Average Error: 0.1 → 0.1
Time: 13.3s
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 r201463 = 841.0;
        double r201464 = 108.0;
        double r201465 = r201463 / r201464;
        double r201466 = x;
        double r201467 = r201465 * r201466;
        double r201468 = 4.0;
        double r201469 = 29.0;
        double r201470 = r201468 / r201469;
        double r201471 = r201467 + r201470;
        return r201471;
}
↓
double f(double x) {
        double r201472 = 841.0;
        double r201473 = 108.0;
        double r201474 = r201472 / r201473;
        double r201475 = x;
        double r201476 = 4.0;
        double r201477 = 29.0;
        double r201478 = r201476 / r201477;
        double r201479 = fma(r201474, r201475, r201478);
        return r201479;
}

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 2019325 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))