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

Average Error: 0.2 → 0.2

Time: 12.1s

Precision: 64

Math

\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y\]

↓

\[\left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right) \cdot y\]

C

double f(double x, double y) {
        double r43275871 = x;
        double r43275872 = 16.0;
        double r43275873 = 116.0;
        double r43275874 = r43275872 / r43275873;
        double r43275875 = r43275871 - r43275874;
        double r43275876 = 3.0;
        double r43275877 = r43275875 * r43275876;
        double r43275878 = y;
        double r43275879 = r43275877 * r43275878;
        return r43275879;
}

↓

double f(double x, double y) {
        double r43275880 = x;
        double r43275881 = 3.0;
        double r43275882 = r43275880 * r43275881;
        double r43275883 = 0.41379310344827586;
        double r43275884 = r43275882 - r43275883;
        double r43275885 = y;
        double r43275886 = r43275884 * r43275885;
        return r43275886;
}

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. Taylor expanded around 0 0.2

   \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right) - 0.4137931034482758563264326312491903081536 \cdot y}\]

3. Simplified 0.2

   \[\leadsto \color{blue}{y \cdot \left(3 \cdot x - 0.4137931034482758563264326312491903081536\right)}\]

4. Final simplification 0.2

   \[\leadsto \left(x \cdot 3 - 0.4137931034482758563264326312491903081536\right) \cdot y\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))