Average Error: 0.1 → 0.1
Time: 3.4s
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 r240801 = 841.0;
        double r240802 = 108.0;
        double r240803 = r240801 / r240802;
        double r240804 = x;
        double r240805 = r240803 * r240804;
        double r240806 = 4.0;
        double r240807 = 29.0;
        double r240808 = r240806 / r240807;
        double r240809 = r240805 + r240808;
        return r240809;
}
↓
double f(double x) {
        double r240810 = 841.0;
        double r240811 = 108.0;
        double r240812 = r240810 / r240811;
        double r240813 = x;
        double r240814 = 4.0;
        double r240815 = 29.0;
        double r240816 = r240814 / r240815;
        double r240817 = fma(r240812, r240813, r240816);
        return r240817;
}

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 2020062 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))