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

Percentage Accurate: 100.0% → 100.0%

Time: 6.4s

Alternatives: 7

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: 60.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;x \leq -1.25:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -9.4 \cdot 10^{-94}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-61}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-30}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+111}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ y x) -1.0)))
   (if (<= x -1.25)
     t_0
     (if (<= x -9.4e-94)
       (* x 0.5)
       (if (<= x 5e-61)
         1.0
         (if (<= x 6.1e-30) (* x 0.5) (if (<= x 2.2e+111) 1.0 t_0)))))))

C

double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double tmp;
	if (x <= -1.25) {
		tmp = t_0;
	} else if (x <= -9.4e-94) {
		tmp = x * 0.5;
	} else if (x <= 5e-61) {
		tmp = 1.0;
	} else if (x <= 6.1e-30) {
		tmp = x * 0.5;
	} else if (x <= 2.2e+111) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y / x) + (-1.0d0)
    if (x <= (-1.25d0)) then
        tmp = t_0
    else if (x <= (-9.4d-94)) then
        tmp = x * 0.5d0
    else if (x <= 5d-61) then
        tmp = 1.0d0
    else if (x <= 6.1d-30) then
        tmp = x * 0.5d0
    else if (x <= 2.2d+111) then
        tmp = 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double tmp;
	if (x <= -1.25) {
		tmp = t_0;
	} else if (x <= -9.4e-94) {
		tmp = x * 0.5;
	} else if (x <= 5e-61) {
		tmp = 1.0;
	} else if (x <= 6.1e-30) {
		tmp = x * 0.5;
	} else if (x <= 2.2e+111) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) + -1.0
	tmp = 0
	if x <= -1.25:
		tmp = t_0
	elif x <= -9.4e-94:
		tmp = x * 0.5
	elif x <= 5e-61:
		tmp = 1.0
	elif x <= 6.1e-30:
		tmp = x * 0.5
	elif x <= 2.2e+111:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / x) + -1.0)
	tmp = 0.0
	if (x <= -1.25)
		tmp = t_0;
	elseif (x <= -9.4e-94)
		tmp = Float64(x * 0.5);
	elseif (x <= 5e-61)
		tmp = 1.0;
	elseif (x <= 6.1e-30)
		tmp = Float64(x * 0.5);
	elseif (x <= 2.2e+111)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y / x) + -1.0;
	tmp = 0.0;
	if (x <= -1.25)
		tmp = t_0;
	elseif (x <= -9.4e-94)
		tmp = x * 0.5;
	elseif (x <= 5e-61)
		tmp = 1.0;
	elseif (x <= 6.1e-30)
		tmp = x * 0.5;
	elseif (x <= 2.2e+111)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision]}, If[LessEqual[x, -1.25], t$95$0, If[LessEqual[x, -9.4e-94], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 5e-61], 1.0, If[LessEqual[x, 6.1e-30], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 2.2e+111], 1.0, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25 or 2.19999999999999999e111 < x

   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/ 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in x around inf 81.7%

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

   5. Taylor expanded in x around 0 81.9%

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

   if -1.25 < x < -9.40000000000000007e-94 or 4.9999999999999999e-61 < x < 6.09999999999999981e-30

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.3%

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

   3. Taylor expanded in x around 0 72.3%

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

      1. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   if -9.40000000000000007e-94 < x < 4.9999999999999999e-61 or 6.09999999999999981e-30 < x < 2.19999999999999999e111

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 55.0%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq -9.4 \cdot 10^{-94}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-61}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-30}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+111}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]

Alternative 3: 59.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-94}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-61}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-33}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+110}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.0)
   -1.0
   (if (<= x -8e-94)
     (* x 0.5)
     (if (<= x 2e-61)
       1.0
       (if (<= x 4e-33) (* x 0.5) (if (<= x 1.7e+110) 1.0 -1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.0) {
		tmp = -1.0;
	} else if (x <= -8e-94) {
		tmp = x * 0.5;
	} else if (x <= 2e-61) {
		tmp = 1.0;
	} else if (x <= 4e-33) {
		tmp = x * 0.5;
	} else if (x <= 1.7e+110) {
		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 <= (-2.0d0)) then
        tmp = -1.0d0
    else if (x <= (-8d-94)) then
        tmp = x * 0.5d0
    else if (x <= 2d-61) then
        tmp = 1.0d0
    else if (x <= 4d-33) then
        tmp = x * 0.5d0
    else if (x <= 1.7d+110) 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 <= -2.0) {
		tmp = -1.0;
	} else if (x <= -8e-94) {
		tmp = x * 0.5;
	} else if (x <= 2e-61) {
		tmp = 1.0;
	} else if (x <= 4e-33) {
		tmp = x * 0.5;
	} else if (x <= 1.7e+110) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.0:
		tmp = -1.0
	elif x <= -8e-94:
		tmp = x * 0.5
	elif x <= 2e-61:
		tmp = 1.0
	elif x <= 4e-33:
		tmp = x * 0.5
	elif x <= 1.7e+110:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.0)
		tmp = -1.0;
	elseif (x <= -8e-94)
		tmp = Float64(x * 0.5);
	elseif (x <= 2e-61)
		tmp = 1.0;
	elseif (x <= 4e-33)
		tmp = Float64(x * 0.5);
	elseif (x <= 1.7e+110)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.0)
		tmp = -1.0;
	elseif (x <= -8e-94)
		tmp = x * 0.5;
	elseif (x <= 2e-61)
		tmp = 1.0;
	elseif (x <= 4e-33)
		tmp = x * 0.5;
	elseif (x <= 1.7e+110)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.0], -1.0, If[LessEqual[x, -8e-94], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 2e-61], 1.0, If[LessEqual[x, 4e-33], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 1.7e+110], 1.0, -1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2 or 1.7000000000000001e110 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 81.4%

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

   if -2 < x < -7.9999999999999996e-94 or 2.0000000000000001e-61 < x < 4.0000000000000002e-33

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.3%

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

   3. Taylor expanded in x around 0 72.3%

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

      1. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   if -7.9999999999999996e-94 < x < 2.0000000000000001e-61 or 4.0000000000000002e-33 < x < 1.7000000000000001e110

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 55.0%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-94}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-61}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-33}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+110}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+41} \lor \neg \left(y \leq 4 \cdot 10^{+21}\right):\\ \;\;\;\;1 - \frac{x \cdot 2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.25e+41) (not (<= y 4e+21)))
   (- 1.0 (/ (* x 2.0) y))
   (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.25e+41) || !(y <= 4e+21)) {
		tmp = 1.0 - ((x * 2.0) / 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 <= (-3.25d+41)) .or. (.not. (y <= 4d+21))) then
        tmp = 1.0d0 - ((x * 2.0d0) / 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 <= -3.25e+41) || !(y <= 4e+21)) {
		tmp = 1.0 - ((x * 2.0) / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.25e+41) or not (y <= 4e+21):
		tmp = 1.0 - ((x * 2.0) / y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3.25e+41) || !(y <= 4e+21))
		tmp = Float64(1.0 - Float64(Float64(x * 2.0) / 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 <= -3.25e+41) || ~((y <= 4e+21)))
		tmp = 1.0 - ((x * 2.0) / y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.25e+41], N[Not[LessEqual[y, 4e+21]], $MachinePrecision]], N[(1.0 - N[(N[(x * 2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.24999999999999988e41 or 4e21 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.4%

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{x}{y}\right) - -1 \cdot \frac{2 - x}{y}} \]
   3. Step-by-step derivation

      1. sub-neg 80.4%

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

      2. mul-1-neg 80.4%

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

      3. unsub-neg 80.4%

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

      4. mul-1-neg 80.4%

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

      5. remove-double-neg 80.4%

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

   4. Simplified 80.4%

      \[\leadsto \color{blue}{\left(1 - \frac{x}{y}\right) + \frac{2 - x}{y}} \]
   5. Step-by-step derivation

      1. associate-+l- 80.4%

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

      2. sub-div 80.4%

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

   6. Applied egg-rr 80.4%

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

   7. Taylor expanded in x around inf 80.4%

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

   if -3.24999999999999988e41 < y < 4e21

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.4%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+41} \lor \neg \left(y \leq 4 \cdot 10^{+21}\right):\\ \;\;\;\;1 - \frac{x \cdot 2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 5: 75.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+41} \lor \neg \left(y \leq 4.8 \cdot 10^{+19}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6e+41) (not (<= y 4.8e+19))) (- 1.0 (/ x y)) (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6e+41) || !(y <= 4.8e+19)) {
		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 <= (-6d+41)) .or. (.not. (y <= 4.8d+19))) 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 <= -6e+41) || !(y <= 4.8e+19)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6e+41) or not (y <= 4.8e+19):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6e+41) || !(y <= 4.8e+19))
		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 <= -6e+41) || ~((y <= 4.8e+19)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6e+41], N[Not[LessEqual[y, 4.8e+19]], $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 < -5.9999999999999997e41 or 4.8e19 < y

   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/ 99.7%

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

   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 79.4%

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

   5. Taylor expanded in y around 0 79.7%

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

      1. mul-1-neg 79.7%

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

      2. unsub-neg 79.7%

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

   7. Simplified 79.7%

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

   if -5.9999999999999997e41 < y < 4.8e19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.4%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+41} \lor \neg \left(y \leq 4.8 \cdot 10^{+19}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 6: 59.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-23}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+110}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.1e-23) -1.0 (if (<= x 1.7e+110) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.1e-23) {
		tmp = -1.0;
	} else if (x <= 1.7e+110) {
		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 <= (-1.1d-23)) then
        tmp = -1.0d0
    else if (x <= 1.7d+110) 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 <= -1.1e-23) {
		tmp = -1.0;
	} else if (x <= 1.7e+110) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.1e-23:
		tmp = -1.0
	elif x <= 1.7e+110:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.1e-23)
		tmp = -1.0;
	elseif (x <= 1.7e+110)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.1e-23)
		tmp = -1.0;
	elseif (x <= 1.7e+110)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.1e-23], -1.0, If[LessEqual[x, 1.7e+110], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1e-23 or 1.7000000000000001e110 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.8%

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

   if -1.1e-23 < x < 1.7000000000000001e110

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 51.6%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-23}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+110}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 7: 38.3% 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 38.8%

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

3. Final simplification 38.8%

   \[\leadsto -1 \]

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 2023331 
(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))))