Question: difficult to search for simplest form of symbolic expression

hi ,friends

  now ,i get a matrix of symbolic expression,it's difficulty to find the simplest forms using the common command  as like simplify or combine

p := Matrix(4, 4, {(1, 1) = (1/2)*exp((1/2)*J[1]-(1/2)*J[2]+(1/2)*J[3])+(1/2)*exp(-(1/2)*J[1]+(1/2)*J[2]+(1/2)*J[3]), (1, 2) = 0, (1, 3) = 0, (1, 4) = (1/2)*exp((1/2)*J[1]-(1/2)*J[2]+(1/2)*J[3])-(1/2)*exp(-(1/2)*J[1]+(1/2)*J[2]+(1/2)*J[3]), (2, 1) = 0, (2, 2) = (1/2)*exp(-(1/2)*J[1]-(1/2)*J[2]-(1/2)*J[3])+(1/2)*exp((1/2)*J[1]+(1/2)*J[2]-(1/2)*J[3]), (2, 3) = -(1/2)*exp(-(1/2)*J[1]-(1/2)*J[2]-(1/2)*J[3])+(1/2)*exp((1/2)*J[1]+(1/2)*J[2]-(1/2)*J[3]), (2, 4) = 0, (3, 1) = 0, (3, 2) = -(1/2)*exp(-(1/2)*J[1]-(1/2)*J[2]-(1/2)*J[3])+(1/2)*exp((1/2)*J[1]+(1/2)*J[2]-(1/2)*J[3]), (3, 3) = (1/2)*exp(-(1/2)*J[1]-(1/2)*J[2]-(1/2)*J[3])+(1/2)*exp((1/2)*J[1]+(1/2)*J[2]-(1/2)*J[3]), (3, 4) = 0, (4, 1) = (1/2)*exp((1/2)*J[1]-(1/2)*J[2]+(1/2)*J[3])-(1/2)*exp(-(1/2)*J[1]+(1/2)*J[2]+(1/2)*J[3]), (4, 2) = 0, (4, 3) = 0, (4, 4) = (1/2)*exp((1/2)*J[1]-(1/2)*J[2]+(1/2)*J[3])+(1/2)*exp(-(1/2)*J[1]+(1/2)*J[2]+(1/2)*J[3])})

how to find the the shortest forms.for example ,

get the result as like this:

              [ cosh(j1/2 - j2/2)*exp(j3/2),                           0,                           0, exp(j3/2)*sinh(j1/2 - j2/2)]
              [                           0, cosh(j1/2 + j2/2)/exp(j3/2), sinh(j1/2 + j2/2)/exp(j3/2),                           0]
              [                           0, sinh(j1/2 + j2/2)/exp(j3/2), cosh(j1/2 + j2/2)/exp(j3/2),                           0]
              [ exp(j3/2)*sinh(j1/2 - j2/2),                           0,                           0, cosh(j1/2 - j2/2)*exp(j3/2)]