Average Error: 0.1 → 0.1
Time: 30.9s
Precision: 64
\[\frac{841.0}{108.0} \cdot x + \frac{4.0}{29.0}\]
↓
\[\mathsf{fma}\left(\frac{841.0}{108.0}, x, \frac{4.0}{29.0}\right)\]
\frac{841.0}{108.0} \cdot x + \frac{4.0}{29.0}
↓
\mathsf{fma}\left(\frac{841.0}{108.0}, x, \frac{4.0}{29.0}\right)
double f(double x) {
        double r14180741 = 841.0;
        double r14180742 = 108.0;
        double r14180743 = r14180741 / r14180742;
        double r14180744 = x;
        double r14180745 = r14180743 * r14180744;
        double r14180746 = 4.0;
        double r14180747 = 29.0;
        double r14180748 = r14180746 / r14180747;
        double r14180749 = r14180745 + r14180748;
        return r14180749;
}
↓
double f(double x) {
        double r14180750 = 841.0;
        double r14180751 = 108.0;
        double r14180752 = r14180750 / r14180751;
        double r14180753 = x;
        double r14180754 = 4.0;
        double r14180755 = 29.0;
        double r14180756 = r14180754 / r14180755;
        double r14180757 = fma(r14180752, r14180753, r14180756);
        return r14180757;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.1

    \[\frac{841.0}{108.0} \cdot x + \frac{4.0}{29.0}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{841.0}{108.0}, x, \frac{4.0}{29.0}\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\frac{841.0}{108.0}, x, \frac{4.0}{29.0}\right)\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))