Average Error: 0.1 → 0.1
Time: 14.1s
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 r207290 = 841.0;
        double r207291 = 108.0;
        double r207292 = r207290 / r207291;
        double r207293 = x;
        double r207294 = r207292 * r207293;
        double r207295 = 4.0;
        double r207296 = 29.0;
        double r207297 = r207295 / r207296;
        double r207298 = r207294 + r207297;
        return r207298;
}
↓
double f(double x) {
        double r207299 = 841.0;
        double r207300 = 108.0;
        double r207301 = r207299 / r207300;
        double r207302 = x;
        double r207303 = 4.0;
        double r207304 = 29.0;
        double r207305 = r207303 / r207304;
        double r207306 = fma(r207301, r207302, r207305);
        return r207306;
}

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 2019303 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))