I just love this performance by Fiona Apple. Must have watched it four or five times in a row already. Production wise, she keeps it fairly classic and does not stray too far from the original, which I always think is kinda risky when covering a song by someone else - in my experience, they tend to fare better when the artist mixes things up a bit and makes its their own.
However, she herself does that in a delivery so intense, so physical (note how completely out of breath she is afterwards), that I was a little startled by the juxtaposition at first, then completely zoned in, goosebumps akimbo, and think this might be the first time I have actually listened to the full lyric, stuff like, "I spoke about wings, you just flew" and "I saw the rain dirty valley, you saw Brigadoon". So simple, yet so poignant - I just never noticed before.
Suffice to say, despite overfamiliarity with the famous hook, I feel like she just opened up the song for me and showed me its treasures - literally "I saw the crescent, you saw the whole of the moon" - which is always a nice feeling after hearing a new cover. Whole new appreciation and all that.