Probably, but hill climbing will avoid loss in the long run. The speed boost is probably more than worth it.
I wouldn't be surprised if we started using lossier math for faster state space search. Once you find a peak, you could swap out the maths to be more exact.
Suppose you have a set membership question. If you approximate yes, you do a more complex inquiry to grab details. If you approximate no, you tell the user no, don't know that face [answer, command, etc]. So this is ripe for approximate methods as you can tune to get very few false negatives (respond no when it's really yes), but allow a healthy dose of false positives.
I wouldn't be surprised if we started using lossier math for faster state space search. Once you find a peak, you could swap out the maths to be more exact.