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From: Damien Wyart on 4 Aug 2010 05:51
Hello,

I am using Mathematica 7.0.2 and playing a bit with an expression
analyzed in the following paper:
http://www.loria.fr/~zimmerma/papers/cise.pdf

I tried many constructions with N and SetPrecision and can't get
Mathematica to output the correct result (I am not very experienced with
Mathematica). Here is the expression :

173746*Sin[10^22]+94228*Log[17.1]-78487*Exp[0.42]

The correct result should be -1.341818958*10^-12 but even forcing each
term with N and a very large number, I am still not getting this value
at all.


Any help will be appreciated. Thanks in advance ; best regards,

--
Damien Wyart

From: Bill Rowe on 5 Aug 2010 06:59
On 8/4/10 at 5:51 AM, damien.wyart(a)free.fr (Damien Wyart) wrote:

>I am using Mathematica 7.0.2 and playing a bit with an expression
>analyzed in the following paper:
>http://www.loria.fr/~zimmerma/papers/cise.pdf

>I tried many constructions with N and SetPrecision and can't get
>Mathematica to output the correct result (I am not very experienced
>with Mathematica). Here is the expression :

>173746*Sin[10^22]+94228*Log[17.1]-78487*Exp[0.42]

>The correct result should be -1.341818958*10^-12 but even forcing
>each term with N and a very large number, I am still not getting
>this value at all.

Actually, the "correct" result for this expression will vary
with different CPUs, different platforms etc. Without being very
specific about hardware and operating system, there is no
assurance whatever you will get the specific value you are expecting.

The problem is due to round off and loss of precision when using
machine precision numbers.

with

In[1]:= $Version

Out[1]= 7.0 for Mac OS X x86 (64-bit) (February 19, 2009)

I get

In[2]:= 173746*Sin[10^22] + 94228*Log[17.1] - 78487*Exp[0.42]

Out[2]= 2.91038*10^-11

I can get the result you are expecting by telling Mathematica to
use exact arithmetic until the final result is converted to a
floating point number. The following result should be repeatable
on all platforms running Mathematica version 7.0.1.

In[3]:= N[
173746*Sin[10^22] + 94228*Log[171/10] - 78487*Exp[42/100], 16]

Out[3]= -1.341818957829620*10^-12


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