Existing pattern-based compiler technology is unable to effectively exploit the full potential of SIMD architectures. We present a new program synthesis based technique for auto-vectorizing performance critical innermost loops. Our synthesis technique is applicable to a wide range of loops, consistently produces performant SIMD code, and generates correctness proofs for the output code. The synthesis technique, which leverages existing work on relational verification methods, is a novel combination of deductive loop restructuring, synthesis condition generation and a new inductive synthesis algorithm for producing loop-free code fragments. The inductive synthesis algorithm wraps an optimized depth-first exploration of code sequences inside a CEGIS loop. Our technique is able to quickly produce SIMD implementations (up to 9 instructions in 0.12 seconds) for a wide range of fundamental looping structures. The resulting SIMD implementations outperform the original loops by 2x-3x.