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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]

2. Taylor expanded in x around 0 100.0%

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

   1. fma-def 100.0%

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

4. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+55} \lor \neg \left(x \leq -5.4 \cdot 10^{+44}\right) \land \left(x \leq -7 \cdot 10^{-41} \lor \neg \left(x \leq 4.2 \cdot 10^{-18}\right)\right):\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-500 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.9e+55)
         (and (not (<= x -5.4e+44)) (or (<= x -7e-41) (not (<= x 4.2e-18)))))
   (* 500.0 x)
   (* -500.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.9e+55) || (!(x <= -5.4e+44) && ((x <= -7e-41) || !(x <= 4.2e-18)))) {
		tmp = 500.0 * x;
	} else {
		tmp = -500.0 * 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 <= (-2.9d+55)) .or. (.not. (x <= (-5.4d+44))) .and. (x <= (-7d-41)) .or. (.not. (x <= 4.2d-18))) then
        tmp = 500.0d0 * x
    else
        tmp = (-500.0d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.9e+55) || (!(x <= -5.4e+44) && ((x <= -7e-41) || !(x <= 4.2e-18)))) {
		tmp = 500.0 * x;
	} else {
		tmp = -500.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.9e+55) or (not (x <= -5.4e+44) and ((x <= -7e-41) or not (x <= 4.2e-18))):
		tmp = 500.0 * x
	else:
		tmp = -500.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.9e+55) || (!(x <= -5.4e+44) && ((x <= -7e-41) || !(x <= 4.2e-18))))
		tmp = Float64(500.0 * x);
	else
		tmp = Float64(-500.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.9e+55) || (~((x <= -5.4e+44)) && ((x <= -7e-41) || ~((x <= 4.2e-18)))))
		tmp = 500.0 * x;
	else
		tmp = -500.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.9e+55], And[N[Not[LessEqual[x, -5.4e+44]], $MachinePrecision], Or[LessEqual[x, -7e-41], N[Not[LessEqual[x, 4.2e-18]], $MachinePrecision]]]], N[(500.0 * x), $MachinePrecision], N[(-500.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8999999999999999e55 or -5.4e44 < x < -6.9999999999999999e-41 or 4.19999999999999999e-18 < x

   1. Initial program 100.0%

      \[500 \cdot \left(x - y\right) \]

   2. Taylor expanded in x around inf 81.5%

      \[\leadsto \color{blue}{500 \cdot x} \]

   if -2.8999999999999999e55 < x < -5.4e44 or -6.9999999999999999e-41 < x < 4.19999999999999999e-18

   1. Initial program 100.0%

      \[500 \cdot \left(x - y\right) \]

   2. Taylor expanded in x around 0 81.5%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+55} \lor \neg \left(x \leq -5.4 \cdot 10^{+44}\right) \land \left(x \leq -7 \cdot 10^{-41} \lor \neg \left(x \leq 4.2 \cdot 10^{-18}\right)\right):\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-500 \cdot y\\ \end{array} \]

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. Final simplification 100.0%

   \[\leadsto 500 \cdot \left(x - y\right) \]

Alternative 4: 50.7% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]

2. Taylor expanded in x around 0 48.1%

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

3. Final simplification 48.1%

   \[\leadsto -500 \cdot y \]

Reproduce

herbie shell --seed 2023340 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))