# Bug? Numerical calculation error with FullSimplify and arbitrary precision

Bug introduced after 5.2, fixed in 8.0, reintroduced in 9.0 and persisting through 11.3

Is this a bug?

If I do

FullSimplify[n E^(010 n)]


then it returns

n/2


which is obviously incorrect.

(I've simplified the example, following a comment.)

[Mathematica Version 10.3.1.0]

• A wild guess: Since the -1.10 in a, b, and nb are independent, the quotient has a great deal of uncertainty in nb/a, represented by 09.698970004336022. Consider Plot[MinMax[1.10.*2.10.^(Interval[09.698970004336022] n) n ]/ n, {n, -10^10, 10^10}]. But I don't understand the 1/2 for a point estimate of the coefficient, or why b/a is presented as an exact result. Note that a/a is not 1 exactly. – Michael E2 Mar 10 '17 at 11:49
• Simpler example: FullSimplify[n E^(0100. n) ], Series[n E^(0100. n) , {n, 0, 0}]. The accuracy 100. does not seem to matter, big or small, positive or negative. – Michael E2 Mar 10 '17 at 12:47
• I don't see how this isn't a bug. n/2 just isn't correct. Can you please contact Wolfram Support and let us know what they said? – Szabolcs Mar 12 '17 at 10:39
• With versions 5.2 and 8.0.4 I get E^(0.*10^-10 n) n as the output (with InputForm being E^(010.*n)*n`). So the bug was introduced in version 9.0. – Alexey Popkov Mar 12 '17 at 14:58
• Sorry to say, but with version 7.0.1 on Win7x64 I get n/2. Incredible. – innaiz Mar 12 '17 at 17:19