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

Average Error: 0.2 → 0.2

Time: 3.8s

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 r872405 = x;
        double r872406 = 16.0;
        double r872407 = 116.0;
        double r872408 = r872406 / r872407;
        double r872409 = r872405 - r872408;
        double r872410 = 3.0;
        double r872411 = r872409 * r872410;
        double r872412 = y;
        double r872413 = r872411 * r872412;
        return r872413;
}

↓

double f(double x, double y) {
        double r872414 = x;
        double r872415 = 16.0;
        double r872416 = 116.0;
        double r872417 = r872415 / r872416;
        double r872418 = r872414 - r872417;
        double r872419 = 3.0;
        double r872420 = r872418 * r872419;
        double r872421 = y;
        double r872422 = r872420 * r872421;
        return r872422;
}

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 2020056 +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))