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

Percentage Accurate: 100.0% → 100.0%

Time: 2.8s

Alternatives: 4

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	return (x + 16.0) / 116.0

Julia

function code(x)
	return Float64(Float64(x + 16.0) / 116.0)
end

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	return (x + 16.0) / 116.0

Julia

function code(x)
	return Float64(Float64(x + 16.0) / 116.0)
end

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x):
	return (x + 16.0) / 116.0

Julia

function code(x)
	return Float64(Float64(x + 16.0) / 116.0)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x + 16}{116} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 97.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -16 \lor \neg \left(x \leq 16\right):\\ \;\;\;\;\frac{x}{116}\\ \mathbf{else}:\\ \;\;\;\;0.13793103448275862\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -16.0) (not (<= x 16.0))) (/ x 116.0) 0.13793103448275862))

C

double code(double x) {
	double tmp;
	if ((x <= -16.0) || !(x <= 16.0)) {
		tmp = x / 116.0;
	} else {
		tmp = 0.13793103448275862;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-16.0d0)) .or. (.not. (x <= 16.0d0))) then
        tmp = x / 116.0d0
    else
        tmp = 0.13793103448275862d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -16.0) || !(x <= 16.0)) {
		tmp = x / 116.0;
	} else {
		tmp = 0.13793103448275862;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -16.0) or not (x <= 16.0):
		tmp = x / 116.0
	else:
		tmp = 0.13793103448275862
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -16.0) || !(x <= 16.0))
		tmp = Float64(x / 116.0);
	else
		tmp = 0.13793103448275862;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -16.0) || ~((x <= 16.0)))
		tmp = x / 116.0;
	else
		tmp = 0.13793103448275862;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -16.0], N[Not[LessEqual[x, 16.0]], $MachinePrecision]], N[(x / 116.0), $MachinePrecision], 0.13793103448275862]

Derivation

1. Split input into 2 regimes

2. if x < -16 or 16 < x

   1. Initial program 100.0%

      \[\frac{x + 16}{116} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.3%

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

   if -16 < x < 16

   1. Initial program 100.0%

      \[\frac{x + 16}{116} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.4%

      \[\leadsto \color{blue}{0.13793103448275862} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -16 \lor \neg \left(x \leq 16\right):\\ \;\;\;\;\frac{x}{116}\\ \mathbf{else}:\\ \;\;\;\;0.13793103448275862\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -16 \lor \neg \left(x \leq 16\right):\\ \;\;\;\;x \cdot 0.008620689655172414\\ \mathbf{else}:\\ \;\;\;\;0.13793103448275862\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -16.0) (not (<= x 16.0)))
   (* x 0.008620689655172414)
   0.13793103448275862))

C

double code(double x) {
	double tmp;
	if ((x <= -16.0) || !(x <= 16.0)) {
		tmp = x * 0.008620689655172414;
	} else {
		tmp = 0.13793103448275862;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-16.0d0)) .or. (.not. (x <= 16.0d0))) then
        tmp = x * 0.008620689655172414d0
    else
        tmp = 0.13793103448275862d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -16.0) || !(x <= 16.0)) {
		tmp = x * 0.008620689655172414;
	} else {
		tmp = 0.13793103448275862;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -16.0) or not (x <= 16.0):
		tmp = x * 0.008620689655172414
	else:
		tmp = 0.13793103448275862
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -16.0) || !(x <= 16.0))
		tmp = Float64(x * 0.008620689655172414);
	else
		tmp = 0.13793103448275862;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -16.0) || ~((x <= 16.0)))
		tmp = x * 0.008620689655172414;
	else
		tmp = 0.13793103448275862;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -16.0], N[Not[LessEqual[x, 16.0]], $MachinePrecision]], N[(x * 0.008620689655172414), $MachinePrecision], 0.13793103448275862]

Derivation

1. Split input into 2 regimes

2. if x < -16 or 16 < x

   1. Initial program 100.0%

      \[\frac{x + 16}{116} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.2%

      \[\leadsto \color{blue}{0.008620689655172414 \cdot x} \]

   if -16 < x < 16

   1. Initial program 100.0%

      \[\frac{x + 16}{116} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.4%

      \[\leadsto \color{blue}{0.13793103448275862} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -16 \lor \neg \left(x \leq 16\right):\\ \;\;\;\;x \cdot 0.008620689655172414\\ \mathbf{else}:\\ \;\;\;\;0.13793103448275862\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.9% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ 0.13793103448275862 \end{array} \]

FPCore

(FPCore (x) :precision binary64 0.13793103448275862)

C

double code(double x) {
	return 0.13793103448275862;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 0.13793103448275862d0
end function

Java

public static double code(double x) {
	return 0.13793103448275862;
}

Python

def code(x):
	return 0.13793103448275862

Julia

function code(x)
	return 0.13793103448275862
end

MATLAB

function tmp = code(x)
	tmp = 0.13793103448275862;
end

Wolfram

code[x_] := 0.13793103448275862

Derivation

1. Initial program 100.0%

   \[\frac{x + 16}{116} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 52.5%

   \[\leadsto \color{blue}{0.13793103448275862} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024154 
(FPCore (x)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, B"
  :precision binary64
  (/ (+ x 16.0) 116.0))