Real-analytic tetration uniqueness criterion?

[mike3]

Ah, so it gives n/2 correct digits (or thereabout), then. So at the 340 or so digits I was using, it should've had around 170 digits correct, which would probably have been enough to get the 32nd derivative provided the epsilon was not too small (I think I used 1e-4 or so, maybe 1e-5 but the last one may have been pushing it, although 1e-4 still produces a graphable approximation of the derivative).