The Twisted-PHS algorithm to solve Approx-SVP for ideal lattices on any number field, based on the PHS algorithm by Pellet-Mary, Hanrot and Stehlé in 2019, was introduced in 2020. The authors performed experiments for prime conductors cyclotomic fields of degrees at most 70, reporting exact approximation factors reached in practice. The main obstacle for these experiments is the computation of a log-S-unit lattice, which requires classical subexponential time.