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

Percentage Accurate: 100.0% → 100.0%

Time: 1.4s

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 100.0%

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

3. Final simplification 100.0%

   \[\leadsto 500 \cdot x + -500 \cdot y \]

Alternative 2: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+51} \lor \neg \left(x \leq -68000000000\right) \land \left(x \leq -1.75 \cdot 10^{-30} \lor \neg \left(x \leq 7 \cdot 10^{-29}\right)\right):\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-500 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5.5e+51)
         (and (not (<= x -68000000000.0))
              (or (<= x -1.75e-30) (not (<= x 7e-29)))))
   (* 500.0 x)
   (* -500.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5.5e+51) || (!(x <= -68000000000.0) && ((x <= -1.75e-30) || !(x <= 7e-29)))) {
		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 <= (-5.5d+51)) .or. (.not. (x <= (-68000000000.0d0))) .and. (x <= (-1.75d-30)) .or. (.not. (x <= 7d-29))) 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 <= -5.5e+51) || (!(x <= -68000000000.0) && ((x <= -1.75e-30) || !(x <= 7e-29)))) {
		tmp = 500.0 * x;
	} else {
		tmp = -500.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5.5e+51) or (not (x <= -68000000000.0) and ((x <= -1.75e-30) or not (x <= 7e-29))):
		tmp = 500.0 * x
	else:
		tmp = -500.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5.5e+51) || (!(x <= -68000000000.0) && ((x <= -1.75e-30) || !(x <= 7e-29))))
		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 <= -5.5e+51) || (~((x <= -68000000000.0)) && ((x <= -1.75e-30) || ~((x <= 7e-29)))))
		tmp = 500.0 * x;
	else
		tmp = -500.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5.5e+51], And[N[Not[LessEqual[x, -68000000000.0]], $MachinePrecision], Or[LessEqual[x, -1.75e-30], N[Not[LessEqual[x, 7e-29]], $MachinePrecision]]]], N[(500.0 * x), $MachinePrecision], N[(-500.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e51 or -6.8e10 < x < -1.7500000000000001e-30 or 6.9999999999999995e-29 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 82.4%

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

   if -5.5e51 < x < -6.8e10 or -1.7500000000000001e-30 < x < 6.9999999999999995e-29

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.0%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+51} \lor \neg \left(x \leq -68000000000\right) \land \left(x \leq -1.75 \cdot 10^{-30} \lor \neg \left(x \leq 7 \cdot 10^{-29}\right)\right):\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-500 \cdot y\\ \end{array} \]

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: 50.9% 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 48.4%

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

3. Final simplification 48.4%

   \[\leadsto -500 \cdot y \]

Reproduce

herbie shell --seed 2023230 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))