Re: //N bug, but WHY?

*To*: mathgroup at smc.vnet.net*Subject*: [mg58649] Re: //N bug, but WHY?*From*: Peter Pein <petsie at dordos.net>*Date*: Tue, 12 Jul 2005 05:21:33 -0400 (EDT)*References*: <data3n$mec$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

symbio schrieb: > Evaluating (using //N) two exact same expressions, gives wrong answer unless > fullsimplify is used first, I spent 2 days on a problem thinking my answer > was wrong, but turned out Mathematica 5 was giving me buggy answers, I > debugged it to this point, but WHY in the world is this happening? Please > help!!! > > cut and paste below to see the test case: > > In[243]:= > \!\(\(Cosh[\(43\ \[Pi]\)\/\@2] + \((1 - Cosh[43\ \@2\ \[Pi]])\)\ Csch[ > 43\ \@2\ \[Pi]]\ Sinh[\(43\ \[Pi]\)\/\@2] // FullSimplify\) // > N\[IndentingNewLine] > Cosh[\(43\ \[Pi]\)\/\@2] + \((1 - Cosh[43\ \@2\ \[Pi]])\)\ Csch[ > 43\ \@2\ \[Pi]]\ Sinh[\(43\ \[Pi]\)\/\@2] // N\) > Out[243]= > \!\(6.551787517854307`*^-42\) > Out[244]= > \!\(\(-1.9342813113834067`*^25\)\) > > > > thanks, > The simplified expression is Sech[(43*Pi)/Sqrt[2]], wich is - with respect to numeric evaluation - completely different from Cosh[(43*Pi)/Sqrt[2]] + (1 - Cosh[43*Sqrt[2]*Pi]) * Csch[43*Sqrt[2]*Pi] * Sinh[(43*Pi)/Sqrt[2]]], where rounding errors occur, which are "blown up" by the large numbers (Exp[43*Pi/Sqrt[2]] is about 3*10^41). You can't expect a correct result using 16-digit numerics. Try instead: Block[{$MaxExtraPrecision = 86}, N[Cosh[(43*Pi)/Sqrt[2]] + (1 - Cosh[43*Sqrt[2]*Pi])*Csch[43*Sqrt[2]*Pi]*Sinh[(43*Pi)/Sqrt[2]], $MachinePrecision]] this will give you: 6.551787517854344014050058*10^-42 -- Peter Pein Berlin http://people.freenet.de/Peter_Berlin/