= Balancing quadrature truncation and round-off error
{title2=$C n^{-p}\approx\delta\ \Longrightarrow\ n\approx(C/\delta)^{1/p}$}
If a <quadrature> error bound is $C n^{-p}$ and the relevant numerical resolution is $\delta$, equating these scales gives an estimate of the strip count beyond which that truncation guarantee reaches the <rounding> scale. For the <composite Simpson's rule>, $p=4$. This estimate is useful for choosing a sensible order of magnitude, but a worst-case bound need not equal the actual <quadrature> error.
For a normal <floating-point number> in base two, the spacing depends on the exponent of the result; half the spacing is a natural final-storage <rounding> scale. <Machine epsilon> instead measures the gap above one. <Function>-evaluation errors, accumulation of summation error, cancellation, and the arithmetic used for the nodes can impose an earlier practical accuracy limit. Thus final storage precision alone cannot give a universal optimal strip count.
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