In this paper we propose a runtime-based selective task replication technique for task-parallel high performance computing applications. Our selective task replication technique is automatic and does not require modification/recompilation of OS, compiler or application code. Our heuristic, we call App_FIT, selects tasks to replicate such that the specified reliability target for an application is achieved. In our experimental evaluation, we show that App FIT selective replication heuristic is low-overhead and highly scalable. In addition, results indicate that complete task replication is overkill for achieving reliability targets. We show that with App FIT, we can tolerate pessimistic exascale error rates with only 53% of the tasks being replicated.