Data.Colour.CIE:cieLAB from colour-2.3.3, C

Percentage Accurate: 100.0% → 100.0%

Time: 2.2s

Alternatives: 3

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ x (/ y 500.0)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x + (y / 500.0)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ x (/ y 500.0)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x + (y / 500.0)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (+ x (/ y 500.0)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x + (y / 500.0)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \frac{y}{500} \]

2. Final simplification 100.0%

   \[\leadsto x + \frac{y}{500} \]

Alternative 2: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-50}:\\ \;\;\;\;y \cdot 0.002\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.002\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.5e-50) (* y 0.002) (if (<= y 7.2e+31) x (* y 0.002))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.5e-50) {
		tmp = y * 0.002;
	} else if (y <= 7.2e+31) {
		tmp = x;
	} else {
		tmp = y * 0.002;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-6.5d-50)) then
        tmp = y * 0.002d0
    else if (y <= 7.2d+31) then
        tmp = x
    else
        tmp = y * 0.002d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6.5e-50) {
		tmp = y * 0.002;
	} else if (y <= 7.2e+31) {
		tmp = x;
	} else {
		tmp = y * 0.002;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.5e-50:
		tmp = y * 0.002
	elif y <= 7.2e+31:
		tmp = x
	else:
		tmp = y * 0.002
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.5e-50)
		tmp = Float64(y * 0.002);
	elseif (y <= 7.2e+31)
		tmp = x;
	else
		tmp = Float64(y * 0.002);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6.5e-50)
		tmp = y * 0.002;
	elseif (y <= 7.2e+31)
		tmp = x;
	else
		tmp = y * 0.002;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.5e-50], N[(y * 0.002), $MachinePrecision], If[LessEqual[y, 7.2e+31], x, N[(y * 0.002), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.49999999999999987e-50 or 7.19999999999999992e31 < y

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]

   2. Taylor expanded in x around 0 75.4%

      \[\leadsto \color{blue}{0.002 \cdot y} \]

   if -6.49999999999999987e-50 < y < 7.19999999999999992e31

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]

   2. Taylor expanded in x around inf 79.9%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-50}:\\ \;\;\;\;y \cdot 0.002\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.002\\ \end{array} \]

Alternative 3: 51.2% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 x)

C

double code(double x, double y) {
	return x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

function tmp = code(x, y)
	tmp = x;
end

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

   \[x + \frac{y}{500} \]

2. Taylor expanded in x around inf 55.4%

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

3. Final simplification 55.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023252 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, C"
  :precision binary64
  (+ x (/ y 500.0)))