Reply to the ``Comment on Reliable operations on oscillatory functions'' by Dr. Ixaru (Q5932765)

\textit{Gh.~Adams} and \textit{S.~Adams} [(AA), Comput. Phys. Commun. 125, No. 1-3, 127-141 (2000; Zbl 0976.65122)] derived formulas for the derivative of oscillatory functions of the form \(\phi(x)=f_1(x)\cos(\omega x+\delta)+f_2(x)\sin(\omega x+\delta)\). They compared it with exponential fitting methods of \textit{L.~Ixaru} [(LI), ibid. 105, No.~1, 1-19 (1997; Zbl 0930.65150)] and found their formulas to be better.NEWLINENEWLINENEWLINEIn the first comment Ixaru states that the (AA) formulas need more information (\(f_1\) and \(f_2\) and \(\delta\)) than the (LI) formulas (only \(\phi\)), and are thus more accurate, but with less information (LI) formulas are optimal as well. In a reply to this comment, the (AA) authors argue that in the specific context of harmonic series (only one term in \(\phi\) with \(\delta\) known), and data known on a (possibly non equispaced) grid, the (AA) formulas can give a better accuracy for the same amount of data. If however only an oscillatory \(\phi\) is given without the specific knowledge of \(f_1\) and \(f_2\), then only the (LI) formulas are applicable.