Average Error: 0.1 → 0.1
Time: 11.3s
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 r184283 = 841.0;
        double r184284 = 108.0;
        double r184285 = r184283 / r184284;
        double r184286 = x;
        double r184287 = r184285 * r184286;
        double r184288 = 4.0;
        double r184289 = 29.0;
        double r184290 = r184288 / r184289;
        double r184291 = r184287 + r184290;
        return r184291;
}
↓
double f(double x) {
        double r184292 = 841.0;
        double r184293 = 108.0;
        double r184294 = r184292 / r184293;
        double r184295 = x;
        double r184296 = 4.0;
        double r184297 = 29.0;
        double r184298 = r184296 / r184297;
        double r184299 = fma(r184294, r184295, r184298);
        return r184299;
}

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 2019208 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))