  We describe and analyze a numerical algorithm for computing the homology
(Betti numbers and torsion coefficients) of semialgebraic sets given by Boolean
formulas. The algorithm works in weak exponential time. This means that outside
a subset of data having exponentially small measure, the cost of the algorithm
is single exponential in the size of the data. This extends the previous work
of the authors in arXiv:1807.06435 to arbitrary semialgebraic sets.
  All previous algorithms proposed for this problem have doubly exponential
complexity.
