daz> this approximation suggests that9^(4^(7*6)) and 3^(2^85) must be fairly good approximations to one another. Indeed! sin(11) is a bit of a cheat, since it takes the closeness of 11 to 7pi/2 and squares it. But sin(2) would be perfectly reasonable, so maybe instead of banning "asymptotic" functions, the problem should be recast as finding the appropriate price (in complexity units). Ed's example of cos(1+cos(1+cos(...))) shows you can square the epsilon at a constant cost, but if we charged according to 1/derivative, this could be fixed. He also hasn't provided for including function definitions, non-named infinite series/products/limits/sups, and functional inverses. MaxCF doesn't seem to be defined. If it's supposed to be the maximum CF partial quotient, some care is needed: it's likely infinite for everything except quadratic surds. If it's the sup of the average p.q., this is usually bounded and can be guessed from the first few CF terms. Rich rcs@cs.arizona.edu