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

Average Error: 0.1 → 0.1

Time: 5.7s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\frac{841}{108} \cdot x + \frac{4}{29}\]

↓

\[\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)\]

C

double f(double x) {
        double r265037 = 841.0;
        double r265038 = 108.0;
        double r265039 = r265037 / r265038;
        double r265040 = x;
        double r265041 = r265039 * r265040;
        double r265042 = 4.0;
        double r265043 = 29.0;
        double r265044 = r265042 / r265043;
        double r265045 = r265041 + r265044;
        return r265045;
}

↓

double f(double x) {
        double r265046 = 841.0;
        double r265047 = 108.0;
        double r265048 = r265046 / r265047;
        double r265049 = x;
        double r265050 = 4.0;
        double r265051 = 29.0;
        double r265052 = r265050 / r265051;
        double r265053 = fma(r265048, r265049, r265052);
        return r265053;
}

Error

Bits error versus x

Derivation

1. Initial program 0.1

   \[\frac{841}{108} \cdot x + \frac{4}{29}\]

2. Simplified 0.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)}\]

3. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)\]

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))