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

Average Error: 0.2 → 0.2

Time: 3.5s

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 r822477 = x;
        double r822478 = 16.0;
        double r822479 = 116.0;
        double r822480 = r822478 / r822479;
        double r822481 = r822477 - r822480;
        double r822482 = 3.0;
        double r822483 = r822481 * r822482;
        double r822484 = y;
        double r822485 = r822483 * r822484;
        return r822485;
}

↓

double f(double x, double y) {
        double r822486 = x;
        double r822487 = 16.0;
        double r822488 = 116.0;
        double r822489 = r822487 / r822488;
        double r822490 = r822486 - r822489;
        double r822491 = 3.0;
        double r822492 = r822490 * r822491;
        double r822493 = y;
        double r822494 = r822492 * r822493;
        return r822494;
}

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 2020003 
(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))