Average Error: 0.1 → 0.1
Time: 14.0s
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 r261296 = 841.0;
        double r261297 = 108.0;
        double r261298 = r261296 / r261297;
        double r261299 = x;
        double r261300 = r261298 * r261299;
        double r261301 = 4.0;
        double r261302 = 29.0;
        double r261303 = r261301 / r261302;
        double r261304 = r261300 + r261303;
        return r261304;
}
↓
double f(double x) {
        double r261305 = 841.0;
        double r261306 = 108.0;
        double r261307 = r261305 / r261306;
        double r261308 = x;
        double r261309 = 4.0;
        double r261310 = 29.0;
        double r261311 = r261309 / r261310;
        double r261312 = fma(r261307, r261308, r261311);
        return r261312;
}

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 2019303 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))