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

Average Error: 0.1 → 0.1

Time: 7.0s

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 r271962 = 841.0;
        double r271963 = 108.0;
        double r271964 = r271962 / r271963;
        double r271965 = x;
        double r271966 = r271964 * r271965;
        double r271967 = 4.0;
        double r271968 = 29.0;
        double r271969 = r271967 / r271968;
        double r271970 = r271966 + r271969;
        return r271970;
}

↓

double f(double x) {
        double r271971 = 841.0;
        double r271972 = 108.0;
        double r271973 = r271971 / r271972;
        double r271974 = x;
        double r271975 = 4.0;
        double r271976 = 29.0;
        double r271977 = r271975 / r271976;
        double r271978 = fma(r271973, r271974, r271977);
        return r271978;
}

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)))