There is no API behind this calculator. The parser, the differentiator, the simplifier, the LaTeX writer and the plotter are all JavaScript that runs on your machine.
What that buys
Your expressions stay on your device — there is nothing to log because nothing is transmitted. Results appear as fast as your machine can compute them, with no round trip. And once the page has loaded, it keeps working without a connection.
What it costs
The whole engine has to be small enough to ship to a browser, which rules out leaning on a large computer-algebra library. Writing the algebra from scratch was more work up front, and it is the reason the engine can name the rule at every node — a general-purpose library would not.
The two exceptions
Fonts come from Google Fonts and the maths typesetting from cdnjs. Both are ordinary CDN requests with no identifiers attached by us, and everything else is local.