A graph transformation stops when its answer has, not only when the graph has

Sources/AngouriMath/Core/Transformations/Saturation.cs

@@ -109,8 +109,18 @@ private static readonly Lazy<IReadOnlyList<MatchedRule>> safeRules
         /// <i>witness</i>, never the answer: what the caller finally extracts is the caller's own
         /// business, and is where a cheapest-form and a canonical-form caller differ.
         /// </param>
+        /// <param name="settled">
+        /// A caller's own stop, asked after every pass that merged something; <see langword="true"/>
+        /// ends the run without the graph's fixed point having been reached. A caller that
+        /// extracts an answer passes "the extraction has not changed for two passes": that is
+        /// the fixed point which matters to it, and it comes where the graph's own may never —
+        /// on a rational coefficient beside a variable, the regrouping rules add a fresh e-node
+        /// to the root's class on every pass while its cheapest member stopped changing on the
+        /// third (<a href="https://github.com/asc-community/AngouriMath/issues/1200">#1200</a>).
+        /// <see cref="ProvesEqual"/> passes nothing: it needs a union, not an extraction.
+        /// </param>
         internal static bool Run(EGraph graph, IReadOnlyList<MatchedRule> rules,
-            BudgetLedger ledger, Func<Entity, double> witnessCost)
+            BudgetLedger ledger, Func<Entity, double> witnessCost, Func<bool>? settled = null)
         {
             var chargedNodes = graph.NodeCount;
             bool ChargeGrowthSinceLastCall()
@@ -220,6 +230,7 @@ bool TryTerm(out Entity value)
                 if (!ledger.Spend()) break;
                 graph.Rebuild();
                 if (!merged) saturated = true;
+                else if (settled is not null && settled()) break;
             }
             return saturated;
         }

Sources/AngouriMath/Core/Transformations/Transformation.Catalogue.cs

@@ -470,10 +470,17 @@ public static Transformation EqualitySaturation(WorkBudget budget, CostModel cos
         /// <b>What this is not.</b> Not a canonical form <i>for the language</i> — no such thing
         /// exists here, since zero-equivalence is undecidable, and
         /// <c>Docs/Contributing/CanonicalForm.md</c> states that boundary. It is a canonical form
-        /// <i>modulo these rules and this budget</i>: equal trees mean the rules proved the two
-        /// expressions equal, different trees mean they did not, and a budget that ran out is
-        /// reported rather than hidden. Nothing in the library calls this — like
-        /// <see cref="Canonicalization"/> it is offered, not applied.
+        /// <i>modulo these rules, this budget, and the answer having settled</i>: equal trees mean
+        /// the rules proved the two expressions equal, different trees mean they did not, and a
+        /// budget that ran out is reported rather than hidden. The run stops once the least
+        /// member of the input's class has survived two passes unchanged, which is the fixed
+        /// point that matters to an extraction and comes where the graph's own may never — on
+        /// a rational coefficient beside a variable the regrouping rules add a member on every
+        /// pass for as long as they are allowed (<a href="https://github.com/asc-community/AngouriMath/issues/1200">#1200</a>),
+        /// and the answer was settled on the third. Measured on the corpus and on those inputs,
+        /// no answer moved and the nine of them went from two seconds to milliseconds. Nothing
+        /// in the library calls this — like <see cref="Canonicalization"/> it is offered, not
+        /// applied.
         /// </para>
         /// </remarks>
         /// <remarks>
@@ -673,10 +680,31 @@ internal EqualitySaturationTransformation(WorkBudget budget, CostModel costModel
                 graph.Rebuild();
 
                 var ledger = BudgetLedger.For(Name, budget);
-                Saturation.Run(graph, SafeRules, ledger, costModel.Cost);
+                // Stop once the answer has: after two passes in which the cheapest member of the
+                // root's class did not change, further merging can only add members this
+                // extraction would not choose. That is the fixed point a caller who extracts
+                // cares about, and on #1200's inputs it comes on the third pass where the
+                // graph's own never does. Measured on the corpus, no answer moves.
+                Entity? last = null;
+                var unchanged = 0;
+                bool Settled()
+                {
+                    var now = graph.Extract(root, costModel.Cost);
+                    unchanged = now is not null && now.Equals(last) ? unchanged + 1 : 0;
+                    last = now;
+                    return unchanged >= SettledPasses;
+                }
+                Saturation.Run(graph, SafeRules, ledger, costModel.Cost, Settled);
                 ledger.Report();
                 return graph.Extract(root, costModel.Cost) ?? input;
             }
+
+            /// <summary>
+            /// How many consecutive passes the extracted answer must survive unchanged before
+            /// the run stops on the answer rather than on the graph. Two, not one: a pass can
+            /// leave the cheapest member alone while adding what the next pass will improve on.
+            /// </summary>
+            private const int SettledPasses = 2;
         }
 
         /// <summary>
@@ -711,7 +739,18 @@ internal GraphCanonicalizationTransformation(WorkBudget budget, RewriteRuleGrowt
                 graph.Rebuild();
 
                 var ledger = BudgetLedger.For(Name, budget);
-                Saturation.Run(graph, rules, ledger, CostModel.Default.Cost);
+                // The same stop as EqualitySaturationTransformation's, on the least member
+                // rather than the cheapest, since that is what this extracts.
+                Entity? last = null;
+                var unchanged = 0;
+                bool Settled()
+                {
+                    var now = graph.ExtractLeast(root, EntityOrder.Canonical);
+                    unchanged = now is not null && now.Equals(last) ? unchanged + 1 : 0;
+                    last = now;
+                    return unchanged >= 2;
+                }
+                Saturation.Run(graph, rules, ledger, CostModel.Default.Cost, Settled);
                 ledger.Report();
 
                 // The least member, not the cheapest: a cost model ties, and a tie would make the