  We present an implementation of the adaptively compressed exchange (ACE)
operator in the LAPW formalism. ACE is a low-rank representation of the Fock
exchange that avoids any loss of precision for the total energy. Our study
shows that this property remains in the all-electron case, as we apply this
method in non-relativistic total-energy calculations with a hybrid
exchange-correlation functional PBE0. The obtained data for light atoms and
molecules are within a few $\mu$Ha off the precise multi-resolution-analysis
calculations. Aside from ACE, another key ingredient to achieve such a high
precision with Fock exchange was the use of high-energy local orbitals.
Finally, we use this implementation to calculate PBE0 gaps in solids and
compare the results to other all-electron results.
