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

Percentage Accurate: 100.0% → 100.0%

Time: 4.0s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{2} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{2} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{2} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{2} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 3.2e-91) (/ x 2.0) (/ y 2.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3.2e-91) {
		tmp = x / 2.0;
	} else {
		tmp = y / 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 3.2d-91) then
        tmp = x / 2.0d0
    else
        tmp = y / 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 3.2e-91) {
		tmp = x / 2.0;
	} else {
		tmp = y / 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3.2e-91:
		tmp = x / 2.0
	else:
		tmp = y / 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3.2e-91)
		tmp = Float64(x / 2.0);
	else
		tmp = Float64(y / 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 3.2e-91)
		tmp = x / 2.0;
	else
		tmp = y / 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3.2e-91], N[(x / 2.0), $MachinePrecision], N[(y / 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.19999999999999996e-91

   1. Initial program 100.0%

      \[\frac{x + y}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 60.3%

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

   if 3.19999999999999996e-91 < y

   1. Initial program 100.0%

      \[\frac{x + y}{2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 72.6%

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

Alternative 3: 50.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \frac{x}{2} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{2} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

5. Simplified 49.7%

   \[\leadsto \frac{\color{blue}{x}}{2} \]
6. Add Preprocessing

Alternative 4: 2.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \frac{x}{-2} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{2} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

5. Simplified 49.7%

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

   1. clear-num N/A

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

   2. inv-pow N/A

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

   3. sqr-pow N/A

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

   4. remove-double-neg N/A

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

   5. neg-mul-1 N/A

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

   6. metadata-eval N/A

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

   7. metadata-eval N/A

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

   8. metadata-eval N/A

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

   9. unpow-prod-down N/A

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

   10. associate-*r* N/A

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

   11. metadata-eval N/A

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

   12. metadata-eval N/A

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

   13. metadata-eval N/A

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

   14. unpow-prod-down N/A

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

   15. *-commutative N/A

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

   16. neg-mul-1 N/A

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

   17. metadata-eval N/A

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

   18. metadata-eval N/A

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

   19. metadata-eval N/A

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

   20. metadata-eval N/A

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

   21. metadata-eval N/A

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

   22. metadata-eval N/A

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

7. Applied egg-rr 2.2%

   \[\leadsto \color{blue}{\frac{x}{-2}} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024192 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, A"
  :precision binary64
  (/ (+ x y) 2.0))