Average Error: 0.1 → 0.1
Time: 2.2s
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 r1395 = 841.0;
        double r1396 = 108.0;
        double r1397 = r1395 / r1396;
        double r1398 = x;
        double r1399 = r1397 * r1398;
        double r1400 = 4.0;
        double r1401 = 29.0;
        double r1402 = r1400 / r1401;
        double r1403 = r1399 + r1402;
        return r1403;
}
↓
double f(double x) {
        double r1404 = 841.0;
        double r1405 = 108.0;
        double r1406 = r1404 / r1405;
        double r1407 = x;
        double r1408 = 4.0;
        double r1409 = 29.0;
        double r1410 = r1408 / r1409;
        double r1411 = fma(r1406, r1407, r1410);
        return r1411;
}

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 2020025 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))