The pilot reported that she departed on a cross-country flight, with a planned duration of about 3 hours and 20 minutes. During the flight she leaned the mixture and switched fuel tanks on the hour. During the approach to the destination airport the engine "coughed and ran rough", the pilot stated that she changed fuel tanks and turned on the boost pump. The engine "coughed" again, and she determined that could not make the runway, which was about 4 miles way. The pilot elected to perform a forced landing in a nearby field. The aircraft was substantially damaged during the forced landing. Air traffic control tower's last radio contact with the aircraft, stated that the pilot reported that she did not have enough gas and would have to land in a field. Aircraft recovery personnel reported that the fuel tanks had not been breeched during the accident and that the fuel tanks were empty.