Changeset 8915 for branches/HeuristicLab.TreeSimplifier/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/SingleObjective/Evaluators/SymbolicRegressionConstantOptimizationEvaluator.cs

Timestamp:

11/15/12 16:47:25 (12 years ago)

Author:

mkommend

Message:

#1763: merged changes from trunk into the tree simplifier branch.

File:

• branches/HeuristicLab.TreeSimplifier/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/SingleObjective/Evaluators/SymbolicRegressionConstantOptimizationEvaluator.cs (modified) (9 diffs)

branches/HeuristicLab.TreeSimplifier/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/SingleObjective/Evaluators/SymbolicRegressionConstantOptimizationEvaluator.cs

@@ -20 +20 @@
 #endregion
 
+using System;
 using System.Collections.Generic;
 using System.Linq;
+using AutoDiff;
 using HeuristicLab.Common;
 using HeuristicLab.Core;
@@ -37 +39 @@
     private const string ConstantOptimizationProbabilityParameterName = "ConstantOptimizationProbability";
     private const string ConstantOptimizationRowsPercentageParameterName = "ConstantOptimizationRowsPercentage";
+    private const string UpdateConstantsInTreeParameterName = "UpdateConstantsInSymbolicExpressionTree";
 
     private const string EvaluatedTreesResultName = "EvaluatedTrees";
@@ -60 +63 @@
       get { return (IFixedValueParameter<PercentValue>)Parameters[ConstantOptimizationRowsPercentageParameterName]; }
     }
+    public IFixedValueParameter<BoolValue> UpdateConstantsInTreeParameter {
+      get { return (IFixedValueParameter<BoolValue>)Parameters[UpdateConstantsInTreeParameterName]; }
+    }
 
     public IntValue ConstantOptimizationIterations {
@@ -72 +78 @@
     public PercentValue ConstantOptimizationRowsPercentage {
       get { return ConstantOptimizationRowsPercentageParameter.Value; }
+    }
+    public bool UpdateConstantsInTree {
+      get { return UpdateConstantsInTreeParameter.Value.Value; }
+      set { UpdateConstantsInTreeParameter.Value.Value = value; }
     }
 
@@ -89 +99 @@
       Parameters.Add(new FixedValueParameter<PercentValue>(ConstantOptimizationProbabilityParameterName, "Determines the probability that the constants are optimized", new PercentValue(1), true));
       Parameters.Add(new FixedValueParameter<PercentValue>(ConstantOptimizationRowsPercentageParameterName, "Determines the percentage of the rows which should be used for constant optimization", new PercentValue(1), true));
+      Parameters.Add(new FixedValueParameter<BoolValue>(UpdateConstantsInTreeParameterName, "Determines if the constants in the tree should be overwritten by the optimized constants.", new BoolValue(true)));
 
       Parameters.Add(new LookupParameter<IntValue>(EvaluatedTreesResultName));
@@ -98 +109 @@
     }
 
+    [StorableHook(HookType.AfterDeserialization)]
+    private void AfterDeserialization() {
+      if (!Parameters.ContainsKey(UpdateConstantsInTreeParameterName))
+        Parameters.Add(new FixedValueParameter<BoolValue>(UpdateConstantsInTreeParameterName, "Determines if the constants in the tree should be overwritten by the optimized constants.", new BoolValue(true)));
+    }
+
     public override IOperation Apply() {
       AddResults();
-      int seed = RandomParameter.ActualValue.Next();
       var solution = SymbolicExpressionTreeParameter.ActualValue;
       double quality;
@@ -106 +122 @@
         IEnumerable<int> constantOptimizationRows = GenerateRowsToEvaluate(ConstantOptimizationRowsPercentage.Value);
         quality = OptimizeConstants(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, ProblemDataParameter.ActualValue,
-           constantOptimizationRows, ConstantOptimizationImprovement.Value, ConstantOptimizationIterations.Value, 0.001,
-           EstimationLimitsParameter.ActualValue.Upper, EstimationLimitsParameter.ActualValue.Lower,
+           constantOptimizationRows, ApplyLinearScalingParameter.ActualValue.Value, ConstantOptimizationIterations.Value,
+           EstimationLimitsParameter.ActualValue.Upper, EstimationLimitsParameter.ActualValue.Lower, UpdateConstantsInTree,
           EvaluatedTreesParameter.ActualValue, EvaluatedTreeNodesParameter.ActualValue);
         if (ConstantOptimizationRowsPercentage.Value != RelativeNumberOfEvaluatedSamplesParameter.ActualValue.Value) {
           var evaluationRows = GenerateRowsToEvaluate();
-          quality = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, ProblemDataParameter.ActualValue, evaluationRows);
+          quality = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, ProblemDataParameter.ActualValue, evaluationRows, ApplyLinearScalingParameter.ActualValue.Value);
         }
       } else {
         var evaluationRows = GenerateRowsToEvaluate();
-        quality = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, ProblemDataParameter.ActualValue, evaluationRows);
+        quality = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, ProblemDataParameter.ActualValue, evaluationRows, ApplyLinearScalingParameter.ActualValue.Value);
       }
       QualityParameter.ActualValue = new DoubleValue(quality);
-      EvaluatedTreesParameter.ActualValue.Value += 1;
-      EvaluatedTreeNodesParameter.ActualValue.Value += solution.Length;
+      lock (locker) {
+        EvaluatedTreesParameter.ActualValue.Value += 1;
+        EvaluatedTreeNodesParameter.ActualValue.Value += solution.Length;
+      }
 
       if (Successor != null)
@@ -127 +145 @@
     }
 
+    private object locker = new object();
     private void AddResults() {
-      if (EvaluatedTreesParameter.ActualValue == null) {
-        var scope = ExecutionContext.Scope;
-        while (scope.Parent != null)
-          scope = scope.Parent;
-        scope.Variables.Add(new Core.Variable(EvaluatedTreesResultName, new IntValue()));
-      }
-      if (EvaluatedTreeNodesParameter.ActualValue == null) {
-        var scope = ExecutionContext.Scope;
-        while (scope.Parent != null)
-          scope = scope.Parent;
-        scope.Variables.Add(new Core.Variable(EvaluatedTreeNodesResultName, new IntValue()));
+      lock (locker) {
+        if (EvaluatedTreesParameter.ActualValue == null) {
+          var scope = ExecutionContext.Scope;
+          while (scope.Parent != null)
+            scope = scope.Parent;
+          scope.Variables.Add(new Core.Variable(EvaluatedTreesResultName, new IntValue()));
+        }
+        if (EvaluatedTreeNodesParameter.ActualValue == null) {
+          var scope = ExecutionContext.Scope;
+          while (scope.Parent != null)
+            scope = scope.Parent;
+          scope.Variables.Add(new Core.Variable(EvaluatedTreeNodesResultName, new IntValue()));
+        }
       }
     }
@@ -145 +166 @@
       SymbolicDataAnalysisTreeInterpreterParameter.ExecutionContext = context;
       EstimationLimitsParameter.ExecutionContext = context;
-
-      double r2 = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, tree, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, problemData, rows);
+      ApplyLinearScalingParameter.ExecutionContext = context;
+
+      double r2 = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, tree, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, problemData, rows, ApplyLinearScalingParameter.ActualValue.Value);
 
       SymbolicDataAnalysisTreeInterpreterParameter.ExecutionContext = null;
       EstimationLimitsParameter.ExecutionContext = null;
+      ApplyLinearScalingParameter.ExecutionContext = context;
 
       return r2;
     }
 
+    #region derivations of functions
+    // create function factory for arctangent
+    private readonly Func<Term, UnaryFunc> arctan = UnaryFunc.Factory(
+      eval: Math.Atan,
+      diff: x => 1 / (1 + x * x));
+    private static readonly Func<Term, UnaryFunc> sin = UnaryFunc.Factory(
+      eval: Math.Sin,
+      diff: Math.Cos);
+    private static readonly Func<Term, UnaryFunc> cos = UnaryFunc.Factory(
+       eval: Math.Cos,
+       diff: x => -Math.Sin(x));
+    private static readonly Func<Term, UnaryFunc> tan = UnaryFunc.Factory(
+      eval: Math.Tan,
+      diff: x => 1 + Math.Tan(x) * Math.Tan(x));
+    private static readonly Func<Term, UnaryFunc> square = UnaryFunc.Factory(
+       eval: x => x * x,
+       diff: x => 2 * x);
+    private static readonly Func<Term, UnaryFunc> erf = UnaryFunc.Factory(
+      eval: alglib.errorfunction,
+      diff: x => 2.0 * Math.Exp(-(x * x)) / Math.Sqrt(Math.PI));
+    private static readonly Func<Term, UnaryFunc> norm = UnaryFunc.Factory(
+      eval: alglib.normaldistribution,
+      diff: x => -(Math.Exp(-(x * x)) * Math.Sqrt(Math.Exp(x * x)) * x) / Math.Sqrt(2 * Math.PI));
+    #endregion
+
+
     public static double OptimizeConstants(ISymbolicDataAnalysisExpressionTreeInterpreter interpreter, ISymbolicExpressionTree tree, IRegressionProblemData problemData,
-      IEnumerable<int> rows, double improvement, int iterations, double differentialStep, double upperEstimationLimit = double.MaxValue, double lowerEstimationLimit = double.MinValue, IntValue evaluatedTrees = null, IntValue evaluatedTreeNodes = null) {
+      IEnumerable<int> rows, bool applyLinearScaling, int maxIterations, double upperEstimationLimit = double.MaxValue, double lowerEstimationLimit = double.MinValue, bool updateConstantsInTree = true, IntValue evaluatedTrees = null, IntValue evaluatedTreeNodes = null) {
+
+      List<AutoDiff.Variable> variables = new List<AutoDiff.Variable>();
+      List<AutoDiff.Variable> parameters = new List<AutoDiff.Variable>();
+      List<string> variableNames = new List<string>();
+
+      AutoDiff.Term func;
+      if (!TryTransformToAutoDiff(tree.Root.GetSubtree(0), variables, parameters, variableNames, out func))
+        throw new NotSupportedException("Could not optimize constants of symbolic expression tree due to not supported symbols used in the tree.");
+      if (variableNames.Count == 0) return 0.0;
+
+      AutoDiff.IParametricCompiledTerm compiledFunc = AutoDiff.TermUtils.Compile(func, variables.ToArray(), parameters.ToArray());
+
       List<SymbolicExpressionTreeTerminalNode> terminalNodes = tree.Root.IterateNodesPrefix().OfType<SymbolicExpressionTreeTerminalNode>().ToList();
-      double[] c = new double[terminalNodes.Count];
-      int treeLength = tree.Length;
-
-      //extract inital constants
-      for (int i = 0; i < terminalNodes.Count; i++) {
-        ConstantTreeNode constantTreeNode = terminalNodes[i] as ConstantTreeNode;
-        if (constantTreeNode != null) c[i] = constantTreeNode.Value;
-        VariableTreeNode variableTreeNode = terminalNodes[i] as VariableTreeNode;
-        if (variableTreeNode != null) c[i] = variableTreeNode.Weight;
-      }
-
-      double epsg = 0;
-      double epsf = improvement;
-      double epsx = 0;
-      int maxits = iterations;
-      double diffstep = differentialStep;
-
-      alglib.minlmstate state;
-      alglib.minlmreport report;
-
-      alglib.minlmcreatev(1, c, diffstep, out state);
-      alglib.minlmsetcond(state, epsg, epsf, epsx, maxits);
-      alglib.minlmoptimize(state, CreateCallBack(interpreter, tree, problemData, rows, upperEstimationLimit, lowerEstimationLimit, treeLength, evaluatedTrees, evaluatedTreeNodes), null, terminalNodes);
-      alglib.minlmresults(state, out c, out report);
-
-      for (int i = 0; i < c.Length; i++) {
-        ConstantTreeNode constantTreeNode = terminalNodes[i] as ConstantTreeNode;
-        if (constantTreeNode != null) constantTreeNode.Value = c[i];
-        VariableTreeNode variableTreeNode = terminalNodes[i] as VariableTreeNode;
-        if (variableTreeNode != null) variableTreeNode.Weight = c[i];
-      }
-
-      return (state.fi[0] - 1) * -1;
-    }
-
-    private static alglib.ndimensional_fvec CreateCallBack(ISymbolicDataAnalysisExpressionTreeInterpreter interpreter, ISymbolicExpressionTree tree, IRegressionProblemData problemData, IEnumerable<int> rows, double upperEstimationLimit, double lowerEstimationLimit, int treeLength, IntValue evaluatedTrees = null, IntValue evaluatedTreeNodes = null) {
-      return (double[] arg, double[] fi, object obj) => {
-        // update constants of tree
-        List<SymbolicExpressionTreeTerminalNode> terminalNodes = (List<SymbolicExpressionTreeTerminalNode>)obj;
-        for (int i = 0; i < terminalNodes.Count; i++) {
-          ConstantTreeNode constantTreeNode = terminalNodes[i] as ConstantTreeNode;
-          if (constantTreeNode != null) constantTreeNode.Value = arg[i];
-          VariableTreeNode variableTreeNode = terminalNodes[i] as VariableTreeNode;
-          if (variableTreeNode != null) variableTreeNode.Weight = arg[i];
-        }
-
-        double quality = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(interpreter, tree, lowerEstimationLimit, upperEstimationLimit, problemData, rows);
-
-        fi[0] = 1 - quality;
-        if (evaluatedTrees != null) evaluatedTrees.Value++;
-        if (evaluatedTreeNodes != null) evaluatedTreeNodes.Value += treeLength;
+      double[] c = new double[variables.Count];
+
+      {
+        c[0] = 0.0;
+        c[1] = 1.0;
+        //extract inital constants
+        int i = 2;
+        foreach (var node in terminalNodes) {
+          ConstantTreeNode constantTreeNode = node as ConstantTreeNode;
+          VariableTreeNode variableTreeNode = node as VariableTreeNode;
+          if (constantTreeNode != null)
+            c[i++] = constantTreeNode.Value;
+          else if (variableTreeNode != null)
+            c[i++] = variableTreeNode.Weight;
+        }
+      }
+
+      alglib.lsfitstate state;
+      alglib.lsfitreport rep;
+      int info;
+
+      Dataset ds = problemData.Dataset;
+      double[,] x = new double[rows.Count(), variableNames.Count];
+      int row = 0;
+      foreach (var r in rows) {
+        for (int col = 0; col < variableNames.Count; col++) {
+          x[row, col] = ds.GetDoubleValue(variableNames[col], r);
+        }
+        row++;
+      }
+      double[] y = ds.GetDoubleValues(problemData.TargetVariable, rows).ToArray();
+      int n = x.GetLength(0);
+      int m = x.GetLength(1);
+      int k = c.Length;
+
+      alglib.ndimensional_pfunc function_cx_1_func = CreatePFunc(compiledFunc);
+      alglib.ndimensional_pgrad function_cx_1_grad = CreatePGrad(compiledFunc);
+
+      try {
+        alglib.lsfitcreatefg(x, y, c, n, m, k, false, out state);
+        alglib.lsfitsetcond(state, 0, 0, maxIterations);
+        alglib.lsfitfit(state, function_cx_1_func, function_cx_1_grad, null, null);
+        alglib.lsfitresults(state, out info, out c, out rep);
+
+      }
+      catch (ArithmeticException) {
+        return 0.0;
+      }
+      catch (alglib.alglibexception) {
+        return 0.0;
+      }
+      var newTree = tree;
+      if (!updateConstantsInTree) newTree = (ISymbolicExpressionTree)tree.Clone();
+      {
+        // only when no error occurred
+        // set constants in tree
+        int i = 2;
+        foreach (var node in newTree.Root.IterateNodesPrefix().OfType<SymbolicExpressionTreeTerminalNode>()) {
+          ConstantTreeNode constantTreeNode = node as ConstantTreeNode;
+          VariableTreeNode variableTreeNode = node as VariableTreeNode;
+          if (constantTreeNode != null)
+            constantTreeNode.Value = c[i++];
+          else if (variableTreeNode != null)
+            variableTreeNode.Weight = c[i++];
+        }
+
+      }
+      return SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(interpreter, newTree, lowerEstimationLimit, upperEstimationLimit, problemData, rows, applyLinearScaling);
+    }
+
+    private static alglib.ndimensional_pfunc CreatePFunc(AutoDiff.IParametricCompiledTerm compiledFunc) {
+      return (double[] c, double[] x, ref double func, object o) => {
+        func = compiledFunc.Evaluate(c, x);
       };
     }
 
+    private static alglib.ndimensional_pgrad CreatePGrad(AutoDiff.IParametricCompiledTerm compiledFunc) {
+      return (double[] c, double[] x, ref double func, double[] grad, object o) => {
+        var tupel = compiledFunc.Differentiate(c, x);
+        func = tupel.Item2;
+        Array.Copy(tupel.Item1, grad, grad.Length);
+      };
+    }
+
+    private static bool TryTransformToAutoDiff(ISymbolicExpressionTreeNode node, List<AutoDiff.Variable> variables, List<AutoDiff.Variable> parameters, List<string> variableNames, out AutoDiff.Term term) {
+      if (node.Symbol is Constant) {
+        var var = new AutoDiff.Variable();
+        variables.Add(var);
+        term = var;
+        return true;
+      }
+      if (node.Symbol is Variable) {
+        var varNode = node as VariableTreeNode;
+        var par = new AutoDiff.Variable();
+        parameters.Add(par);
+        variableNames.Add(varNode.VariableName);
+        var w = new AutoDiff.Variable();
+        variables.Add(w);
+        term = AutoDiff.TermBuilder.Product(w, par);
+        return true;
+      }
+      if (node.Symbol is Addition) {
+        List<AutoDiff.Term> terms = new List<Term>();
+        foreach (var subTree in node.Subtrees) {
+          AutoDiff.Term t;
+          if (!TryTransformToAutoDiff(subTree, variables, parameters, variableNames, out t)) {
+            term = null;
+            return false;
+          }
+          terms.Add(t);
+        }
+        term = AutoDiff.TermBuilder.Sum(terms);
+        return true;
+      }
+      if (node.Symbol is Subtraction) {
+        List<AutoDiff.Term> terms = new List<Term>();
+        for (int i = 0; i < node.SubtreeCount; i++) {
+          AutoDiff.Term t;
+          if (!TryTransformToAutoDiff(node.GetSubtree(i), variables, parameters, variableNames, out t)) {
+            term = null;
+            return false;
+          }
+          if (i > 0) t = -t;
+          terms.Add(t);
+        }
+        term = AutoDiff.TermBuilder.Sum(terms);
+        return true;
+      }
+      if (node.Symbol is Multiplication) {
+        AutoDiff.Term a, b;
+        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, out a) ||
+          !TryTransformToAutoDiff(node.GetSubtree(1), variables, parameters, variableNames, out b)) {
+          term = null;
+          return false;
+        } else {
+          List<AutoDiff.Term> factors = new List<Term>();
+          foreach (var subTree in node.Subtrees.Skip(2)) {
+            AutoDiff.Term f;
+            if (!TryTransformToAutoDiff(subTree, variables, parameters, variableNames, out f)) {
+              term = null;
+              return false;
+            }
+            factors.Add(f);
+          }
+          term = AutoDiff.TermBuilder.Product(a, b, factors.ToArray());
+          return true;
+        }
+      }
+      if (node.Symbol is Division) {
+        // only works for at least two subtrees
+        AutoDiff.Term a, b;
+        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, out a) ||
+          !TryTransformToAutoDiff(node.GetSubtree(1), variables, parameters, variableNames, out b)) {
+          term = null;
+          return false;
+        } else {
+          List<AutoDiff.Term> factors = new List<Term>();
+          foreach (var subTree in node.Subtrees.Skip(2)) {
+            AutoDiff.Term f;
+            if (!TryTransformToAutoDiff(subTree, variables, parameters, variableNames, out f)) {
+              term = null;
+              return false;
+            }
+            factors.Add(1.0 / f);
+          }
+          term = AutoDiff.TermBuilder.Product(a, 1.0 / b, factors.ToArray());
+          return true;
+        }
+      }
+      if (node.Symbol is Logarithm) {
+        AutoDiff.Term t;
+        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, out t)) {
+          term = null;
+          return false;
+        } else {
+          term = AutoDiff.TermBuilder.Log(t);
+          return true;
+        }
+      }
+      if (node.Symbol is Exponential) {
+        AutoDiff.Term t;
+        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, out t)) {
+          term = null;
+          return false;
+        } else {
+          term = AutoDiff.TermBuilder.Exp(t);
+          return true;
+        }
+      } if (node.Symbol is Sine) {
+        AutoDiff.Term t;
+        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, out t)) {
+          term = null;
+          return false;
+        } else {
+          term = sin(t);
+          return true;
+        }
+      } if (node.Symbol is Cosine) {
+        AutoDiff.Term t;
+        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, out t)) {
+          term = null;
+          return false;
+        } else {
+          term = cos(t);
+          return true;
+        }
+      } if (node.Symbol is Tangent) {
+        AutoDiff.Term t;
+        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, out t)) {
+          term = null;
+          return false;
+        } else {
+          term = tan(t);
+          return true;
+        }
+      }
+      if (node.Symbol is Square) {
+        AutoDiff.Term t;
+        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, out t)) {
+          term = null;
+          return false;
+        } else {
+          term = square(t);
+          return true;
+        }
+      } if (node.Symbol is Erf) {
+        AutoDiff.Term t;
+        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, out t)) {
+          term = null;
+          return false;
+        } else {
+          term = erf(t);
+          return true;
+        }
+      } if (node.Symbol is Norm) {
+        AutoDiff.Term t;
+        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, out t)) {
+          term = null;
+          return false;
+        } else {
+          term = norm(t);
+          return true;
+        }
+      }
+      if (node.Symbol is StartSymbol) {
+        var alpha = new AutoDiff.Variable();
+        var beta = new AutoDiff.Variable();
+        variables.Add(beta);
+        variables.Add(alpha);
+        AutoDiff.Term branchTerm;
+        if (TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, out branchTerm)) {
+          term = branchTerm * alpha + beta;
+          return true;
+        } else {
+          term = null;
+          return false;
+        }
+      }
+      term = null;
+      return false;
+    }
+
+    public static bool CanOptimizeConstants(ISymbolicExpressionTree tree) {
+      var containsUnknownSymbol = (
+        from n in tree.Root.GetSubtree(0).IterateNodesPrefix()
+        where
+         !(n.Symbol is Variable) &&
+         !(n.Symbol is Constant) &&
+         !(n.Symbol is Addition) &&
+         !(n.Symbol is Subtraction) &&
+         !(n.Symbol is Multiplication) &&
+         !(n.Symbol is Division) &&
+         !(n.Symbol is Logarithm) &&
+         !(n.Symbol is Exponential) &&
+         !(n.Symbol is Sine) &&
+         !(n.Symbol is Cosine) &&
+         !(n.Symbol is Tangent) &&
+         !(n.Symbol is Square) &&
+         !(n.Symbol is Erf) &&
+         !(n.Symbol is Norm) &&
+         !(n.Symbol is StartSymbol)
+        select n).
+      Any();
+      return !containsUnknownSymbol;
+    }
   }
 }