Average Error: 0.1 → 0.1
Time: 12.6s
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 r163650 = 841.0;
        double r163651 = 108.0;
        double r163652 = r163650 / r163651;
        double r163653 = x;
        double r163654 = r163652 * r163653;
        double r163655 = 4.0;
        double r163656 = 29.0;
        double r163657 = r163655 / r163656;
        double r163658 = r163654 + r163657;
        return r163658;
}
↓
double f(double x) {
        double r163659 = 841.0;
        double r163660 = 108.0;
        double r163661 = r163659 / r163660;
        double r163662 = x;
        double r163663 = 4.0;
        double r163664 = 29.0;
        double r163665 = r163663 / r163664;
        double r163666 = fma(r163661, r163662, r163665);
        return r163666;
}

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 2019235 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))