# Simple arithmetic with Irrationals fails [closed]

While solving a simple puzzle that asked for a few calculations in plane geometry, I ended up with this expression:

$-\frac{55}{2}+\frac{\sqrt{27233}}{2}+\frac{1}{2}(55-\sqrt{27233})$

Or, in InputForm:

-55/2 + Sqrt/2 + (55 - Sqrt)/2


Obviously, the result is an exact 0. But the expression just sits there (Mathematica 10.1.0 64-bit, Win7) and looks at me challengingly instead of being evaluated to zero. Let's help it along a little:

-55/2 + Sqrt/2 + (55 - Sqrt)/2 // Apart
(* 0 *)


Good. Together, Simplify and probably a bunch of other functions deliver the same small incentive that Mathematica needs to get cracking. But the original expression that I encountered was larger, and the relevant portion was this (note the absolute-value function):

$\left|{-\frac{55}{2}+\frac{\sqrt{27233}}{2}+\frac{1}{2}(55-\sqrt{27233})}\right|$

Or, in InputForm:

Abs[-55/2 + Sqrt/2 + (55 - Sqrt)/2]


Expected result: Still 0, of course. Actual result:

N::meprec: "Internal precision limit \$MaxExtraPrecision = 50. reached while evaluating -(55/2)+Sqrt/2+1/2 (55-Sqrt)."


Clearly, applying Simplify, Together or any other operation to the expression inside Abs[] will make this work, as long as the expression's structure is changed in some way, as that will collapse the expression to zero.

What puzzles me is why Mathematica wouldn't evaluate it on its own? I always thought that Mathematica does an automatic "light-weight Simplify", so to speak, which would cover such a simple case.

The real question is, though, whether this is a bug. After all, unless I manually start editing intermediate results, this perfectly good evaluatable expression remains unevaluated, botching the rest of my puzzle solution. :)

• I think you answered your own question, haven't you? It's obvious that 1-1 evaluates to zero, but also that more complicated expressions require "user intervention" such as Simplify. So what's the question here? – yohbs Sep 20 '15 at 6:51
• what-should-we-do-about-the-abbreviation-mma – Sjoerd C. de Vries Sep 20 '15 at 11:00
• The Abs` issue is listed in the Possible Issues section of its help page: "Abs can stay unevaluated for some complicated numeric arguments:". The example include the error message you list in your question. – Sjoerd C. de Vries Sep 20 '15 at 11:06
• Quick answer: It's not a bug. – Daniel Lichtblau Sep 20 '15 at 22:27
• I'm voting to close this question as off-topic because the question is rhetorical rather than real -- this is just a rant about something doesn't like about Mathematica's evaluation process. – m_goldberg Oct 28 '15 at 17:01