Accuracy of Sun and Moon Calculations

[infinite-happiness]

Hi!
I'm using the functions Astronomy.SearchMoonPhase, Astronomy.SearchAltitude('Sun',...) and Astronomy.SearchRiseSet('Sun',...), and I'm wondering about the precision of Astronomy Engine and if there are other easily available javascript tools that have better precision for calculating moon phase and sunrise/dawn. I do not want to use an API or online service, but rather something based on math or something that can be saved in the project and used offline.

I have been trying to understand the precision of Astronomy Engine, regarding the sun and the moon, reading about VSOP87 and NOVAS C 3.1, and asking AI. It is difficult to get an understanding with my limited knowledge.

I understand that "Real-world refraction varies based on air temperature, pressure, and humidity; such weather-based conditions are outside the scope of Astronomy Engine.", and I'm not looking for more accuracy in such everyday fluctuations, since I do not want to depend on equipment that measures those things,

So I would like a statement, an understanding of how accurate Astronomy Engine is for these calculations, and if I find another library, how much more accurate it is.

For example, a very good statement for accuracy that I'm looking for is 'VSOP87 guarantees for Mercury, Venus, the Earth-Moon barycenter and Mars a precision of 1" for 4000 years before and after the 2000 epoch'. But I suppose this does not apply to the functions I'm using?

Thank you in advance!