  Suzuki-Trotter decompositions of exponential operators like $\exp(Ht)$ are
required in almost every branch of numerical physics. Often the exponent under
consideration has to be split into more than two operators, for instance as
local gates on quantum computers. In this work, we demonstrate how highly
optimised schemes originally derived for exactly two operators can be applied
to such generic Suzuki-Trotter decompositions. After this first trick, we
explain what makes an efficient decomposition and how to choose from the large
variety available. Furthermore we demonstrate that many problems for which a
Suzuki-Trotter decomposition might appear to be the canonical ansatz, are
better approached with different methods like Taylor or Chebyshev expansions.
In particular, we derive an efficient and numerically stable method to
implement truncated polynomial expansions based on a linear factorisation using
their complex zeros.
