Average Error: 0.1 → 0.1
Time: 15.9s
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 r175042 = 841.0;
        double r175043 = 108.0;
        double r175044 = r175042 / r175043;
        double r175045 = x;
        double r175046 = r175044 * r175045;
        double r175047 = 4.0;
        double r175048 = 29.0;
        double r175049 = r175047 / r175048;
        double r175050 = r175046 + r175049;
        return r175050;
}
↓
double f(double x) {
        double r175051 = 841.0;
        double r175052 = 108.0;
        double r175053 = r175051 / r175052;
        double r175054 = x;
        double r175055 = 4.0;
        double r175056 = 29.0;
        double r175057 = r175055 / r175056;
        double r175058 = fma(r175053, r175054, r175057);
        return r175058;
}

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 2019323 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))