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

Average Error: 0.2 → 0.2

Time: 2.7s

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 r1038841 = x;
        double r1038842 = 16.0;
        double r1038843 = 116.0;
        double r1038844 = r1038842 / r1038843;
        double r1038845 = r1038841 - r1038844;
        double r1038846 = 3.0;
        double r1038847 = r1038845 * r1038846;
        double r1038848 = y;
        double r1038849 = r1038847 * r1038848;
        return r1038849;
}

↓

double f(double x, double y) {
        double r1038850 = x;
        double r1038851 = 16.0;
        double r1038852 = 116.0;
        double r1038853 = r1038851 / r1038852;
        double r1038854 = r1038850 - r1038853;
        double r1038855 = 3.0;
        double r1038856 = r1038854 * r1038855;
        double r1038857 = y;
        double r1038858 = r1038856 * r1038857;
        return r1038858;
}

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. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020056 
(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))