Average Error: 0.1 → 0.1
Time: 13.9s
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 r211400 = 841.0;
        double r211401 = 108.0;
        double r211402 = r211400 / r211401;
        double r211403 = x;
        double r211404 = r211402 * r211403;
        double r211405 = 4.0;
        double r211406 = 29.0;
        double r211407 = r211405 / r211406;
        double r211408 = r211404 + r211407;
        return r211408;
}
↓
double f(double x) {
        double r211409 = 841.0;
        double r211410 = 108.0;
        double r211411 = r211409 / r211410;
        double r211412 = x;
        double r211413 = 4.0;
        double r211414 = 29.0;
        double r211415 = r211413 / r211414;
        double r211416 = fma(r211411, r211412, r211415);
        return r211416;
}

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 2019323 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))