https://cadxfem.org/cao/Compensation-horner.pdf was the reference I was using.
The assumption I made was that the higher order terms are smaller than the current polynomial coeficient, ie |p[i]|>= |evalpoly(x, p[i+1:end])|. This is true for |x|<1 and monotonically decreasing |p[i]|. The good news is that that is the scenario that you encounter for evaluating special functions.
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