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

Percentage Accurate: 100.0% → 100.0%

Time: 10.8s

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

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

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: 85.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + -2}\\ t_1 := \frac{x - y}{2 - \left(x + y\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;t\_1 \leq 10^{-199}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-27}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y -2.0))) (t_1 (/ (- x y) (- 2.0 (+ x y)))))
   (if (<= t_1 -2e-5)
     (/ x (- 2.0 x))
     (if (<= t_1 1e-199) t_0 (if (<= t_1 5e-27) (* x 0.5) t_0)))))

C

double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double t_1 = (x - y) / (2.0 - (x + y));
	double tmp;
	if (t_1 <= -2e-5) {
		tmp = x / (2.0 - x);
	} else if (t_1 <= 1e-199) {
		tmp = t_0;
	} else if (t_1 <= 5e-27) {
		tmp = x * 0.5;
	} 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 = y / (y + (-2.0d0))
    t_1 = (x - y) / (2.0d0 - (x + y))
    if (t_1 <= (-2d-5)) then
        tmp = x / (2.0d0 - x)
    else if (t_1 <= 1d-199) then
        tmp = t_0
    else if (t_1 <= 5d-27) then
        tmp = x * 0.5d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double t_1 = (x - y) / (2.0 - (x + y));
	double tmp;
	if (t_1 <= -2e-5) {
		tmp = x / (2.0 - x);
	} else if (t_1 <= 1e-199) {
		tmp = t_0;
	} else if (t_1 <= 5e-27) {
		tmp = x * 0.5;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + -2.0)
	t_1 = (x - y) / (2.0 - (x + y))
	tmp = 0
	if t_1 <= -2e-5:
		tmp = x / (2.0 - x)
	elif t_1 <= 1e-199:
		tmp = t_0
	elif t_1 <= 5e-27:
		tmp = x * 0.5
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + -2.0))
	t_1 = Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
	tmp = 0.0
	if (t_1 <= -2e-5)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (t_1 <= 1e-199)
		tmp = t_0;
	elseif (t_1 <= 5e-27)
		tmp = Float64(x * 0.5);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + -2.0);
	t_1 = (x - y) / (2.0 - (x + y));
	tmp = 0.0;
	if (t_1 <= -2e-5)
		tmp = x / (2.0 - x);
	elseif (t_1 <= 1e-199)
		tmp = t_0;
	elseif (t_1 <= 5e-27)
		tmp = x * 0.5;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-5], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-199], t$95$0, If[LessEqual[t$95$1, 5e-27], N[(x * 0.5), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < -2.00000000000000016e-5

   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. lower-/.f64 N/A

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

      2. lower--.f64 98.3

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

   5. Applied rewrites 98.3%

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

   if -2.00000000000000016e-5 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 9.99999999999999982e-200 or 5.0000000000000002e-27 < (/.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 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. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. mul-1-neg N/A

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

      11. associate-*r* N/A

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

      12. metadata-eval N/A

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

      13. *-lft-identity N/A

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

      14. lower-+.f64 N/A

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

      15. metadata-eval 82.9

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

   5. Applied rewrites 82.9%

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

   if 9.99999999999999982e-200 < (/.f64 (-.f64 x y) (-.f64 #s(literal 2 binary64) (+.f64 x y))) < 5.0000000000000002e-27

   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. lower-/.f64 N/A

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

      2. lower--.f64 48.9

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

   5. Applied rewrites 48.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 48.9%

      \[\leadsto x \cdot \color{blue}{0.5} \]
3. Recombined 3 regimes into one program.
4. 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 2024226 
(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))))