What is the best state-of-the-art numerical integral algorithm? I'm trying to implement a numerical integrator that should have the minimum relative error and is not slow. So I was looking for the best accepted state-of-the-art algorithm to do so but there seems to be so many approaches that I could not understand which one should I choose. So I'm turning to you for a recommendation.
Thank you for your attention,

As @J.M noted, there are many methods, each suited for a certain purpose.
If you don't know what the function is in advance, then for low-dimensional ($d < 3$) integrals a adaptive Gauss–Kronrod rule quadrature is probably the fastest.
In higher dimensions, you can really only use Monte-Carlo methods.
If you know apriori that the functions have a very large range, you can use a weighted Monte-Carlo approach, in which you select more points in the "large" regions, than in the "smaller" ones.
