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 r264439 = 841.0;
        double r264440 = 108.0;
        double r264441 = r264439 / r264440;
        double r264442 = x;
        double r264443 = r264441 * r264442;
        double r264444 = 4.0;
        double r264445 = 29.0;
        double r264446 = r264444 / r264445;
        double r264447 = r264443 + r264446;
        return r264447;
}
↓
double f(double x) {
        double r264448 = 841.0;
        double r264449 = 108.0;
        double r264450 = r264448 / r264449;
        double r264451 = x;
        double r264452 = 4.0;
        double r264453 = 29.0;
        double r264454 = r264452 / r264453;
        double r264455 = fma(r264450, r264451, r264454);
        return r264455;
}

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)))