Average Error: 0.1 → 0.1
Time: 4.6s
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 r235410 = 841.0;
        double r235411 = 108.0;
        double r235412 = r235410 / r235411;
        double r235413 = x;
        double r235414 = r235412 * r235413;
        double r235415 = 4.0;
        double r235416 = 29.0;
        double r235417 = r235415 / r235416;
        double r235418 = r235414 + r235417;
        return r235418;
}
↓
double f(double x) {
        double r235419 = 841.0;
        double r235420 = 108.0;
        double r235421 = r235419 / r235420;
        double r235422 = x;
        double r235423 = 4.0;
        double r235424 = 29.0;
        double r235425 = r235423 / r235424;
        double r235426 = fma(r235421, r235422, r235425);
        return r235426;
}

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 2020034 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))