Deterministic multithreading (DMT) eliminates many pernicious software problems caused by nondeterminism. It works by constraining a program to repeat the same thread interleavings, or schedules, when given same input. Despite much recent research, it remains an open challenge to build both deterministic and efficient DMT systems for general programs on commodity hardware. To deterministically resolve a data race, a DMT system must enforce a deterministic schedule of shared memory accesses, or memschedule, which can incur prohibitive overhead. By using schedules consisting only of synchronization operations, or sync-schedule, this overhead can be avoided. However, a sync-schedule is deterministic only for race-free programs, but most programs have races.Our key insight is that races tend to occur only within minor portions of an execution, and a dominant majority of the execution is still race-free. Thus, we can resort to a mem-schedule only for the "racy" portions and enforce a sync-schedule otherwise, combining the efficiency of sync-schedules and the determinism of memschedules. We call these combined schedules hybrid schedules.Based on this insight, we have built PEREGRINE, an efficient deterministic multithreading system. When a program first runs on an input, PEREGRINE records an execution trace. It then relaxes this trace into a hybrid schedule and reuses the schedule on future compatible inputs efficiently and deterministically. PEREGRINE further improves efficiency with two new techniques: determinismpreserving slicing to generalize a schedule to more inputs while preserving determinism, and schedule-guided simplification to precisely analyze a program according to a specific schedule. Our evaluation on a diverse set of programs shows that PEREGRINE is deterministic and efficient, and can frequently reuse schedules for half of the evaluated programs.