Mysterious RegionDistanceFunction::regp message

Question

Bug introduced in 12.3.1 or earlier and persisting through 13.1.0 [CASE:4853257]

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I encountered a strange problem with RegionDistanceFunction. Consider this list of points (I'm forced to use Compress, because with direct input the problem doesn't reproduce):

pts = Uncompress@"1:eJx11l1Ik1EYB3BNAwsqDLqwomZ+lCvNPtA+Bp0wuihvKr14T5lQtlzFClYxLWd+\
VfYJkVBZpF1ILMoIgojUi6n50dbMLZtZqQsv+hCDdtMH9p6HPWcHfHpBj/B75/u85/\
lzniXuO7rTbI6KirLF6r9yLbbjB6L1P6bpP607el31Fs4O/zlh3erTmATf3ecNATNnG/L1y6/\
A4hsz2os4Z4liHVRgnbgzn7Prc7c0zxpSIM7K6zu2cVboap6YP6xAcFK/\
NnE20OP02IIKlDpydm03cZaaNv43NKbASF/\
d3rZszq469euLAoaK243tmXpVYp1Q4Iq408jZrSJrdF5IgcvHOu3dyZwFOxZ4Fv1SIP9ncfb+hZx9FtVNKtAScm+\
8lsBZcYN9zBTLI7BevPg8zr6xH69K4hTob7mf5ZjDGa4S8E78pAT83/gsCVgNVhfZxHD9+\
D4S6sNvjDsgAfcI90wC7irusgTsA/ZFAnYOOykBe429l4DpwLREqgrnCfMlAROIiZSAmcUMS/\
D7mo509etbIt7nkPrwJMPBeI/GTJ6e+Bd2Bbzur4bSHo2NivcoV2Bi+oWSe90a+\
y7WWgWqyvJGeZfGskV1dQo4qkeePXipMW8ga3b0HQUazA83p3Rq7JKoyqlAzZPW340dGltRYGnKfaxCb6F/\
wKX3Q1TVRkAFrARkwZ4R8Nbw1JgeIOAi9J6A5SdnnqkcJ2AYEkmAUXwiY/dU+\
AQpIaBcrDkErIWUEOAT76ERUAs9JyBNVGUl4CP0nACHWKsIWAM9J6BfVHWTgPPQcwKWiaoeEfABek5AGawErIaeE/\
AGek7AOeg5AUuh5wQMQc8JOC3WmD1TYRWccAT0iaoSCDgL5xUBqZArAt5Drgg4BbkiIBNyRYAXckVADeSKgBTIFQGD\
kCsCSiFXBKyEXBHwGnJFQDXkioBkyBUBAciVAtVhsMNKQAbkigA35IqAKsgV8fAkyBUB7yBXBEBVMQVTIR1yRQBUlU\
BAJeSKgCWQKwIGIFcK4NGNR3lkfoQPezz8JeB4wHEhAQcKDhgJOIJwJEnAoYVDLPJNJjzmcOz998vdP0c/e4c=";

Now create a RegionDistanceFunction and apply it to the points:

df = RegionDistance[Line[pts[[{1, -1}]]]];

df /@ pts[[2 ;; -2]]

I get two RegionDistanceFunction::regp messages during the evaluation of this code:

RegionDistanceFunction::regp: A correctly specified region expected at position 1 of RegionDistanceFunction[Line[{Compile`$4,Compile`$4}],2,Sqrt[(-105.65+Subscript[Slot[<<1>>], <<1>>])^2+(-103.317+Subscript[Slot[<<1>>], <<1>>])^2]&].

What is even more strange, I don't get these messages when I use the RegionDistanceFunction inside of a Function:

df[#] & /@ pts[[2 ;; -2]]

Why does this happen? How can it be explained?

I'm using Mathematica 12.3.1 on Windows 10 x64. The problem persists after restarting Mathematica.

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UPDATE

I've found that the problem is related to auto-compilation performed by Map, and can be boiled down to

df = RegionDistance[
   Line[Uncompress[
     "1:eJxTTMoPSmNiYGAoZgESPpnFJamMQAZIZF/g6cOzM6Mcsv+U5rldiXTAKQEAX1wVAA=="]]];

SetSystemOptions["CompileOptions" -> {"MapCompileLength" -> 1}];

df /@ {{105., 103.}}

RegionDistanceFunction::regp: A correctly specified region expected at position 1 of RegionDistanceFunction[Line[{Compile`$1,Compile`$1}],2,Sqrt[(-105.65+Subscript[Slot[<<1>>], <<1>>])^2+(-103.317+Subscript[Slot[<<1>>], <<1>>])^2]&].

RegionDistanceFunction::regp: A correctly specified region expected at position 1 of RegionDistanceFunction[Line[{Compile`$1,Compile`$1}],2,Sqrt[(-105.65+Subscript[Slot[<<1>>], <<1>>])^2+(-103.317+Subscript[Slot[<<1>>], <<1>>])^2]&].

{0.72321}

Is it a bug? Is there a workaround?

Answer 1

Looks something is going wrong with the automatic compilation process. You observe:

df /@ pts[[2 ;; -2]];

RegionDistanceFunction::regp: A correctly specified region expected at position 1 of RegionDistanceFunction[Line[{Compile$8,Compile$8}],2,Sqrt[(-105.65+Subscript[Slot[<<1>>], <<1>>])^2+(-103.317+Subscript[Slot[<<1>>], <<1>>])^2]&].

RegionDistanceFunction::regp: A correctly specified region expected at position 1 of RegionDistanceFunction[Line[{Compile$8,Compile$8}],2.,Sqrt[(-105.65+Subscript[Slot[<<1>>], <<1>>])^2+(-103.317+Subscript[Slot[<<1>>], <<1>>])^2]&].

Increase the length to start automatic compilation:

SetSystemOptions["CompileOptions" -> "MapCompileLength" -> 111];
df /@ pts[[2 ;; -2]];

I think this is worth reporting to support as a bug.