Add regression test

Closes sympy/sympy#13645

diofant/core/tests/test_expr.py

@@ -1619,3 +1619,25 @@ def test_sympyissue_7426():
 def test_pow_rewrite():
     assert (2**x).rewrite(sin) == 2**x
     assert (2**x).rewrite(tanh) == 2**x
+
+
+def test_sympyissue_13645():
+    r, r_m = symbols('r r_m', positive=True)
+    th = symbols('th', extended_real=True)
+    a, M = symbols('a M', extended_real=True)
+    kappa, gamma = symbols('kappa gamma', extended_real=True)
+
+    l = sqrt(M/r_m**3)*(r_m**4 + r_m**2*a**2 - 2*M*r_m*a**2 -
+                        a*sqrt(M*r_m)*(r_m**2-a**2))
+    l /= r_m**2 - 3*M*r_m + 2*a*sqrt(M*r_m)
+
+    Delta = r**2 - 2*M*r + a**2
+    Sigma = r**2 + a**2*cos(th)**2
+    A = (r**2 + a**2)**2 - Delta*a**2*sin(th)**2
+
+    tmp3 = sqrt(1 + l**2*Sigma**2*Delta/(sin(th))**2)
+    ln_h = log((1 + tmp3) / (Sigma*Delta/A)) - tmp3
+    hm1 = exp(ln_h) - 1
+
+    # not hangs
+    (hm1*(gamma-1)/(kappa*gamma))**(1/(gamma - 1))

docs/release/notes-0.9.rst

@@ -178,3 +178,4 @@ These Sympy issues also were addressed:
 * :sympyissue:`13071` meijerg.is_number is wrong
 * :sympyissue:`13575` limit(acos(erfi(x)), x, 1) causes recursion error
 * :sympyissue:`13629` bug in rsolve
+* :sympyissue:`13645` sympy hangs on evaluating expression