 comparison are "certain"; it is probably the most used type
  of comparison, and the other comparisons are still accessible by the
  explicit comparison functions. The checking forbid empty interval; they are
  not needed since there would be an empty interval at end of the computation
  if an empty interval is created during the computation, and no root would
  be inside. The checking also forbid invalid numbers (NaN for floating-point
  numbers). It can be a minor performance hit if you only use exact
  