I forgot to mention how you'd actually use that specific "wheel" to evaluate expressions. I know it's not the point of this meditation to just use the existing tools, but comparison might still be sensible.

#!/usr/bin/perl
use strict;
use warnings;
use Math::Symbolic;
my $parser = Math::Symbolic::Parser->new();

while (1) {
  print "\n> ";
  my $line = <STDIN>;
  my $tree = $parser->parse($line);
  print("Parse error.\n"), next if not defined $tree;
  print "Entered: $tree\n";
  my $result = $tree->value();
  print("Evaluation error.\n"), next if not defined $result;
  print "Result: $result\n";
}
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The output would look like this:

> 3*4.2e3+5^(3.1+2)
Entered: (3 * 4.2e3) + (5 ^ (3.1 + 2))
Result: 16270.6841971501

> a*b+c
Entered: (a * b) + c
Evaluation error.
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That last bit shows that the parser is actually intended to be used with variables, too. So it's not a parse error but an evaluation error.

Switching to using the YAPP based parser is rather straightforward, too. Just add "implementation => 'Yapp'" to the call to the constructor.

Cheers,
Steffen