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 r208969 = 841.0;
        double r208970 = 108.0;
        double r208971 = r208969 / r208970;
        double r208972 = x;
        double r208973 = r208971 * r208972;
        double r208974 = 4.0;
        double r208975 = 29.0;
        double r208976 = r208974 / r208975;
        double r208977 = r208973 + r208976;
        return r208977;
}
↓
double f(double x) {
        double r208978 = 841.0;
        double r208979 = 108.0;
        double r208980 = r208978 / r208979;
        double r208981 = x;
        double r208982 = 4.0;
        double r208983 = 29.0;
        double r208984 = r208982 / r208983;
        double r208985 = fma(r208980, r208981, r208984);
        return r208985;
}

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 2020047 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))