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

Percentage Accurate: 100.0% → 100.0%

Time: 7.5s

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. Add Preprocessing

Alternative 2: 87.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+22}:\\ \;\;\;\;1 + \frac{2 - x}{y}\\ \mathbf{elif}\;y \leq 5.4:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5e+22)
   (+ 1.0 (/ (- 2.0 x) y))
   (if (<= y 5.4) (/ (- x y) (- 2.0 x)) (/ (- x y) (- 2.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e+22) {
		tmp = 1.0 + ((2.0 - x) / y);
	} else if (y <= 5.4) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = (x - 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 (y <= (-5d+22)) then
        tmp = 1.0d0 + ((2.0d0 - x) / y)
    else if (y <= 5.4d0) then
        tmp = (x - y) / (2.0d0 - x)
    else
        tmp = (x - y) / (2.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5e+22) {
		tmp = 1.0 + ((2.0 - x) / y);
	} else if (y <= 5.4) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = (x - y) / (2.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e+22:
		tmp = 1.0 + ((2.0 - x) / y)
	elif y <= 5.4:
		tmp = (x - y) / (2.0 - x)
	else:
		tmp = (x - y) / (2.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e+22)
		tmp = Float64(1.0 + Float64(Float64(2.0 - x) / y));
	elseif (y <= 5.4)
		tmp = Float64(Float64(x - y) / Float64(2.0 - x));
	else
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5e+22)
		tmp = 1.0 + ((2.0 - x) / y);
	elseif (y <= 5.4)
		tmp = (x - y) / (2.0 - x);
	else
		tmp = (x - y) / (2.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e+22], N[(1.0 + N[(N[(2.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4], N[(N[(x - y), $MachinePrecision] / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999996e22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \color{blue}{\left(2 - y\right)}\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 83.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \color{blue}{y}\right)\right) \]

   5. Simplified 83.5%

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

   6. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

         \[\leadsto 1 + \left(2 \cdot \frac{1}{y} + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right) \]

      3. unsub-neg N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. div-sub N/A

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

      7. unsub-neg N/A

         \[\leadsto 1 + \frac{2 + \left(\mathsf{neg}\left(x\right)\right)}{y} \]

      8. mul-1-neg N/A

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

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{2 + -1 \cdot x}{y}\right)}\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(2 + -1 \cdot x\right), \color{blue}{y}\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(2 + \left(\mathsf{neg}\left(x\right)\right)\right), y\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(2 - x\right), y\right)\right) \]

      13. --lowering--.f64 83.5%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(2, x\right), y\right)\right) \]

   8. Simplified 83.5%

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

   if -4.9999999999999996e22 < y < 5.4000000000000004

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \color{blue}{\left(2 - x\right)}\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 98.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \color{blue}{x}\right)\right) \]

   5. Simplified 98.2%

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

   if 5.4000000000000004 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \color{blue}{\left(2 - y\right)}\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 71.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \color{blue}{y}\right)\right) \]

   5. Simplified 71.7%

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

Alternative 3: 86.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{2 - x}{y}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+22}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (- 2.0 x) y))))
   (if (<= y -5.2e+22) t_0 (if (<= y 2.5e+15) (/ (- x y) (- 2.0 x)) t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 + ((2.0 - x) / y);
	double tmp;
	if (y <= -5.2e+22) {
		tmp = t_0;
	} else if (y <= 2.5e+15) {
		tmp = (x - y) / (2.0 - x);
	} 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 = 1.0d0 + ((2.0d0 - x) / y)
    if (y <= (-5.2d+22)) then
        tmp = t_0
    else if (y <= 2.5d+15) then
        tmp = (x - y) / (2.0d0 - x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + ((2.0 - x) / y);
	double tmp;
	if (y <= -5.2e+22) {
		tmp = t_0;
	} else if (y <= 2.5e+15) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + ((2.0 - x) / y)
	tmp = 0
	if y <= -5.2e+22:
		tmp = t_0
	elif y <= 2.5e+15:
		tmp = (x - y) / (2.0 - x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(Float64(2.0 - x) / y))
	tmp = 0.0
	if (y <= -5.2e+22)
		tmp = t_0;
	elseif (y <= 2.5e+15)
		tmp = Float64(Float64(x - y) / Float64(2.0 - x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + ((2.0 - x) / y);
	tmp = 0.0;
	if (y <= -5.2e+22)
		tmp = t_0;
	elseif (y <= 2.5e+15)
		tmp = (x - y) / (2.0 - x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(N[(2.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+22], t$95$0, If[LessEqual[y, 2.5e+15], N[(N[(x - y), $MachinePrecision] / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2e22 or 2.5e15 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \color{blue}{\left(2 - y\right)}\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 79.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \color{blue}{y}\right)\right) \]

   5. Simplified 79.3%

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

   6. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

         \[\leadsto 1 + \left(2 \cdot \frac{1}{y} + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right) \]

      3. unsub-neg N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. div-sub N/A

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

      7. unsub-neg N/A

         \[\leadsto 1 + \frac{2 + \left(\mathsf{neg}\left(x\right)\right)}{y} \]

      8. mul-1-neg N/A

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

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{2 + -1 \cdot x}{y}\right)}\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(2 + -1 \cdot x\right), \color{blue}{y}\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(2 + \left(\mathsf{neg}\left(x\right)\right)\right), y\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(2 - x\right), y\right)\right) \]

      13. --lowering--.f64 79.3%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(2, x\right), y\right)\right) \]

   8. Simplified 79.3%

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

   if -5.2e22 < y < 2.5e15

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \color{blue}{\left(2 - x\right)}\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 95.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \color{blue}{x}\right)\right) \]

   5. Simplified 95.5%

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

Alternative 4: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{2 - x}{y}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+22}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (- 2.0 x) y))))
   (if (<= y -5.2e+22) t_0 (if (<= y 2.2e+19) (/ x (- 2.0 x)) t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 + ((2.0 - x) / y);
	double tmp;
	if (y <= -5.2e+22) {
		tmp = t_0;
	} else if (y <= 2.2e+19) {
		tmp = x / (2.0 - x);
	} 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 = 1.0d0 + ((2.0d0 - x) / y)
    if (y <= (-5.2d+22)) then
        tmp = t_0
    else if (y <= 2.2d+19) then
        tmp = x / (2.0d0 - x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + ((2.0 - x) / y);
	double tmp;
	if (y <= -5.2e+22) {
		tmp = t_0;
	} else if (y <= 2.2e+19) {
		tmp = x / (2.0 - x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + ((2.0 - x) / y)
	tmp = 0
	if y <= -5.2e+22:
		tmp = t_0
	elif y <= 2.2e+19:
		tmp = x / (2.0 - x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(Float64(2.0 - x) / y))
	tmp = 0.0
	if (y <= -5.2e+22)
		tmp = t_0;
	elseif (y <= 2.2e+19)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + ((2.0 - x) / y);
	tmp = 0.0;
	if (y <= -5.2e+22)
		tmp = t_0;
	elseif (y <= 2.2e+19)
		tmp = x / (2.0 - x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(N[(2.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+22], t$95$0, If[LessEqual[y, 2.2e+19], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2e22 or 2.2e19 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \color{blue}{\left(2 - y\right)}\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 79.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(x, y\right), \mathsf{\_.f64}\left(2, \color{blue}{y}\right)\right) \]

   5. Simplified 79.3%

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

   6. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

         \[\leadsto 1 + \left(2 \cdot \frac{1}{y} + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right) \]

      3. unsub-neg N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. div-sub N/A

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

      7. unsub-neg N/A

         \[\leadsto 1 + \frac{2 + \left(\mathsf{neg}\left(x\right)\right)}{y} \]

      8. mul-1-neg N/A

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

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{2 + -1 \cdot x}{y}\right)}\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(2 + -1 \cdot x\right), \color{blue}{y}\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(2 + \left(\mathsf{neg}\left(x\right)\right)\right), y\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(2 - x\right), y\right)\right) \]

      13. --lowering--.f64 79.3%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(2, x\right), y\right)\right) \]

   8. Simplified 79.3%

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

   if -5.2e22 < y < 2.2e19

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(2 - x\right)}\right) \]

      2. --lowering--.f64 74.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(2, \color{blue}{x}\right)\right) \]

   5. Simplified 74.2%

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

Alternative 5: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.2e+22) 1.0 (if (<= y 7.6e+17) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.2e+22) {
		tmp = 1.0;
	} else if (y <= 7.6e+17) {
		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 <= (-5.2d+22)) then
        tmp = 1.0d0
    else if (y <= 7.6d+17) 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 <= -5.2e+22) {
		tmp = 1.0;
	} else if (y <= 7.6e+17) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.2e+22:
		tmp = 1.0
	elif y <= 7.6e+17:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.2e+22)
		tmp = 1.0;
	elseif (y <= 7.6e+17)
		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 <= -5.2e+22)
		tmp = 1.0;
	elseif (y <= 7.6e+17)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.2e+22], 1.0, If[LessEqual[y, 7.6e+17], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2e22 or 7.6e17 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 78.6%

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

   if -5.2e22 < y < 7.6e17

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(2 - x\right)}\right) \]

      2. --lowering--.f64 74.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(2, \color{blue}{x}\right)\right) \]

   5. Simplified 74.2%

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

Alternative 6: 62.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+16}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5e+22) 1.0 (if (<= y 2.2e+16) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e+22) {
		tmp = 1.0;
	} else if (y <= 2.2e+16) {
		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 <= (-5d+22)) then
        tmp = 1.0d0
    else if (y <= 2.2d+16) 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 <= -5e+22) {
		tmp = 1.0;
	} else if (y <= 2.2e+16) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e+22:
		tmp = 1.0
	elif y <= 2.2e+16:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e+22)
		tmp = 1.0;
	elseif (y <= 2.2e+16)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5e+22)
		tmp = 1.0;
	elseif (y <= 2.2e+16)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e+22], 1.0, If[LessEqual[y, 2.2e+16], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9999999999999996e22 or 2.2e16 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 78.6%

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

   if -4.9999999999999996e22 < y < 2.2e16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 50.9%

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

Alternative 7: 37.3% 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

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

5. Simplified 36.4%

   \[\leadsto \color{blue}{-1} \]
6. Add Preprocessing

Developer Target 1: 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 2024192 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ x (- 2 (+ x y))) (/ y (- 2 (+ x y)))))

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