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

Average Error: 0.2 → 0.2

Time: 3.5s

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 r822972 = x;
        double r822973 = 16.0;
        double r822974 = 116.0;
        double r822975 = r822973 / r822974;
        double r822976 = r822972 - r822975;
        double r822977 = 3.0;
        double r822978 = r822976 * r822977;
        double r822979 = y;
        double r822980 = r822978 * r822979;
        return r822980;
}

↓

double f(double x, double y) {
        double r822981 = x;
        double r822982 = 16.0;
        double r822983 = 116.0;
        double r822984 = r822982 / r822983;
        double r822985 = r822981 - r822984;
        double r822986 = 3.0;
        double r822987 = r822985 * r822986;
        double r822988 = y;
        double r822989 = r822987 * r822988;
        return r822989;
}

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 2020083 
(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))