formula match. Calculations were done using extended precision (`long double` in C) while horizontal line mark machine epsilon for IEEE 754-2008 (binary64). ](figs/Convergence1){width="50.00000%"}

Two types of behavior can be observed in Fig. \[SmokingGun\]. Vertical absolute error $\epsilon$ scale is adjusted to range $\{ 2^{-63}, 1 \}$, i.e., `long double` machine epsilon for this and related Figs. \[Convergence2\], \[Convergence3\]. In typical situation absolute error $\epsilon$ for best approximation decreases exponentially with code length. However, if ”true” $\exp-\log$ formula is encountered, error instantly drops off to limiting value. In example from Fig. \[SmokingGun\] it is small multiple of machine epsilon for `long double` precision ($2^{-63}$) or binary zero.

Criterion directly based on Kolmogorov complexity is inconvenient, if one deals with languages of various size, like our calculators 1-4, eq. (\[CALC\]). Convergence rate also depends on language size $n$, cf. Fig. \[SmokingGun\]. One could use Kolmogorov complexity corrected for language size, or compile formulas generated in extended calculators or down to one of primitive forms given by or . The former approach usually underestimate, and the latter heavily overestimates true complexity. Therefore we propose another criterion, independent of the language used to generate formulas. Instead of plotting error as a function complexity, we 