“Simi” is used if the root word is Latin based; “Himi” is used if the word is Greek based.
“Dimi” is used if the word came in to use when the English were adopting words from the French.
One of Chimp Stuart’s (Lancelot Link’s professional translator) favorite words covers all the bases: hemidemisemiquaver—a 64th note.
Source: (Note the author’s post has a “Naus-like” troll overtone in his writing style and vocabulary)
https://www.quora.com/Whats-the-difference-between-the-prefixes-semi-hemi-and-demi-notably-seen-in-hemidemisemiquaver-i-e-a-64th-note