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

Percentage Accurate: 100.0% → 100.0%

Time: 3.6s

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   2. flip-+ N/A

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

   3. div-sub N/A

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

   4. sub-neg N/A

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

   5. associate-/l* N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-/.f64 N/A

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

   8. lower--.f64 N/A

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

   9. lift-/.f64 N/A

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

   10. metadata-eval N/A

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

   11. distribute-neg-frac N/A

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

   12. lower-/.f64 N/A

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

   13. lift-/.f64 N/A

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

   14. metadata-eval N/A

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

   15. lift-/.f64 N/A

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

   16. metadata-eval N/A

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

   17. metadata-eval N/A

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

   18. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(x, \frac{x}{x - \frac{1}{3}}, \frac{\color{blue}{\frac{-1}{9}}}{x - \frac{1}{3}}\right) \]

   19. lower--.f64 100.0

       \[\leadsto \mathsf{fma}\left(x, \frac{x}{x - 0.3333333333333333}, \frac{-0.1111111111111111}{\color{blue}{x - \frac{1}{3}}}\right) \]

   20. lift-/.f64 N/A

       \[\leadsto \mathsf{fma}\left(x, \frac{x}{x - \frac{1}{3}}, \frac{\frac{-1}{9}}{x - \color{blue}{\frac{1}{3}}}\right) \]

   21. metadata-eval 100.0

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

4. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{x}{x - 0.3333333333333333}, \frac{-0.1111111111111111}{x - 0.3333333333333333}\right)} \]
5. 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

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

   2. lift-/.f64 N/A

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

   3. metadata-eval N/A

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

   4. metadata-eval N/A

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

   5. metadata-eval N/A

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

   6. metadata-eval N/A

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

   7. lift-/.f64 N/A

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

   8. sub-neg N/A

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

   9. lower--.f64 N/A

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

   10. lift-/.f64 N/A

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

   11. metadata-eval N/A

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

   12. metadata-eval 100.0

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

4. Applied rewrites 100.0%

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

Alternative 3: 49.9% 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 51.0%

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

Reproduce

herbie shell --seed 2024296 
(FPCore (x)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, F"
  :precision binary64
  (+ x (/ 1.0 3.0)))