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

Percentage Accurate: 100.0% → 100.0%

Time: 1.5s

Alternatives: 5

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. Final simplification 100.0%

   \[\leadsto \frac{x + 16}{116} \]

Alternative 2: 97.8% accurate, 0.6× 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(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. Taylor expanded in x around inf 96.8%

      \[\leadsto \color{blue}{0.008620689655172414 \cdot x} \]
   3. Step-by-step derivation

      1. *-commutative 96.8%

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

      2. metadata-eval 96.8%

         \[\leadsto x \cdot \color{blue}{\left(--0.008620689655172414\right)} \]

      3. metadata-eval 96.8%

         \[\leadsto x \cdot \left(-\color{blue}{\frac{1}{-116}}\right) \]

      4. distribute-rgt-neg-in 96.8%

         \[\leadsto \color{blue}{-x \cdot \frac{1}{-116}} \]

      5. div-inv 96.8%

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

      6. distribute-neg-frac 96.8%

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

   4. Applied egg-rr 96.8%

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

   if -16 < x < 16

   1. Initial program 100.0%

      \[\frac{x + 16}{116} \]

   2. Taylor expanded in x around 0 97.2%

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

4. Final simplification 97.0%

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

Alternative 3: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -16:\\ \;\;\;\;x \cdot 0.008620689655172414\\ \mathbf{elif}\;x \leq 16:\\ \;\;\;\;0.13793103448275862\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.008620689655172414\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -16.0)
   (* x 0.008620689655172414)
   (if (<= x 16.0) 0.13793103448275862 (* x 0.008620689655172414))))

C

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

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-16.0d0)) then
        tmp = x * 0.008620689655172414d0
    else if (x <= 16.0d0) then
        tmp = 0.13793103448275862d0
    else
        tmp = x * 0.008620689655172414d0
    end if
    code = tmp
end function

Java

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

Python

def code(x):
	tmp = 0
	if x <= -16.0:
		tmp = x * 0.008620689655172414
	elif x <= 16.0:
		tmp = 0.13793103448275862
	else:
		tmp = x * 0.008620689655172414
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_] := If[LessEqual[x, -16.0], N[(x * 0.008620689655172414), $MachinePrecision], If[LessEqual[x, 16.0], 0.13793103448275862, N[(x * 0.008620689655172414), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -16 or 16 < x

   1. Initial program 100.0%

      \[\frac{x + 16}{116} \]

   2. Taylor expanded in x around inf 96.8%

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

   if -16 < x < 16

   1. Initial program 100.0%

      \[\frac{x + 16}{116} \]

   2. Taylor expanded in x around 0 97.2%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -16:\\ \;\;\;\;x \cdot 0.008620689655172414\\ \mathbf{elif}\;x \leq 16:\\ \;\;\;\;0.13793103448275862\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.008620689655172414\\ \end{array} \]

Alternative 4: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.13793103448275862 - \frac{x}{-116} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- 0.13793103448275862 (/ x -116.0)))

C

double code(double x) {
	return 0.13793103448275862 - (x / -116.0);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 0.13793103448275862d0 - (x / (-116.0d0))
end function

Java

public static double code(double x) {
	return 0.13793103448275862 - (x / -116.0);
}

Python

def code(x):
	return 0.13793103448275862 - (x / -116.0)

Julia

function code(x)
	return Float64(0.13793103448275862 - Float64(x / -116.0))
end

MATLAB

function tmp = code(x)
	tmp = 0.13793103448275862 - (x / -116.0);
end

Wolfram

code[x_] := N[(0.13793103448275862 - N[(x / -116.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x + 16}{116} \]
2. Step-by-step derivation

   1. frac-2neg 100.0%

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

   2. distribute-frac-neg 100.0%

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

   3. metadata-eval 100.0%

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

3. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{-\frac{x + 16}{-116}} \]
4. Step-by-step derivation

   1. distribute-neg-frac 100.0%

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

   2. distribute-neg-in 100.0%

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

   3. metadata-eval 100.0%

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

   4. +-commutative 100.0%

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

   5. unsub-neg 100.0%

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

   6. div-sub 100.0%

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

   7. metadata-eval 100.0%

      \[\leadsto \color{blue}{0.13793103448275862} - \frac{x}{-116} \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{0.13793103448275862 - \frac{x}{-116}} \]

6. Final simplification 100.0%

   \[\leadsto 0.13793103448275862 - \frac{x}{-116} \]

Alternative 5: 51.4% 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. Taylor expanded in x around 0 50.1%

   \[\leadsto \color{blue}{0.13793103448275862} \]

3. Final simplification 50.1%

   \[\leadsto 0.13793103448275862 \]

Reproduce

herbie shell --seed 2023196 
(FPCore (x)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, B"
  :precision binary64
  (/ (+ x 16.0) 116.0))