Third-order　methods　can　be　used　to　solve　efficiently　the　unconstrained　optimization　problems,　and　they,　in　most　cases,　use　fewer　iterations　but　more　computational　cost　per　iteration　than　a　second-order　method　to　reach　the　same　accuracy.　Recently,　it　has　been　shown　by　an　article　that　under　some　conditions　the　ratio　of　the　number　of　arithmetic　operations　of　a　third-order　method　(the　Halley　class　of　methods)　and　Newton＇s　method　is　constant　(at　most　5)　per　iteration.　Automatic　differentiation　(AD)　can　compute　fast　and　accurate　derivatives　such　as　the　Jacobian,　Hessian　matrix　and　the　tensor　of　the　function.　The　Halley　class　of　methods　includes　these　high-order　derivatives.　In　this　paper,　we　apply　AD　efficiently　to　the　methods　and　investigate　the　computational　complexity　of　them.　The　results　show　that　under　general　conditions　even　including　the　computation　of　the　function　and　its　derivative　terms,　the　upper　bound　of　the　ratio　can　be　reduced　to　3.5.