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

Percentage Accurate: 100.0% → 100.0%

Time: 2.2s

Alternatives: 4

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, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

      \[\leadsto 500 \cdot \color{blue}{\left(x + \left(-y\right)\right)} \]

   2. distribute-rgt-in 100.0%

      \[\leadsto \color{blue}{x \cdot 500 + \left(-y\right) \cdot 500} \]

   3. fma-def 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, 500, 500 \cdot \left(-y\right)\right) \]
6. Add Preprocessing

Alternative 2: 75.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-41} \lor \neg \left(y \leq 4500000\right):\\ \;\;\;\;y \cdot -500\\ \mathbf{else}:\\ \;\;\;\;x \cdot 500\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1e-41) (not (<= y 4500000.0))) (* y -500.0) (* x 500.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1e-41) || !(y <= 4500000.0)) {
		tmp = y * -500.0;
	} else {
		tmp = x * 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 <= (-1d-41)) .or. (.not. (y <= 4500000.0d0))) then
        tmp = y * (-500.0d0)
    else
        tmp = x * 500.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1e-41) || !(y <= 4500000.0)) {
		tmp = y * -500.0;
	} else {
		tmp = x * 500.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1e-41) or not (y <= 4500000.0):
		tmp = y * -500.0
	else:
		tmp = x * 500.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1e-41) || !(y <= 4500000.0))
		tmp = Float64(y * -500.0);
	else
		tmp = Float64(x * 500.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1e-41) || ~((y <= 4500000.0)))
		tmp = y * -500.0;
	else
		tmp = x * 500.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1e-41], N[Not[LessEqual[y, 4500000.0]], $MachinePrecision]], N[(y * -500.0), $MachinePrecision], N[(x * 500.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000001e-41 or 4.5e6 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.3%

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

   if -1.00000000000000001e-41 < y < 4.5e6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.1%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-41} \lor \neg \left(y \leq 4500000\right):\\ \;\;\;\;y \cdot -500\\ \mathbf{else}:\\ \;\;\;\;x \cdot 500\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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. Final simplification 100.0%

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

Alternative 4: 51.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ y \cdot -500 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 52.1%

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

4. Final simplification 52.1%

   \[\leadsto y \cdot -500 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024040 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))