Bug introduced in 12.1 or earlier and persisting through 13.2

Consider the following region:

region = BooleanRegion[#1 || #2 &, {Circle[{0, 0}, 
   63.01771474209481`, {-0.3085423746716913`, 0}], 
  Circle[{0, 0}, 63.01771474209481`, {0, 0.3085423746716913`}]}]

Why in Mathematica 12.1 RegionMeasure[region] returns a complex value, and how to avoid it without dealing with explicit calculations (despite the fact that it is possible to make this easily)?


38.8873 + 0.0000128693 I

  • $\begingroup$ Machine precision calculations neither track nor control precision. You get what you get. Arbitrary precision will track and attempt to control precision. Exact numbers will give exact results. $\endgroup$
    – Bob Hanlon
    Commented Feb 4, 2022 at 15:50
  • $\begingroup$ Per the tag wiki for bugs: "Please do not use this tag for new questions." -- Now, does the community think it's a bug? $\endgroup$
    – Michael E2
    Commented Feb 4, 2022 at 18:00
  • $\begingroup$ I think it is a bug. Worth reporting to the support. Added the BUG header and the tag. $\endgroup$ Commented Feb 5, 2022 at 4:03

1 Answer 1


This is numerical inaccuracy stemming from your machine precision inputs. Setting a WorkingPrecision for RegionMeasure takes care of the problem:

RegionMeasure[region, WorkingPrecision -> 10]

(* Out: 38.88727071 *)
  • 1
    $\begingroup$ Why not WorkingPrecision -> $MachinePrecision? (Why so much less than?) -- Oh, bizarre. It makes no difference. But I usually use WorkingPrecision -> 16 because it's shorter to type, and that works. -- Oh, wow, WorkingPrecision -> 10. fails, too. That's wierd. $\endgroup$
    – Michael E2
    Commented Feb 4, 2022 at 18:00
  • 3
    $\begingroup$ Hmm, WorkingPrecision -> p seems to work only if p is an integer (fails for Real and Rational). $\endgroup$
    – Michael E2
    Commented Feb 4, 2022 at 18:07
  • $\begingroup$ @MichaelE2 This looks like a bug in WorkingPrecision functionality. Worth reporting to support. $\endgroup$ Commented Feb 5, 2022 at 3:58

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