \]

Developer target: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 - \left(x + y\right)\\ \frac{x}{t_0} - \frac{y}{t_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 2.0 (+ x y)))) (- (/ x t_0) (/ y t_0))))

C

double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = 2.0d0 - (x + y)
    code = (x / t_0) - (y / t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Python

def code(x, y):
	t_0 = 2.0 - (x + y)
	return (x / t_0) - (y / t_0)

Julia

function code(x, y)
	t_0 = Float64(2.0 - Float64(x + y))
	return Float64(Float64(x / t_0) - Float64(y / t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = 2.0 - (x + y);
	tmp = (x / t_0) - (y / t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(N[(x / t$95$0), $MachinePrecision] - N[(y / t$95$0), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023332 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))

  (/ (- x y) (- 2.0 (+ x y))))