You sure didn't say much about what your formulas look like, but here's a little parser for what you did show (and a few extras, like * and parens).

#!/usr/bin/perl

# http://perlmonks.org/?node_id=1211295

use strict;
use warnings;
use Data::Dump 'pp';

while(<DATA>)
  {
  print "\nformula $_";
  my %data = qw( a 2 b 3 ); # for testing, set from your other file
  pp 'before', \%data;
  calc($_, \%data);
  pp 'after ', \%data;
  }

sub error { die s/\G/ *** Expected @_ -->/r, "\n" }
sub want { /\G\s+/gc; /\G\Q$_[1]\E/gc ? shift : error "'$_[1]'" }

sub calc
  {
  local $_ = shift;
  our $dataref = shift;
  expr(0);
  pos($_) == length $_ or error 'End of Source';
  }

sub expr
  {
  our $dataref;
  /\G\s+/gc;
  my $value =
    /\G(\w+)\s*=/gc ? do { my $t = $1; $dataref->{$t} = expr(0) } :
    /\G(\w+)/gc ? $dataref->{$&} // 0 :
    /\G\(/gc ? want expr(0), ')' :
    error 'Operand';
  $value =
    /\G\s+/gc ? $value :
    $_[0] <= 1 && /\G\+/gc ? $value + expr(2) :
    $_[0] <= 2 && /\G\*/gc ? $value * expr(3) :
    return $value while 1;
  }

__DATA__
z = a + b
z = a * b
z = a * b + a * b
z = a + b * a + b
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