plot $N$-th best approximation (Fig. \[Convergence2\]). Now all curves nearly overlap, and observed lower error limit is $\epsilon > e^{-N}$.

Above considerations provide the first criterion for constant identification:

Criterion 1:\
Identification candidate: *if absolute error $\epsilon$ in subsequence of progressively better approximations in terms of $\exp-\log$ formulas deviates ”significantly” from estimated upper limit $e^{-N}$ (drops to numerical ”zero”/machine epsilon in particular) we can stop search and return formula code, as possible identification candidate.*

Failure of search: *if absolute error in subsequence of progressively better approximations in terms of $\exp-\log$ formulas follow $e^{-N}$ and reach numerical precision limit, or computational resources are exhausted, search failed.*

Candidate code must be then verified using symbolic methods, high-precision numerical confirmation test, and ultimately proved using standard mathematical techniques. Above criterion do not provide any numerical estimate for probability of successful identification. However, we point out, that even in case of possible misidentification, unexpected drop of error to machine epsilon marks stop of the search anyway. This is because finding better approximation would require formula with complexity already above threshold, given by intersection of dotted lines in Fig. \[Convergence2\]. Beyond that, number of formulas with identical decimal expansion grows exponentially. This behavior mark search 