The compiler is responsible for the implementation of the matmul intrinsic. Most of them have a “decent for small matrices and easy to inline” version by defaul

The compiler is responsible for the implementation of the matmul intrinsic. Most of them have a “decent for small matrices and easy to inline” version by default and an option to convert it to call to BLAS under certain conditions (like larger matrices). Then, the performance is that of your BLAS library. The assumption (quite good in my experience) is that people use the intrinsic naturally because it is easy and natural, but turn to BLAS calls when performance becomes important. Which is not the case for the vast majority of matrix multiplication, even in high performance computing. There is no universal optimal algorithm.