Billy Joel -- Movin' Out ... of His $14 Million Miami Palace

Billy Joel must be INSANE -- like certifiably insane -- 'cause the Piano Man has grown tired of his INCREDIBLE Miami Beach estate ... and put the place up for sale for the low low price of $14.75 mil.

The 8,881 square foot oceanfront palace -- located on the ultra-exclusive La Gorce Island -- boasts 7 bedrooms, 8.5 baths ... and happens to be surrounded by famous neighbors like Cher and Lil Wayne.

Joel bought the place in 2006 for $13.5 mil -- it's unclear why he's decided to leave.

But if you've got the cash ... this place is a dream pad ...with a gourmet chef kitchen, wine cellar, bad-ass swimming pool and of course 150 feet of water frontage.

... 'cause everyone needs a place to park their boat.