Average Error: 0.1 → 0.1
Time: 7.2s
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 r4174432 = 841.0;
        double r4174433 = 108.0;
        double r4174434 = r4174432 / r4174433;
        double r4174435 = x;
        double r4174436 = r4174434 * r4174435;
        double r4174437 = 4.0;
        double r4174438 = 29.0;
        double r4174439 = r4174437 / r4174438;
        double r4174440 = r4174436 + r4174439;
        return r4174440;
}
↓
double f(double x) {
        double r4174441 = 841.0;
        double r4174442 = 108.0;
        double r4174443 = r4174441 / r4174442;
        double r4174444 = x;
        double r4174445 = 4.0;
        double r4174446 = 29.0;
        double r4174447 = r4174445 / r4174446;
        double r4174448 = fma(r4174443, r4174444, r4174447);
        return r4174448;
}

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 2019156 +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)))