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 r1016756 = x;
        double r1016757 = 16.0;
        double r1016758 = 116.0;
        double r1016759 = r1016757 / r1016758;
        double r1016760 = r1016756 - r1016759;
        double r1016761 = 3.0;
        double r1016762 = r1016760 * r1016761;
        double r1016763 = y;
        double r1016764 = r1016762 * r1016763;
        return r1016764;
}

↓

double f(double x, double y) {
        double r1016765 = x;
        double r1016766 = 16.0;
        double r1016767 = 116.0;
        double r1016768 = r1016766 / r1016767;
        double r1016769 = r1016765 - r1016768;
        double r1016770 = 3.0;
        double r1016771 = r1016769 * r1016770;
        double r1016772 = y;
        double r1016773 = r1016771 * r1016772;
        return r1016773;
}

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 2019362 
(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))