Average Error: 0.1 → 0.1
Time: 13.1s
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 r169841 = 841.0;
        double r169842 = 108.0;
        double r169843 = r169841 / r169842;
        double r169844 = x;
        double r169845 = r169843 * r169844;
        double r169846 = 4.0;
        double r169847 = 29.0;
        double r169848 = r169846 / r169847;
        double r169849 = r169845 + r169848;
        return r169849;
}
↓
double f(double x) {
        double r169850 = 841.0;
        double r169851 = 108.0;
        double r169852 = r169850 / r169851;
        double r169853 = x;
        double r169854 = 4.0;
        double r169855 = 29.0;
        double r169856 = r169854 / r169855;
        double r169857 = fma(r169852, r169853, r169856);
        return r169857;
}

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 2019306 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))