Fail-stop and silent errors are unavoidable on large-scale platforms. Efficient resilience techniques must accommodate both error sources. A traditional checkpointing and rollback recovery approach can be used, with added veri-fications to detect silent errors. A fail-stop error leads to the loss of the whole memory content, hence the obligation to checkpoint on a stable storage (e.g., an external disk). On the contrary, it is possible to use in-memory checkpoints for silent errors, which provide a much smaller checkpoint and recovery overhead. Furthermore, recent detectors offer partial verification mechanisms, which are less costly than guaranteed verifications but do not detect all silent errors. In this paper, we show how to combine all these techniques for HPC applications whose dependence graph is a chain of tasks, and provide a sophisticated dynamic programming algorithm returning the optimal solution in polynomial time. Simulations demonstrate that the combined use of multi-level checkpointing and partial verifications further improves performance.