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I notice the following weird results with MMA version 12.1 on Mac. I restart MMA and still get the same.

FullSimplify[Exp[-2 (x - 3.1)^2]]  (* 0, obviously wrong*)
FullSimplify[Exp[-2 (x - 3.0)^2]]  (* nonzero, correct *)
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    $\begingroup$ Same on 12.1.0 for Linux x86 (64-bit) (March 4, 2020) Changing to 3.100000000000000000000000000000000000000000000000000 makes the problem go away $\endgroup$
    – Bill
    Aug 19 '20 at 0:14
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    $\begingroup$ @Bill - specifying any arbitrary-precision will work, e.g., Exp[-2 (x - 3.11)^2] // FullSimplify` or Exp[-2 (x - SetPrecision[3.1, 1])^2] // FullSimplify $\endgroup$
    – Bob Hanlon
    Aug 19 '20 at 0:22
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    $\begingroup$ It's the same on win10 (V12.1.1). It's a strange mistake. $\endgroup$ Aug 19 '20 at 1:11
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    $\begingroup$ Also on V9.0. Anything constant from 3.0 to 18.83856036 gets simplified to 0. $\endgroup$
    – wxffles
    Aug 19 '20 at 1:25
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    $\begingroup$ This type of problem is thorny (I've commented on similar in past). We are looking into one possi ble improvement for version 12.2. Not sure if it will survive testing though. $\endgroup$ Aug 19 '20 at 15:53