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

Average Error: 0.2 → 0.2

Time: 1.7s

Precision: 64

Math

\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]

↓

\[\left(3 \cdot x - 0.413793103448275856\right) \cdot y\]

C

double f(double x, double y) {
        double r978916 = x;
        double r978917 = 16.0;
        double r978918 = 116.0;
        double r978919 = r978917 / r978918;
        double r978920 = r978916 - r978919;
        double r978921 = 3.0;
        double r978922 = r978920 * r978921;
        double r978923 = y;
        double r978924 = r978922 * r978923;
        return r978924;
}

↓

double f(double x, double y) {
        double r978925 = 3.0;
        double r978926 = x;
        double r978927 = r978925 * r978926;
        double r978928 = 0.41379310344827586;
        double r978929 = r978927 - r978928;
        double r978930 = y;
        double r978931 = r978929 * r978930;
        return r978931;
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.2
Target	0.2
Herbie	0.2

\[y \cdot \left(x \cdot 3 - 0.413793103448275856\right)\]

Derivation

1. Initial program 0.2

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]

2. Taylor expanded around 0 0.2

   \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right) - 0.413793103448275856 \cdot y}\]

3. Simplified 0.2

   \[\leadsto \color{blue}{y \cdot \left(3 \cdot x - 0.413793103448275856\right)}\]
4. Using strategy rm

5. Applied *-un-lft-identity 0.2

   \[\leadsto y \cdot \color{blue}{\left(1 \cdot \left(3 \cdot x - 0.413793103448275856\right)\right)}\]

6. Final simplification 0.2

   \[\leadsto \left(3 \cdot x - 0.413793103448275856\right) \cdot y\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.41379310344827586))

  (* (* (- x (/ 16 116)) 3) y))