import math

class ParseError(Exception):
    pass

vars = { 'e'  : math.exp(1),
         'pi' : math.pi }

funcs = { 'sin':   math.sin,
          'cos':   math.cos,
          'exp':   math.exp,
          'log':   math.log,
          'sqrt':  math.sqrt,
          'floor': math.floor,
          'abs':   abs,
          'sgn':   lambda x: (x<0 and -1) or (x>0 and 1) or 0 }

binops = { '^': ( 1, 'r', lambda a,b: a**b),
           '*': ( 2, 'l', lambda a,b: a*b),
           '/': ( 2, 'l', lambda a,b: a/b),
           '+': ( 3, 'l', lambda a,b: a+b),
           '-': ( 3, 'l', lambda a,b: a-b) }

expr_level = 3

def calc_term(s):
    while s[0].isspace(): s.pop(0)
    if s[0].isdigit():
        acc = 0.0
        while s[0].isdigit():
            acc = acc*10 + int(s.pop(0))
        if s[0] == '.':
            den = 10.0
            s.pop(0)
            while s[0].isdigit():
                acc = acc + int(s.pop(0))/den
                den *= 10.0
        if s[0].upper() == 'E':
            s.pop(0)
            if s[0] == '-':
                sign = -1
            elif s[0] == '+':
                sign = +1
            else:
                raise ParseError("Exponent sign is required")
            s.pop(0)
            if not s[0].isdigit():
                raise ParseError("Exponent value required")
            exp = 0
            while s[0].isdigit():
                exp = exp*10 + int(s.pop(0))
            acc *= 10 ** (sign*exp)
        return acc
    if s[0] == '-':
        s.pop(0)
        return - calc_term(s)
    if s[0] == '(':
        s.pop(0)
        v = calc_expr(s)
        while s[0].isspace(): s.pop(0)
        if s[0] != ')':
            raise ParseError("')' expected")
        s.pop(0)
        return v
    if s[0].isalpha():
        t = ""
        while s[0].isalnum() or s[0]=='_':
            t += s.pop(0)
        while s[0].isspace(): s.pop(0)
        if t in funcs:
            if s[0] != '(':
                raise ParseError("'(' expected")
            x = calc_term(s)
            return funcs[t](x)
        elif s[0] == '=':
            s.pop(0)
            x = calc_expr(s)
            vars[t] = x
            return x
        if t in vars:
            return vars[t]
        raise ParseError("Undefined symbol %s" % repr(t))
    raise ParseError("Syntax error: %s" % repr(s[0]))

def calc_expr(s,level = expr_level):
    if level == 0:
        return calc_term(s)
    a = calc_expr(s,level-1)
    while True:
        while s[0].isspace(): s.pop(0)
        if s[0] in binops:
            (lv, gr, op) = binops[s[0]]
            if level != lv:
                break
            s.pop(0)
            if gr == 'r':
                a = op(a,calc_expr(s,level))
            else:
                a = op(a,calc_expr(s,level-1))
        else:
            break
    return a

if __name__ == "__main__":
    def test(s):
        print repr(s),"==>",
        try:
            charlist = list(s) + ["#END#"]
            result = calc_expr(charlist)
            if charlist[0] != "#END#":
                raise ParseError("Extra charaters at end of expression: %s" %
                                 repr(charlist[0]))
            print result
        except ParseError,e:
            print "Error: %s"%e
            print " "*(len(s)-len(charlist)+2)+"^"
    test("2+2")
    test("  2 + 2")
    test("(2+2)*3")
    test("2+2*3")
    test("pi")
    test("pi_2 = 2*pi")
    test("cos(pi/3)")
    test("cos+2")
    test("x=pi*11+2")
    test("cos(x)")
    test("cos(x - floor(x/pi_2)*pi_2)")
    test("eps = 1E-5")
    test("der = (cos(x+eps)-cos(x))/eps")
    test("sin(x)")
    test("x=1+1/(1+1/x)")
    test("x=1+1/(1+1/x)")
    test("x=1+1/(1+1/x)")
    test("x=1+1/(1+1/x)")
    test("x=1+1/(1+1/x)")
    test("x=1+1/(1+1/x)")
    test("x=1+1/(1+1/x)")
    test("x=1+1/(1+1/x)")
    test("x=1+1/(1+1/x)")
    test("x - (1+sqrt(y))/2")
    test("y = 2^(1+1)+1")
    test("x - (1+sqrt(y))/2")
    test("2^3^4")
    test("(2^3)^4")