Average Error: 0.1 → 0.1
Time: 14.1s
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 r243347 = 841.0;
        double r243348 = 108.0;
        double r243349 = r243347 / r243348;
        double r243350 = x;
        double r243351 = r243349 * r243350;
        double r243352 = 4.0;
        double r243353 = 29.0;
        double r243354 = r243352 / r243353;
        double r243355 = r243351 + r243354;
        return r243355;
}
↓
double f(double x) {
        double r243356 = 841.0;
        double r243357 = 108.0;
        double r243358 = r243356 / r243357;
        double r243359 = x;
        double r243360 = 4.0;
        double r243361 = 29.0;
        double r243362 = r243360 / r243361;
        double r243363 = fma(r243358, r243359, r243362);
        return r243363;
}

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 2019347 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))