Use rustdoc instead, somehow, so the code only exists in one place

It's getting tedious getting the code and tests working in the main.rs file and then copy-pasting them to the index.html file. I haven't used rustdoc yet, but I know it can execute code examples as tests that the docs are right... I don't know how easy it is to customize the output into this table format, though.

Start by comparing the examples and tests in main.rs with the generated content in index.html. Research rustdoc's executable documentation examples and whether its output can support the existing table format. Done means the code and tests have one source of truth without losing the current index.html presentation.

Written by the indexing model from the issue text.