Composed in Hebrew at Tarascon on the Rhone, the Sepher Shesh Kenaphayim (Book of Six Wings) presents six tables for predicting eclipses, largely based on the parameters and methods of al-Battani. This work, composed by the Rabbi Immanuel ben Jacob Bonfils, enjoyed considerable distribution and remains extant in 35 Hebrew manuscripts, 12 Greek manuscripts, and two Latin versions. Gassendi and Peiresc were even discussing the tables in the 1630s. The most complex table in the set gives the correction in time from mean to true syzygy, in a double-entry format. This table does not derive from al-Battani; its computational foundations have not been discovered. By using computerized versions of the Toledan and Alfonsine Tables, I shall show how we might search for the hidden algorithm by which Bonfils composed his syzygy table.