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

Average Error: 0.2 → 0.2

Time: 12.3s

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 r483632 = x;
        double r483633 = 16.0;
        double r483634 = 116.0;
        double r483635 = r483633 / r483634;
        double r483636 = r483632 - r483635;
        double r483637 = 3.0;
        double r483638 = r483636 * r483637;
        double r483639 = y;
        double r483640 = r483638 * r483639;
        return r483640;
}

↓

double f(double x, double y) {
        double r483641 = x;
        double r483642 = 16.0;
        double r483643 = 116.0;
        double r483644 = r483642 / r483643;
        double r483645 = r483641 - r483644;
        double r483646 = 3.0;
        double r483647 = r483645 * r483646;
        double r483648 = y;
        double r483649 = r483647 * r483648;
        return r483649;
}

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 2019305 +o rules:numerics
(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))