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

Percentage Accurate: 100.0% → 100.0%

Time: 8.2s

Alternatives: 11

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

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(y + x\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ y x))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (y + x));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (y + x))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (y + x));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (y + x))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(y + x)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (y + x));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(y + x), $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%

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

Alternative 2: 85.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{2 - \left(y + x\right)}\\ \mathbf{if}\;t\_0 \leq -0.5:\\ \;\;\;\;-1\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-241}:\\ \;\;\;\;\mathsf{fma}\left(0.25, x, 0.5\right) \cdot x\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, y, -0.5\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- 2.0 (+ y x)))))
   (if (<= t_0 -0.5)
     -1.0
     (if (<= t_0 5e-241)
       (* (fma 0.25 x 0.5) x)
       (if (<= t_0 5e-17) (* (fma -0.25 y -0.5) y) 1.0)))))

C

double code(double x, double y) {
	double t_0 = (x - y) / (2.0 - (y + x));
	double tmp;
	if (t_0 <= -0.5) {
		tmp = -1.0;
	} else if (t_0 <= 5e-241) {
		tmp = fma(0.25, x, 0.5) * x;
	} else if (t_0 <= 5e-17) {
		tmp = fma(-0.25, y, -0.5) * y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(2.0 - Float64(y + x)))
	tmp = 0.0
	if (t_0 <= -0.5)
		tmp = -1.0;
	elseif (t_0 <= 5e-241)
		tmp = Float64(fma(0.25, x, 0.5) * x);
	elseif (t_0 <= 5e-17)
		tmp = Float64(fma(-0.25, y, -0.5) * y);
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], -1.0, If[LessEqual[t$95$0, 5e-241], N[(N[(0.25 * x + 0.5), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$0, 5e-17], N[(N[(-0.25 * y + -0.5), $MachinePrecision] * y), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < -0.5

   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. Applied rewrites 97.3%

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

   if -0.5 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 4.9999999999999998e-241

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 50.6

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

   5. Applied rewrites 50.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto x \cdot \color{blue}{\left(\frac{1}{2} + \frac{1}{4} \cdot x\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.6%

      \[\leadsto \mathsf{fma}\left(0.25, x, 0.5\right) \cdot \color{blue}{x} \]

   if 4.9999999999999998e-241 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 4.9999999999999999e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. distribute-neg-in N/A

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

      8. mul-1-neg N/A

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

      9. mul-1-neg N/A

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

      10. associate-*r* N/A

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

      11. metadata-eval N/A

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

      12. *-lft-identity N/A

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

      13. lower-+.f64 N/A

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

      14. metadata-eval 51.0

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

   5. Applied rewrites 51.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 51.0%

      \[\leadsto \mathsf{fma}\left(-0.25, y, -0.5\right) \cdot \color{blue}{y} \]

   if 4.9999999999999999e-17 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x 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. Applied rewrites 94.8%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{2 - \left(y + x\right)} \leq -0.5:\\ \;\;\;\;-1\\ \mathbf{elif}\;\frac{x - y}{2 - \left(y + x\right)} \leq 5 \cdot 10^{-241}:\\ \;\;\;\;\mathsf{fma}\left(0.25, x, 0.5\right) \cdot x\\ \mathbf{elif}\;\frac{x - y}{2 - \left(y + x\right)} \leq 5 \cdot 10^{-17}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, y, -0.5\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. 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 2024230 
(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))))