import re

def max_nested_braces(expr):
    count = 0
    while True:
        expr, no_of_subs = re.subn(r'\{[^{}]*\}', '', expr)
        if no_of_subs == 0:
            break
        count += 1

    if re.search(r'[{}]', expr):
        return -1
    return count

def test_cases():
    assert max_nested_braces('a*b') == 0
    assert max_nested_braces('a*b+{}') == 1
    assert max_nested_braces('a*{b+c}') == 1
    assert max_nested_braces('{a+2}*{b+c}') == 1
    assert max_nested_braces('a*{b+c*{e*3.14}}') == 2
    assert max_nested_braces('{{a+2}*{b+c}+e}') == 2
    assert max_nested_braces('{{a+2}*{b+{c*d}}+e}') == 3
    assert max_nested_braces('{{a+2}*{{b+{c*d}}+e*d}}') == 4
    assert max_nested_braces('a*b{') == -1
    assert max_nested_braces('a*{b+c}}') == -1
    assert max_nested_braces('}a+b{') == -1
    assert max_nested_braces('a*{b+c*{e*3.14}}}') == -1
    assert max_nested_braces('{{a+2}*{{b}+{c*d}}+e*d}}') == -1

if __name__ == '__main__':
    test_cases()
    print('all tests passed')