From many verbs one can derive an agent noun for each gender:
Some of these derivatives are rarely found, but it is easy enough to derive productively when needed — when the perfect participle stem ends in a t. It is easy to speak about male and female lectureres, for example (lector and lectrix).
How to derive feminine an neuter agents from a verb whose perfect participle stem ends in an s?The masculine derivative is common and easy (eg. profiteri > professor), but how to form the feminine and neuter versions? I would like this to be analogous with the derivatives for computare and scribere above, so using the present participle (eg. profitens) is unsatisfactory.
If you can give a way to derive feminine and neuter agents, please give actual use examples. Examples should preferably be classical. If there are no classical examples, are there later ones and did ancient grammarians notice that such words are missing?
Here is a feeble attempt to derive in feminine and neuter: The stem of profiteri is profit- and when we add a t for perfect participle, we get profitt- which has turned into profett- and then profess-. It seems easier to derive before making the subsitution tt > ss. The companions of profettor would then be profettrix and profettrum. Intervocalic tt should become ss, but it feels more natural to take ttr > tr. This leaves me with professor, profetrix and profetrum. This is my best guess, but I have no idea if this is consistent with classical (or any other) use of Latin.
There are indeed a few examples of such words from ancient texts, but they are very rare. They are still formed from the supine stem, meaning that the original dental consonant (d or t) is replaced with s, to which -trix or -trum is then appended.
The Perseus Project provides a search tool for its dictionaries (in particular, Lewis & Short) which allows searching for lemmas by their last few letters. The search results for -strix and -strum list all candidate words; beware, though, that each result also contains a number of unrelated entries (i.e. words derived in other ways).
For the feminine, the least uncommon word (according to Perseus) is tonstrix, which appears three times in Plautus (preclassical), once in Martial (postclassical), and also in one inscription. (Furthermore, there is the variant tonsrix mentioned once by the grammarian Charisius.) According to the grammarian Priscian, Cicero once used defenstrix. Hence, there is relatively good evidence for this derivation having been used over a long period.
Of specific interest regarding profiteri, which has a double -ss- in its supine, are assestrix (compare assessor) and possestrix (compare possessor), demonstrating that -ss- is simplified to -s-. Both words were used by the poet Afranius (early first century BC), according to grammarian Nonius Marcellus.
We can therefore conclude that the female equivalent to professor would likely have been profestrix.
Among the words ending in -strum found in the search, I can only identify two examples that actually match the pattern and are derived from a supine stem ending in -s: claustrum (from claudere) and rostrum (from rodere). On the plus side, both are quite common, at least in plural. There are no examples for verbs with -ss in the supine. Still, it seems plausible to me that the corresponding word derived from profiteri would have been profestrum.