ColPivHouseholderQR vs FullPivLU speed documentation

Dear Eigen team

In the table from this page https://eigen.tuxfamily.org/dox/group__TutorialLinearAlgebra.html, the speed of FullPivLU is - for small-to-medium size and -- for large problems. For colPivHouseholderQr it is + and -. So from this table, I would expect than colPivHouseholderQr is faster than FullPivLU. However, from this second page https://eigen.tuxfamily.org/dox/group__DenseDecompositionBenchmark.html and my own test, I found the opposite.

So should this page https://eigen.tuxfamily.org/dox/group__TutorialLinearAlgebra.html be updated?

In the same page, it is also indicated that If your matrix is of a very small fixed size (at most 4x4) this allows Eigen to avoid performing a LU decomposition, and instead use formulas that are more efficient on such small matrices.

For a 3x3 matrix, for me A.fullPivLu().solve( b ) is faster than A.inverse()*b , so should this sentence be also updated or is there something I am doing wrong?