Sure, I added an early return for the twinless case.
I agree the retrieval of twins is a bit awkward; I think the proper fix this would be to move the storage of twinning info into a better data structure that keeps the ordering info as well (OTOH we may not need the asymptotic complexity guarantees of a union-find in practice...).

Edit: done as a separate commit: I switched Grouper so that it handles the ordering.

Did you try playing with it (e.g. plot(); twinx() and move the mouse around) with a ", " separator? I think " / " is more readable, but certainly that's subjective and I can go with whatever separator has the approval of most.

Reducing the "duplicate" work seems not so easy without introducing some layers of caching and cache invalidation, which I'm not particularly keen to do.

I just tested it out and it seemed pretty good performance wise to me.

I would vote for pipe "|" instead of the slant for the separator.

Sure, works for me.

This was discussed during the call today. Looks like the preferred option is Tim's last one ((x, y) = (x1, y1) | (x2, y2)), also changing for the non-twinned case and paying attention to make that also work for the 3d case.
Polar axes don't work too well with this format because they already display theta both in degrees and in radians, but we chose not to worry too much about them as twinned polar axes seem extremely rare.

Meeting consensus: switch everything (regular and twinned) to @timhoffm's last suggestion above.

🤣 Three of us posting notes about the meeting consensus.

I implemented the (x, y) = (..., ...) | (..., ...) output format in the last commit, but it turns out that's quite wide and tends to overflow the toolbar (depending on the exact axes limits); perhaps the reviewers can give it a try.

Here is what it can look like for plt.plot([1, 2]); plt.twinx().plot([4, 3]):

Did a rebase, partially to rerun tests since logs were removed.

Test failures are real, and related to the change at hand.

Ping @anntzer on the above.

Fixed.

Python 3.12 error seems related.

Fixed for real this time? Sorry for the back and forth.

I also figured out that it would be much cleaner for Grouper to keep track of the ordering info in a separate dict rather than sticking everything in _mapping; moved that to a new _ordering dict instead.