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

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

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, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 100.0%

   \[\leadsto \color{blue}{-500 \cdot y + 500 \cdot x} \]
4. Add Preprocessing

Alternative 2: 73.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+79} \lor \neg \left(x \leq -2.5 \cdot 10^{+28}\right) \land \left(x \leq -1.15 \cdot 10^{-46} \lor \neg \left(x \leq 6 \cdot 10^{-35}\right)\right):\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-500 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.8e+79)
         (and (not (<= x -2.5e+28)) (or (<= x -1.15e-46) (not (<= x 6e-35)))))
   (* 500.0 x)
   (* -500.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8e+79) || (!(x <= -2.5e+28) && ((x <= -1.15e-46) || !(x <= 6e-35)))) {
		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 <= (-3.8d+79)) .or. (.not. (x <= (-2.5d+28))) .and. (x <= (-1.15d-46)) .or. (.not. (x <= 6d-35))) 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 <= -3.8e+79) || (!(x <= -2.5e+28) && ((x <= -1.15e-46) || !(x <= 6e-35)))) {
		tmp = 500.0 * x;
	} else {
		tmp = -500.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.8e+79) or (not (x <= -2.5e+28) and ((x <= -1.15e-46) or not (x <= 6e-35))):
		tmp = 500.0 * x
	else:
		tmp = -500.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.8e+79) || (!(x <= -2.5e+28) && ((x <= -1.15e-46) || !(x <= 6e-35))))
		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 <= -3.8e+79) || (~((x <= -2.5e+28)) && ((x <= -1.15e-46) || ~((x <= 6e-35)))))
		tmp = 500.0 * x;
	else
		tmp = -500.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.8e+79], And[N[Not[LessEqual[x, -2.5e+28]], $MachinePrecision], Or[LessEqual[x, -1.15e-46], N[Not[LessEqual[x, 6e-35]], $MachinePrecision]]]], N[(500.0 * x), $MachinePrecision], N[(-500.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.8000000000000002e79 or -2.49999999999999979e28 < x < -1.15e-46 or 5.99999999999999978e-35 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.1%

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

   if -3.8000000000000002e79 < x < -2.49999999999999979e28 or -1.15e-46 < x < 5.99999999999999978e-35

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.5%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+79} \lor \neg \left(x \leq -2.5 \cdot 10^{+28}\right) \land \left(x \leq -1.15 \cdot 10^{-46} \lor \neg \left(x \leq 6 \cdot 10^{-35}\right)\right):\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-500 \cdot y\\ \end{array} \]
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. Add Preprocessing

Alternative 4: 50.1% 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. Add Preprocessing

3. Taylor expanded in x around 0 48.5%

   \[\leadsto \color{blue}{-500 \cdot y} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))