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

Average Error: 0.2 → 0.2

Time: 3.3s

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 r1016224 = x;
        double r1016225 = 16.0;
        double r1016226 = 116.0;
        double r1016227 = r1016225 / r1016226;
        double r1016228 = r1016224 - r1016227;
        double r1016229 = 3.0;
        double r1016230 = r1016228 * r1016229;
        double r1016231 = y;
        double r1016232 = r1016230 * r1016231;
        return r1016232;
}

↓

double f(double x, double y) {
        double r1016233 = x;
        double r1016234 = 16.0;
        double r1016235 = 116.0;
        double r1016236 = r1016234 / r1016235;
        double r1016237 = r1016233 - r1016236;
        double r1016238 = 3.0;
        double r1016239 = r1016237 * r1016238;
        double r1016240 = y;
        double r1016241 = r1016239 * r1016240;
        return r1016241;
}

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 2020060 +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))