1
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 Simplify[E^(-0.2` (1 - τ2)) (2^-(-21 + τ1)^2 Sin[
          1.256` + π (-21 + τ1)] + 
        2^-(-20 + τ1)^2 Sin[
          1.256` + π (-20 + τ1)]) (2^-(-21 + τ2)^2 Sin[
          1.256` + π (-21 + τ2)] + 
        2^-(-20 + τ2)^2 Sin[1.256` + π (-20 + τ2)]) Sin[
       0.9797958971132712` (1 - τ2)] (1/2 E^(-0.2` (1 - τ1))
          Sin[0.9797958971132712` (1 - τ1)] + 
        E^(-0.2` (-τ1 + τ2))
          Sin[0.9797958971132712` (-τ1 + τ2)])]

(mma11 win7 64bit)

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  • 1
    $\begingroup$ A related question. $\endgroup$ – J. M. will be back soon Oct 15 '16 at 2:51
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    $\begingroup$ Use Simplify[expr] // Chop $\endgroup$ – Bob Hanlon Oct 15 '16 at 2:58
  • $\begingroup$ @Bob Hanlon It may not be that problem. $\endgroup$ – WateSoyan Oct 15 '16 at 3:00
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    $\begingroup$ @WateSoyan well, it is your job to state the problem well. So what did you expect, 12? $\endgroup$ – Kuba Dec 14 '16 at 9:26
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    $\begingroup$ Probably precision-related. For any value of the parameters that I try, I get extremely small values, effectively zero. Remember that any number that has a decimal point is considered inexact, so the argument that "but it's not exactly zero!" doesn't apply. A counterargument is: Have you investigated how much precision would be lost to roundoff during such a calculation? Perhaps more than the magnitude of the result. $\endgroup$ – Szabolcs Dec 14 '16 at 9:33
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I understand that you are not very sure about the purpose of Simplify[] function. Take it out of the expression and you will get the long full result.

    E^(-0.2` (1 - τ2)) (2^-(-21 + τ1)^2 Sin[
     1.256` + π (-21 + τ1)] + 
   2^-(-20 + τ1)^2 Sin[
     1.256` + π (-20 + τ1)]) (2^-(-21 + τ2)^2 Sin[
     1.256` + π (-21 + τ2)] + 
   2^-(-20 + τ2)^2 Sin[1.256` + π (-20 + τ2)]) Sin[
  0.9797958971132712` (1 - τ2)] (1/2 E^(-0.2` (1 - τ1)) Sin[
     0.9797958971132712` (1 - τ1)] + 
   E^(-0.2` (-τ1 + τ2)) Sin[
     0.9797958971132712` (-τ1 + τ2)])

Which results in a long expression that you may inspect. Also try substitute Simplify with N and also eliminate some precision from the code.

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