Python (without importing anything)
Number of characters: 222
I stole many tricks from Dave's answer, but I managed to shave off some more characters.
def e(s,l=0,n=0,f='+'):
if s:l=[c for c in s+')'if' '!=c]
while f!=')':
p=l.pop;m=p(0)
if m=='(':m=e(0,l)
while l[0]not in'+-*/)':m+=p(0)
m=float(m);n={'+':n+m,'-':n-m,'*':n*m,'/':n/(m or 1)}[f];f=p(0)
return n
Commented version:
def evaluate(stringexpr, listexpr=0, n=0, f_operation='+'):
# start out as taking 0 + the expression... (or could use 1 * ;)
# We'll prefer to keep the expression as a list of characters,
# so we can use .pop(0) to eat up the expression as we go.
if stringexpr:
listexpr = [c for c in stringexpr+')' if c!=' ']
# use ')' as sentinel to return the answer
while f_operation != ')':
m_next = listexpr.pop(0)
if m_next == '(':
# lists are passed by reference, so this call will eat the (parexp)
m_next = evaluate(None, listexpr)
else:
# rebuild any upcoming numeric chars into a string
while listexpr[0] not in '+-*/)':
m_next += listexpr.pop(0)
# Update n as the current answer. But never divide by 0.
m = float(m_next)
n = {'+':n+m, '-':n-m, '*':n*m, '/':n/(m or 1)}[f_operation]
# prepare the next operation (known to be one of '+-*/)')
f_operation = listexpr.pop(0)
return n
