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

Average Error: 0.2 → 0.3

Time: 43.5s

Precision: 64

Math

\[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]

↓

\[3.0 \cdot \left(\left(x - \frac{16.0}{116.0}\right) \cdot y\right)\]

C

double f(double x, double y) {
        double r35812984 = x;
        double r35812985 = 16.0;
        double r35812986 = 116.0;
        double r35812987 = r35812985 / r35812986;
        double r35812988 = r35812984 - r35812987;
        double r35812989 = 3.0;
        double r35812990 = r35812988 * r35812989;
        double r35812991 = y;
        double r35812992 = r35812990 * r35812991;
        return r35812992;
}

↓

double f(double x, double y) {
        double r35812993 = 3.0;
        double r35812994 = x;
        double r35812995 = 16.0;
        double r35812996 = 116.0;
        double r35812997 = r35812995 / r35812996;
        double r35812998 = r35812994 - r35812997;
        double r35812999 = y;
        double r35813000 = r35812998 * r35812999;
        double r35813001 = r35812993 * r35813000;
        return r35813001;
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.2
Target	0.2
Herbie	0.3

\[y \cdot \left(x \cdot 3.0 - 0.41379310344827586\right)\]

Derivation

1. Initial program 0.2

   \[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]
2. Using strategy rm

3. Applied add-sqr-sqrt 1.0

   \[\leadsto \left(\left(x - \frac{16.0}{116.0}\right) \cdot \color{blue}{\left(\sqrt{3.0} \cdot \sqrt{3.0}\right)}\right) \cdot y\]

4. Applied associate-*r* 0.9

   \[\leadsto \color{blue}{\left(\left(\left(x - \frac{16.0}{116.0}\right) \cdot \sqrt{3.0}\right) \cdot \sqrt{3.0}\right)} \cdot y\]
5. Using strategy rm

6. Applied pow1 0.9

   \[\leadsto \left(\left(\left(x - \frac{16.0}{116.0}\right) \cdot \sqrt{3.0}\right) \cdot \sqrt{3.0}\right) \cdot \color{blue}{{y}^{1}}\]

7. Applied pow1 0.9

   \[\leadsto \left(\left(\left(x - \frac{16.0}{116.0}\right) \cdot \sqrt{3.0}\right) \cdot \color{blue}{{\left(\sqrt{3.0}\right)}^{1}}\right) \cdot {y}^{1}\]

8. Applied pow1 0.9

   \[\leadsto \left(\left(\left(x - \frac{16.0}{116.0}\right) \cdot \color{blue}{{\left(\sqrt{3.0}\right)}^{1}}\right) \cdot {\left(\sqrt{3.0}\right)}^{1}\right) \cdot {y}^{1}\]

9. Applied pow1 0.9

   \[\leadsto \left(\left(\color{blue}{{\left(x - \frac{16.0}{116.0}\right)}^{1}} \cdot {\left(\sqrt{3.0}\right)}^{1}\right) \cdot {\left(\sqrt{3.0}\right)}^{1}\right) \cdot {y}^{1}\]

10. Applied pow-prod-down 0.9

    \[\leadsto \left(\color{blue}{{\left(\left(x - \frac{16.0}{116.0}\right) \cdot \sqrt{3.0}\right)}^{1}} \cdot {\left(\sqrt{3.0}\right)}^{1}\right) \cdot {y}^{1}\]

11. Applied pow-prod-down 0.9

    \[\leadsto \color{blue}{{\left(\left(\left(x - \frac{16.0}{116.0}\right) \cdot \sqrt{3.0}\right) \cdot \sqrt{3.0}\right)}^{1}} \cdot {y}^{1}\]

12. Applied pow-prod-down 0.9

    \[\leadsto \color{blue}{{\left(\left(\left(\left(x - \frac{16.0}{116.0}\right) \cdot \sqrt{3.0}\right) \cdot \sqrt{3.0}\right) \cdot y\right)}^{1}}\]

13. Simplified 0.3

    \[\leadsto {\color{blue}{\left(\left(\left(x - \frac{16.0}{116.0}\right) \cdot y\right) \cdot 3.0\right)}}^{1}\]

14. Final simplification 0.3

    \[\leadsto 3.0 \cdot \left(\left(x - \frac{16.0}{116.0}\right) \cdot y\right)\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))