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

Percentage Accurate: 100.0% → 100.0%

Time: 7.2s

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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 2: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+42}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-134}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 58:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))) (t_1 (/ x (- 2.0 x))))
   (if (<= y -1.7e+42)
     t_0
     (if (<= y -1.6e-101)
       t_1
       (if (<= y -6.7e-134) (* y -0.5) (if (<= y 58.0) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -1.7e+42) {
		tmp = t_0;
	} else if (y <= -1.6e-101) {
		tmp = t_1;
	} else if (y <= -6.7e-134) {
		tmp = y * -0.5;
	} else if (y <= 58.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    t_1 = x / (2.0d0 - x)
    if (y <= (-1.7d+42)) then
        tmp = t_0
    else if (y <= (-1.6d-101)) then
        tmp = t_1
    else if (y <= (-6.7d-134)) then
        tmp = y * (-0.5d0)
    else if (y <= 58.0d0) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -1.7e+42) {
		tmp = t_0;
	} else if (y <= -1.6e-101) {
		tmp = t_1;
	} else if (y <= -6.7e-134) {
		tmp = y * -0.5;
	} else if (y <= 58.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	t_1 = x / (2.0 - x)
	tmp = 0
	if y <= -1.7e+42:
		tmp = t_0
	elif y <= -1.6e-101:
		tmp = t_1
	elif y <= -6.7e-134:
		tmp = y * -0.5
	elif y <= 58.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	t_1 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -1.7e+42)
		tmp = t_0;
	elseif (y <= -1.6e-101)
		tmp = t_1;
	elseif (y <= -6.7e-134)
		tmp = Float64(y * -0.5);
	elseif (y <= 58.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x / y);
	t_1 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -1.7e+42)
		tmp = t_0;
	elseif (y <= -1.6e-101)
		tmp = t_1;
	elseif (y <= -6.7e-134)
		tmp = y * -0.5;
	elseif (y <= 58.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+42], t$95$0, If[LessEqual[y, -1.6e-101], t$95$1, If[LessEqual[y, -6.7e-134], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 58.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.69999999999999988e42 or 58 < y

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing
   3. 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%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 76.9%

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

   6. Taylor expanded in y around 0 77.0%

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

      1. mul-1-neg 77.0%

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

      2. unsub-neg 77.0%

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

   8. Simplified 77.0%

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

   if -1.69999999999999988e42 < y < -1.59999999999999989e-101 or -6.69999999999999996e-134 < y < 58

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.9%

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

   if -1.59999999999999989e-101 < y < -6.69999999999999996e-134

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-neg-frac 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+42}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-134}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 58:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+41}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-102}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-134}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -3.1e+41)
     (- 1.0 (/ x y))
     (if (<= y -8.5e-102)
       t_0
       (if (<= y -6.7e-134)
         (* y -0.5)
         (if (<= y 1.15e-7) t_0 (/ y (+ y -2.0))))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -3.1e+41) {
		tmp = 1.0 - (x / y);
	} else if (y <= -8.5e-102) {
		tmp = t_0;
	} else if (y <= -6.7e-134) {
		tmp = y * -0.5;
	} else if (y <= 1.15e-7) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x / (2.0d0 - x)
    if (y <= (-3.1d+41)) then
        tmp = 1.0d0 - (x / y)
    else if (y <= (-8.5d-102)) then
        tmp = t_0
    else if (y <= (-6.7d-134)) then
        tmp = y * (-0.5d0)
    else if (y <= 1.15d-7) then
        tmp = t_0
    else
        tmp = y / (y + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -3.1e+41) {
		tmp = 1.0 - (x / y);
	} else if (y <= -8.5e-102) {
		tmp = t_0;
	} else if (y <= -6.7e-134) {
		tmp = y * -0.5;
	} else if (y <= 1.15e-7) {
		tmp = t_0;
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if y <= -3.1e+41:
		tmp = 1.0 - (x / y)
	elif y <= -8.5e-102:
		tmp = t_0
	elif y <= -6.7e-134:
		tmp = y * -0.5
	elif y <= 1.15e-7:
		tmp = t_0
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -3.1e+41)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (y <= -8.5e-102)
		tmp = t_0;
	elseif (y <= -6.7e-134)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.15e-7)
		tmp = t_0;
	else
		tmp = Float64(y / Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -3.1e+41)
		tmp = 1.0 - (x / y);
	elseif (y <= -8.5e-102)
		tmp = t_0;
	elseif (y <= -6.7e-134)
		tmp = y * -0.5;
	elseif (y <= 1.15e-7)
		tmp = t_0;
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+41], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.5e-102], t$95$0, If[LessEqual[y, -6.7e-134], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.15e-7], t$95$0, N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.1e41

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing
   3. 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%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 86.4%

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

   6. Taylor expanded in y around 0 86.6%

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

      1. mul-1-neg 86.6%

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

      2. unsub-neg 86.6%

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

   8. Simplified 86.6%

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

   if -3.1e41 < y < -8.49999999999999973e-102 or -6.69999999999999996e-134 < y < 1.14999999999999997e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.9%

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

   if -8.49999999999999973e-102 < y < -6.69999999999999996e-134

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-neg-frac 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if 1.14999999999999997e-7 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. distribute-neg-frac 72.4%

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

   5. Simplified 72.4%

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

      1. frac-2neg 72.4%

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

      2. div-inv 72.2%

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

      3. remove-double-neg 72.2%

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

      4. sub-neg 72.2%

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

      5. distribute-neg-in 72.2%

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

      6. metadata-eval 72.2%

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

      7. remove-double-neg 72.2%

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

   7. Applied egg-rr 72.2%

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

      1. associate-*r/ 72.4%

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

      2. *-rgt-identity 72.4%

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

      3. +-commutative 72.4%

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

   9. Simplified 72.4%

      \[\leadsto \color{blue}{\frac{y}{y + -2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+41}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-134}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+41}:\\ \;\;\;\;1 + \frac{\left(2 - x\right) - x}{y}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-102}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-134}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -1e+41)
     (+ 1.0 (/ (- (- 2.0 x) x) y))
     (if (<= y -4.5e-102)
       t_0
       (if (<= y -6.7e-134)
         (* y -0.5)
         (if (<= y 1.9e-9) t_0 (/ y (+ y -2.0))))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -1e+41) {
		tmp = 1.0 + (((2.0 - x) - x) / y);
	} else if (y <= -4.5e-102) {
		tmp = t_0;
	} else if (y <= -6.7e-134) {
		tmp = y * -0.5;
	} else if (y <= 1.9e-9) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x / (2.0d0 - x)
    if (y <= (-1d+41)) then
        tmp = 1.0d0 + (((2.0d0 - x) - x) / y)
    else if (y <= (-4.5d-102)) then
        tmp = t_0
    else if (y <= (-6.7d-134)) then
        tmp = y * (-0.5d0)
    else if (y <= 1.9d-9) then
        tmp = t_0
    else
        tmp = y / (y + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -1e+41) {
		tmp = 1.0 + (((2.0 - x) - x) / y);
	} else if (y <= -4.5e-102) {
		tmp = t_0;
	} else if (y <= -6.7e-134) {
		tmp = y * -0.5;
	} else if (y <= 1.9e-9) {
		tmp = t_0;
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if y <= -1e+41:
		tmp = 1.0 + (((2.0 - x) - x) / y)
	elif y <= -4.5e-102:
		tmp = t_0
	elif y <= -6.7e-134:
		tmp = y * -0.5
	elif y <= 1.9e-9:
		tmp = t_0
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -1e+41)
		tmp = Float64(1.0 + Float64(Float64(Float64(2.0 - x) - x) / y));
	elseif (y <= -4.5e-102)
		tmp = t_0;
	elseif (y <= -6.7e-134)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.9e-9)
		tmp = t_0;
	else
		tmp = Float64(y / Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -1e+41)
		tmp = 1.0 + (((2.0 - x) - x) / y);
	elseif (y <= -4.5e-102)
		tmp = t_0;
	elseif (y <= -6.7e-134)
		tmp = y * -0.5;
	elseif (y <= 1.9e-9)
		tmp = t_0;
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+41], N[(1.0 + N[(N[(N[(2.0 - x), $MachinePrecision] - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5e-102], t$95$0, If[LessEqual[y, -6.7e-134], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.9e-9], t$95$0, N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.00000000000000001e41

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing
   3. 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%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 87.0%

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

      1. associate--l+ 87.0%

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

      2. associate-*r/ 87.0%

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

      3. neg-mul-1 87.0%

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

      4. associate-*r/ 87.0%

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

      5. div-sub 87.0%

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

      6. cancel-sign-sub-inv 87.0%

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

      7. metadata-eval 87.0%

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

      8. *-lft-identity 87.0%

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

      9. +-commutative 87.0%

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

      10. unsub-neg 87.0%

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

   7. Simplified 87.0%

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

   if -1.00000000000000001e41 < y < -4.49999999999999999e-102 or -6.69999999999999996e-134 < y < 1.90000000000000006e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.9%

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

   if -4.49999999999999999e-102 < y < -6.69999999999999996e-134

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-neg-frac 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if 1.90000000000000006e-9 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. distribute-neg-frac 72.4%

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

   5. Simplified 72.4%

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

      1. frac-2neg 72.4%

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

      2. div-inv 72.2%

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

      3. remove-double-neg 72.2%

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

      4. sub-neg 72.2%

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

      5. distribute-neg-in 72.2%

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

      6. metadata-eval 72.2%

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

      7. remove-double-neg 72.2%

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

   7. Applied egg-rr 72.2%

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

      1. associate-*r/ 72.4%

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

      2. *-rgt-identity 72.4%

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

      3. +-commutative 72.4%

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

   9. Simplified 72.4%

      \[\leadsto \color{blue}{\frac{y}{y + -2}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+41}:\\ \;\;\;\;1 + \frac{\left(2 - x\right) - x}{y}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-134}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+54} \lor \neg \left(x \leq 235000000\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.1e+54) (not (<= x 235000000.0))) (+ (/ y x) -1.0) 1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.1e+54) || !(x <= 235000000.0)) {
		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 <= (-3.1d+54)) .or. (.not. (x <= 235000000.0d0))) 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 <= -3.1e+54) || !(x <= 235000000.0)) {
		tmp = (y / x) + -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.1e+54) or not (x <= 235000000.0):
		tmp = (y / x) + -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.1e+54) || !(x <= 235000000.0))
		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 <= -3.1e+54) || ~((x <= 235000000.0)))
		tmp = (y / x) + -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.1e+54], N[Not[LessEqual[x, 235000000.0]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -3.0999999999999999e54 or 2.35e8 < x

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing
   3. 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%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 82.8%

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

   6. Taylor expanded in x around 0 83.0%

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

   if -3.0999999999999999e54 < x < 2.35e8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 48.9%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+54} \lor \neg \left(x \leq 235000000\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+48}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 105000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7.8e+48) -1.0 (if (<= x 105000000.0) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7.8e+48) {
		tmp = -1.0;
	} else if (x <= 105000000.0) {
		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 <= (-7.8d+48)) then
        tmp = -1.0d0
    else if (x <= 105000000.0d0) 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 <= -7.8e+48) {
		tmp = -1.0;
	} else if (x <= 105000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7.8e+48:
		tmp = -1.0
	elif x <= 105000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7.8e+48)
		tmp = -1.0;
	elseif (x <= 105000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -7.8e+48)
		tmp = -1.0;
	elseif (x <= 105000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7.8e+48], -1.0, If[LessEqual[x, 105000000.0], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -7.8000000000000002e48 or 1.05e8 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.4%

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

   if -7.8000000000000002e48 < x < 1.05e8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 48.9%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+48}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 105000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing

3. Taylor expanded in x around inf 40.3%

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

4. Final simplification 40.3%

   \[\leadsto -1 \]
5. Add Preprocessing

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 2024041 
(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))))