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Re: //N bug, but WHY?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg58645] Re: [mg58634] //N bug, but WHY?
*From*: Bob Hanlon <hanlonr at cox.net>
*Date*: Tue, 12 Jul 2005 05:21:30 -0400 (EDT)
*Reply-to*: hanlonr at cox.net
*Sender*: owner-wri-mathgroup at wolfram.com
expr=Cosh[(43*Pi)/Sqrt[2]]+(1-Cosh[
43*Sqrt[2]*Pi])*Csch[43*Sqrt[2]*Pi]*Sinh[(43*Pi)/Sqrt[2]];
You are trying to take the difference of two very large numbers. Precision is
an issue
term1=expr[[1]]
Cosh[(43*Pi)/Sqrt[2]]
term2=expr[[2]]
(1 - Cosh[43*Sqrt[2]*Pi])*Csch[43*Sqrt[2]*Pi]*Sinh[(43*Pi)/Sqrt[2]]
term1//N
1.526301024376754*^41
term2//N
-1.5263010243767541*^41
%+%%
-1.9342813113834067*^25
expr//N
-1.9342813113834067*^25
Using explicit precision will eliminate the problem
N[expr,20]
6.55178751785434401405005796823578794`20.*^-42
However, if you simplify, there is only one small term
FullSimplify[expr]
Sech[(43*Pi)/Sqrt[2]]
%//N
6.5517875178544*^-42
Bob Hanlon
>
> From: "symbio" <symbio at has.com>
To: mathgroup at smc.vnet.net
> Date: 2005/07/11 Mon AM 04:19:20 EDT
> Subject: [mg58645] [mg58634] //N bug, but WHY?
>
> 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,
>
>
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