calculators with $x$ as well, but only for it is visible *explicite* in definition. In presentation of results we used $x=2$.

Calculator 3 is designed to mimic *Mathematica* behavior. Constants beyond $\pi,e$ and $i$ were chosen as follows. To enable rapid integer generation via addition, multiplication and exponentiation we use -1 and 2. Incidentally, these numbers are also are initial values for Lucas numbers. Rational numbers are easily generated via continued fractions, thanks to $-1$ constant, allowing for construction of reciprocal $1/x \equiv x^{-1}$. Rational constant $1/2$ together with $i$ form trigonometric functions $e^{ix} = \cos{x} + i \sin{x}$ and square roots $\sqrt{x} = x^{1/2}$. Number of instructions equal to ten is selected intentionally. It will allow for instant estimate of the compression factor in Sect. \[Criterion3\]. Both target numerical constant and RPN calculator code can be expressed as string of base-10 digits `0123456789`, see next Sect. \[enum\].

Fourth calculator is the largest one. Maximum number of 36 buttons is limited by a current implementation of the fast `itoa` function used to convert string variables into base-36 numbers, i.e. alphanumeric lowercase digits and letters. It is the most close to what people usually expect from scientific hand-held device. Full list 