There are a few good general options to extract more ILP for latency-dominated contexts, though all of them trade additional register pressure and usually some additional operation count; Estrin's scheme is the most commonly used. Factoring medium-order polynomials into quadratics is sometimes a good option (not all such factorizations are well behaved wrt numerical stability, but it also can give you the ability to synthesize selected extra-precise coefficients naturally without doing head-tail arithmetic). Quadratic factorizations are a favorite of mine because (when they work) they yield good performance in _both_ latency- and throughput-dominated contexts, which makes it easier to deliver identical results for scalar and vectorized functions.

There's no general form "best" option for optimizing latency; when I wrote math library functions day-to-day we just built a table of the optimal evaluation sequence for each order of polynomial up to 8 or so and each microarchitecture and grabbed the one we needed unless there were special constraints that required a different choice.

Though... they are allowed to cache common subexpressions, and my point about dependency chains is quite relevant on modern hardware. So x*x, x*x*x, etc may each be computed once. And since arithmetic operators are left-to-right associative, the rather ugly code, as written, is fast and not as wasteful as it appears.