Abstract shape analysis allows efficient computation of a representative sample of low-energy foldings of an RNA molecule. More comprehensive information is obtained by computing shape probabilities, accumulating the Boltzmann probabilities of all structures within each abstract shape. Such information is superior to free energies because it is independent of sequence length and base composition. However, up to this point, computation of shape probabilities evaluates all shapes simultaneously and comes with a computation cost which is exponential in the length of the sequence.