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

Percentage Accurate: 100.0% → 100.0%

Time: 7.9s

Alternatives: 8

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: 60.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+45}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -9.4 \cdot 10^{-144}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ y x) -1.0)))
   (if (<= x -7.5e+45)
     t_0
     (if (<= x -5e-17)
       1.0
       (if (<= x -9.4e-144) (* x 0.5) (if (<= x 6.2e+46) 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double tmp;
	if (x <= -7.5e+45) {
		tmp = t_0;
	} else if (x <= -5e-17) {
		tmp = 1.0;
	} else if (x <= -9.4e-144) {
		tmp = x * 0.5;
	} else if (x <= 6.2e+46) {
		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 <= (-7.5d+45)) then
        tmp = t_0
    else if (x <= (-5d-17)) then
        tmp = 1.0d0
    else if (x <= (-9.4d-144)) then
        tmp = x * 0.5d0
    else if (x <= 6.2d+46) 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 <= -7.5e+45) {
		tmp = t_0;
	} else if (x <= -5e-17) {
		tmp = 1.0;
	} else if (x <= -9.4e-144) {
		tmp = x * 0.5;
	} else if (x <= 6.2e+46) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) + -1.0
	tmp = 0
	if x <= -7.5e+45:
		tmp = t_0
	elif x <= -5e-17:
		tmp = 1.0
	elif x <= -9.4e-144:
		tmp = x * 0.5
	elif x <= 6.2e+46:
		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 <= -7.5e+45)
		tmp = t_0;
	elseif (x <= -5e-17)
		tmp = 1.0;
	elseif (x <= -9.4e-144)
		tmp = Float64(x * 0.5);
	elseif (x <= 6.2e+46)
		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 <= -7.5e+45)
		tmp = t_0;
	elseif (x <= -5e-17)
		tmp = 1.0;
	elseif (x <= -9.4e-144)
		tmp = x * 0.5;
	elseif (x <= 6.2e+46)
		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, -7.5e+45], t$95$0, If[LessEqual[x, -5e-17], 1.0, If[LessEqual[x, -9.4e-144], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 6.2e+46], 1.0, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.50000000000000058e45 or 6.1999999999999995e46 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 82.8%

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

      1. mul-1-neg 82.8%

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

   4. Simplified 82.8%

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

   5. Taylor expanded in x around 0 82.8%

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

   if -7.50000000000000058e45 < x < -4.9999999999999999e-17 or -9.4000000000000004e-144 < x < 6.1999999999999995e46

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 58.8%

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

   if -4.9999999999999999e-17 < x < -9.4000000000000004e-144

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.0%

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

   3. Taylor expanded in x around 0 75.0%

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

      1. *-commutative 75.0%

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

   5. Simplified 75.0%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+45}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -9.4 \cdot 10^{-144}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]

Alternative 3: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+47}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{y}{x} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7.2e+46)
   (+ (/ y x) -1.0)
   (if (<= x 3.4e+47) (/ (- x y) (- 2.0 y)) (+ (* 2.0 (/ y x)) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7.2e+46) {
		tmp = (y / x) + -1.0;
	} else if (x <= 3.4e+47) {
		tmp = (x - y) / (2.0 - y);
	} else {
		tmp = (2.0 * (y / x)) + -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 <= (-7.2d+46)) then
        tmp = (y / x) + (-1.0d0)
    else if (x <= 3.4d+47) then
        tmp = (x - y) / (2.0d0 - y)
    else
        tmp = (2.0d0 * (y / x)) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -7.2e+46) {
		tmp = (y / x) + -1.0;
	} else if (x <= 3.4e+47) {
		tmp = (x - y) / (2.0 - y);
	} else {
		tmp = (2.0 * (y / x)) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7.2e+46:
		tmp = (y / x) + -1.0
	elif x <= 3.4e+47:
		tmp = (x - y) / (2.0 - y)
	else:
		tmp = (2.0 * (y / x)) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7.2e+46)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (x <= 3.4e+47)
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	else
		tmp = Float64(Float64(2.0 * Float64(y / x)) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -7.2e+46)
		tmp = (y / x) + -1.0;
	elseif (x <= 3.4e+47)
		tmp = (x - y) / (2.0 - y);
	else
		tmp = (2.0 * (y / x)) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7.2e+46], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[x, 3.4e+47], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.1999999999999997e46

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 87.6%

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

      1. mul-1-neg 87.6%

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

   4. Simplified 87.6%

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

   5. Taylor expanded in x around 0 87.6%

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

   if -7.1999999999999997e46 < x < 3.3999999999999998e47

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 92.9%

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

   if 3.3999999999999998e47 < 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. inv-pow 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around -inf 78.2%

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

      1. sub-neg 78.2%

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

   6. Simplified 78.2%

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

   7. Taylor expanded in y around inf 78.2%

      \[\leadsto \color{blue}{2 \cdot \frac{y}{x}} + -1 \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+47}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{y}{x} + -1\\ \end{array} \]

Alternative 4: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+46}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-16}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -9.4 \cdot 10^{-144}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 10^{+41}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.6e+46)
   -1.0
   (if (<= x -1.2e-16)
     1.0
     (if (<= x -9.4e-144) (* x 0.5) (if (<= x 1e+41) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.6e+46) {
		tmp = -1.0;
	} else if (x <= -1.2e-16) {
		tmp = 1.0;
	} else if (x <= -9.4e-144) {
		tmp = x * 0.5;
	} else if (x <= 1e+41) {
		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 <= (-1.6d+46)) then
        tmp = -1.0d0
    else if (x <= (-1.2d-16)) then
        tmp = 1.0d0
    else if (x <= (-9.4d-144)) then
        tmp = x * 0.5d0
    else if (x <= 1d+41) 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 <= -1.6e+46) {
		tmp = -1.0;
	} else if (x <= -1.2e-16) {
		tmp = 1.0;
	} else if (x <= -9.4e-144) {
		tmp = x * 0.5;
	} else if (x <= 1e+41) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.6e+46:
		tmp = -1.0
	elif x <= -1.2e-16:
		tmp = 1.0
	elif x <= -9.4e-144:
		tmp = x * 0.5
	elif x <= 1e+41:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.6e+46)
		tmp = -1.0;
	elseif (x <= -1.2e-16)
		tmp = 1.0;
	elseif (x <= -9.4e-144)
		tmp = Float64(x * 0.5);
	elseif (x <= 1e+41)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.6e+46)
		tmp = -1.0;
	elseif (x <= -1.2e-16)
		tmp = 1.0;
	elseif (x <= -9.4e-144)
		tmp = x * 0.5;
	elseif (x <= 1e+41)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.6e+46], -1.0, If[LessEqual[x, -1.2e-16], 1.0, If[LessEqual[x, -9.4e-144], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 1e+41], 1.0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5999999999999999e46 or 1.00000000000000001e41 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 81.7%

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

   if -1.5999999999999999e46 < x < -1.20000000000000002e-16 or -9.4000000000000004e-144 < x < 1.00000000000000001e41

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 58.9%

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

   if -1.20000000000000002e-16 < x < -9.4000000000000004e-144

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.0%

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

   3. Taylor expanded in x around 0 75.0%

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

      1. *-commutative 75.0%

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

   5. Simplified 75.0%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+46}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-16}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -9.4 \cdot 10^{-144}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 10^{+41}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5: 72.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+16} \lor \neg \left(y \leq 4.5 \cdot 10^{+109}\right):\\ \;\;\;\;\frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.45e+16) (not (<= y 4.5e+109)))
   (/ (- y x) y)
   (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.45e+16) || !(y <= 4.5e+109)) {
		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 <= (-1.45d+16)) .or. (.not. (y <= 4.5d+109))) 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 <= -1.45e+16) || !(y <= 4.5e+109)) {
		tmp = (y - x) / y;
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.45e+16) or not (y <= 4.5e+109):
		tmp = (y - x) / y
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.45e+16) || !(y <= 4.5e+109))
		tmp = Float64(Float64(y - 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 <= -1.45e+16) || ~((y <= 4.5e+109)))
		tmp = (y - x) / y;
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.45e+16], N[Not[LessEqual[y, 4.5e+109]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e16 or 4.4999999999999996e109 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 85.6%

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

      1. neg-mul-1 85.6%

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

   4. Simplified 85.6%

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

      1. frac-2neg 85.6%

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

      2. div-inv 85.3%

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

      3. sub-neg 85.3%

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

      4. distribute-neg-in 85.3%

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

      5. remove-double-neg 85.3%

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

      6. remove-double-neg 85.3%

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

   6. Applied egg-rr 85.3%

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

      1. associate-*r/ 85.6%

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

      2. +-commutative 85.6%

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

      3. sub-neg 85.6%

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

      4. *-rgt-identity 85.6%

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

   8. Simplified 85.6%

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

   if -1.45e16 < y < 4.4999999999999996e109

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.7%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+16} \lor \neg \left(y \leq 4.5 \cdot 10^{+109}\right):\\ \;\;\;\;\frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 6: 73.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+16}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+95}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.3e+16) 1.0 (if (<= y 5.2e+95) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.3e+16) {
		tmp = 1.0;
	} else if (y <= 5.2e+95) {
		tmp = x / (2.0 - x);
	} 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 (y <= (-1.3d+16)) then
        tmp = 1.0d0
    else if (y <= 5.2d+95) then
        tmp = x / (2.0d0 - x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.3e+16) {
		tmp = 1.0;
	} else if (y <= 5.2e+95) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.3e+16:
		tmp = 1.0
	elif y <= 5.2e+95:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.3e+16)
		tmp = 1.0;
	elseif (y <= 5.2e+95)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.3e+16)
		tmp = 1.0;
	elseif (y <= 5.2e+95)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.3e+16], 1.0, If[LessEqual[y, 5.2e+95], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e16 or 5.19999999999999981e95 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 84.5%

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

   if -1.3e16 < y < 5.19999999999999981e95

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+16}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+95}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 60.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+98}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.2e+15) 1.0 (if (<= y 1.3e+98) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.2e+15) {
		tmp = 1.0;
	} else if (y <= 1.3e+98) {
		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 (y <= (-1.2d+15)) then
        tmp = 1.0d0
    else if (y <= 1.3d+98) 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 (y <= -1.2e+15) {
		tmp = 1.0;
	} else if (y <= 1.3e+98) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.2e+15:
		tmp = 1.0
	elif y <= 1.3e+98:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.2e+15)
		tmp = 1.0;
	elseif (y <= 1.3e+98)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.2e+15)
		tmp = 1.0;
	elseif (y <= 1.3e+98)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.2e+15], 1.0, If[LessEqual[y, 1.3e+98], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e15 or 1.3e98 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 84.5%

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

   if -1.2e15 < y < 1.3e98

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 52.9%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+98}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 37.9% 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 38.0%

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

3. Final simplification 38.0%

   \[\leadsto -1 \]

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 2023334 
(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))))