Right now I am writing a technical report, where I describe asymptotic(al) curves, expansions etc. My understanding after a bit of web browsing is that asymptotic and asymptotical are near-synonymous but the former is much more common (please correct me if I am wrong), so I will replace all instances of asymptotical by asymptotic.
Is there any general rule for those X vs. X-al situations? I can handle the most common cases (such as "Economic" vs. "economical") because I have seen them enough times, but I have not inferred a general rule, so I am at a loss when presented with an uncommon word (such as “asymptotic”).
(I am not a native speaker.)
There are historical reasons behind the choice of the suffixes -ic – ical as explained here:
compound adjectival word-forming element, usually interchangeable with -ic but sometimes with specialized sense (such as historic/historical, politic/political), Middle English, from Late Latin -icalis, from Latin -icus + -alis (see -al (1)).
Probably it was needed because the forms in -ic often took on a noun sense (for example physic). Forms in -ical tend to be attested earlier in English than their twins in -ic.