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

Average Accuracy: 100.0% → 100.0%

Time: 2.3s

Precision: binary64

Cost: 320

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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 (x + 16.0) / 116.0;
}

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 100.0%

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

2. Applied egg-rr 100.0%

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

   [Start] 100.0	\[ \frac{x + 16}{116} \]
   frac-2neg [=>] 100.0	\[ \color{blue}{\frac{-\left(x + 16\right)}{-116}} \]
   distribute-frac-neg [=>] 100.0	\[ \color{blue}{-\frac{x + 16}{-116}} \]
   metadata-eval [=>] 100.0	\[ -\frac{x + 16}{\color{blue}{-116}} \]

3. Simplified 100.0%

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

   [Start] 100.0	\[ -\frac{x + 16}{-116} \]
   distribute-neg-frac [=>] 100.0	\[ \color{blue}{\frac{-\left(x + 16\right)}{-116}} \]
   distribute-neg-in [=>] 100.0	\[ \frac{\color{blue}{\left(-x\right) + \left(-16\right)}}{-116} \]
   metadata-eval [=>] 100.0	\[ \frac{\left(-x\right) + \color{blue}{-16}}{-116} \]
   +-commutative [<=] 100.0	\[ \frac{\color{blue}{-16 + \left(-x\right)}}{-116} \]
   unsub-neg [=>] 100.0	\[ \frac{\color{blue}{-16 - x}}{-116} \]
   div-sub [=>] 100.0	\[ \color{blue}{\frac{-16}{-116} - \frac{x}{-116}} \]
   metadata-eval [=>] 100.0	\[ \color{blue}{0.13793103448275862} - \frac{x}{-116} \]

4. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	97.9%
Cost	456

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

Alternative 2
Accuracy	50.4%
Cost	64

\[0.13793103448275862 \]

Reproduce

herbie shell --seed 2023160 
(FPCore (x)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, B"
  :precision binary64
  (/ (+ x 16.0) 116.0))