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

Average Error: 0.2 → 0.2

Time: 16.9s

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 r269949237 = x;
        double r269949238 = 16.0;
        double r269949239 = 116.0;
        double r269949240 = r269949238 / r269949239;
        double r269949241 = r269949237 - r269949240;
        double r269949242 = 3.0;
        double r269949243 = r269949241 * r269949242;
        double r269949244 = y;
        double r269949245 = r269949243 * r269949244;
        return r269949245;
}

↓

double f(double x, double y) {
        double r269949246 = x;
        double r269949247 = 16.0;
        double r269949248 = 116.0;
        double r269949249 = r269949247 / r269949248;
        double r269949250 = r269949246 - r269949249;
        double r269949251 = 3.0;
        double r269949252 = r269949250 * r269949251;
        double r269949253 = y;
        double r269949254 = r269949252 * r269949253;
        return r269949254;
}

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 2019173 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))