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