Average Error: 0.1 → 0.1
Time: 13.4s
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 r162699 = 841.0;
        double r162700 = 108.0;
        double r162701 = r162699 / r162700;
        double r162702 = x;
        double r162703 = r162701 * r162702;
        double r162704 = 4.0;
        double r162705 = 29.0;
        double r162706 = r162704 / r162705;
        double r162707 = r162703 + r162706;
        return r162707;
}
↓
double f(double x) {
        double r162708 = 841.0;
        double r162709 = 108.0;
        double r162710 = r162708 / r162709;
        double r162711 = x;
        double r162712 = 4.0;
        double r162713 = 29.0;
        double r162714 = r162712 / r162713;
        double r162715 = fma(r162710, r162711, r162714);
        return r162715;
}

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 2019322 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))