Average Error: 0.1 → 0.1
Time: 7.6s
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 r179320 = 841.0;
        double r179321 = 108.0;
        double r179322 = r179320 / r179321;
        double r179323 = x;
        double r179324 = r179322 * r179323;
        double r179325 = 4.0;
        double r179326 = 29.0;
        double r179327 = r179325 / r179326;
        double r179328 = r179324 + r179327;
        return r179328;
}
↓
double f(double x) {
        double r179329 = 841.0;
        double r179330 = 108.0;
        double r179331 = r179329 / r179330;
        double r179332 = x;
        double r179333 = 4.0;
        double r179334 = 29.0;
        double r179335 = r179333 / r179334;
        double r179336 = fma(r179331, r179332, r179335);
        return r179336;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.1

    \[\frac{841}{108} \cdot x + \frac{4}{29}\]
  2. Using strategy rm

  3. Applied fma-def0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)}\]

  4. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))