  Counts of holomorphic disks are at the heart of the SYZ approach to mirror
symmetry. In the non archimedean framework, these counts are expressed as
counts of analytic cylinders. In simple cases, such as cluster varieties, these
counts can be extracted from a combinatorial algorithm encoded by a scattering
diagram. The relevant scattering diagram encodes information about
infinitesimal analytic cylinders. In this paper, we give a formula relating
counts of a restricted class of cylinders on affine log Calabi Yau surfaces to
counts on a single blowup of a toric surface, using non archimedean Gromov
Witten theory and a degeneration procedure parametrized by tropical data. This
closed form formula constrasts with the scattering diagram approach.
