  The current dependence of the spin torque switching rate in a thermally
activated region of an in-plane magnetized system was studied. The logarithm of
the switching rate depended nonlinearly on current in the high-current region,
I_{c} < I < I_{c}^{*}, where I_{c} and I_{c}^{*} are critical currents
distinguishing the stability of the magnetization. We also found that the
attempt frequency had a minimum around I_{c}, and that the attempt frequency at
I_{c} was three orders of magnitude smaller than that at zero current, contrary
to the assumption in previous analyses of experiments that it remains constant.
