Average Error: 0.1 → 0.1
Time: 14.4s
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 r240283 = 841.0;
        double r240284 = 108.0;
        double r240285 = r240283 / r240284;
        double r240286 = x;
        double r240287 = r240285 * r240286;
        double r240288 = 4.0;
        double r240289 = 29.0;
        double r240290 = r240288 / r240289;
        double r240291 = r240287 + r240290;
        return r240291;
}
↓
double f(double x) {
        double r240292 = 841.0;
        double r240293 = 108.0;
        double r240294 = r240292 / r240293;
        double r240295 = x;
        double r240296 = 4.0;
        double r240297 = 29.0;
        double r240298 = r240296 / r240297;
        double r240299 = fma(r240294, r240295, r240298);
        return r240299;
}

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 2019304 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))