  Given an observable and its operator product expansion (OPE), we present
expressions that carefully disentangle truncated sums of the perturbative
series in powers of $\alpha$ from the non-perturbative (NP) corrections. This
splitting is done with NP power accuracy. Analytic control of the splitting is
achieved and the organization of the different terms is done along an
super/hyper-asymptotic expansion. As a test we apply the methods to the static
potential in the large $\beta_0$ approximation. We see the superasymptotic and
hyperasymptotic structure of the observable in full glory.
