Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, G

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

Alternatives: 3

Speedup: 3.8×

Specification

Math

\[\begin{array}{l} \\ x - \frac{1}{3} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- x (/ 1.0 3.0)))

C

double code(double x) {
	return x - (1.0 / 3.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x - (1.0d0 / 3.0d0)
end function

Java

public static double code(double x) {
	return x - (1.0 / 3.0);
}

Python

def code(x):
	return x - (1.0 / 3.0)

Julia

function code(x)
	return Float64(x - Float64(1.0 / 3.0))
end

MATLAB

function tmp = code(x)
	tmp = x - (1.0 / 3.0);
end

Wolfram

code[x_] := N[(x - N[(1.0 / 3.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{1}{3} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- x (/ 1.0 3.0)))

C

double code(double x) {
	return x - (1.0 / 3.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x - (1.0d0 / 3.0d0)
end function

Java

public static double code(double x) {
	return x - (1.0 / 3.0);
}

Python

def code(x):
	return x - (1.0 / 3.0)

Julia

function code(x)
	return Float64(x - Float64(1.0 / 3.0))
end

MATLAB

function tmp = code(x)
	tmp = x - (1.0 / 3.0);
end

Wolfram

code[x_] := N[(x - N[(1.0 / 3.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{x}{0.3333333333333333 + x}, x, \frac{-0.1111111111111111}{0.3333333333333333 + x}\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (fma
  (/ x (+ 0.3333333333333333 x))
  x
  (/ -0.1111111111111111 (+ 0.3333333333333333 x))))

C

double code(double x) {
	return fma((x / (0.3333333333333333 + x)), x, (-0.1111111111111111 / (0.3333333333333333 + x)));
}

Julia

function code(x)
	return fma(Float64(x / Float64(0.3333333333333333 + x)), x, Float64(-0.1111111111111111 / Float64(0.3333333333333333 + x)))
end

Wolfram

code[x_] := N[(N[(x / N[(0.3333333333333333 + x), $MachinePrecision]), $MachinePrecision] * x + N[(-0.1111111111111111 / N[(0.3333333333333333 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \frac{1}{3} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto x - \color{blue}{\frac{1}{3}} \]

   2. metadata-eval 100.0

      \[\leadsto x - \color{blue}{0.3333333333333333} \]

4. Applied rewrites 100.0%

   \[\leadsto x - \color{blue}{0.3333333333333333} \]
5. Step-by-step derivation

   1. lift--.f64 N/A

      \[\leadsto \color{blue}{x - \frac{1}{3}} \]

   2. flip-- N/A

      \[\leadsto \color{blue}{\frac{x \cdot x - \frac{1}{3} \cdot \frac{1}{3}}{x + \frac{1}{3}}} \]

   3. lift-*.f64 N/A

      \[\leadsto \frac{\color{blue}{x \cdot x} - \frac{1}{3} \cdot \frac{1}{3}}{x + \frac{1}{3}} \]

   4. metadata-eval N/A

      \[\leadsto \frac{x \cdot x - \color{blue}{\frac{1}{9}}}{x + \frac{1}{3}} \]

   5. lift-+.f64 N/A

      \[\leadsto \frac{x \cdot x - \frac{1}{9}}{\color{blue}{x + \frac{1}{3}}} \]

   6. div-sub N/A

      \[\leadsto \color{blue}{\frac{x \cdot x}{x + \frac{1}{3}} - \frac{\frac{1}{9}}{x + \frac{1}{3}}} \]

   7. lift-*.f64 N/A

      \[\leadsto \frac{\color{blue}{x \cdot x}}{x + \frac{1}{3}} - \frac{\frac{1}{9}}{x + \frac{1}{3}} \]

   8. associate-*r/ N/A

      \[\leadsto \color{blue}{x \cdot \frac{x}{x + \frac{1}{3}}} - \frac{\frac{1}{9}}{x + \frac{1}{3}} \]

   9. lift-/.f64 N/A

      \[\leadsto x \cdot \color{blue}{\frac{x}{x + \frac{1}{3}}} - \frac{\frac{1}{9}}{x + \frac{1}{3}} \]

   10. lift-*.f64 N/A

       \[\leadsto \color{blue}{x \cdot \frac{x}{x + \frac{1}{3}}} - \frac{\frac{1}{9}}{x + \frac{1}{3}} \]

   11. lift-+.f64 N/A

       \[\leadsto x \cdot \frac{x}{x + \frac{1}{3}} - \frac{\frac{1}{9}}{\color{blue}{x + \frac{1}{3}}} \]

   12. flip3-+ N/A

       \[\leadsto x \cdot \frac{x}{x + \frac{1}{3}} - \frac{\frac{1}{9}}{\color{blue}{\frac{{x}^{3} + {\frac{1}{3}}^{3}}{x \cdot x + \left(\frac{1}{3} \cdot \frac{1}{3} - x \cdot \frac{1}{3}\right)}}} \]

   13. associate-/r/ N/A

       \[\leadsto x \cdot \frac{x}{x + \frac{1}{3}} - \color{blue}{\frac{\frac{1}{9}}{{x}^{3} + {\frac{1}{3}}^{3}} \cdot \left(x \cdot x + \left(\frac{1}{3} \cdot \frac{1}{3} - x \cdot \frac{1}{3}\right)\right)} \]

   14. fp-cancel-sub-sign-inv N/A

       \[\leadsto \color{blue}{x \cdot \frac{x}{x + \frac{1}{3}} + \left(\mathsf{neg}\left(\frac{\frac{1}{9}}{{x}^{3} + {\frac{1}{3}}^{3}}\right)\right) \cdot \left(x \cdot x + \left(\frac{1}{3} \cdot \frac{1}{3} - x \cdot \frac{1}{3}\right)\right)} \]

   15. lift-*.f64 N/A

       \[\leadsto \color{blue}{x \cdot \frac{x}{x + \frac{1}{3}}} + \left(\mathsf{neg}\left(\frac{\frac{1}{9}}{{x}^{3} + {\frac{1}{3}}^{3}}\right)\right) \cdot \left(x \cdot x + \left(\frac{1}{3} \cdot \frac{1}{3} - x \cdot \frac{1}{3}\right)\right) \]

   16. distribute-lft-neg-in N/A

       \[\leadsto x \cdot \frac{x}{x + \frac{1}{3}} + \color{blue}{\left(\mathsf{neg}\left(\frac{\frac{1}{9}}{{x}^{3} + {\frac{1}{3}}^{3}} \cdot \left(x \cdot x + \left(\frac{1}{3} \cdot \frac{1}{3} - x \cdot \frac{1}{3}\right)\right)\right)\right)} \]

   17. associate-/r/ N/A

       \[\leadsto x \cdot \frac{x}{x + \frac{1}{3}} + \left(\mathsf{neg}\left(\color{blue}{\frac{\frac{1}{9}}{\frac{{x}^{3} + {\frac{1}{3}}^{3}}{x \cdot x + \left(\frac{1}{3} \cdot \frac{1}{3} - x \cdot \frac{1}{3}\right)}}}\right)\right) \]

   18. flip3-+ N/A

       \[\leadsto x \cdot \frac{x}{x + \frac{1}{3}} + \left(\mathsf{neg}\left(\frac{\frac{1}{9}}{\color{blue}{x + \frac{1}{3}}}\right)\right) \]

   19. lift-+.f64 N/A

       \[\leadsto x \cdot \frac{x}{x + \frac{1}{3}} + \left(\mathsf{neg}\left(\frac{\frac{1}{9}}{\color{blue}{x + \frac{1}{3}}}\right)\right) \]

6. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{0.3333333333333333 + x}, x, \frac{-0.1111111111111111}{0.3333333333333333 + x}\right)} \]
7. Add Preprocessing

Alternative 2: 100.0% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ x - 0.3333333333333333 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- x 0.3333333333333333))

C

double code(double x) {
	return x - 0.3333333333333333;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x - 0.3333333333333333d0
end function

Java

public static double code(double x) {
	return x - 0.3333333333333333;
}

Python

def code(x):
	return x - 0.3333333333333333

Julia

function code(x)
	return Float64(x - 0.3333333333333333)
end

MATLAB

function tmp = code(x)
	tmp = x - 0.3333333333333333;
end

Wolfram

code[x_] := N[(x - 0.3333333333333333), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \frac{1}{3} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto x - \color{blue}{\frac{1}{3}} \]

   2. metadata-eval 100.0

      \[\leadsto x - \color{blue}{0.3333333333333333} \]

4. Applied rewrites 100.0%

   \[\leadsto x - \color{blue}{0.3333333333333333} \]
5. Add Preprocessing

Alternative 3: 50.8% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ -0.3333333333333333 \end{array} \]

FPCore

(FPCore (x) :precision binary64 -0.3333333333333333)

C

double code(double x) {
	return -0.3333333333333333;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = -0.3333333333333333d0
end function

Java

public static double code(double x) {
	return -0.3333333333333333;
}

Python

def code(x):
	return -0.3333333333333333

Julia

function code(x)
	return -0.3333333333333333
end

MATLAB

function tmp = code(x)
	tmp = -0.3333333333333333;
end

Wolfram

code[x_] := -0.3333333333333333

Derivation

1. Initial program 100.0%

   \[x - \frac{1}{3} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 48.3%

   \[\leadsto \color{blue}{-0.3333333333333333} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024338 
(FPCore (x)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, G"
  :precision binary64
  (- x (/ 1.0 3.0)))