The proposed C++ tricks are useful and I think that its reasonably well-known (at least to people who do numerics) that a C++ compiler, with the right flags, can beautifully unroll loops when array sizes are known at compile-time.

> brute force Cramer's rule solution

This isn't really a fair comparison: trusty old DGESV will yield far more accurate results for badly conditioned problems since it does row swaps (partial pivoting). It might also rescale values; I don't remember the details. It would be much more reasonable to compare a hypothetical DGEC (double precision general matrix cramer's rule) routine.