Average Error: 0.1 → 0.1
Time: 10.4s
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 r171635 = 841.0;
        double r171636 = 108.0;
        double r171637 = r171635 / r171636;
        double r171638 = x;
        double r171639 = r171637 * r171638;
        double r171640 = 4.0;
        double r171641 = 29.0;
        double r171642 = r171640 / r171641;
        double r171643 = r171639 + r171642;
        return r171643;
}
↓
double f(double x) {
        double r171644 = 841.0;
        double r171645 = 108.0;
        double r171646 = r171644 / r171645;
        double r171647 = x;
        double r171648 = 4.0;
        double r171649 = 29.0;
        double r171650 = r171648 / r171649;
        double r171651 = fma(r171646, r171647, r171650);
        return r171651;
}

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 2019305 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))