Mladenovic, with one championship to her credit on the WTA Tour, advanced when Petra Martic retired from their match in the second set. Mladenovic captured the first set 6-3.
Safarova had an unexpectedly difficult time earning her quarterfinal berth, eventually outlasting Mirjana Lucic-Baroni 7-6 (7-4), 7-6 (12-10).
In other second-round matches Thursday Eugenie Bouchard defeated Sesil Karatantcheva 7-6 (7-2), 6-4; Lauren Davis ousted Andrea Hlavackova 6-1, 2-6, 6-3 and Ajla Tomljanovic moved on when Bethanie Mattek-Sands retired in the third set trailing 7-5, 3-6, 4-1.
Mladenovic will meet Bouchard in the quarterfinals, Davis will face Safarova, Tomljanovic will play No. 6 seed Marina Erakovic, and Polona Hercog will take on Christina McHale.
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