Average Error: 0.1 → 0.1
Time: 12.6s
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 r176462 = 841.0;
        double r176463 = 108.0;
        double r176464 = r176462 / r176463;
        double r176465 = x;
        double r176466 = r176464 * r176465;
        double r176467 = 4.0;
        double r176468 = 29.0;
        double r176469 = r176467 / r176468;
        double r176470 = r176466 + r176469;
        return r176470;
}
↓
double f(double x) {
        double r176471 = 841.0;
        double r176472 = 108.0;
        double r176473 = r176471 / r176472;
        double r176474 = x;
        double r176475 = 4.0;
        double r176476 = 29.0;
        double r176477 = r176475 / r176476;
        double r176478 = fma(r176473, r176474, r176477);
        return r176478;
}

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)))