Programming heterogeneous multiprocessor architectures combining multiple processor cores and hardware accelerators is a real challenge. Computer-aided design and development tools try to reduce the large design space by simplifying hardware-software mapping mechanisms. However, energy consumption is not well supported in most of design space exploration methodologies due to the difficulty to estimate energy consumption fast and accurately. To this aim, this paper proposes and validates an exploration method for partitioning tilling-based parallel applications on software cores and hardware accelerators under energy-efficiency constraints. The methodology is based on energy and performance measurement of a tiny subset of the design space and an analytical formulation of the performance and energy of an application kernel mapped onto a heterogeneous architecture. This closed-form expression is captured and solved using Mixed Integer Linear Programming, which allows for very fast exploration and results in the best hardware and software partitioning under energy constraint. The approach is validated on two application kernels using a Zynq-based architecture showing more than 12% acceleration speed-up and energy saving compared to standard approaches. Results also show that the most energy-efficient solution is application-and platform-dependent and moreover hardly predictable, which highlights the need for fast exploration tools as in this paper.