Average Error: 0.1 → 0.1
Time: 1.3s
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 r208907 = 841.0;
        double r208908 = 108.0;
        double r208909 = r208907 / r208908;
        double r208910 = x;
        double r208911 = r208909 * r208910;
        double r208912 = 4.0;
        double r208913 = 29.0;
        double r208914 = r208912 / r208913;
        double r208915 = r208911 + r208914;
        return r208915;
}
↓
double f(double x) {
        double r208916 = 841.0;
        double r208917 = 108.0;
        double r208918 = r208916 / r208917;
        double r208919 = x;
        double r208920 = 4.0;
        double r208921 = 29.0;
        double r208922 = r208920 / r208921;
        double r208923 = fma(r208918, r208919, r208922);
        return r208923;
}

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 2020002 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))