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

Average Error: 0.2 → 0.2

Time: 3.0s

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 r967237 = x;
        double r967238 = 16.0;
        double r967239 = 116.0;
        double r967240 = r967238 / r967239;
        double r967241 = r967237 - r967240;
        double r967242 = 3.0;
        double r967243 = r967241 * r967242;
        double r967244 = y;
        double r967245 = r967243 * r967244;
        return r967245;
}

↓

double f(double x, double y) {
        double r967246 = x;
        double r967247 = 16.0;
        double r967248 = 116.0;
        double r967249 = r967247 / r967248;
        double r967250 = r967246 - r967249;
        double r967251 = 3.0;
        double r967252 = r967250 * r967251;
        double r967253 = y;
        double r967254 = r967252 * r967253;
        return r967254;
}

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 2020035 
(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))