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

Average Error: 0.2 → 0.2

Time: 4.8s

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 r751542 = x;
        double r751543 = 16.0;
        double r751544 = 116.0;
        double r751545 = r751543 / r751544;
        double r751546 = r751542 - r751545;
        double r751547 = 3.0;
        double r751548 = r751546 * r751547;
        double r751549 = y;
        double r751550 = r751548 * r751549;
        return r751550;
}

↓

double f(double x, double y) {
        double r751551 = x;
        double r751552 = 16.0;
        double r751553 = 116.0;
        double r751554 = r751552 / r751553;
        double r751555 = r751551 - r751554;
        double r751556 = 3.0;
        double r751557 = r751555 * r751556;
        double r751558 = y;
        double r751559 = r751557 * r751558;
        return r751559;
}

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 2019304 
(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))