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

Average Error: 0.2 → 0.2

Time: 10.2s

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 r602968 = x;
        double r602969 = 16.0;
        double r602970 = 116.0;
        double r602971 = r602969 / r602970;
        double r602972 = r602968 - r602971;
        double r602973 = 3.0;
        double r602974 = r602972 * r602973;
        double r602975 = y;
        double r602976 = r602974 * r602975;
        return r602976;
}

↓

double f(double x, double y) {
        double r602977 = x;
        double r602978 = 16.0;
        double r602979 = 116.0;
        double r602980 = r602978 / r602979;
        double r602981 = r602977 - r602980;
        double r602982 = 3.0;
        double r602983 = r602981 * r602982;
        double r602984 = y;
        double r602985 = r602983 * r602984;
        return r602985;
}

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 2019209 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.413793103448275856))

  (* (* (- x (/ 16 116)) 3) y))