Average Error: 0.1 → 0.1
Time: 4.0s
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 r366760 = 841.0;
        double r366761 = 108.0;
        double r366762 = r366760 / r366761;
        double r366763 = x;
        double r366764 = r366762 * r366763;
        double r366765 = 4.0;
        double r366766 = 29.0;
        double r366767 = r366765 / r366766;
        double r366768 = r366764 + r366767;
        return r366768;
}
↓
double f(double x) {
        double r366769 = 841.0;
        double r366770 = 108.0;
        double r366771 = r366769 / r366770;
        double r366772 = x;
        double r366773 = 4.0;
        double r366774 = 29.0;
        double r366775 = r366773 / r366774;
        double r366776 = fma(r366771, r366772, r366775);
        return r366776;
}

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 2020100 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))