compare performance MathJax vs MathQuill vs Katex

So the questions is, is MathQuill async?

Based on the MathQuill source, it renders elements on document ready, synchronously, but it can also render elements on the fly, through the .mathquill() API. Technically though, you could call the method yourself and do it asynchronously.

And is this is good performance test?

I can't really speak to the usefulness of the test because it's unclear what you're trying to do, but I can provide you with some general background on the issue.

MathQuill's main strength is the ability to render math on the fly, with pretty, user-friendly textboxes. They themselves admit that it's not a good option for rendering static math, due to it's limited LaTeX support.

KaTeX, according to most benchmarks I've seen, is faster than MathJax, by a long shot. However, it has somewhat incomplete support for LaTeX, so that may be an issue.

MathJax is pretty slow, relative to the others, but it has almost complete support for LaTeX. If that's the price you're willing to pay, then go for it.

In short, choose MathQuill for editing, KaTeX for speed, for MathJax for comprehensiveness.

And is there maybe a better formula renderer?

These three are the only ones I've heard of. Based on a previous question, the only other option is jsMath, MathJax's predecessor. It's from 2004, so there's no reason that you should use it.

You can use mathlive for both editing and static TeX content.