  It has been observed that some working principles of evolutionary algorithms,
in particular, the influence of the parameters, cannot be understood from
results on the asymptotic order of the runtime, but only from more precise
results. In this work, we complement the emerging topic of precise runtime
analysis with a first precise complexity theoretic result. Our vision is that
the interplay between algorithm analysis and complexity theory becomes a
fruitful tool also for analyses more precise than asymptotic orders of
magnitude.
  As particular result, we prove that the unary unbiased black-box complexity
of the OneMax benchmark function class is $n \ln(n) - cn \pm o(n)$ for a
constant $c$ which is between $0.2539$ and $0.2665$. This runtime can be
achieved with a simple (1+1)-type algorithm using a fitness-dependent mutation
strength. When translated into the fixed-budget perspective, our algorithm
finds solutions which are roughly 13\% closer to the optimum than those of the
best previously known algorithms. To prove our results, we formulate several
new versions of the variable drift theorems, which also might be of independent
interest.
