Average Error: 0.1 → 0.1
Time: 3.7s
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 r261440 = 841.0;
        double r261441 = 108.0;
        double r261442 = r261440 / r261441;
        double r261443 = x;
        double r261444 = r261442 * r261443;
        double r261445 = 4.0;
        double r261446 = 29.0;
        double r261447 = r261445 / r261446;
        double r261448 = r261444 + r261447;
        return r261448;
}
↓
double f(double x) {
        double r261449 = 841.0;
        double r261450 = 108.0;
        double r261451 = r261449 / r261450;
        double r261452 = x;
        double r261453 = 4.0;
        double r261454 = 29.0;
        double r261455 = r261453 / r261454;
        double r261456 = fma(r261451, r261452, r261455);
        return r261456;
}

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 2020089 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))