By the way, is there a rule to how these short forms are formed?

Yep! Most Japanese verbs (with a few exceptions like ‘shimasu’ becoming suru) use one of the ‘i’ variants (‘i’, ‘ni’, ‘ki’, or ‘ri’) after the kanji, that indicates they are verbs. Yakimasu (to burn/ cook), shirimasu (to know), arukimasu (to walk), arimasu (to be), shinimasu (to die). Ki will become ku in the shortened version, and ri will become ru, ni -> nu: yaku, shiru, aruku, aru, shinu.

I believe the verbs that don’t end in one of those like tabemasu (to eat) will default to ‘ru’ (taberu), but I don’t know if that’s a rule off the top of my head, or if I just can’t think of any others right now.

In the cases where rendaku applies, such as yogimasu (to swim), the end kana will also have rendaku applied, e.g. yogu. Ki -> ku, gi -> gu.