Average Error: 0.1 → 0.1
Time: 3.9s
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 r248103 = 841.0;
        double r248104 = 108.0;
        double r248105 = r248103 / r248104;
        double r248106 = x;
        double r248107 = r248105 * r248106;
        double r248108 = 4.0;
        double r248109 = 29.0;
        double r248110 = r248108 / r248109;
        double r248111 = r248107 + r248110;
        return r248111;
}
↓
double f(double x) {
        double r248112 = 841.0;
        double r248113 = 108.0;
        double r248114 = r248112 / r248113;
        double r248115 = x;
        double r248116 = 4.0;
        double r248117 = 29.0;
        double r248118 = r248116 / r248117;
        double r248119 = fma(r248114, r248115, r248118);
        return r248119;
}

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 2020057 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))