Average Error: 0.1 → 0.1
Time: 11.0s
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 r232309 = 841.0;
        double r232310 = 108.0;
        double r232311 = r232309 / r232310;
        double r232312 = x;
        double r232313 = r232311 * r232312;
        double r232314 = 4.0;
        double r232315 = 29.0;
        double r232316 = r232314 / r232315;
        double r232317 = r232313 + r232316;
        return r232317;
}
↓
double f(double x) {
        double r232318 = 841.0;
        double r232319 = 108.0;
        double r232320 = r232318 / r232319;
        double r232321 = x;
        double r232322 = 4.0;
        double r232323 = 29.0;
        double r232324 = r232322 / r232323;
        double r232325 = fma(r232320, r232321, r232324);
        return r232325;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.1

    \[\frac{841}{108} \cdot x + \frac{4}{29}\]
  2. Using strategy rm

  3. Applied fma-def0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)}\]

  4. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)\]

Reproduce

herbie shell --seed 2019196 +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)))