Average Error: 0.1 → 0.1
Time: 15.6s
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 r11210310 = 841.0;
        double r11210311 = 108.0;
        double r11210312 = r11210310 / r11210311;
        double r11210313 = x;
        double r11210314 = r11210312 * r11210313;
        double r11210315 = 4.0;
        double r11210316 = 29.0;
        double r11210317 = r11210315 / r11210316;
        double r11210318 = r11210314 + r11210317;
        return r11210318;
}
↓
double f(double x) {
        double r11210319 = 841.0;
        double r11210320 = 108.0;
        double r11210321 = r11210319 / r11210320;
        double r11210322 = x;
        double r11210323 = 4.0;
        double r11210324 = 29.0;
        double r11210325 = r11210323 / r11210324;
        double r11210326 = fma(r11210321, r11210322, r11210325);
        return r11210326;
}

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 2019169 +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)))