A system and method for high-speed execution of graphics application programs, including shading language instructions, that utilize 3D graphics hardware. The method involves expressing a graphics computation in a platform-independent procedural shading expression, converting the expression (i.e., user application program) into an intermediate representation such as a tree, and then translating it into a sequence of parametric shading expressions. The method can alternatively processes the intermediate tree representation using a cost-based, tree-grammar recognizer such as iburg. The result is a platform-specific and least-cost, in terms of the underlying hardware, sequence of parametric shading expressions that realizes the graphics computation. The system and method is useful in translating platform-independent RenderMan.TM. Shading Language programs into fast-executing, platform-specific OpenGL.TM. or Direct3D.TM. executable code.