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: 74.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-7}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.005\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7e-7) (* y -0.005) (if (<= y 8.5e-7) x (* y -0.005))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7e-7) {
		tmp = y * -0.005;
	} else if (y <= 8.5e-7) {
		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 <= (-7d-7)) then
        tmp = y * (-0.005d0)
    else if (y <= 8.5d-7) 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 <= -7e-7) {
		tmp = y * -0.005;
	} else if (y <= 8.5e-7) {
		tmp = x;
	} else {
		tmp = y * -0.005;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7e-7:
		tmp = y * -0.005
	elif y <= 8.5e-7:
		tmp = x
	else:
		tmp = y * -0.005
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7e-7)
		tmp = Float64(y * -0.005);
	elseif (y <= 8.5e-7)
		tmp = x;
	else
		tmp = Float64(y * -0.005);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -7e-7)
		tmp = y * -0.005;
	elseif (y <= 8.5e-7)
		tmp = x;
	else
		tmp = y * -0.005;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7e-7], N[(y * -0.005), $MachinePrecision], If[LessEqual[y, 8.5e-7], x, N[(y * -0.005), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.99999999999999968e-7 or 8.50000000000000014e-7 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.1%

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

   if -6.99999999999999968e-7 < y < 8.50000000000000014e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.0%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-7}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.005\\ \end{array} \]

Alternative 3: 50.8% 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 52.9%

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

3. Final simplification 52.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023238 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))