Average Error: 0.1 → 0.1
Time: 3.0s
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 r241170 = 841.0;
        double r241171 = 108.0;
        double r241172 = r241170 / r241171;
        double r241173 = x;
        double r241174 = r241172 * r241173;
        double r241175 = 4.0;
        double r241176 = 29.0;
        double r241177 = r241175 / r241176;
        double r241178 = r241174 + r241177;
        return r241178;
}
↓
double f(double x) {
        double r241179 = 841.0;
        double r241180 = 108.0;
        double r241181 = r241179 / r241180;
        double r241182 = x;
        double r241183 = 4.0;
        double r241184 = 29.0;
        double r241185 = r241183 / r241184;
        double r241186 = fma(r241181, r241182, r241185);
        return r241186;
}

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 2019353 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))