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~μHa and 0.2~μHa, 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 $α$-iron we demonstrate the capability of LAPW+lo of reaching μHa/atom precision also for periodic systems, which allows also for distinction between numerical precision and the accuracy of a given functional.

6 pages, 3 figures