Osaka, 21, admitted she over-thought about the need to win the match in order to retain her ranking at the top of the women's game as she went down 3-6 6-2 7-5.
The 21-year-old Japanese was a break up in the final set against Bencic, but was broken when serving for the match at 5-4 as the wind swirled despite the blue skies in the Spanish capital.

Naomi Osaka of Japan shakes hands with winner and opponent Belinda Bencic of Switzerland during day six of the Mutua Madrid Open at La Caja Magica on May 09, 2019 in Madrid, Spain.

Image credit: Getty Images

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"People have been telling me that if I get to the semis I stay at number one so I wanted to do that," Osaka said.
"I wanted to do that and was thinking about it while I was playing, which wasn't a good thing. I play my best when I'm calm and today I wasn't, so that's the biggest thing I can learn."
Bencic will face two-times Madrid champion Halep in the last four after the Romanian beat ninth seed Ashleigh Barty 7-5 7-5.

Belinda Bencic of Switzerland seen in action against Naomi Osaka of Japan during day six of the Mutua Madrid Open at La Caja Magica in Madrid, Spain.

Image credit: Getty Images

If Halep wins the tournament she will replace Osaka at the top of the WTA rankings heading into the French Open.
Stephens comfortably saw off Croatian Petra Martic 6-4 6-3 to set up a semi-final with Bertens after the Dutch seventh seed stunned world number two Petra Kvitova 6-2 6-3 in Thursday's late match under the floodlights.
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