Two phone screens, one terrible, one amazing -- thoughts?

TLDR: two phone interviews for same company scheduled for different days. Independent interviews (one did not lead to other). First one terrible. Second one amazing. Should I email the recruiter that first one wasn't at the right time? I recently had two back to back phone screens for a new grad position at a fairly difficult company (one of Dropbox, Airbnb, Uber, Palantir, Facebook). They were scheduled for two different days. I got my first screen scheduled the day before (less than 24 hours). I was pulling multiple all-nighters due to a school project, and was in a wretched bodily and mental condition. I took the phone screen in the morning and I was super tired. I didn't do well and I could tell from the interviewer's tone that it wasn't a pass. We ran out of time without me completing the problem and I didn't ask questions about the company. After resting for the weekend, I had the second phone screen. And it was probably the best went phone screen in my recruiting life. Since I already kinda gave up due to the first screen, I was in a zen mode. Not only did I complete the coding assignment to the interviewer's satisfaction, we had a nice chitchat about the company's culture and future. It was supposed to be a 45 minute interview but we went over 30 minutes. That never happened to me before. I could kind of tell the interviewer was trying to sell the position to me to, like "our company is a good place to start a career." I had an actual connection with him, and I felt so bad I messed up on the first screen. When companies have two back to back phone screens, do they want both to have gone well to go to next round (onsite)? Do you think it is a good idea to email the recruiter and explain how the first phone screen wasn't at the best time for me? Or should I just keep quiet?