California, March 15, 2018 - World No 1 Roger Federer's remarkable run continued as he booked his quarterfinal berth in the ATP Indian Wells Masters with a 7-5, 6-4 win over Jeremy Chardy. The 36-year-old Federer, who won his 20th Grand Slam when he captured the Australian Open in January, is off to one of his strongest career starts and is now 15-0 in 2018. It is his best beginning to the season since 2006 when he started 16-0 and won 33 of his first 34 matches. "It has been great. It is a totally different year, and so many years after that," he said. "For so many years I have felt good actually in Australia already. "I don't know if it's Australia per se or, taking the benefits from the hard work I put into the new season." Federer, who also won at Rotterdam in February, is gunning for a record sixth Indian Wells title. "Yeah, and then also Rotterdam was great. I was very happy that I was able to win the tournament there, not just get to the semis and get world No 1. "And here now I'm relieved that I was able to win three matches already. Because in a big, tough draw like here at Indian Wells, you're never quite sure what to expect. "So I'm just happy I'm on a good run." The defending Indian Wells champion Federer put on a serving clinic against Chardy as he hit two aces and won 100 percent of his first serve points. He dropped just three serve points overall with those coming on his second serve. Federer advances to the quarterfinals where he will face South Korea's Chung Hyeon who defeated 30th-seeded Pablo Cuevas 6-1, 6-3 earlier on Wednesday. Federer only needed to break Chardy once in each set to get the win in 82 minutes. The first break of serve came in the 11th game of the opening set to take a 6-5 lead. In the second set he broke Chardy in the ninth game to lead 5-4. Each time he got the break he then served for the set. Federer clinched the victory on the first match point when Chardy pounded a forehand into the net. Chardy hit four aces but made 46 unforced errors compared to just 29 for Federer. Federer is now 4-1 overall against Chardy, having beaten the Frenchman the last two times they played. Federer picked up seven titles in 2017, comprising the Australian Open, Halle, Wimbledon, Miami, Shanghai, Basle and Indian Wells. Federer will face the 21-year-old Chung for the second time this year. Chung made a Grand Slam breakthrough when he reached the semifinals of the Australian Open in January but had to retire in his match with Federer because of a foot blister. "He was actually struggling going into the match," Federer said. "Seeing the blister after, that wasn't very nice. I can just imagine how much pain there is to it. "You kind of want to go out and give it a shot, but then you're like, probably shouldn't. So I felt for him." Chung survived a late rally from Uruguay's Cuevas, who fended off a total of nine match points before eventually losing in the first-ever meeting between the pair. Down a set and behind 5-0 in the second set, Cuevas miraculously saved seven match points to win the game. He then served out the next game to cut Chung's lead to 5-2 and then broke the South Korean in the game after that. Cuevas saved two more match points in the ninth game but his luck finally ran out. In other men's fourth round action, Croatia's Borna Coric blasted nine aces as he outlasted American Taylor Fritz 6-2, 6-7 (6/8), 6-4. Unseeded Coric moves to the quarterfinals, where he will play red-hot South African Kevin Anderson who defeated Spaniard Pablo Carreno Busta 4-6, 6-3, 7-6 (8/6). Meanwhile, world No 1 Simona Halep punched her ticket to the Indian Wells semifinals with a 6-4, 6-7 (5/7), 6-3 win over Croatia's Petra Martic. The 26-year-old Halep improved to 18-1 on the season and is looking to win her second WTA Tour title of 2018. Halep, of Romania, needed two hours and 23 minutes to put Martic away under taxing conditions as strong winds swirled around the main stadium court. "It was difficult conditions to play in today because of the wind," she said. "It was tough to play, because the ball was really moving. "But I just tried everything. I tried also to push a little bit the ball and then to hit it. I tried to mix it up. Was not easy at all. For both of us it was difficult." Halep moves on to the semifinals where she will face Japan's Naomi Osaka who beat fifth-seeded Karolina Pliskova 6-2, 6-3. Halep is guaranteed to hold onto her No 1 ranking at the end of this event after world No 2 Caroline Wozniacki was eliminated on Tuesday. Halep blasted two aces and broke Martic's serve four times. "I just fought and that's maybe why I won because I refuse to lose," Halep said. Halep won the final five games of the third set after being broken once and falling behind 3-1 early. The turning point in the third set came for Halep after she won a challenge in the eighth game with Martic holding serve. On the very next point Martic hit a forehand wide as Halep took the game and a 5-3 set lead. Halep then served for the match, winning five of the final six points after the challenge. Halep said her early struggles in the final set were from nerves and frustration with the playing conditions. "I calmed myself down a little bit more, and I just was more focused on what I have to do, and not thinking that much about the wind and what is going on on court. "I just fought till the end, and I think that's why I could win." Halep is seeking her second Indian Wells title after beating Jelena Jankovic in 2015. In the evening session, world No 44 Osaka broke Pliskova's serve six times in her 78-minute upset on the main stadium court. "I returned the ball well," said Osaka. "She is one of the best servers on tour and I was able to break her quite a few times so I am really happy about that." Pliskova, who reached the quarterfinals at the Australian Open in January, smashed five aces but made six double faults. Pliskova was trying to reach the semifinals in this event for the third consecutive year. "Everything was a little bit off from my side," Pliskova said. "She was playing very well. Hitting her spots, forehands, even the backhands. "I just battling all the way, even in serving and returning. I was definitely not feeling the best."