NEW YORK — Gael Monfils follows his own rules.

The guy does things on a tennis court no one else has — or can. Just search his name on YouTube and watch any of many video clips showcasing his speed and agility; start with the parallel-to-the-ground, a-few-feet-in-the-air dive at this year’s French Open.

He sips soda during breaks in his matches, raising the can in a toast to his agent.

He is currently without any coach at all, in an era when some players have two.

What Monfils has never done, despite all his talent — and in some cases, because he has appeared to value style over substance right there on court, in the middle of a point, preferring the spectacular to the sufficient — is reach a Grand Slam final. He took a step closer Tuesday at the U.S. Open during a surprisingly matter-of-fact 7-5, 7-6 (6), 7-5 victory in the fourth round over No. 7-seeded Grigor Dimitrov, a man considered one of the sport’s up-and-comers.

There is a narrative building around the 20th-seeded Monfils’ success so far this year at Flushing Meadows, where he hasn’t dropped a set en route to reaching the quarterfinals for the first time since 2010.

The Frenchman will face Roger Federer for a spot in the semifinals.

Federer advanced to the U.S. Open quarterfinals for the 10th time in 11 years by eliminating 17th-seeded Roberto Bautista Agut 6-4, 6-3, 6-2 Tuesday night. Federer won the point on 35 of 52 trips to the net.

The other quarterfinal matchup on that half of the draw will be No. 6 Tomas Berdych against No. 14 Marin Cilic. Berdych beat 20-year-old Dominic Thiem 6-1, 6-2, 6-4; Cilic was a 5-7, 7-6 (3), 6-4, 3-6, 6-3 winner against No. 26 Gilles Simon, who was treated for a back problem early on.