Average Error: 0.1 → 0.1
Time: 3.8s
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 r326563 = 841.0;
        double r326564 = 108.0;
        double r326565 = r326563 / r326564;
        double r326566 = x;
        double r326567 = r326565 * r326566;
        double r326568 = 4.0;
        double r326569 = 29.0;
        double r326570 = r326568 / r326569;
        double r326571 = r326567 + r326570;
        return r326571;
}
↓
double f(double x) {
        double r326572 = 841.0;
        double r326573 = 108.0;
        double r326574 = r326572 / r326573;
        double r326575 = x;
        double r326576 = 4.0;
        double r326577 = 29.0;
        double r326578 = r326576 / r326577;
        double r326579 = fma(r326574, r326575, r326578);
        return r326579;
}

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 2020060 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))