Finely tuning MPI applications (number of processes, granularity, collective operation algorithms, topology and process placement) is critical to obtain good performance on supercomputers. With a rising cost of modern supercomputers, running parallel applications at scale solely to optimize their performance is extremely expensive. Having inexpensive but faithful predictions of expected performance could be a great help for researchers and system administrators. The methodology we propose captures the complexity of adaptive applications by emulating the MPI code while skipping insignificant parts. We demonstrate its capability with High Performance Linpack (HPL), the benchmark used to rank supercomputers in the TOP500 and which requires a careful tuning. We explain (1) how we both extended the SimGrid's SMPI simulator and slightly modified the open-source version of HPL to allow a fast emulation on a single commodity server at the scale of a supercomputer and (2) how to model the different components (network, BLAS, ...) of the system. We show that a careful modeling of both spatial and temporal node variability allows us to obtain predictions within a few percents of real experiments (see Figure 1).