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 r242590 = 841.0;
        double r242591 = 108.0;
        double r242592 = r242590 / r242591;
        double r242593 = x;
        double r242594 = r242592 * r242593;
        double r242595 = 4.0;
        double r242596 = 29.0;
        double r242597 = r242595 / r242596;
        double r242598 = r242594 + r242597;
        return r242598;
}
↓
double f(double x) {
        double r242599 = 841.0;
        double r242600 = 108.0;
        double r242601 = r242599 / r242600;
        double r242602 = x;
        double r242603 = 4.0;
        double r242604 = 29.0;
        double r242605 = r242603 / r242604;
        double r242606 = fma(r242601, r242602, r242605);
        return r242606;
}

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 2020021 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))