An　new　inexact　method　of　tangent　hyperbolas　(NIMTH)　has　been　proposed　recently.　In　NIMTH,　the　Newton　equation　and　the　Newton-like　equation　are　solved　respectively　by　one　Cholesky　factorization　(CF)　step　and　p　preconditioned　conjugate　gradient　(PCG)　steps,　periodically.　The　algorithm　is　efficient　in　theory.　But　its　implementation　is　still　restricted.　In　this　paper,　an　efficient　version　of　NIMTH　is　presented,　in　which　the　parameter　p　is　independent　of　the　complexity　of　the　objective　function,　and　its　tensor　terms　can　be　efficiently　evaluated　by　automatic　differentiation.　Further　theoretical　analysis　and　numerical　experiments　show　that　this　version　of　NIMTH　is　of　great　competition　for　the　middle　and　large　scale　unconstrained　optimization　problems.　©　Springer-Verlag　Berlin　Heidelberg　2007.