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Re: Re: Loss of precision when using Simplify

• To: mathgroup at smc.vnet.net
• Subject: [mg37019] Re: [mg36996] Re: Loss of precision when using Simplify
• From: Bill Rowe <listuser at earthlink.net>
• Date: Sun, 6 Oct 2002 05:33:26 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

On 10/4/02 at 5:01 AM, carlw at u.washington.edu (Carl K. Woll) wrote:

>It seems to me that you are arguing that if you have an expression
>consisting of one term which is very inprecise and another term which
>is very precise or exact, then the total expression is only as precise
>as the least precise portion of the expression. 

Yes. 

>This is total nonsense. 

Not exactly.

>Consider adding the following terms:

>1.234567890123456`16 + 0.00000000000000001`1

>consisting of one term with precision 16 and another term with
>precision 1. By your argument, Mathematica should return an answer
>with only a single digit of precision. Of course, Mathematica does no
>such thing.

I had not considered adding two terms with much different magnitude and much different precision.

Consider a different example i.e.,

1.234567890123456`16 + 0.1`1

Mathematica does not and should not return a result with 16 digits of precision