Numeric vs symbolic arithmetic

numeric arithmetic

• normally inexact
• usually produces some sort of answer (may suffer loss of accuracy, fail to converge, etc.)
• arithmetic relatively cheap
• zeroes usually not given special treatment except to avoid computational singularities
• zero detection: number sufficiently small?
• maximize size of pivots to promote stability

symbolic arithmetic

• always exact
• frequently cannot produce an answer (problem is intractable, expression swell, etc.)
• arithmetic often expensive
• zeroes can greatly simplify calculations by making some of them unnecessary
• zero detection: expression equivalent to zero?
• minimize complexity of
  pivots to stunt expression growth