"Second set, it was definitely better".
Both the Spaniard and Federer have looked in supreme form since the start of the tournament, with both players yet to drop a set.
At the tournament in the United States, which is a Masters 1000 event and widely considered as one of the biggest events outside of the four Grand Slams, 37-year-old Federer eased through with a 6-1, 6-4 win over Great Britain's Kyle Edmund.
Speaking of their first meeting, Federer admitted the windy conditions of the match were tough but said Edmund still had what it takes to achieve great things in the future.
The victor of that match will face either 18th-seeded Frenchman Gael Monfils or unseeded German Philipp Kohlschreiber - who stunned world number one Novak Djokovic 6-4, 6-4 on Tuesday. He never really got going.
Three-time champion Nadal crushed Filip Krajinovic of Serbia 6-3, 6-4, while five-time champion Federer defeated Kyle Edmund of the United Kingdom 6-1, 6-4.
"I felt like every time I was trying something different she was coming up with better shots", Muguruza said. "It's small gaps", Nadal said about the upsets.
"The previous days here in Indian Wells helped me a lot to get back to my top level physically and also to play good tennis again", Thiem said.More news: Former Cardinals WR J.J. Nelson signs with Oakland Raiders
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"Probably played a little bit worse today than yesterday", Nadal said of his performance. Naomi Osaka, the world's top-ranked woman, also lost in straight sets a day earlier.
Awaiting Raonic in today's quarterfinals is 19-year-old Miomir Kecmanovic who earned a retirement from Yoshihito Nishioka. 2 has finally reached the quarter finals of ATP Indian Wells for the first time in three years.
"It will be amusing that somebody other than Novak is still in", Kecmanovic said of top-ranked Djokovic, his famous countryman who was upset on Tuesday.
The multiple Grand Slam champions both won their quarter-finals on Friday, although Nadal in particular had to work hard to overcome Russian Karen Khachanov 7-6 (2) 7-6 (2) in a match during which he required treatment on the knee.
Kecmanovic got into the main draw when world No.6 Kevin Anderson withdrew before his opening match with an elbow injury.
Raonic will be Kecmanovic's next opponent after the big-serving 13th seed accounted for German Jan-Lennard Struff 6-4 6-3.