#! perl -slw
use strict;
use List::Util qw[ reduce ]; $a=$b;

our $XLATE ||= 0;

sub nestedOk{ 
    index( $_[ 0 ], '(' ) <= index( $_[ 0 ], ')' ) and
    0 == reduce{
        $a + ( $b eq '(' ) - ( $b eq ')' ) 
    } 0, split'[^()]*', $_[ 0 ] 
}

my $re_var   = qr[ [a-zA-Z]\w* ]x;
my $re_subex = qr[ \{\d+\} ]x;
my $re_func  = qr[ $re_var $re_subex ]x;
my $re_num   = qr[ -? \d+ (?: \. \d+ )? (?: [Ee] [+-]? \d+ )? ]x;
my $re_term  = qr[ $re_num | $re_func | $re_subex | $re_var ]x;
my $re_op    = qr[[,%+*/^-]];
my %ops = ( qw[ % MOD + ADD * MULT / DIV ^ POW - SUBT ] );

sub exp2rpn {
    my( $exp, $aStack, $aBits ) = @_;
    die "Unbalanced parens: '$exp'" unless nestedOk $exp;
    my $varargs = 0;
    {
        my( $left, $op, $right, $rest ) = $exp =~ m[
            ^ (?: ( $re_term )? ( $re_op ) )? ( $re_term ) ( .* ) $
        ]x or die "malformed (sub)expression '$exp'";
        $varargs++ if $op and $op eq ',';
        for ( $left, $right ) {
            next unless $_;
            if( my( $func, $subex ) = m[^ ( $re_var )? \{ ( \d+ ) \} $
+]x ) {
                exp2rpn( $aBits->[ $subex ], $aStack, $aBits ); 
                push @$aStack, $func if $func 
            }
            else{
                push( @$aStack, $_  );
            }
        }
        push @$aStack, ++$varargs if $op and $op eq ',' and not $rest;
        push @$aStack, $XLATE ? $ops{ $op } : $op
            if $op and $op ne ',';
        $exp = $rest, redo if $rest;
    }    
    return $aStack;
}

sub parseExp {
    local $_ = $_[ 0 ];
    s[\s+][]g;
    my( $bit, @bits ) = 0;
    s[\( ( [^()]+ )  \)]{ push @bits, $1; "{${ \( $bit++ ) }}"; }ex 
        while m[[()]];
    my $toplvl = $_;
    return @{ exp2rpn $toplvl, [], \@bits };
}

#die "No expression given\n" unless @ARGV;
while( <DATA> ) {
    chomp;
    printf "%s \n\t %s\n\n", $_, join', ',  parseExp $_;
}

__END__
1+2+3
a+b+c
abc+def+Efg_hij
2.0+1e-2/0.01E-21 
max( a, b, c, d ) * atan( pi*4, -1 )
sin( cos( x ) - tan( y ) ) + f( g( z ) )
2*(somevar+other) + max(this, that)
A+(B*C-D)/E
(a*(b)-c^(3.4e-2))
5^((-2e-3+x)*sin(p+4.0)/fred)
sin(a) + sin(ab) + sin( a, b )
Func_1( 1, Func_2( Func3( 1* 2 * 3) * aFunc( 3 ) )+FuNc(4,5,6), -2,e, 
+-10, -2e-10 ) +1
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