Average Error: 0.1 → 0.1
Time: 15.5s
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 r13237440 = 841.0;
        double r13237441 = 108.0;
        double r13237442 = r13237440 / r13237441;
        double r13237443 = x;
        double r13237444 = r13237442 * r13237443;
        double r13237445 = 4.0;
        double r13237446 = 29.0;
        double r13237447 = r13237445 / r13237446;
        double r13237448 = r13237444 + r13237447;
        return r13237448;
}
↓
double f(double x) {
        double r13237449 = 841.0;
        double r13237450 = 108.0;
        double r13237451 = r13237449 / r13237450;
        double r13237452 = x;
        double r13237453 = 4.0;
        double r13237454 = 29.0;
        double r13237455 = r13237453 / r13237454;
        double r13237456 = fma(r13237451, r13237452, r13237455);
        return r13237456;
}

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 2019170 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))