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

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

Alternatives: 3

Speedup: 1.7×

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, 1.7× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(y + x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 0.5 (+ y x)))

C

double code(double x, double y) {
	return 0.5 * (y + x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * (y + x)
end function

Java

public static double code(double x, double y) {
	return 0.5 * (y + x);
}

Python

def code(x, y):
	return 0.5 * (y + x)

Julia

function code(x, y)
	return Float64(0.5 * Float64(y + x))
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * (y + x);
end

Wolfram

code[x_, y_] := N[(0.5 * N[(y + x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

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

   1. *-commutative N/A

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

   2. *-lft-identity N/A

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

   3. *-inverses N/A

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

   4. associate-*l/ N/A

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

   5. associate-*r/ N/A

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

   6. associate-*r* N/A

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

   7. *-commutative N/A

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

   8. *-commutative N/A

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

   9. distribute-rgt-in N/A

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

   10. *-commutative N/A

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

   11. distribute-lft1-in N/A

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

   12. +-commutative N/A

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

   13. associate-*r* N/A

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

   14. lower-*.f64 N/A

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

   15. distribute-lft-in N/A

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

   16. *-rgt-identity N/A

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

   17. associate-*r/ N/A

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

   18. associate-*l/ N/A

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

   19. *-inverses N/A

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

   20. *-lft-identity N/A

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

   21. lower-+.f64 100.0

       \[\leadsto \color{blue}{\left(y + x\right)} \cdot 0.5 \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{\left(y + x\right) \cdot 0.5} \]

6. Final simplification 100.0%

   \[\leadsto 0.5 \cdot \left(y + x\right) \]
7. Add Preprocessing

Alternative 2: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + x \leq -2 \cdot 10^{-272}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (+ y x) -2e-272) (* x 0.5) (* y 0.5)))

C

double code(double x, double y) {
	double tmp;
	if ((y + x) <= -2e-272) {
		tmp = x * 0.5;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y + x) <= (-2d-272)) then
        tmp = x * 0.5d0
    else
        tmp = y * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y + x) <= -2e-272) {
		tmp = x * 0.5;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y + x) <= -2e-272:
		tmp = x * 0.5
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y + x) <= -2e-272)
		tmp = Float64(x * 0.5);
	else
		tmp = Float64(y * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y + x) <= -2e-272)
		tmp = x * 0.5;
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y + x), $MachinePrecision], -2e-272], N[(x * 0.5), $MachinePrecision], N[(y * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.99999999999999986e-272

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 47.2

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   5. Simplified 47.2%

      \[\leadsto \color{blue}{x \cdot 0.5} \]

   if -1.99999999999999986e-272 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot \frac{1}{2}} \]

      2. lower-*.f64 48.4

         \[\leadsto \color{blue}{y \cdot 0.5} \]

   5. Simplified 48.4%

      \[\leadsto \color{blue}{y \cdot 0.5} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + x \leq -2 \cdot 10^{-272}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x 0.5))

C

double code(double x, double y) {
	return x * 0.5;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * 0.5d0
end function

Java

public static double code(double x, double y) {
	return x * 0.5;
}

Python

def code(x, y):
	return x * 0.5

Julia

function code(x, y)
	return Float64(x * 0.5)
end

MATLAB

function tmp = code(x, y)
	tmp = x * 0.5;
end

Wolfram

code[x_, y_] := N[(x * 0.5), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 50.4

      \[\leadsto \color{blue}{x \cdot 0.5} \]

5. Simplified 50.4%

   \[\leadsto \color{blue}{x \cdot 0.5} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024215 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, A"
  :precision binary64
  (/ (+ x y) 2.0))