Multi-Access Edge Computing (MEC) is a promising paradigm that providing cloud-like service for handling the high-complexity and latency-sensitive applications on user equipment (UE) via computation offloading. However, the execution reliability is rarely considered in current MEC studies, which is an important factor to guarantee the quality of service (QoS). For that, this paper considers an energy-saving offloading to satisfy the reliability and latency requirements of the application. Specifically, we formulate an optimization problem to minimize the UE's energy consumption with reliability and latency constraints. To tackle this NP-hard problem, we first divide the entire application into multiple directed-acyclic-graph-(DAG)-based subtasks, where the subtask can be executed on the UE locally or MEC server remotely. Then, we decompose the overall reliability and latency requirements into multiple constraints for each subtask. Finally, we propose a fast heuristic algorithm to find a solution satisfying the constraints. Simulation results demonstrate the proposed algorithm obtains lower energy consumption compared with the local execution and random assignment and costs less runtime compared with the greedy algorithm. INDEX TERMS Multi-access edge computing, computation offloading, energy consumption minimization, reliability guarantee.