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

Percentage Accurate: 100.0% → 100.0%

Time: 5.8s

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_] := N[(500.0 * x + 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. Step-by-step derivation

   1. fma-def 100.0%

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

4. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+52}:\\ \;\;\;\;-500 \cdot y\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-31}:\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-500 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.6e+52)
   (* -500.0 y)
   (if (<= y 1.65e-31) (* 500.0 x) (* -500.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.6e+52) {
		tmp = -500.0 * y;
	} else if (y <= 1.65e-31) {
		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 (y <= (-2.6d+52)) then
        tmp = (-500.0d0) * y
    else if (y <= 1.65d-31) 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 (y <= -2.6e+52) {
		tmp = -500.0 * y;
	} else if (y <= 1.65e-31) {
		tmp = 500.0 * x;
	} else {
		tmp = -500.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.6e+52:
		tmp = -500.0 * y
	elif y <= 1.65e-31:
		tmp = 500.0 * x
	else:
		tmp = -500.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.6e+52)
		tmp = Float64(-500.0 * y);
	elseif (y <= 1.65e-31)
		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 (y <= -2.6e+52)
		tmp = -500.0 * y;
	elseif (y <= 1.65e-31)
		tmp = 500.0 * x;
	else
		tmp = -500.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.6e+52], N[(-500.0 * y), $MachinePrecision], If[LessEqual[y, 1.65e-31], N[(500.0 * x), $MachinePrecision], N[(-500.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e52 or 1.65e-31 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.4%

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

   if -2.6e52 < y < 1.65e-31

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 79.5%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+52}:\\ \;\;\;\;-500 \cdot y\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-31}:\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-500 \cdot y\\ \end{array} \]

Alternative 3: 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. Taylor expanded in x around 0 100.0%

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

3. Final simplification 100.0%

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

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: 50.6% 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 50.5%

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

3. Final simplification 50.5%

   \[\leadsto -500 \cdot y \]

Reproduce

herbie shell --seed 2023176 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))