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

Average Error: 0.2 → 0.2

Time: 18.8s

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 r729701 = x;
        double r729702 = 16.0;
        double r729703 = 116.0;
        double r729704 = r729702 / r729703;
        double r729705 = r729701 - r729704;
        double r729706 = 3.0;
        double r729707 = r729705 * r729706;
        double r729708 = y;
        double r729709 = r729707 * r729708;
        return r729709;
}

↓

double f(double x, double y) {
        double r729710 = x;
        double r729711 = 16.0;
        double r729712 = 116.0;
        double r729713 = r729711 / r729712;
        double r729714 = r729710 - r729713;
        double r729715 = 3.0;
        double r729716 = r729714 * r729715;
        double r729717 = y;
        double r729718 = r729716 * r729717;
        return r729718;
}

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 2019303 
(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))