Yeah, I just recently learned about Estrin's method when fooling around with some polynomial approximations. I'd been scaling the output by a sqrt term to get better accuracy at small degrees, but it turned out that polynomials of very large degrees can be calculated in the same time as a single correctly-rounded sqrt, especially when fma is available. Seemingly, the only real cost is the added register pressure.

The length of an expression when written out can definitely be deceiving when pipelining is added to the mix.