Data.Colour.CIE:cieLABView from colour-2.3.3, B

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

Alternatives: 3

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ 500 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 500.0 (- x y)))

C

double code(double x, double y) {
	return 500.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 500.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 500.0 * (x - y);
}

Python

def code(x, y):
	return 500.0 * (x - y)

Julia

function code(x, y)
	return Float64(500.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 500.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(500.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 500 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 500.0 (- x y)))

C

double code(double x, double y) {
	return 500.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 500.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 500.0 * (x - y);
}

Python

def code(x, y):
	return 500.0 * (x - y)

Julia

function code(x, y)
	return Float64(500.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 500.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(500.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 500 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 500.0 (- x y)))

C

double code(double x, double y) {
	return 500.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 500.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 500.0 * (x - y);
}

Python

def code(x, y):
	return 500.0 * (x - y)

Julia

function code(x, y)
	return Float64(500.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 500.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(500.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0146:\\ \;\;\;\;y \cdot -500\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-24}:\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -500\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.0146) (* y -500.0) (if (<= y 3.8e-24) (* 500.0 x) (* y -500.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.0146) {
		tmp = y * -500.0;
	} else if (y <= 3.8e-24) {
		tmp = 500.0 * x;
	} else {
		tmp = y * -500.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-0.0146d0)) then
        tmp = y * (-500.0d0)
    else if (y <= 3.8d-24) then
        tmp = 500.0d0 * x
    else
        tmp = y * (-500.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -0.0146) {
		tmp = y * -500.0;
	} else if (y <= 3.8e-24) {
		tmp = 500.0 * x;
	} else {
		tmp = y * -500.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.0146:
		tmp = y * -500.0
	elif y <= 3.8e-24:
		tmp = 500.0 * x
	else:
		tmp = y * -500.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.0146)
		tmp = Float64(y * -500.0);
	elseif (y <= 3.8e-24)
		tmp = Float64(500.0 * x);
	else
		tmp = Float64(y * -500.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.0146)
		tmp = y * -500.0;
	elseif (y <= 3.8e-24)
		tmp = 500.0 * x;
	else
		tmp = y * -500.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.0146], N[(y * -500.0), $MachinePrecision], If[LessEqual[y, 3.8e-24], N[(500.0 * x), $MachinePrecision], N[(y * -500.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0146000000000000001 or 3.80000000000000026e-24 < y

   1. Initial program 100.0%

      \[500 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-500 \cdot y} \]
   4. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto \color{blue}{-500 \cdot y + 0} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot -500} + 0 \]

      3. accelerator-lowering-fma.f64 74.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, -500, 0\right)} \]

   5. Simplified 74.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, -500, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

         \[\leadsto \color{blue}{y \cdot -500} \]

      2. *-lowering-*.f64 74.8

         \[\leadsto \color{blue}{y \cdot -500} \]

   7. Applied egg-rr 74.8%

      \[\leadsto \color{blue}{y \cdot -500} \]

   if -0.0146000000000000001 < y < 3.80000000000000026e-24

   1. Initial program 100.0%

      \[500 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto 500 \cdot \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 83.9%

      \[\leadsto 500 \cdot \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 50.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ 500 \cdot x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 500.0 x))

C

double code(double x, double y) {
	return 500.0 * x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 500.0d0 * x
end function

Java

public static double code(double x, double y) {
	return 500.0 * x;
}

Python

def code(x, y):
	return 500.0 * x

Julia

function code(x, y)
	return Float64(500.0 * x)
end

MATLAB

function tmp = code(x, y)
	tmp = 500.0 * x;
end

Wolfram

code[x_, y_] := N[(500.0 * x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto 500 \cdot \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 54.4%

   \[\leadsto 500 \cdot \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024198 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))