Multivariate functions of continuous variables arise in countless
branches of science. Numerical computations with such functions
typically involve a compromise between two contrary desiderata: accurate
resolution of the functional dependence, versus parsimonious memory
usage. Recently, two promising strategies have emerged for satisfying
both requirements: (i) The quantics representation, which expresses
functions as multi-index tensors, with each index representing one bit
of a binary encoding of one of the variables; and (ii) tensor cross
interpolation (TCI), which, if applicable, yields parsimonious
interpolations for multi-index tensors. Here, we present a strategy,
quantics TCI, which combines the advantages of both schemes. We
illustrate its potential with an application from condensed matter
physics: the computation of Brillouin zone integrals.