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

Average Error: 0.2 → 0.2

Time: 13.8s

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 r525186 = x;
        double r525187 = 16.0;
        double r525188 = 116.0;
        double r525189 = r525187 / r525188;
        double r525190 = r525186 - r525189;
        double r525191 = 3.0;
        double r525192 = r525190 * r525191;
        double r525193 = y;
        double r525194 = r525192 * r525193;
        return r525194;
}

↓

double f(double x, double y) {
        double r525195 = x;
        double r525196 = 16.0;
        double r525197 = 116.0;
        double r525198 = r525196 / r525197;
        double r525199 = r525195 - r525198;
        double r525200 = 3.0;
        double r525201 = r525199 * r525200;
        double r525202 = y;
        double r525203 = r525201 * r525202;
        return r525203;
}

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 2019325 +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))