Average Error: 0.1 → 0.1
Time: 11.5s
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 r196552 = 841.0;
        double r196553 = 108.0;
        double r196554 = r196552 / r196553;
        double r196555 = x;
        double r196556 = r196554 * r196555;
        double r196557 = 4.0;
        double r196558 = 29.0;
        double r196559 = r196557 / r196558;
        double r196560 = r196556 + r196559;
        return r196560;
}
↓
double f(double x) {
        double r196561 = 841.0;
        double r196562 = 108.0;
        double r196563 = r196561 / r196562;
        double r196564 = x;
        double r196565 = 4.0;
        double r196566 = 29.0;
        double r196567 = r196565 / r196566;
        double r196568 = fma(r196563, r196564, r196567);
        return r196568;
}

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 2019212 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))