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

Average Error: 0.2 → 0.2

Time: 8.2s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r660281 = x;
        double r660282 = 16.0;
        double r660283 = 116.0;
        double r660284 = r660282 / r660283;
        double r660285 = r660281 - r660284;
        double r660286 = 3.0;
        double r660287 = r660285 * r660286;
        double r660288 = y;
        double r660289 = r660287 * r660288;
        return r660289;
}

↓

double f(double x, double y) {
        double r660290 = x;
        double r660291 = 16.0;
        double r660292 = 116.0;
        double r660293 = r660291 / r660292;
        double r660294 = r660290 - r660293;
        double r660295 = 3.0;
        double r660296 = r660294 * r660295;
        double r660297 = y;
        double r660298 = r660296 * r660297;
        return r660298;
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.2
Target	0.2
Herbie	0.2

\[y \cdot \left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right)\]

Derivation

1. Initial program 0.2

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]
2. Using strategy rm

3. Applied associate-*l* 0.3

   \[\leadsto \color{blue}{\left(x - \frac{16}{116}\right) \cdot \left(3 \cdot y\right)}\]
4. Using strategy rm

5. Applied associate-*r* 0.2

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

6. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019297 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.413793103448275856))

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