This work is concerned with approximating a trivariate function defined on tensor-product domain via evaluations. Combining tensorized Chebyshev interpolation Tucker decomposition of low multilinear rank yields approximations that can be computed and stored very efficiently. The existing Chebfun3 algorithm [Hashemi Trefethen, SIAM J. Sci. Comput., 39 (2017)]uses similar format but the construct...