Many useful tasks in data science and machine learning applications can be written as simple variations of matrix multiplication. However, users have difficulty performing such tasks as existing matrix/vector libraries support only a limited class of computations hand-tuned for each unique hardware platform. Users can alternatively write the task as a simple nested loop but current compilers are not sophisticated enough to generate fast code for the task written in this way. To address these issues, we extend an open-source compiler to recognize and optimize these matrix multiplication-like tasks. Our framework, called Amulet, uses both database-style and compiler optimization techniques to generate fast code tailored to its execution environment. We show through experiments that Amulet achieves speedups on a variety of matrix multiplication-like tasks compared to existing compilers. For large matrices Amulet typically performs within 15% of hand-tuned matrix multiplication libraries, while handling a much broader class of computations.