User blog comment:Hyp cos/Growth Rate ε(0)−1/@comment-30754445-20170714141844

Very illuminating. Nice indeed.

So LittlePeng's analytic ε₀-level function would have a 2-level cost.

By the way, I think your definition of "comparable" is too strict.

Would you say that 2↑↑n is comparable to f3(n)? Or to "n in a square" in Steinhous-Moser notation?

The relations between any pair of these functions can be approximated as f(x)~g(x+k) where k grows very slowly to infinity.