Average Error: 0.1 → 0.1
Time: 3.5s
Precision: 64
\[\frac{841}{108} \cdot x + \frac{4}{29}\]
↓
\[\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)\]
\frac{841}{108} \cdot x + \frac{4}{29}
↓
\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)
double f(double x) {
        double r265978 = 841.0;
        double r265979 = 108.0;
        double r265980 = r265978 / r265979;
        double r265981 = x;
        double r265982 = r265980 * r265981;
        double r265983 = 4.0;
        double r265984 = 29.0;
        double r265985 = r265983 / r265984;
        double r265986 = r265982 + r265985;
        return r265986;
}
↓
double f(double x) {
        double r265987 = 841.0;
        double r265988 = 108.0;
        double r265989 = r265987 / r265988;
        double r265990 = x;
        double r265991 = 4.0;
        double r265992 = 29.0;
        double r265993 = r265991 / r265992;
        double r265994 = fma(r265989, r265990, r265993);
        return r265994;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))