internal PivotsExpression Simplify(Dictionary<string, Pivots.Pivot> pivotVsPivotValues) {
     if (invariant)
         return this;
     if (matching_combinations.Count == 0)
         return False;
     int possible_combinations = 1;
     foreach (string pivot in relevant_pivots) {
         possible_combinations *= pivotVsPivotValues[pivot].Choices.Keys.Count;
     }
     if (matching_combinations.Count == possible_combinations)
         return True;
     foreach (string pivot in relevant_pivots) {
         var values = pivotVsPivotValues[pivot].Choices.Keys;
         if (matching_combinations.Count % values.Count != 0)
             continue;
         int reduced_combinations = matching_combinations.Count / values.Count;
         ComparableHashSet<ComparableHashSet<string>> new_combinations = new ComparableHashSet<ComparableHashSet<string>>();
         foreach (var combination in matching_combinations) {
             ComparableHashSet<string> reduced_combination = new ComparableHashSet<string>(combination);
             reduced_combination.ExceptWith(values);
             new_combinations.Add(reduced_combination);
             if (new_combinations.Count > reduced_combinations)
                 break;
         }
         if (new_combinations.Count == reduced_combinations) {
             PivotsExpression result = new PivotsExpression();
             result.relevant_pivots = new HashSet<string>(relevant_pivots);
             result.relevant_pivots.Remove(pivot);
             result.matching_combinations = new_combinations;
             return result.Simplify(pivotVsPivotValues);
         }
     }
     return this;
 }
            internal override PivotsExpression ToPivotsExpression(Dictionary<string, Pivots.Pivot> pivotVsPivotValues, GetChoiceDelegate get_choice_fn) {
                PivotsExpression left, right;

                left = left_child.ToPivotsExpression(pivotVsPivotValues, get_choice_fn);
                if (left.invariant) {
                    if (left.invariant_result)
                        return right_child.ToPivotsExpression(pivotVsPivotValues, get_choice_fn);
                    else
                        return left;
                }
                right = right_child.ToPivotsExpression(pivotVsPivotValues, get_choice_fn);
                if (right.invariant) {
                    if (right.invariant_result)
                        return left;
                    else
                        return right;
                }

                HashSet<string> shared_pivots = new HashSet<string>(left.relevant_pivots);
                shared_pivots.IntersectWith(right.relevant_pivots);

                if (shared_pivots.Count == left.relevant_pivots.Count) {
                    // All pivots are shared, just intersect the sets.
                    PivotsExpression result = new PivotsExpression();
                    result.relevant_pivots = left.relevant_pivots;
                    result.matching_combinations = new ComparableHashSet<ComparableHashSet<string>>(left.matching_combinations);
                    result.matching_combinations.IntersectWith(right.matching_combinations);
                    return result.Simplify(pivotVsPivotValues);
                }

                if (shared_pivots.Count == 0) {
                    // No shared pivots, so do a cross product
                    PivotsExpression result = new PivotsExpression();
                    result.relevant_pivots = new HashSet<string>(left.relevant_pivots);
                    result.relevant_pivots.UnionWith(right.relevant_pivots);

                    result.matching_combinations = new ComparableHashSet<ComparableHashSet<string>>();

                    foreach (var left_combination in left.matching_combinations) {
                        foreach (var right_combination in right.matching_combinations) {
                            ComparableHashSet<string> new_combination = new ComparableHashSet<string>(left_combination);
                            new_combination.UnionWith(right_combination);
                            result.matching_combinations.Add(new_combination);
                        }
                    }
                    // It shouldn't be necessary to simplify in this case, as any independent pivots should have been removed already
                    return result;
                }

                HashSet<string> shared_pivot_values = new HashSet<string>();
                foreach (string pivot in shared_pivots) {
                    shared_pivot_values.UnionWith(pivotVsPivotValues[pivot].Choices.Keys);
                }

                // Sort by relevant pivot count
                if (left.relevant_pivots.Count > right.relevant_pivots.Count) {
                    var tmp = left;
                    left = right;
                    right = tmp;
                }

                if (right.relevant_pivots.IsSupersetOf(left.relevant_pivots)) {
                    // Filter the combintions in right by what's in left.
                    PivotsExpression result = new PivotsExpression();
                    result.relevant_pivots = right.relevant_pivots;

                    result.matching_combinations = new ComparableHashSet<ComparableHashSet<string>>();

                    foreach (var right_combination in right.matching_combinations) {
                        ComparableHashSet<string> reduced_combination = new ComparableHashSet<string>(right_combination);
                        reduced_combination.IntersectWith(shared_pivot_values);
                        if (left.matching_combinations.Contains(reduced_combination))
                            result.matching_combinations.Add(right_combination);
                    }
                    return result.Simplify(pivotVsPivotValues);
                }
                else {
                    Dictionary<ComparableHashSet<string>, List<ComparableHashSet<string>>> shared_values_to_left_values = new Dictionary<ComparableHashSet<string>, List<ComparableHashSet<string>>>();

                    foreach (var left_combination in left.matching_combinations) {
                        ComparableHashSet<string> shared_values = new ComparableHashSet<string>();
                        foreach (var value in left_combination) {
                            if (shared_pivot_values.Contains(value))
                                shared_values.Add(value);
                        }
                        List<ComparableHashSet<string>> combination_list;
                        if (!shared_values_to_left_values.TryGetValue(shared_values, out combination_list))
                            combination_list = shared_values_to_left_values[shared_values] = new List<ComparableHashSet<string>>();
                        combination_list.Add(left_combination);
                    }

                    PivotsExpression result = new PivotsExpression();

                    result.relevant_pivots = new HashSet<string>(left.relevant_pivots);
                    result.relevant_pivots.UnionWith(right.relevant_pivots);

                    result.matching_combinations = new ComparableHashSet<ComparableHashSet<string>>();

                    foreach (var right_combination in right.matching_combinations) {
                        ComparableHashSet<string> shared_values = new ComparableHashSet<string>();
                        foreach (var value in right_combination) {
                            if (shared_pivot_values.Contains(value))
                                shared_values.Add(value);
                        }
                        List<ComparableHashSet<string>> left_combinations;
                        if (shared_values_to_left_values.TryGetValue(shared_values, out left_combinations)) {
                            foreach (var left_combination in left_combinations) {
                                ComparableHashSet<string> new_combination = new ComparableHashSet<string>(right_combination);
                                new_combination.UnionWith(left_combination);
                                result.matching_combinations.Add(new_combination);
                            }
                        }
                    }
                    return result.Simplify(pivotVsPivotValues);
                }
            }
            internal override PivotsExpression ToPivotsExpression(Dictionary<string, Pivots.Pivot> pivotVsPivotValues, GetChoiceDelegate get_choice_fn) {
                var result = new PivotsExpression();

                result.relevant_pivots = new HashSet<string>();
                result.relevant_pivots.Add(pivot_name);

                result.matching_combinations = new ComparableHashSet<ComparableHashSet<string>>();

                if (inverted) {
                    foreach (string pivotValue in pivotVsPivotValues[pivot_name].Choices.Keys) {
                        if (pivotValue != pivot_choice) {
                            ComparableHashSet<string> choice = new ComparableHashSet<string>();
                            choice.Add(pivotValue);
                            result.matching_combinations.Add(choice);
                        }
                    }
                }
                else {
                    ComparableHashSet<string> choice = new ComparableHashSet<string>();
                    choice.Add(pivot_choice);
                    result.matching_combinations.Add(choice);
                }

                return result;
            }
 internal ComparableHashSet<ComparableHashSet<string>> GetExpandedChoices(PivotsExpression expr, HashSet<string> pivots, Dictionary<string, Pivots.Pivot> pivotVsPivotValues) {
     ComparableHashSet<ComparableHashSet<string>> result = expr.matching_combinations;
     foreach (string pivot in pivots) {
         if (expr.relevant_pivots.Contains(pivot))
             continue;
         ComparableHashSet<ComparableHashSet<string>> new_result = new ComparableHashSet<ComparableHashSet<string>>();
         var pivot_choices = pivotVsPivotValues[pivot].Choices.Keys;
         foreach (var matching_combination in result) {
             foreach (string pivot_choice in pivot_choices) {
                 ComparableHashSet<string> choices = new ComparableHashSet<string>(matching_combination);
                 choices.Add(pivot_choice);
                 new_result.Add(choices);
             }
         }
         result = new_result;
     }
     return result;
 }