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

Percentage Accurate: 100.0% → 100.0%

Time: 2.8s

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift-/.f64 N/A

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

   2. div-inv N/A

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

   3. lower-*.f64 N/A

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

   4. lift-+.f64 N/A

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

   5. +-commutative N/A

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

   6. lower-+.f64 N/A

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

   7. metadata-eval 100.0

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

4. Applied rewrites 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 50.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-239}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (+ x y) -2e-239) (* 0.5 x) (* 0.5 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x + y) <= -2e-239) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x + y) <= (-2d-239)) then
        tmp = 0.5d0 * x
    else
        tmp = 0.5d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x + y) <= -2e-239) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x + y) <= -2e-239:
		tmp = 0.5 * x
	else:
		tmp = 0.5 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(x + y) <= -2e-239)
		tmp = Float64(0.5 * x);
	else
		tmp = Float64(0.5 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x + y) <= -2e-239)
		tmp = 0.5 * x;
	else
		tmp = 0.5 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(x + y), $MachinePrecision], -2e-239], N[(0.5 * x), $MachinePrecision], N[(0.5 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -2.0000000000000002e-239

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 50.1

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

   5. Applied rewrites 50.1%

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

   if -2.0000000000000002e-239 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 53.5

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

   5. Applied rewrites 53.5%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-239}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.9% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 49.1

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

5. Applied rewrites 49.1%

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

6. Final simplification 49.1%

   \[\leadsto 0.5 \cdot x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024273 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, A"
  :precision binary64
  (/ (+ x y) 2.0))