Parsing inflected forms may not always work as expected. If the following does not give the correct word, try Latin Words or Perseus.
convertĭbĭlis (convers-), e, adj. [converto], changeable (post-class.): propositiones, App. Dogm. Plat. 3, p. 33, 1 and 2 (al. conversibilis): deus convertibilis et demutabilis, Prud. Apoth. 344.
Hence, con-vertĭbĭlĭter, adv., changeably (late Lat.), Aug. Music. 5, 13.