define Kolmogorov complexity of the formulas. In Sect. \[enum\] we discuss some practical issues regarding numerical implementation of the sequential formula generators. Then, we combine experience/knowledge of Sect. \[ELnumbers\] and \[enum\] to find properties and typical behavior of the constructed EL numbers. Sections \[Criterion1\]-\[Criterion3\] propose three criteria for number recognition: (1) instant error drop-off to machine epsilon instead statistically expected $e$-folding; exponential growth of number of formulas indicates failure of search (2) maximum likelihood formula in the view of statistical process (3) compression ratio of the decimal constant in terms of RPN calculator code.

[Elementary complex $\exp-\log$ numbers \[ELnumbers\]]{}

Our first task is to precisely define set of formulas/numbers we want to identify using decimal expansion. We restrict ourselves to explicit formulas [@chow] i.e. those computable using hand-held scientific calculator. We assume root-finding procedure is absent. Therefore, as notable exception, most of algebraic numbers are not in above class, because polynomials of the order 5 and larger are not explicitly solvable in general. To be specific, we consider any complex number created from:

1.  integers: $0,1,-1,2,-2, \ldots$

2.  rationals: $\frac{1}{2},\frac{1}{3}, \frac{3}{2}, \ldots$

3.  mathematical constants: $0, 1, 2, e,\pi, i, \phi, \ldots$

4.  addition/subtraction, multiplication/division, exponentiation/logarithm (arbitrary base)

5.  elementary 