This report compares the Unified Substitution Method (USM) with Mathematica’s native Integrate function across five families of integrals involving quadratic radicals and trigonometric half-angle structures. For each transform family, the document includes the Wolfram code used, timing data, expression-size measurements, verification tests, and commentary on successes, timeouts, and branch-related behavior. The goal is to document how the USM rationalization framework performs in controlled benchmark examples, especially in terms of speed, correctness, and avoidance of expression swell.
Overall, the benchmarks show that the USM framework is especially effective when the direct Mathematica integration path leads to timeouts, unevaluated integrals, or large antiderivative expressions. The report also documents cases where Mathematica performs competitively, making the comparison useful as a technical reference rather than a one-sided performance claim.
No hay comentarios:
Publicar un comentario