Is there an algorithm for solar eclipse duration?

[StephenG1CMZ]

Thanks for the many interesting suggestions.

It seems like the Elements... book will be most useful, though it will take some time to get it.

I have noticed something curious (perhaps a bug?) in my calculation of the eclipse magnitude (the fraction eclipsed, not brightness) for a solar eclipse.

My calculation of this magnitude for the example used by Jean Meeus is OK (edition 2 formula 54.2, example 54.a).
But my calculation for tomorrow's 14 October 2023 solar eclipse is 2.0, whereas online sources are giving a value of 0.9 - and of course one would expect a value less than 1 given the visible ring (although the calculation is not limited to 1).

I am wondering whether this is a problem with the calculation, or a misunderstanding of categorisation.

Jean Meeus states that the formula for the calculation for the solar eclipse applies to a partial eclipse. But the eclipse is categorised as an annular one.

I would have assumed that an annular eclipse is obviously partial, but since the categorisation is "annular" not "partial" perhaps the formula should not be used? (implying a None should be returned rather than a number). [-My code lazily always returns a number even when total.]

Or is the "partial" formula valid for annular eclipses too, in which case my calculation may be in error despite yielding a reasonable result for the example (1993 May 21)
Update: Comparing several magnitudes for 1900-2023 with online values, it seems only partial solar magnitudes are valid using this formula - not annular, hybrid or total (but all lunar eclipse values are OK).