Of course one can. Just ask Donald Knuth. :-)

For the case of arbitrary polynomials, Horner's method minimizes the number of operations, but doesn't minimize latency, which is in most applications much more important. On an ancient PPC 604, better schemes allow about three times faster evaluation; on modern processors that ratio is worse. And in the special case of evaluating p (x + k y) for many consecutive values k, Horner's method is decidedly suboptimal, even considering just the number of operations.

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