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Jan 13 at 22:00 comment added Steven Stadnicki @CommandMaster It can, but that's actually baked into the $O(B^2)$ estimate — you're doing operations on numbers of shrinking length. Note that this also means that the necessary $B$ can be $O(r)$ or so, too — in other words, you need an approximation to $f$ of closeness roughly $\exp(-r)$ to be able to find $r$ with any confidence.
Jan 13 at 21:18 comment added Daniel Weber Can't the length of this segment be $O(\sqrt r)$, though?
Jan 13 at 19:40 history answered Steven Stadnicki CC BY-SA 4.0