The physician started to perform the operation but the patient was not yet completely under anesthesia. which part of sentence is wrong?

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I'd say this is wordy: there are two adverbs right next to each other, and one is unnecessary. There is also a comma missing.

completely under

Right.

The part of the sentence that is wrong is "not yet completely under anesthesia." When a patient is undergoing a surgical operation, it is crucial for them to be fully under anesthesia to ensure they do not feel any pain or discomfort during the procedure. Therefore, the correct sentence should be: "The physician started to perform the operation, ensuring that the patient was completely under anesthesia."