\frac{\sin{x}}{\cos{x}}.$$ Scientific calculators sometimes distinguish less important, secondary functions which require pressing two buttons. But mathematically they are completely equivalent. You can compute $\sinh, \cosh$ using $\exp$, or *vice versa*. This is especially true in complex domain, where all elementary functions are reducible to $\exp$ and $\ln$.

Reduction is possible for binary operations as well, e.g: $$x \times y = e^{\ln{x} + \ln{y}}, \quad   x \cdot y = \log_x{\left[ (x^y)^x \right] }.$$ Replacing multiplication by logarithms and addition is an achievement of medieval mathematics [@briggs] used without changes for 300 years. It was replaced with slide rule used in XX century. They both went extinct with modern computers. However, we point out, that using logarithms and addition you can not only do bottom-up translation to multiplication/exponentiation. You might go opposite way as well, from high-rank (grade) hyper-operation down do additions. Expressing addition/multiplication by exponentiation/logarithms only (up-bottom) is therefore possible, but tricky, see Appendix C in Supplemental Material.

Taking above considerations into account, important question arises: how many constants, functions and binary operations are required for our virtual calculator to be still fully operational? How far reduction process can go, without impairing our computational abilities? This is also known as ,,broken 