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

Average Error: 0.2 → 0.2

Time: 3.7s

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 r425763 = x;
        double r425764 = 16.0;
        double r425765 = 116.0;
        double r425766 = r425764 / r425765;
        double r425767 = r425763 - r425766;
        double r425768 = 3.0;
        double r425769 = r425767 * r425768;
        double r425770 = y;
        double r425771 = r425769 * r425770;
        return r425771;
}

↓

double f(double x, double y) {
        double r425772 = x;
        double r425773 = 16.0;
        double r425774 = 116.0;
        double r425775 = r425773 / r425774;
        double r425776 = r425772 - r425775;
        double r425777 = 3.0;
        double r425778 = r425776 * r425777;
        double r425779 = y;
        double r425780 = r425778 * r425779;
        return r425780;
}

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 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3) 0.41379310344827586))

  (* (* (- x (/ 16 116)) 3) y))