Back when
Billy Joel was writing this song he brought his new creation to a recording session with his band. During a break in recording he said he had a new song and wanted the band's opinion. They listened as
Joel played the song, and when it was over
Liberty DeVitto, the drummer said, "You
schmuck. That's
Laughter In The Rain by
Neil Sedaka!"
Billy Joel had ripped off another melody and hadn't even realized it.
"You mean I wrote all these words for nothing?!" he replied back.
Joel took his lyrics home at the end of the day and was so mad about having subconsciously stealing another song that he wrote a new melody: the "angry" one we know and love today.
References:
Billy Joel told this story at a 1996 lecture. I was in the audience that night.