Wow, this is mighty strange... I added some more prints of calculations, as so:

printf "%3.5g %3.5g %3.5g %3.5g\n",
  ($e+0), (0+$e), (0-$e),($e-0);

printf "%3.5g %3.5g %3.5g %3.5g\n",
  ($e+1), (1+$e), (1-$e),($e-1);

printf "%3.5g %3.5g %3.5g %3.5g\n",
  ($e+$e), ($e-$e), ($e*$e),($e/$e);

printf "%3.5g %3.5g %3.5g %3.5g\n",
  ($e**2), ($e**0), (0/$e),($e/0);
[download]

The output was:

  0   0   0   0
  1   1   1  -1
  2   0   1   1
  0   1   0   0
[download]

In particular, note that the final calculation is ($e/0). The anomaly is more than just $e having an ambiguous value, it seems.