Re: Accuracy and Precision

*To*: mathgroup at smc.vnet.net*Subject*: [mg36983] Re: Accuracy and Precision*From*: pkosta2002 at yahoo.com (Peter Kosta)*Date*: Fri, 4 Oct 2002 05:01:21 -0400 (EDT)*References*: <anggkb$prg$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

The more I play with the example the more depressing it gets. Start with floating point numbers but explicitely arbitrary-precision ones. In[1]:= a=77617.00000000000000000000000000000; b=33095.00000000000000000000000000000; In[3]:= \!\(333.7500000000000000000000000000000\ b\^6 + a\^2\ \((11\ a\^2\ b\^2 - \ b\^6 - 121\ b\^4 - 2)\) + 5.500000000000000000000000000000\ b\^8 + a\/\(2\ b\)\) Out[3]= \!\(\(-4.78339168666055402578083604864320577443814`26.6715*^32\)\) In[4]:= Accuracy[%] Out[4]= -6 Due to the manual section 3.1.6: "When you do calculations with arbitrary-precision numbers, as discussed in the previous section, Mathematica always keeps track of the precision of your results, and gives only those digits which are known to be correct, given the precision of your input. When you do calculations with machine-precision numbers, however, Mathematica always gives you a machineprecision result, whether or not all the digits in the result can, in fact, be determined to be correct on the basis of your input. " Because I started with arbitrary-precision numbers Mathematica should display only those digits that are correct, that is none. To relax a bit, set a new input cell to StandardForm and type 77617.000000000000000000000000000000000 Convert it to InputForm. You get 77616.999999999999999999999999999999999999999999952771`37.9031 Convert back to StandardForm 77616.99999999999999999999999999999999999999999976637`37.9031 Again to InputForm 77616.99999999999999999999999999999999999999999963735`37.9031 Back to StandardForm 77616.99999999999999999999999999999999999999999951376`37.9031 See what you can get if you have enough patience or a small program. PK

**Follow-Ups**:**Re: Re: Accuracy and Precision***From:*Daniel Lichtblau <danl@wolfram.com>