Perl (no eval)
Number of characters: 167 106 (see below for the 106 character version)
Fully obfuscated function: (167 characters if you join these three lines into one)
sub e{my$_="($_[0])";s/\s//g;$n=q"(-?\d++(\.\d+)?+)";
@a=(sub{$1},1,sub{$3*$6},sub{$3+$6},4,sub{$3-$6},6,sub{$3/$6});
while(s:\($n\)|(?<=\()$n(.)$n:$a[7&ord$5]():e){}$_}
Clear/deobfuscated version:
sub e {
my $_ = "($_[0])";
s/\s//g;
$n=q"(-?\d++(\.\d+)?+)"; # a regex for "number", including capturing groups
# q"foo" in perl means the same as 'foo'
# Note the use of ++ and ?+ to tell perl
# "no backtracking"
@a=(sub{$1}, # 0 - no operator found
1, # placeholder
sub{$3*$6}, # 2 - ord('*') = 052
sub{$3+$6}, # 3 - ord('+') = 053
4, # placeholder
sub{$3-$6}, # 5 - ord('-') = 055
6, # placeholder
sub{$3/$6}); # 7 - ord('/') = 057
# The (?<=... bit means "find a NUM WHATEVER NUM sequence that happens
# immediately after a left paren", without including the left
# paren. The while loop repeatedly replaces "(" NUM WHATEVER NUM with
# "(" RESULT and "(" NUM ")" with NUM. The while loop keeps going
# so long as those replacements can be made.
while(s:\($n\)|(?<=\()$n(.)$n:$a[7&ord$5]():e){}
# A perl function returns the value of the last statement
$_
}
I had misread the rules initially, so I'd submitted a version with "eval". Here's a version without it.
The latest bit of insight came when I realized that the last octal digit in the character codes for +, -, /, and * is different, and that ord(undef) is 0. This lets me set up the dispatch table @a as an array, and just invoke the code at the location 7 & ord($3).
There's an obvious spot to shave off one more character - change q"" into '' - but that would make it harder to cut-and-paste into the shell.
Even shorter
Number of characters: 124 106
Taking edits by ephemient into account, it's now down to 124 characters: (join the two lines into one)
sub e{$_=$_[0];s/\s//g;$n=q"(-?\d++(\.\d+)?+)";
1while s:\($n\)|$n(.)$n:($1,1,$3*$6,$3+$6,4,$3-$6,6,$6&&$3/$6)[7&ord$5]:e;$_}
Shorter still
Number of characters: 110 106
The ruby solution down below is pushing me further, though I can't reach its 104 characters:
sub e{($_)=@_;$n='( *-?[.\d]++ *)';
s:\($n\)|$n(.)$n:(($1,$2-$4,$4&&$2/$4,$2*$4,$2+$4)x9)[.8*ord$3]:e?e($_):$_}
I had to give in and use ''. That ruby send trick is really useful for this problem.
Squeezing water from a stone
Number of characters: 106
A small contortion to avoid the divide-by-zero check.
sub e{($_)=@_;$n='( *-?[.\d]++ *)';
s:\($n\)|$n(.)$n:($1,0,$2*$4,$2+$4,0,$2-$4)[7&ord$3]//$2/$4:e?e($_):$_}
Here's the test harness for this function:
perl -le 'sub e{($_)=@_;$n='\''( *-?[.\d]++ *)'\'';s:\($n\)|$n(.)$n:($1,0,$2*$4,$2+$4,0,$2-$4)[7&ord$3]//$2/$4:e?e($_):$_}' -e 'print e($_) for @ARGV' '1 + 3' '1 + ((123 * 3 - 69) / 100)' '4 * (9 - 4) / (2 * 6 - 2) + 8' '2*3*4*5+99' '2.45/8.5*9.27+(5*0.0023) ' '1 + 3 / -8'
