The work this builds on was discussed here (121 comments):
It's quite interesting to delve into how special functions like `sin` and the like are actually implemented and the lengths people go to to make them "correctly rounded" (see, for example, crlibm). Even something as simple as linear interpolation between two floating point endpoints can be quite subtle if you want an implementation that is exactly correctly rounded and also fast.
This assertion is however wrong. Closed form solutions at worse accumulate rounding errors of a single expression, while iterative solutions not only pile on rounding errors throughout the iterations but they also have to stop by truncating the rest of the solution, leading to results which not only is approximate but also amplifies rounding errors.
Not that meaningful indeed, until, as the abstract states, it outperforms existing series and root-finding solutions by a factor of at least 2. QED. QED.
The link is also on the arxiv page but a bit hidden.