Can only agree with the man who said that the Easyout was most misnamed tool in the shop.
SOMETIMES, if you can access the nut or parent metal into which the screw id tapped, a succesion of blows around the outside when placed on a suitable "anvil" will break any rust/corrosion.
Obviously can't be used on a casting of any size.
+1 for the left hand drill, probably a mixture of torque with a little local heating.
On larger sizes, if a hardened screw, the tipped drills used at high speed with lots of pressure will work. But you no longer see them at Shows, (i have some that need replacing. Trying to use a small masonry drill, instead, did not work, and it wrecked the masonry drill!)
Howard