Daria Kasatkina learns the hard way how good “hurricane” Serena Williams is

Bencic beat world number 17 Madison Keys, 2014 Wimbledon finalist Eugenie Bouchard, the fast-improving Briton, Johanna Konta, double US Open finalist Caroline Wozniacki, and world number four Agnieszka Radwanska in order to win at Eastbourne.

To reach the last eight would be an extraordinary effort; she would be the first British player to make the quarter-finals of a slam since Jo Durie at Wimbledon in 1984.

She has assured her interviewers, when asked, that she still has vivid childhood memories of her early years in Australia, where she played under-12 nationals during the heat of an Australian summer.

Her win means she will climb around 11 places from her ranking of 47 and at this rate, she is destined for much higher.

“I think players find it hard to know how to get after her mentally, as well as physically”.

Federer, a four-time Australian Open champion, beat Dimitrov in the quarterfinals at the Brisbane International two weeks ago, dropping a set to the Bulgarian player for the first time. Her success at the season’s first Grand Slam has given the Brits and Aussies something to celebrate, and scrutinize. “Everything I’ve been trying to work on was kind of clicking today”, said the buoyant world No 1, who is seeking a record-equalling 22nd Grand Slam title.

The Russian fifth seed needed two hours, 14 minutes to see off the hard-working 103rd-ranked American 6-1, 6-7 (5/7), 6-0 with the roof closed on Rod Laver Arena on a wet Melbourne day.

The 25-year-old, who put out Venus Williams in round one, was far too strong for the Czech Denisa Allertova, her 6-2, 6-2 victory putting her through to the last 16 for the second consecutive Grand Slam event.

To Konta’s way of thinking, no match matters except the next one.

“I had a tough match against her at the French Open so I knew I had to run every ball down and fight for every point”. “It’s very exciting, I must tell you”, said the Swiss, who also became the oldest man to reach the round of 16 since Andre Agassi in 2005.

“She has the mental side to complement her tennis now, she’s very consistent, she does believe so much more in herself and you can see it clearly on court”.

Kasatkina managed to get on the scoreboard in holding serve for 1-3 but she had no answers to Williams’ serve as she rattled through the set in just 22 minutes.

Her opponent has also been in good form, but Allertova was wearing heavy strapping around her left thigh and, whether fully fit or not, never really gained a foothold in the contest.

“My second match (against Hseih Su-Wei) I thought, under the circumstances, I thought I played well. I’m just happy I’m competing at the event I’m at which happens to be the Australian Open, which is pretty cool”.