Always run Gauss-Seidel at tiny sizes to rule out fake solutions

brush-strokes/src/lib/Math/Root/Isolation.hs

@@ -250,26 +250,27 @@ defaultRootIsolationAlgorithms
   :: forall n d
   .  BoxCt n d
   => Double -> Double -> Box n -> BoxHistory n -> Either String ( NE.NonEmpty ( RootIsolationAlgorithm n d ) )
-defaultRootIsolationAlgorithms minWidth ε_eq box history
-  -- All the box widths are lower than the minimum width: give up.
-  | and $ ( \ cd -> width cd <= minWidth ) <$> coordinates box
-  = Left $ "widths <= " ++ show minWidth
-  | otherwise
-  = Right $ case history of
+defaultRootIsolationAlgorithms minWidth ε_eq box history =
+  case history of
     lastRoundBoxes : _
       -- If, in the last round of strategies, we didn't try bisection...
       | any ( \case { BisectionStep {} -> False; _ -> True } . fst ) lastRoundBoxes
       , ( _step, lastRoundFirstBox ) <- NE.last lastRoundBoxes
       -- ...and the last round didn't sufficiently reduce the size of the box...
       , not $ box `sufficientlySmallerThan` lastRoundFirstBox
-        -- ...then try bisecting the box.
-        -> NE.singleton $ Bisection ( defaultBisectionOptions minWidth ε_eq box )
+      -- ...then try bisecting the box...
+      -- ...unless the box is already too small, in which case we give up.
+      -> if verySmall
+         then Left $ "widths <= " ++ show minWidth
+         else Right $ NE.singleton $ Bisection ( defaultBisectionOptions minWidth ε_eq box )
     -- Otherwise, do a normal round.
     -- Currently: we try an interval Gauss–Seidel step followed by box(1)-consistency.
-      _ -> GaussSeidel _gaussSeidelOptions
-              NE.:| [ Box1 _box1Options ]
+    _ -> Right $ GaussSeidel _gaussSeidelOptions
+            NE.:| [ Box1 _box1Options | not verySmall ]
 
   where
+    verySmall = and $ ( \ cd -> width cd <= minWidth ) <$> coordinates box
+
     _box1Options :: Box1Options n d
     _box1Options =
       Box1Options