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

Percentage Accurate: 100.0% → 100.0%

Time: 7.6s

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: 75.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3000000000 \lor \neg \left(x \leq 6.2 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3000000000.0) (not (<= x 6.2e+25)))
   (+ (/ y x) -1.0)
   (/ (- y) (- 2.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3000000000.0) || !(x <= 6.2e+25)) {
		tmp = (y / x) + -1.0;
	} else {
		tmp = -y / (2.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-3000000000.0d0)) .or. (.not. (x <= 6.2d+25))) then
        tmp = (y / x) + (-1.0d0)
    else
        tmp = -y / (2.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -3000000000.0) || !(x <= 6.2e+25)) {
		tmp = (y / x) + -1.0;
	} else {
		tmp = -y / (2.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3000000000.0) or not (x <= 6.2e+25):
		tmp = (y / x) + -1.0
	else:
		tmp = -y / (2.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3000000000.0) || !(x <= 6.2e+25))
		tmp = Float64(Float64(y / x) + -1.0);
	else
		tmp = Float64(Float64(-y) / Float64(2.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3000000000.0) || ~((x <= 6.2e+25)))
		tmp = (y / x) + -1.0;
	else
		tmp = -y / (2.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3000000000.0], N[Not[LessEqual[x, 6.2e+25]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], N[((-y) / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3e9 or 6.1999999999999996e25 < x

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

      1. expm1-log1p-u 97.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x - y}{\left(2 - x\right) - y}\right)\right)} \]

      2. associate--l- 97.0%

         \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x - y}{\color{blue}{2 - \left(x + y\right)}}\right)\right) \]

   5. Applied egg-rr 97.0%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x - y}{2 - \left(x + y\right)}\right)\right)} \]
   6. Step-by-step derivation

      1. expm1-log1p-u 100.0%

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

      2. div-inv 99.7%

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

      3. flip-- 46.2%

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

      4. associate-*l/ 46.2%

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

      5. difference-of-squares 46.6%

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

   7. Applied egg-rr 46.6%

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

   8. Taylor expanded in x around inf 82.8%

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

      1. neg-mul-1 82.8%

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

   10. Simplified 82.8%

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

   11. Taylor expanded in x around inf 83.1%

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

   if -3e9 < x < 6.1999999999999996e25

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. distribute-neg-frac 71.9%

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

   6. Simplified 71.9%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3000000000 \lor \neg \left(x \leq 6.2 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{2 - y}\\ \end{array} \]

Alternative 3: 63.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2850000000 \lor \neg \left(x \leq 4.6 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2850000000.0) (not (<= x 4.6e+25))) (+ (/ y x) -1.0) 1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2850000000.0) || !(x <= 4.6e+25)) {
		tmp = (y / x) + -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 <= (-2850000000.0d0)) .or. (.not. (x <= 4.6d+25))) then
        tmp = (y / x) + (-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 <= -2850000000.0) || !(x <= 4.6e+25)) {
		tmp = (y / x) + -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2850000000.0) or not (x <= 4.6e+25):
		tmp = (y / x) + -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2850000000.0) || !(x <= 4.6e+25))
		tmp = Float64(Float64(y / x) + -1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2850000000.0) || ~((x <= 4.6e+25)))
		tmp = (y / x) + -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2850000000.0], N[Not[LessEqual[x, 4.6e+25]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -2.85e9 or 4.5999999999999996e25 < x

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

      1. expm1-log1p-u 97.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x - y}{\left(2 - x\right) - y}\right)\right)} \]

      2. associate--l- 97.0%

         \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x - y}{\color{blue}{2 - \left(x + y\right)}}\right)\right) \]

   5. Applied egg-rr 97.0%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x - y}{2 - \left(x + y\right)}\right)\right)} \]
   6. Step-by-step derivation

      1. expm1-log1p-u 100.0%

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

      2. div-inv 99.7%

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

      3. flip-- 46.2%

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

      4. associate-*l/ 46.2%

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

      5. difference-of-squares 46.6%

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

   7. Applied egg-rr 46.6%

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

   8. Taylor expanded in x around inf 82.8%

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

      1. neg-mul-1 82.8%

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

   10. Simplified 82.8%

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

   11. Taylor expanded in x around inf 83.1%

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

   if -2.85e9 < x < 4.5999999999999996e25

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 48.1%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2850000000 \lor \neg \left(x \leq 4.6 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 74.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+49} \lor \neg \left(y \leq 2.7 \cdot 10^{+65}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.6e+49) (not (<= y 2.7e+65)))
   (- 1.0 (/ x y))
   (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.6e+49) || !(y <= 2.7e+65)) {
		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 <= (-5.6d+49)) .or. (.not. (y <= 2.7d+65))) 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 <= -5.6e+49) || !(y <= 2.7e+65)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.6e+49) or not (y <= 2.7e+65):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5.6e+49) || !(y <= 2.7e+65))
		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 <= -5.6e+49) || ~((y <= 2.7e+65)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5.6e+49], N[Not[LessEqual[y, 2.7e+65]], $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 < -5.5999999999999996e49 or 2.70000000000000019e65 < y

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

      1. expm1-log1p-u 98.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x - y}{\left(2 - x\right) - y}\right)\right)} \]

      2. associate--l- 98.9%

         \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x - y}{\color{blue}{2 - \left(x + y\right)}}\right)\right) \]

   5. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x - y}{2 - \left(x + y\right)}\right)\right)} \]
   6. Step-by-step derivation

      1. expm1-log1p-u 100.0%

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

      2. div-inv 99.8%

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

      3. flip-- 37.9%

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

      4. associate-*l/ 38.0%

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

      5. difference-of-squares 38.6%

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

   7. Applied egg-rr 38.6%

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

   8. Taylor expanded in y around inf 77.3%

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

   9. Taylor expanded in y around inf 77.0%

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

       1. mul-1-neg 77.0%

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

       2. unsub-neg 77.0%

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

   11. Simplified 77.0%

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

   if -5.5999999999999996e49 < y < 2.70000000000000019e65

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 74.4%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+49} \lor \neg \left(y \leq 2.7 \cdot 10^{+65}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 5: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+46} \lor \neg \left(y \leq 5.5 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.1e+46) (not (<= y 5.5e+65))) (/ y (+ x y)) (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.1e+46) || !(y <= 5.5e+65)) {
		tmp = y / (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 <= (-5.1d+46)) .or. (.not. (y <= 5.5d+65))) then
        tmp = y / (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 <= -5.1e+46) || !(y <= 5.5e+65)) {
		tmp = y / (x + y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.1e+46) or not (y <= 5.5e+65):
		tmp = y / (x + y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5.1e+46) || !(y <= 5.5e+65))
		tmp = Float64(y / 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 <= -5.1e+46) || ~((y <= 5.5e+65)))
		tmp = y / (x + y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5.1e+46], N[Not[LessEqual[y, 5.5e+65]], $MachinePrecision]], N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0999999999999997e46 or 5.4999999999999996e65 < y

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

      1. expm1-log1p-u 98.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x - y}{\left(2 - x\right) - y}\right)\right)} \]

      2. associate--l- 98.9%

         \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x - y}{\color{blue}{2 - \left(x + y\right)}}\right)\right) \]

   5. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x - y}{2 - \left(x + y\right)}\right)\right)} \]
   6. Step-by-step derivation

      1. expm1-log1p-u 100.0%

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

      2. div-inv 99.8%

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

      3. flip-- 37.9%

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

      4. associate-*l/ 38.0%

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

      5. difference-of-squares 38.6%

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

   7. Applied egg-rr 38.6%

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

   8. Taylor expanded in y around inf 77.3%

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

   if -5.0999999999999997e46 < y < 5.4999999999999996e65

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 74.4%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+46} \lor \neg \left(y \leq 5.5 \cdot 10^{+65}\right):\\ \;\;\;\;\frac{y}{x + y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 6: 63.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3500000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+25}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3500000000.0) -1.0 (if (<= x 5.6e+25) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3500000000.0) {
		tmp = -1.0;
	} else if (x <= 5.6e+25) {
		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 <= (-3500000000.0d0)) then
        tmp = -1.0d0
    else if (x <= 5.6d+25) 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 <= -3500000000.0) {
		tmp = -1.0;
	} else if (x <= 5.6e+25) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3500000000.0:
		tmp = -1.0
	elif x <= 5.6e+25:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3500000000.0)
		tmp = -1.0;
	elseif (x <= 5.6e+25)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3500000000.0)
		tmp = -1.0;
	elseif (x <= 5.6e+25)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3500000000.0], -1.0, If[LessEqual[x, 5.6e+25], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5e9 or 5.6000000000000003e25 < x

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 82.4%

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

   if -3.5e9 < x < 5.6000000000000003e25

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 48.1%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3500000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+25}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 7: 38.7% 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. Step-by-step derivation

   1. associate--r+ 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around inf 45.0%

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

5. Final simplification 45.0%

   \[\leadsto -1 \]

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 2023182 
(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))))