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

Average Error: 0.2 → 0.2

Time: 6.3s

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 r844900 = x;
        double r844901 = 16.0;
        double r844902 = 116.0;
        double r844903 = r844901 / r844902;
        double r844904 = r844900 - r844903;
        double r844905 = 3.0;
        double r844906 = r844904 * r844905;
        double r844907 = y;
        double r844908 = r844906 * r844907;
        return r844908;
}

↓

double f(double x, double y) {
        double r844909 = x;
        double r844910 = 16.0;
        double r844911 = 116.0;
        double r844912 = r844910 / r844911;
        double r844913 = r844909 - r844912;
        double r844914 = 3.0;
        double r844915 = r844913 * r844914;
        double r844916 = y;
        double r844917 = r844915 * r844916;
        return r844917;
}

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. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(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))