At Rice University, we have undertaken a project to construct a framework for generating high-level problem solving languages that can achieve high performance on a variety of platforms. The underlying strategy, called telescoping languages, builds problem-solving systems from domain-specific libraries and scripting languages by extensively preanalyzing libraries to produce a precompiler that optimizes library calls within the scripts as if they were primitives in the underlying language. Our study of applications written in Matlab by the signal processing group at Rice University has identified a collection of old and new optimizations that show promise for this particular domain. Two promising new optimizations are procedure vectorization and procedure strength reduction. By transforming these programs, at source level, according to the strategies described in this paper, we were able to achieve speedups ranging from a factor of 1.1 to 1.6 over the entire applications—with speedups for individual functions as high as 3.3.