Principles behind?

in your calculation, you are calculating escape angle theta as theta = v_lateral / (v_bullet - v_retreat)

however, imo this formula is only true when you are moving orbital exactly ;)

Else, you have to calculate some integral, as the change rate of theta is changing everytime the distance changes. (Like my version)

imo if you really want to calculate the max escape in a brute force way — try every possible paths a robot can move.

And that would be, for an estimated hit time of 50ticks, if you try 360 angles — 360^50 angles in total (~10^128). Anyway, you can always prune a lot of them.