The formula parser sometimes was not able to parse a user's formula quickly, or took a long time to determine that a formula was in error. Ideally, parsing should take no more than ten or twenty seconds, but it can take many minutes. Also, there were interpretation problems that increased the parsing time, or returned erroneous interpretations of formulae.
As the parser makes the initial assumption that the first matching rule it finds in the grammar is the correct one to apply, well formed formulae parse well. It is only when it has to backtrack and generate all the children of a node that it takes a significant amount of time. The backtracking occurs either when there is an error in the formula and it has to exhaust all possible paths of derivation before it determines it is unparsable or, more commonly, the parser makes a mistake in its initial interpretation.
To reduce the chance of the parser incorrectly parsing formulae, the formula parser can be made more selective about the relationships between items, making the regions accepted by the geometric tests, as described in Section 3.1.4, smaller. Thus, the x2 in Figure 6.9 would be too far from the 2 to be combined. Unfortunately, doing this also limits the parser's ability to cope with the unpredictable nature of handwritten input. It also does not eliminate the pro