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|Romania's Simona Halep has won two Grand Slam titles, but never the Australian Open. (Photo: AFP/William West)|
History-chasing Serena Williams and defending champion Naomi Osaka were chief among six of the top 10 women's seeds who tumbled out in round three.
After top seed Ashleigh Barty, Halep is the highest remaining seed at four and is in full flow, not dropping a set in reaching the last eight.
Despite several shocks in Melbourne, Halep will be expected to defeat 28th seed Anett Kontaveit of Estonia and the Romanian's coach said she has learnt to better control her emotions.
"She's still as stressed on the court as she always is, but she's learning ways to deal with it and to handle it," said the Australian Darren Cahill.
Halep, the beaten 2018 finalist, has come up with a novel way of attempting to keep herself in check.
All aces by players at the Australian Open earn a donation to a bushfire relief fund, but Halep has promised to give $200 each time that she berates Cahill during a match.
Cahill, who is totting up how much Halep owes, sees another change in the 28-year-old Halep, who won the French Open in 2018 and Wimbledon last year.
"What I'm most proud of is that fight that she's showing when a few things go against her," he said.
"That's been the big change in her I have seen over the last two or three years."
Like Halep, the 26-year-old Muguruza has also won the French Open and Wimbledon, in 2016 and 2017 respectively.
But she has gone in the opposite direction to Halep, who is set to move up a spot to two in the world rankings next week.
Muguruza, like Halep a former number one, is now down at 32nd in the world.
But with fellow Spaniard Conchita Martinez back as her coach as of November, she is finally returning to form.
It was with Martinez - the first Spanish woman to win Wimbledon, in 1994 - in her corner that Muguruza triumphed at Wimbledon.
Muguruza arrived in Melbourne with a virus and lost the first set of her opener 6-0 to the American qualifier Shelby Rogers.
But she won the next two sets 6-1, 6-0, and in Monday's last 16 brushed aside the ninth seed Kiki Bertens 6-3, 6-3.
Muguruza faces 30th-seeded Anastasia Pavlyuchenkova in the quarter-finals - the third time in four years the Russian has reached the last eight. She has never gone any farther.
The 47-year-old Martinez is trying to temper expectations of what she and Muguruza can achieve together.
But she said: "I feel like pre-season was very, very good.
"There was a lot of time actually to work on things, on things that were needed. I think the results are here."
That includes encouraging Muguruza to be aggressive, "finishing at the net a lot", but also working on the mental side of her game.
"Not only coaching... the experience as a player, the mental part, I went through that and more things," said Martinez.
"We talk a lot, but we understand each other."