Automatic program parallelization has been an elusive goal for many years. It has recently become more important due to the widespread introduction of multi-cores in PCs. Automatic parallelization could not be achieved because classic compiler analysis was neither powerful enough and program behavior was found to be in many cases input dependent. Run-time thread level parallelization, introduced in 1995, was a welcome but somewhat different avenue for advancing parallelization coverage. In this paper we introduce a novel analysis, Hybrid Analysis (HA), which unifies static and dynamic memory reference techniques into a seamless compiler framework which extracts almost maximum available parallelism from scientific codes and generates minimum run-time overhead. In this paper we will present how we can extract maximum information from the quantities that could not be sufficiently analyzed through static compiler methods and generate sufficient conditions which, when evaluated dynamically can validate optimizations. A large number of experiments confirm the viability of our techniques, which have been implemented in the Polaris compiler.