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

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

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. div-inv N/A

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

   2. *-lowering-*.f64 N/A

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

   3. +-lowering-+.f64 N/A

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

   4. metadata-eval 100.0

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

4. Applied egg-rr 100.0%

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

Alternative 2: 62.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.8 \cdot 10^{-53}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 7.8e-53) (* x 0.5) (* y 0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 7.8e-53) {
		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 <= 7.8d-53) 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 <= 7.8e-53) {
		tmp = x * 0.5;
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 7.8e-53:
		tmp = x * 0.5
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 7.8e-53)
		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 <= 7.8e-53)
		tmp = x * 0.5;
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 7.8e-53], N[(x * 0.5), $MachinePrecision], N[(y * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.8000000000000004e-53

   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. +-rgt-identity N/A

         \[\leadsto \color{blue}{\frac{1}{2} \cdot x + 0} \]

      2. accelerator-lowering-fma.f64 53.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, x, 0\right)} \]

   5. Simplified 53.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, x, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 53.7

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

   7. Applied egg-rr 53.7%

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

   if 7.8000000000000004e-53 < 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. +-rgt-identity N/A

         \[\leadsto \color{blue}{\frac{1}{2} \cdot y + 0} \]

      2. accelerator-lowering-fma.f64 63.6

         \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, y, 0\right)} \]

   5. Simplified 63.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, y, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 63.6

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

   7. Applied egg-rr 63.6%

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

Alternative 3: 51.4% 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. +-rgt-identity N/A

      \[\leadsto \color{blue}{\frac{1}{2} \cdot x + 0} \]

   2. accelerator-lowering-fma.f64 48.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, x, 0\right)} \]

5. Simplified 48.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.5, x, 0\right)} \]
6. Step-by-step derivation

   1. +-rgt-identity N/A

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

   2. *-commutative N/A

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

   3. *-lowering-*.f64 48.8

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

7. Applied egg-rr 48.8%

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

Reproduce

herbie shell --seed 2024196 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, A"
  :precision binary64
  (/ (+ x y) 2.0))