Average Error: 0.1 → 0.1
Time: 3.2s
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 r242860 = 841.0;
        double r242861 = 108.0;
        double r242862 = r242860 / r242861;
        double r242863 = x;
        double r242864 = r242862 * r242863;
        double r242865 = 4.0;
        double r242866 = 29.0;
        double r242867 = r242865 / r242866;
        double r242868 = r242864 + r242867;
        return r242868;
}
↓
double f(double x) {
        double r242869 = 841.0;
        double r242870 = 108.0;
        double r242871 = r242869 / r242870;
        double r242872 = x;
        double r242873 = 4.0;
        double r242874 = 29.0;
        double r242875 = r242873 / r242874;
        double r242876 = fma(r242871, r242872, r242875);
        return r242876;
}

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 2020065 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))