Average Error: 0.1 → 0.1
Time: 4.1s
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 r319002 = 841.0;
        double r319003 = 108.0;
        double r319004 = r319002 / r319003;
        double r319005 = x;
        double r319006 = r319004 * r319005;
        double r319007 = 4.0;
        double r319008 = 29.0;
        double r319009 = r319007 / r319008;
        double r319010 = r319006 + r319009;
        return r319010;
}
↓
double f(double x) {
        double r319011 = 841.0;
        double r319012 = 108.0;
        double r319013 = r319011 / r319012;
        double r319014 = x;
        double r319015 = 4.0;
        double r319016 = 29.0;
        double r319017 = r319015 / r319016;
        double r319018 = fma(r319013, r319014, r319017);
        return r319018;
}

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 2019362 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))