Re: Loss of precision when using Simplify

*To*: mathgroup at smc.vnet.net*Subject*: [mg36988] Re: Loss of precision when using Simplify*From*: "Carl K. Woll" <carlw at u.washington.edu>*Date*: Fri, 4 Oct 2002 05:01:31 -0400 (EDT)*Organization*: University of Washington*References*: <angi42$q06$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Bill, Let's step through the expansion here. 9*(0.546+x[2]))/16 can be expanded to 9*0.546/16 + 9*x[2]/16 which becomes .307125 + 9*x[2]/16 My question was why the 9/16 gets converted to .5625, as I see no reason to do so. Even more troubling (to me, at least) is the following: x[0]+3x[1]/4+9x[2]/16+.4//Simplify 0.4 + x[0] + 0.75 x[1] + 0.5625 x[2] I don't want Simplify to change my nice rational numbers to machine number approximations. Carl Woll Physics Dept U of Washington "Bill Rowe" <listuser at earthlink.net> wrote in message news:angi42$q06$1 at smc.vnet.net... > On 10/2/02 at 3:32 AM, carlw at u.washington.edu (Carl K. Woll) wrote: > > >I'm writing to report what I consider to be a bug. First, I want to > >show a simplified example of the problem. Consider the following > >expression: > > > >expr=0.22 + x[0] + (3*(-0.16+ x[1]))/4 + (9*(0.546 + x[2]))/16; > > > >When simplified I expected to get some real number plus > >x[0]+3x[1]/4+9x[2]/16, but instead I get the following: > > > >Simplify[expr] 0.407125 + x[0] + 0.75 x[1] + 0.5625 x[2] > > > >As you can see, for some reason Mathematica converted the fractions > >3/4 and 9/16 to real machine numbers. I consider this to be a bug. > > You really are not seeing a loss of precision here. When simplify carries out the indicated multiplication such as 9*.546/16 a machine precision number is returned because on of the arguments only has machine precision. It would be incorrect for Mathematica to return a result with greater precision than the arguements. It would also be incorrect for Mathematica to refuse to preform the required multiplications when simplifying this expression. > > Or said differently, if you want an exact result from Mathematica *all* of the information you supply Mathematica must also be exact. It is not sensible for Mathematica to do otherwise. >