To little/no purpose
Definition 1 of 2
Pro Tip 1/3Effort Wasted
Used to express efforts that fail to achieve their intended result. 
He studied all night to little purpose, since the exam was postponed.
Pro Tip 2/3Subtle Negativity
Implies disappointment or disillusionment with the outcome. 
Their negotiations continued to little purpose.
Pro Tip 3/3Not Always Literal
Sometimes used figuratively to express futility, not just physically doing something. 
Arguing about the past is to little purpose.