Solid gold(I) fluoride remains as an unsynthesized and uncharacterized compound. We have performed a search for potential gold(I) fluoride crystal structures using USPEX evolutionary algorithm and dispersion-corrected hybrid density functional methods. Over 4000 AuF crystal structures have been investigated. Behavior of the AuF crystal structures under pressure was studied up to 25 GPa, and we also evaluated the thermodynamic stability of the hypothetical AuF crystal structures with respect to AuF3, AuF5, and Au3F8. Mixed-valence compound Au3[AuF4] with Au atoms in various formal oxidation states emerged as the thermodynamically most stable AuF species.