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

Percentage Accurate: 99.7% → 99.7%

Time: 1.1s

Alternatives: 4

Speedup: 1.0×

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

\[\begin{array}{l} \\ \left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* (- x (/ 16.0 116.0)) 3.0) y))

C

double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x - (16.0d0 / 116.0d0)) * 3.0d0) * y
end function

Java

public static double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

Python

def code(x, y):
	return ((x - (16.0 / 116.0)) * 3.0) * y

Julia

function code(x, y)
	return Float64(Float64(Float64(x - Float64(16.0 / 116.0)) * 3.0) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x - (16.0 / 116.0)) * 3.0) * y;
end

Wolfram

code[x_, y_] := N[(N[(N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] * y), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* (- x (/ 16.0 116.0)) 3.0) y))

C

double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x - (16.0d0 / 116.0d0)) * 3.0d0) * y
end function

Java

public static double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

Python

def code(x, y):
	return ((x - (16.0 / 116.0)) * 3.0) * y

Julia

function code(x, y)
	return Float64(Float64(Float64(x - Float64(16.0 / 116.0)) * 3.0) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x - (16.0 / 116.0)) * 3.0) * y;
end

Wolfram

code[x_, y_] := N[(N[(N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] * y), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (* (- x (/ 16.0 116.0)) 3.0) y))

C

double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x - (16.0d0 / 116.0d0)) * 3.0d0) * y
end function

Java

public static double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

Python

def code(x, y):
	return ((x - (16.0 / 116.0)) * 3.0) * y

Julia

function code(x, y)
	return Float64(Float64(Float64(x - Float64(16.0 / 116.0)) * 3.0) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x - (16.0 / 116.0)) * 3.0) * y;
end

Wolfram

code[x_, y_] := N[(N[(N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] * y), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 5.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{-246}:\\ \;\;\;\;\frac{16}{116}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{16}{116}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 4e-246) (/ 16.0 116.0) (- x (/ 16.0 116.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4e-246) {
		tmp = 16.0 / 116.0;
	} else {
		tmp = x - (16.0 / 116.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 4d-246) then
        tmp = 16.0d0 / 116.0d0
    else
        tmp = x - (16.0d0 / 116.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 4e-246) {
		tmp = 16.0 / 116.0;
	} else {
		tmp = x - (16.0 / 116.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4e-246:
		tmp = 16.0 / 116.0
	else:
		tmp = x - (16.0 / 116.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4e-246)
		tmp = Float64(16.0 / 116.0);
	else
		tmp = Float64(x - Float64(16.0 / 116.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 4e-246)
		tmp = 16.0 / 116.0;
	else
		tmp = x - (16.0 / 116.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4e-246], N[(16.0 / 116.0), $MachinePrecision], N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.99999999999999982e-246

   1. Initial program 99.8%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-12}{29}} \cdot y \]

   5. Applied rewrites 28.6%

      \[\leadsto \color{blue}{\left(x - \frac{16}{116}\right)} \cdot y \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-12}{29} \cdot y + 3 \cdot \left(x \cdot y\right)} \]

   8. Applied rewrites 1.5%

      \[\leadsto \color{blue}{x - \frac{16}{116}} \]

   9. Taylor expanded in x around 0

      \[\leadsto 3 \cdot x - \color{blue}{\frac{12}{29}} \]

   11. Applied rewrites 4.5%

       \[\leadsto \frac{16}{\color{blue}{116}} \]

   if 3.99999999999999982e-246 < y

   1. Initial program 99.0%

      \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-12}{29}} \cdot y \]

   5. Applied rewrites 30.8%

      \[\leadsto \color{blue}{\left(x - \frac{16}{116}\right)} \cdot y \]

   6. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-12}{29} \cdot y + 3 \cdot \left(x \cdot y\right)} \]

   8. Applied rewrites 6.1%

      \[\leadsto \color{blue}{x - \frac{16}{116}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 28.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{16}{116}\right) \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (- x (/ 16.0 116.0)) y))

C

double code(double x, double y) {
	return (x - (16.0 / 116.0)) * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - (16.0d0 / 116.0d0)) * y
end function

Java

public static double code(double x, double y) {
	return (x - (16.0 / 116.0)) * y;
}

Python

def code(x, y):
	return (x - (16.0 / 116.0)) * y

Julia

function code(x, y)
	return Float64(Float64(x - Float64(16.0 / 116.0)) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = (x - (16.0 / 116.0)) * y;
end

Wolfram

code[x_, y_] := N[(N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-12}{29}} \cdot y \]

5. Applied rewrites 29.6%

   \[\leadsto \color{blue}{\left(x - \frac{16}{116}\right)} \cdot y \]
6. Add Preprocessing

Alternative 4: 3.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \frac{16}{116} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ 16.0 116.0))

C

double code(double x, double y) {
	return 16.0 / 116.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 16.0d0 / 116.0d0
end function

Java

public static double code(double x, double y) {
	return 16.0 / 116.0;
}

Python

def code(x, y):
	return 16.0 / 116.0

Julia

function code(x, y)
	return Float64(16.0 / 116.0)
end

MATLAB

function tmp = code(x, y)
	tmp = 16.0 / 116.0;
end

Wolfram

code[x_, y_] := N[(16.0 / 116.0), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-12}{29}} \cdot y \]

5. Applied rewrites 29.6%

   \[\leadsto \color{blue}{\left(x - \frac{16}{116}\right)} \cdot y \]

6. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{-12}{29} \cdot y + 3 \cdot \left(x \cdot y\right)} \]

8. Applied rewrites 3.7%

   \[\leadsto \color{blue}{x - \frac{16}{116}} \]

9. Taylor expanded in x around 0

   \[\leadsto 3 \cdot x - \color{blue}{\frac{12}{29}} \]

11. Applied rewrites 3.4%

    \[\leadsto \frac{16}{\color{blue}{116}} \]
12. Add Preprocessing

Developer Target 1: 99.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(x \cdot 3 - 0.41379310344827586\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* y (- (* x 3.0) 0.41379310344827586)))

C

double code(double x, double y) {
	return y * ((x * 3.0) - 0.41379310344827586);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y * ((x * 3.0d0) - 0.41379310344827586d0)
end function

Java

public static double code(double x, double y) {
	return y * ((x * 3.0) - 0.41379310344827586);
}

Python

def code(x, y):
	return y * ((x * 3.0) - 0.41379310344827586)

Julia

function code(x, y)
	return Float64(y * Float64(Float64(x * 3.0) - 0.41379310344827586))
end

MATLAB

function tmp = code(x, y)
	tmp = y * ((x * 3.0) - 0.41379310344827586);
end

Wolfram

code[x_, y_] := N[(y * N[(N[(x * 3.0), $MachinePrecision] - 0.41379310344827586), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024321 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64
  :pre (TRUE)

  :alt
  (! :herbie-platform default (* y (- (* x 3) 20689655172413793/50000000000000000)))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))