def test_automatic_rewrite():
assert octave_code(Li(x)) == 'logint(x) - logint(2)'
assert octave_code(erf2(x, y)) == '-erf(x) + erf(y)'
def test_erf2():
assert erf2(0, 0) is S.Zero
assert erf2(x, x) is S.Zero
assert erf2(nan, 0) is nan
assert erf2(-oo, y) == erf(y) + 1
assert erf2( oo, y) == erf(y) - 1
assert erf2( x, oo) == 1 - erf(x)
assert erf2( x,-oo) == -1 - erf(x)
assert erf2(x, erf2inv(x, y)) == y
assert erf2(-x, -y) == -erf2(x,y)
assert erf2(-x, y) == erf(y) + erf(x)
assert erf2( x, -y) == -erf(y) - erf(x)
assert erf2(x, y).rewrite('fresnels') == erf(y).rewrite(fresnels)-erf(x).rewrite(fresnels)
assert erf2(x, y).rewrite('fresnelc') == erf(y).rewrite(fresnelc)-erf(x).rewrite(fresnelc)
assert erf2(x, y).rewrite('hyper') == erf(y).rewrite(hyper)-erf(x).rewrite(hyper)
assert erf2(x, y).rewrite('meijerg') == erf(y).rewrite(meijerg)-erf(x).rewrite(meijerg)
assert erf2(x, y).rewrite('uppergamma') == erf(y).rewrite(uppergamma) - erf(x).rewrite(uppergamma)
assert erf2(x, y).rewrite('expint') == erf(y).rewrite(expint)-erf(x).rewrite(expint)
assert erf2(I, 0).is_real is False
assert erf2(0, 0, evaluate=False).is_real
assert erf2(0, 0, evaluate=False).is_zero
assert erf2(x, x, evaluate=False).is_zero
assert erf2(x, y).is_zero is None
assert expand_func(erf(x) + erf2(x, y)) == erf(y)
assert conjugate(erf2(x, y)) == erf2(conjugate(x), conjugate(y))
assert erf2(x, y).rewrite('erf') == erf(y) - erf(x)
assert erf2(x, y).rewrite('erfc') == erfc(x) - erfc(y)
assert erf2(x, y).rewrite('erfi') == I*(erfi(I*x) - erfi(I*y))
assert erf2(x, y).diff(x) == erf2(x, y).fdiff(1)
assert erf2(x, y).diff(y) == erf2(x, y).fdiff(2)
assert erf2(x, y).diff(x) == -2*exp(-x**2)/sqrt(pi)
assert erf2(x, y).diff(y) == 2*exp(-y**2)/sqrt(pi)
raises(ArgumentIndexError, lambda: erf2(x, y).fdiff(3))
assert erf2(x, y).is_extended_real is None
xr, yr = symbols('xr yr', extended_real=True)
assert erf2(xr, yr).is_extended_real is True