The BBMM algorithm

I had a doubt regarding the Black Box Matrix Matrix Multiplication (BBMM) algorithm
from what I read there was no mention of mathematical proof that this approximation is better than the one used right now because it was mentioned that this algorithm had better or comparable accuracy for given dataset in the research paper given in the wiki page for GSOC of pymc so can anyone please explain where I can find a proof regarding this ? or is it so that this approach doesn’t always have better results ?
If possible please share the resources for that. here is the link for the paper given in the wiki page.
thank you.