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

Average Error: 0.01% → 0.01%

Time: 1.4s

Precision: binary64

Cost: 320

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

↓

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;
}

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.01

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

2. Final simplification 0.01

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

Alternatives

Alternative 1
Error	2.18%
Cost	457

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

Alternative 2
Error	48.98%
Cost	64

\[0.13793103448275862 \]

Reproduce

herbie shell --seed 2023089 
(FPCore (x)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, B"
  :precision binary64
  (/ (+ x 16.0) 116.0))