  To address ultimate precision in density-functional-theory calculations we
employ the full-potential linearized augmented planewave + local-orbital
(LAPW+lo) method and justify its usage as a benchmark method. LAPW+lo and two
completely unrelated numerical approaches, multi-resolution analysis (MRA) and
linear combination of atomic orbitals, yield total energies of atoms with a
mean deviation of 0.9~{\mu}Ha and 0.2~{\mu}Ha, respectively. Spectacular
agreement with the MRA is reached also for total and atomization energies of
the G2-1 set consisting of 55 molecules. With the example of $\alpha$-iron we
demonstrate the capability of LAPW+lo of reaching {\mu}Ha/atom precision also
for periodic systems, which allows also for distinction between numerical
precision and the accuracy of a given functional.
