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: He has matured and is playing more carefully, more seriously.
The Frenchman, who will face Roger Federer for a spot in the semifinals, rejected that notion after Tuesday's win.
"I'm the same. So I will say I'm a bit more lucky than I was maybe sometime in the past. I think I haven't changed a lot, to be honest," Monfils said. "I just play maybe solid today, but I'm still the same."
As if to prove that, there was the unusual sequence in the second set. Trailing 40-love as Dimitrov served, Monfils stood halfway between the baseline and the service line to receive, and then casually and halfheartedly flicked a return long to lose the game. He walked to the changeover to a chorus of boos from the spectators in Arthur Ashe Stadium, plopped down for the break, chucked a towel at the adjacent chair and started barking something toward his guest box in the stands.
Monfils said he was angry at himself at that moment and just wanted to get that game over with.
"I was like, 'Just serve, because obviously I give you the game. So it's OK,'" he said. "It's nothing against anyone. I was upset."
Monfils' lone Grand Slam semifinal appearance came at the 2008 French Open, when he lost to Federer, part of a 2-7 career mark against the 17-time major champion.
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 in the match.
In women's quarterfinal action Tuesday, 39th-ranked Peng Shuai of China ended the precocious run of 17-year-old Belinda Bencic of Switzerland 6-2, 6-1. Peng's next opponent will be No. 10 Caroline Wozniacki or No. 13 Sara Errani, who met late Tuesday.
Peng, 28, advanced to her first Grand Slam semifinal in the 37th major tournament of her career; only five women took longer to get to the final four at one of the sport's top four events.
Her voice choking with emotion during an on-court interview, Peng said she had pondered giving up professional tennis in the past, but "my coach, my parents — they always tell me to try to keep going and never ever, give up."
In the afternoon, with the temperature topping 90 degrees and the humidity at about 50 percent, Monfils and Dimitrov appeared sluggish at times.
"Where should I begin?" said Dimitrov, a Wimbledon semifinalist in July. "Just a bad match for me."
A key moment came in the second-set tiebreaker, when Dimitrov went ahead 6-4. On the first set point, Dimitrov nearly lost his balance as he shanked a forehand off Monfils' mediocre drop shot.
"One of the worst drop shots I ever hit," Monfils said, grinning, "and he hit a frame."
On the second, a 13-stroke exchange, Dimitrov dropped a backhand into the net.
That was part of four-point run for Monfils thanks to miscues by his opponent. While Monfils essentially kept the ball in play, taking some pace off and pushing shots over the net, Dimitrov sailed forehands long to end the set.
"He defended when he had to," Dimitrov said. "But if you think about it, I did a lot of unforced errors."
What mattered in the end, of course, was who won, something that has not always seemed to matter to Monfils.
"For me, tennis is a sport, you know," he said. "It's not a job, you know. It's a sport."