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

Average Error: 0.2 → 0.2

Time: 3.1s

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 r2331635 = x;
        double r2331636 = 16.0;
        double r2331637 = 116.0;
        double r2331638 = r2331636 / r2331637;
        double r2331639 = r2331635 - r2331638;
        double r2331640 = 3.0;
        double r2331641 = r2331639 * r2331640;
        double r2331642 = y;
        double r2331643 = r2331641 * r2331642;
        return r2331643;
}

↓

double f(double x, double y) {
        double r2331644 = x;
        double r2331645 = 16.0;
        double r2331646 = 116.0;
        double r2331647 = r2331645 / r2331646;
        double r2331648 = r2331644 - r2331647;
        double r2331649 = 3.0;
        double r2331650 = r2331648 * r2331649;
        double r2331651 = y;
        double r2331652 = r2331650 * r2331651;
        return r2331652;
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.2
Target	0.2
Herbie	0.2

\[y \cdot \left(x \cdot 3 - 0.413793103448275856\right)\]

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 2020018 +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))