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

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

Alternatives: 5

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_] := N[(y * -500.0 + 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%

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

   1. +-commutative 100.0%

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

   2. *-commutative 100.0%

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

   3. fma-def 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-52} \lor \neg \left(x \leq 3.5 \cdot 10^{-64}\right) \land \left(x \leq 5.5 \cdot 10^{-22} \lor \neg \left(x \leq 2.6 \cdot 10^{+17}\right)\right):\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -500\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.1e-52)
         (and (not (<= x 3.5e-64)) (or (<= x 5.5e-22) (not (<= x 2.6e+17)))))
   (* 500.0 x)
   (* y -500.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.1e-52) || (!(x <= 3.5e-64) && ((x <= 5.5e-22) || !(x <= 2.6e+17)))) {
		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 ((x <= (-3.1d-52)) .or. (.not. (x <= 3.5d-64)) .and. (x <= 5.5d-22) .or. (.not. (x <= 2.6d+17))) 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 ((x <= -3.1e-52) || (!(x <= 3.5e-64) && ((x <= 5.5e-22) || !(x <= 2.6e+17)))) {
		tmp = 500.0 * x;
	} else {
		tmp = y * -500.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.1e-52) or (not (x <= 3.5e-64) and ((x <= 5.5e-22) or not (x <= 2.6e+17))):
		tmp = 500.0 * x
	else:
		tmp = y * -500.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.1e-52) || (!(x <= 3.5e-64) && ((x <= 5.5e-22) || !(x <= 2.6e+17))))
		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 ((x <= -3.1e-52) || (~((x <= 3.5e-64)) && ((x <= 5.5e-22) || ~((x <= 2.6e+17)))))
		tmp = 500.0 * x;
	else
		tmp = y * -500.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.1e-52], And[N[Not[LessEqual[x, 3.5e-64]], $MachinePrecision], Or[LessEqual[x, 5.5e-22], N[Not[LessEqual[x, 2.6e+17]], $MachinePrecision]]]], N[(500.0 * x), $MachinePrecision], N[(y * -500.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0999999999999999e-52 or 3.5000000000000003e-64 < x < 5.5000000000000001e-22 or 2.6e17 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 76.5%

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

   if -3.0999999999999999e-52 < x < 3.5000000000000003e-64 or 5.5000000000000001e-22 < x < 2.6e17

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 83.6%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-52} \lor \neg \left(x \leq 3.5 \cdot 10^{-64}\right) \land \left(x \leq 5.5 \cdot 10^{-22} \lor \neg \left(x \leq 2.6 \cdot 10^{+17}\right)\right):\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -500\\ \end{array} \]

Alternative 3: 100.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 4: 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 5: 50.2% 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. Taylor expanded in x around 0 52.6%

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

3. Final simplification 52.6%

   \[\leadsto y \cdot -500 \]

Reproduce

herbie shell --seed 2023221 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))