X vs. X-al adjectives (asymptotic vs asymptotical, etc.)

Question

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.)

Answer 1

There are historical reasons behind the choice of the suffixes -ic - ical as explained here:

-ical

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.

(Etymonline)

Answer 2

I have been thinking about this a lot recently and i have decided that perhaps the general rule is:

a single element is -ic, a battle is historic, a light switch is electric, 2+2=4 is arithmetic, Gandalf is Fantastic, a money saving tip is economic, a piece of logic is well, logic.

A more complex thing made of many -ic elements is -ical. a War is historical, the wiring in a whole house is electrical, a system made up of many pieces of arithmetic is arithmetical, Lord of the Rings is Fantastical, living your life following money saving tips is economical, and carrying out a task using logic is logical.