Redundancy elimination is a key optimization direction, and loop nests are the main optimization target in modern compilers. Previous work on redundancy elimination of array computations in loop nests either targets specific computation patterns or fails to recognize redundancies with complex structures. This paper proposes RACE (Redundant Array Computation Elimination), a hash-based technique that utilizes a novel two-level scheme to identify the data reuse between array references and the computation redundancies between expressions, enabling hierarchical redundancy detection beyond pattern-specific methods. It traverses the expression trees in loop nests to detect redundancies hierarchically in linear time and generates efficient code with optimized auxiliary arrays that store redundant computation results. Furthermore, RACE supports the expression reassociation with various aggressive strategies to improve the redundancy opportunities. Experimental results demonstrate the effectiveness of RACE.