I have seen this Taylor bug before:
(%i2) qqq : %e^(%e^(1/x)*gamma(x-%e^(-x)))-%e^gamma(x);
(%o2) %e^(%e^(1/x)*gamma(x-%e^-x))-%e^gamma(x)
(%i3) limit(qqq,x,inf);
debugger invoked on a SIMPLE-CONDITION in thread
#<THREAD"main thread" RUNNING {1007DC0183}>:
Undefined limit product $INF * $ZEROA in lim-times
0]
A recent build gives
It's nice that we don't get thrown into the debugger, but the answer is wrong--I'm pretty sure that the correct value is
infinity.