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

Percentage Accurate: 100.0% → 100.0%

Time: 1.4s

Alternatives: 3

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x - \frac{y}{200} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x (/ y 200.0)))

C

double code(double x, double y) {
	return x - (y / 200.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x - (y / 200.0d0)
end function

Java

public static double code(double x, double y) {
	return x - (y / 200.0);
}

Python

def code(x, y):
	return x - (y / 200.0)

Julia

function code(x, y)
	return Float64(x - Float64(y / 200.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x - (y / 200.0);
end

Wolfram

code[x_, y_] := N[(x - N[(y / 200.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y}{200} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x (/ y 200.0)))

C

double code(double x, double y) {
	return x - (y / 200.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x - (y / 200.0d0)
end function

Java

public static double code(double x, double y) {
	return x - (y / 200.0);
}

Python

def code(x, y):
	return x - (y / 200.0)

Julia

function code(x, y)
	return Float64(x - Float64(y / 200.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x - (y / 200.0);
end

Wolfram

code[x_, y_] := N[(x - N[(y / 200.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y}{200} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x (/ y 200.0)))

C

double code(double x, double y) {
	return x - (y / 200.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x - (y / 200.0d0)
end function

Java

public static double code(double x, double y) {
	return x - (y / 200.0);
}

Python

def code(x, y):
	return x - (y / 200.0)

Julia

function code(x, y)
	return Float64(x - Float64(y / 200.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x - (y / 200.0);
end

Wolfram

code[x_, y_] := N[(x - N[(y / 200.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]

2. Final simplification 100.0%

   \[\leadsto x - \frac{y}{200} \]

Alternative 2: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3000000:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.005\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3000000.0) (* y -0.005) (if (<= y 3.3e-57) x (* y -0.005))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3000000.0) {
		tmp = y * -0.005;
	} else if (y <= 3.3e-57) {
		tmp = x;
	} else {
		tmp = y * -0.005;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3000000.0d0)) then
        tmp = y * (-0.005d0)
    else if (y <= 3.3d-57) then
        tmp = x
    else
        tmp = y * (-0.005d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3000000.0) {
		tmp = y * -0.005;
	} else if (y <= 3.3e-57) {
		tmp = x;
	} else {
		tmp = y * -0.005;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3000000.0:
		tmp = y * -0.005
	elif y <= 3.3e-57:
		tmp = x
	else:
		tmp = y * -0.005
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3000000.0)
		tmp = Float64(y * -0.005);
	elseif (y <= 3.3e-57)
		tmp = x;
	else
		tmp = Float64(y * -0.005);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3000000.0)
		tmp = y * -0.005;
	elseif (y <= 3.3e-57)
		tmp = x;
	else
		tmp = y * -0.005;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3000000.0], N[(y * -0.005), $MachinePrecision], If[LessEqual[y, 3.3e-57], x, N[(y * -0.005), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3e6 or 3.2999999999999998e-57 < y

   1. Initial program 100.0%

      \[x - \frac{y}{200} \]

   2. Taylor expanded in x around 0 72.6%

      \[\leadsto \color{blue}{-0.005 \cdot y} \]

   if -3e6 < y < 3.2999999999999998e-57

   1. Initial program 100.0%

      \[x - \frac{y}{200} \]

   2. Taylor expanded in x around inf 83.5%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3000000:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.005\\ \end{array} \]

Alternative 3: 51.8% 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%

   \[x - \frac{y}{200} \]

2. Taylor expanded in x around inf 53.3%

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

3. Final simplification 53.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))