Average Error: 0.1 → 0.1
Time: 15.0s
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 r17512053 = 841.0;
        double r17512054 = 108.0;
        double r17512055 = r17512053 / r17512054;
        double r17512056 = x;
        double r17512057 = r17512055 * r17512056;
        double r17512058 = 4.0;
        double r17512059 = 29.0;
        double r17512060 = r17512058 / r17512059;
        double r17512061 = r17512057 + r17512060;
        return r17512061;
}
↓
double f(double x) {
        double r17512062 = 841.0;
        double r17512063 = 108.0;
        double r17512064 = r17512062 / r17512063;
        double r17512065 = x;
        double r17512066 = 4.0;
        double r17512067 = 29.0;
        double r17512068 = r17512066 / r17512067;
        double r17512069 = fma(r17512064, r17512065, r17512068);
        return r17512069;
}

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 2019172 +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)))