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

Average Error: 0.2 → 0.2

Time: 3.7s

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 r880055 = x;
        double r880056 = 16.0;
        double r880057 = 116.0;
        double r880058 = r880056 / r880057;
        double r880059 = r880055 - r880058;
        double r880060 = 3.0;
        double r880061 = r880059 * r880060;
        double r880062 = y;
        double r880063 = r880061 * r880062;
        return r880063;
}

↓

double f(double x, double y) {
        double r880064 = x;
        double r880065 = 16.0;
        double r880066 = 116.0;
        double r880067 = r880065 / r880066;
        double r880068 = r880064 - r880067;
        double r880069 = 3.0;
        double r880070 = r880068 * r880069;
        double r880071 = y;
        double r880072 = r880070 * r880071;
        return r880072;
}

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 2020036 
(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))