def METHOD_NAME():
    R = Rational
    assert combsimp(gamma(x)) == gamma(x)
    assert combsimp(gamma(x + 1)/x) == gamma(x)
    assert combsimp(gamma(x)/(x - 1)) == gamma(x - 1)
    assert combsimp(x*gamma(x)) == gamma(x + 1)
    assert combsimp((x + 1)*gamma(x + 1)) == gamma(x + 2)
    assert combsimp(gamma(x + y)*(x + y)) == gamma(x + y + 1)
    assert combsimp(x/gamma(x + 1)) == 1/gamma(x)
    assert combsimp((x + 1)**2/gamma(x + 2)) == (x + 1)/gamma(x + 1)
    assert combsimp(x*gamma(x) + gamma(x + 3)/(x + 2)) == \
        (x + 2)*gamma(x + 1)
    assert combsimp(gamma(2*x)*x) == gamma(2*x + 1)/2
    assert combsimp(gamma(2*x)/(x - Rational(1, 2))) == 2*gamma(2*x - 1)
    assert combsimp(gamma(x)*gamma(1 - x)) == pi/sin(pi*x)
    assert combsimp(gamma(x)*gamma(-x)) == -pi/(x*sin(pi*x))
    assert combsimp(1/gamma(x + 3)/gamma(1 - x)) == \
        sin(pi*x)/(pi*x*(x + 1)*(x + 2))
    assert powsimp(combsimp(
        gamma(x)*gamma(x + Rational(1, 2))*gamma(y)/gamma(x + y))) == \
        2**(-2*x + 1)*sqrt(pi)*gamma(2*x)*gamma(y)/gamma(x + y)
    assert combsimp(1/gamma(x)/gamma(x - Rational(1, 3))/gamma(x + Rational(1, 3))) == \
        3**(3*x - Rational(3, 2))/(2*pi*gamma(3*x - 1))
    assert simplify(
        gamma(Rational(1, 2) + x/2)*gamma(1 + x/2)/gamma(1 + x)/sqrt(pi)*2**x) == 1
    assert combsimp(gamma(Rational(-1, 4))*gamma(Rational(-3, 4))) == 16*sqrt(2)*pi/3
    assert powsimp(combsimp(gamma(2*x)/gamma(x))) == \
        2**(2*x - 1)*gamma(x + Rational(1, 2))/sqrt(pi)
    # issue sympy/sympy#6792
    e = (-gamma(k)*gamma(k + 2) + gamma(k + 1)**2)/gamma(k)**2
    assert combsimp(e) == -k
    assert combsimp(1/e) == -1/k
    e = (gamma(x) + gamma(x + 1))/gamma(x)
    assert combsimp(e) == x + 1
    assert combsimp(1/e) == 1/(x + 1)
    e = (gamma(x) + gamma(x + 2))*(gamma(x - 1) + gamma(x))/gamma(x)
    assert combsimp(e) == (x**2 + x + 1)*gamma(x + 1)/(x - 1)
    e = (-gamma(k)*gamma(k + 2) + gamma(k + 1)**2)/gamma(k)**2
    assert combsimp(e**2) == k**2
    assert combsimp(e**2/gamma(k + 1)) == k/gamma(k)
    a = R(1, 2) + R(1, 3)
    b = a + R(1, 3)
    assert combsimp(gamma(2*k)/gamma(k)*gamma(k + a)*gamma(k + b)) == \
        3*2**(2*k + 1)*3**(-3*k - 2)*sqrt(pi)*gamma(3*k + R(3, 2))/2
    A, B = symbols('A B', commutative=False)
    assert combsimp(e*B*A) == combsimp(e)*B*A
    # check iteration
    assert combsimp(gamma(2*k)/gamma(k)*gamma(-k - R(1, 2))) == (
        -2**(2*k + 1)*sqrt(pi)/(2*((2*k + 1)*cos(pi*k))))
    assert combsimp(
        gamma(k)*gamma(k + R(1, 3))*gamma(k + R(2, 3))/gamma(3*k/2)) == (
        3*2**(3*k + 1)*3**(-3*k - Rational(1, 2))*sqrt(pi)*gamma(3*k/2 + Rational(1, 2))/2)