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Re: Bug ??????

• To: mathgroup at smc.vnet.net
• Subject: [mg105352] Re: Bug ??????
• From: sashap <pavlyk at gmail.com>
• Date: Sun, 29 Nov 2009 05:10:06 -0500 (EST)
• References: <heqf01$1m4$1@smc.vnet.net>

On Nov 28, 12:12 am, ynb <wkfkh... at yahoo.co.jp> wrote:
> F[x_]:=34880228747203264624081936 -
> 464212176939061350196344960*x^2 +
> 4201844995162976506469882880*x^4 -
> 36736184611200699915890392480*x^6 +
> 245136733977616412716801297320*x^8 -
> 1144143594851571569661248433072*x^10 +
> 3682862525053500791559515638600*x^12 -
> 8693355704402316431096075720520*x^14 +
> 16394872503384952006491292949865*x^16 -
> 26387316917169915527289585290460*x^18 +
> 37452280566060594746358503070858*x^20 -
> 47740404486181766316209780642820*x^22 +
> 55423947476122401752437921213065*x^24 -
> 58870208625780045323379674540820*x^26 +
> 58030587837504412314635631719520*x^28 -
> 54472073947308977321830018366176*x^30 +
> 49239457796351067392552601696240*x^32 -
> 43012853616400258712689244528460*x^34 +
> 36323948931672906173046609029970*x^36 -
> 29377569489403484765569859203920*x^38 +
> 22788548915181561726713932258680*x^40 -
> 16857194550514400031853658104200*x^42 +
> 11584615647879044636617246631070*x^44 -
> 7411292928519764848064641481820*x^46 +
> 4455112744096674126517658718330*x^48 -
> 2438996599504313974964504461440*x^50 +
> 1194689292448727425260627641460*x^52 -
> 524949326441431396920558140380*x^54 +
> 201021537824162724562860099525*x^56 -
> 61015761298172117757282456180*x^58 +
> 8304189679978507974953617206*x^60 +
> 2576525048464159376125949700*x^62 -
> 2090208393662742383940297195*x^64 +
> 1986814425386740056472178280*x^66 -
> 689825144661940289046969960*x^68 -
> 74165160041784503310561360*x^70 -
> 43639409581797171854387880*x^72 -
> 306779359014073038922080*x^74 +
> 29021239224919123514667120*x^76 +
> 3148715202822489687194520*x^78 -
> 1180110005143725763548459*x^80 -
> 1198749024197941338242580*x^82 -
> 491140297003511546045670*x^84 +
> 69048887622760819121580*x^86 +
> 69823737459557420754765*x^88 +
> 14776899216873553079620*x^90 -
> 1463855286795400794960*x^92 -
> 2352108554547064743120*x^94 -
> 381175702618028601675*x^96 +
> 126522213276402173400*x^98 +
> 35845283140073787252*x^100 -
> 2394735843271729380*x^102 -
> 1421523086424723225*x^104 -
> 37328586803289300*x^106 +
> 29410426690606450*x^108 +
> 2647220666999700*x^110 -
> 300290705882655*x^112 - 51254703758400*
> x^114 + 500254901760*x^116 +
> 403671859200*x^118  + 18339659776  + 18339659776 *x^120
>
> (*  Bug ?; F[Sqrt[Sqrt[2] + 3^(1/3)] + 1/Sqrt[3^(1/3) + 5^(1/5)]]
> //N
> =3.828176627860558*^38<---Bug ?  *)
>
> (* =0? *)

In[13]:= z =
  RootReduce[Sqrt[Sqrt[2] + 3^(1/3)] + 1/Sqrt[3^(1/3) + 5^(1/5)]];

In[14]:= RootReduce[F[z]]

Out[14]= 18339659776

You can also verify the result numerically using extended precision:

In[16]:= N[F[Sqrt[Sqrt[2] + 3^(1/3)] + 1/Sqrt[3^(1/3) + 5^(1/5)]], 50]

Out[16]= 1.8339659776`50.*^10

Machine precision numerical evaluation gives garbage due to
catastrophic
cancellation, i.e. subtraction of two close large numbers canceling
all significant
digits.

Hope this helps,
Oleksandr Pavlyk

Wolfram Research