Found 22 equivalence classes:

Class 1 (6 trees):
  mul(mul(mul(0,mul(0,0)),0),mul(0,0)) (6 leaves)
  0 (1 leaves)
  mul(mul(0,0),mul(0,mul(mul(0,0),0))) (6 leaves)
  mul(mul(mul(0,0),0),mul(0,mul(0,0))) (6 leaves)
  mul(mul(mul(0,0),0),mul(0,0)) (5 leaves)
  mul(mul(0,0),mul(0,mul(0,0))) (5 leaves)

Class 2 (9 trees):
  mul(0,mul(mul(0,0),mul(0,0))) (5 leaves)
  mul(0,mul(mul(0,0),mul(0,mul(0,0)))) (6 leaves)
  mul(mul(mul(0,0),mul(0,mul(0,0))),0) (6 leaves)
  mul(mul(0,0),mul(mul(0,0),mul(0,0))) (6 leaves)
  mul(0,0) (2 leaves)
  mul(mul(mul(0,0),mul(0,0)),mul(0,0)) (6 leaves)
  mul(mul(mul(mul(0,0),0),mul(0,0)),0) (6 leaves)
  mul(0,mul(mul(mul(0,0),0),mul(0,0))) (6 leaves)
  mul(mul(mul(0,0),mul(0,0)),0) (5 leaves)

Class 3 (11 trees):
  mul(0,mul(mul(0,mul(0,0)),mul(0,0))) (6 leaves)
  mul(0,mul(mul(0,mul(0,0)),0)) (5 leaves)
  mul(0,mul(mul(0,mul(0,mul(0,0))),0)) (6 leaves)
  mul(0,mul(mul(0,mul(mul(0,0),0)),0)) (6 leaves)
  mul(0,mul(mul(mul(0,0),mul(0,0)),0)) (6 leaves)
  mul(0,mul(mul(mul(0,mul(0,0)),0),0)) (6 leaves)
  mul(0,mul(mul(mul(0,0),0),0)) (5 leaves)
  mul(0,mul(mul(mul(mul(0,0),0),0),0)) (6 leaves)
  mul(0,mul(0,0)) (3 leaves)
  mul(0,mul(0,mul(mul(0,0),mul(0,0)))) (6 leaves)
  mul(0,mul(mul(0,0),0)) (4 leaves)

Class 4 (11 trees):
  mul(mul(0,mul(mul(mul(0,0),0),0)),0) (6 leaves)
  mul(mul(0,mul(0,mul(0,0))),0) (5 leaves)
  mul(mul(0,mul(mul(0,mul(0,0)),0)),0) (6 leaves)
  mul(mul(mul(mul(0,0),mul(0,0)),0),0) (6 leaves)
  mul(mul(0,mul(mul(0,0),0)),0) (5 leaves)
  mul(mul(mul(0,0),mul(mul(0,0),0)),0) (6 leaves)
  mul(mul(0,0),0) (3 leaves)
  mul(mul(0,mul(mul(0,0),mul(0,0))),0) (6 leaves)
  mul(mul(0,mul(0,mul(mul(0,0),0))),0) (6 leaves)
  mul(mul(0,mul(0,0)),0) (4 leaves)
  mul(mul(0,mul(0,mul(0,mul(0,0)))),0) (6 leaves)

Class 5 (4 trees):
  mul(0,mul(0,mul(mul(0,mul(0,0)),0))) (6 leaves)
  mul(0,mul(0,mul(0,0))) (4 leaves)
  mul(0,mul(0,mul(mul(mul(0,0),0),0))) (6 leaves)
  mul(0,mul(0,mul(mul(0,0),0))) (5 leaves)

Class 6 (1 trees):
  mul(mul(0,0),mul(0,0)) (4 leaves)

Class 7 (4 trees):
  mul(mul(mul(0,0),0),0) (4 leaves)
  mul(mul(mul(0,mul(0,mul(0,0))),0),0) (6 leaves)
  mul(mul(mul(0,mul(0,0)),0),0) (5 leaves)
  mul(mul(mul(0,mul(mul(0,0),0)),0),0) (6 leaves)

Class 8 (2 trees):
  mul(0,mul(0,mul(0,mul(0,0)))) (5 leaves)
  mul(0,mul(0,mul(0,mul(mul(0,0),0)))) (6 leaves)

Class 9 (2 trees):
  mul(mul(0,0),mul(mul(0,mul(0,0)),0)) (6 leaves)
  mul(mul(0,0),mul(mul(0,0),0)) (5 leaves)

Class 10 (2 trees):
  mul(mul(0,mul(mul(0,0),0)),mul(0,0)) (6 leaves)
  mul(mul(0,mul(0,0)),mul(0,0)) (5 leaves)

Class 11 (2 trees):
  mul(mul(mul(mul(0,0),0),0),0) (5 leaves)
  mul(mul(mul(mul(0,mul(0,0)),0),0),0) (6 leaves)

Class 12 (1 trees):
  mul(0,mul(0,mul(0,mul(0,mul(0,0))))) (6 leaves)

Class 13 (1 trees):
  mul(0,mul(mul(0,0),mul(mul(0,0),0))) (6 leaves)

Class 14 (1 trees):
  mul(mul(0,0),mul(0,mul(0,mul(0,0)))) (6 leaves)

Class 15 (1 trees):
  mul(mul(0,0),mul(mul(mul(0,0),0),0)) (6 leaves)

Class 16 (1 trees):
  mul(mul(0,mul(0,0)),mul(0,mul(0,0))) (6 leaves)

Class 17 (1 trees):
  mul(mul(0,mul(0,0)),mul(mul(0,0),0)) (6 leaves)

Class 18 (1 trees):
  mul(mul(mul(0,0),0),mul(mul(0,0),0)) (6 leaves)

Class 19 (1 trees):
  mul(mul(0,mul(0,mul(0,0))),mul(0,0)) (6 leaves)

Class 20 (1 trees):
  mul(mul(mul(mul(0,0),0),0),mul(0,0)) (6 leaves)

Class 21 (1 trees):
  mul(mul(mul(0,mul(0,0)),mul(0,0)),0) (6 leaves)

Class 22 (1 trees):
  mul(mul(mul(mul(mul(0,0),0),0),0),0) (6 leaves)