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

Average Error: 0.2 → 0.2

Time: 3.1s

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 r798878 = x;
        double r798879 = 16.0;
        double r798880 = 116.0;
        double r798881 = r798879 / r798880;
        double r798882 = r798878 - r798881;
        double r798883 = 3.0;
        double r798884 = r798882 * r798883;
        double r798885 = y;
        double r798886 = r798884 * r798885;
        return r798886;
}

↓

double f(double x, double y) {
        double r798887 = x;
        double r798888 = 16.0;
        double r798889 = 116.0;
        double r798890 = r798888 / r798889;
        double r798891 = r798887 - r798890;
        double r798892 = 3.0;
        double r798893 = r798891 * r798892;
        double r798894 = y;
        double r798895 = r798893 * r798894;
        return r798895;
}

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 2020060 
(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))