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

Average Error: 0.1 → 0.1

Time: 3.0s

Precision: binary64

Math

\[\frac{841}{108} \cdot x + \frac{4}{29} \]

↓

\[\mathsf{fma}\left(7.787037037037037, x, 0.13793103448275862\right) \]

FPCore

(FPCore (x) :precision binary64 (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))

↓

(FPCore (x) :precision binary64 (fma 7.787037037037037 x 0.13793103448275862))

C

double code(double x) {
	return ((841.0 / 108.0) * x) + (4.0 / 29.0);
}

↓

double code(double x) {
	return fma(7.787037037037037, x, 0.13793103448275862);
}

Error

Bits error versus x

Derivation

1. Initial program 0.1

   \[\frac{841}{108} \cdot x + \frac{4}{29} \]

2. Simplified 0.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(7.787037037037037, x, 0.13793103448275862\right)} \]

3. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(7.787037037037037, x, 0.13793103448275862\right) \]

Reproduce

herbie shell --seed 2022067 
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))