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Redundancy elimination is an important compiler optimization, which deals with the elimination of unnecessary reevaluations of the same computation. This optimization requires two passes - one pass to detect the redundant computations and the second pass to eliminate the redundancies. A Simple Algorithm for Global Value Numbering (GVN) (Saleena and Paleri, 2014) is a simple and efficient method for redundancy detection. This work is extended by devising an algorithm for redundancy elimination. The elimination pass makes use of the information computed by the GVN algorithm. New algorithm has been implemented as an optimization pass in the LLVM compiler framework.