Right. OP here, FWIW, in my colloquial English (right or wrong:) "Perfect" is, well, perfect; does everything I want and cannot be meaningfully improved.

"Perfectly Fine" on the other hand, the key word is "fine". It is "eh. It mostly does the job. I cannot begrudge it too much. I have bigger things to rant about. It's perfectly fine."

"Fine" is like "Nice". It's fine. It's nice. Note quite "Good", let alone "Amazing". But it's fine. Perfectly so :)

(I empathize with all of your pain points, particularly the stopping of generation if my screen locks. I have employer-mandated iPhone which has draconian locking policies which are pretty close to average time of query generation. I wonder if app will have the same issue?)

So 'fine' is better than 'perfectly fine'?

(I’m not a native speaker.)

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No, but perfect is much better than perfectly fine.

Yep, this is also my interpretation of the phrase.

I best equated it to "usable" since I agree it's "not quite good".