Average Error: 0.1 → 0.1
Time: 3.9s
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 r274195 = 841.0;
        double r274196 = 108.0;
        double r274197 = r274195 / r274196;
        double r274198 = x;
        double r274199 = r274197 * r274198;
        double r274200 = 4.0;
        double r274201 = 29.0;
        double r274202 = r274200 / r274201;
        double r274203 = r274199 + r274202;
        return r274203;
}
↓
double f(double x) {
        double r274204 = 841.0;
        double r274205 = 108.0;
        double r274206 = r274204 / r274205;
        double r274207 = x;
        double r274208 = 4.0;
        double r274209 = 29.0;
        double r274210 = r274208 / r274209;
        double r274211 = fma(r274206, r274207, r274210);
        return r274211;
}

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 2020060 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))