diff --git a/src/form/expression.cpp b/src/form/expression.cpp
index 4966f354..a317c714 100644
--- a/src/form/expression.cpp
+++ b/src/form/expression.cpp
@@ -1,6 +1,7 @@
 #include "form/expression.hpp"
 
 #include <algorithm>
+#include <iostream>
 #include <sstream>
 
 Expression::Expression()
@@ -202,6 +203,28 @@ void Expression::replaceName(const std::string& from, const std::string& to) {
   }
 }
 
+void Expression::substituteFunction(const std::string& from,
+                                    const Expression& to,
+                                    const std::string& param) {
+  if (type == Type::FUNCTION && name == from) {
+    // sanity check
+    if (to.type != Type::FUNCTION || to.children.size() != 1) {
+      throw std::runtime_error("invalid function substitution: " +
+                               to.toString());
+    }
+    name = to.name;
+    Expression& arg = *children.front();
+    Expression newArg = *to.children.front();  // copy
+    newArg.replaceAll(Expression(Type::PARAMETER, param), arg);
+    arg = newArg;
+    std::cout << "result " << toString() << std::endl;
+    return;
+  }
+  for (auto& c : children) {
+    c->substituteFunction(from, to, param);
+  }
+}
+
 std::ostream& operator<<(std::ostream& out, const Expression& e) {
   e.print(out, 0, true, Expression::Type::CONSTANT);
   return out;
diff --git a/src/form/expression.hpp b/src/form/expression.hpp
index af2865ec..2e92bb67 100644
--- a/src/form/expression.hpp
+++ b/src/form/expression.hpp
@@ -62,6 +62,9 @@ class Expression {
 
   void replaceName(const std::string& from, const std::string& to);
 
+  void substituteFunction(const std::string& from, const Expression& to,
+                          const std::string& param);
+
   friend std::ostream& operator<<(std::ostream& out, const Expression& e);
 
   std::string toString() const;
diff --git a/src/form/formula.cpp b/src/form/formula.cpp
index 8904781c..b89cde78 100644
--- a/src/form/formula.cpp
+++ b/src/form/formula.cpp
@@ -1,5 +1,6 @@
 #include "form/formula.hpp"
 
+#include <iostream>
 #include <set>
 
 #include "form/expression_util.hpp"
@@ -138,6 +139,17 @@ void Formula::replaceName(const std::string& from, const std::string& to) {
   entries = newEntries;
 }
 
+void Formula::substituteFunction(const std::string& from,
+                                 const Expression& to) {
+  const auto param = ExpressionUtil::newParameter();
+  for (auto& e : entries) {
+    std::cout << "subst " << from << " -> " << to.toString() << " in "
+              << e.second.toString() << std::endl;
+    e.second.substituteFunction(from, to, param.name);
+    ExpressionUtil::normalize(e.second);
+  }
+}
+
 void Formula::collectEntries(const std::string& name, Formula& target) {
   for (auto& e : entries) {
     if (e.first.name == name) {
@@ -159,14 +171,21 @@ void Formula::collectEntries(const Expression& e, Formula& target) {
   }
 }
 
-void Formula::resolveIdentities() {
+void Formula::resolveIdentities(const std::string& main) {
   auto copy = entries;
   for (auto& e : copy) {
-    if (ExpressionUtil::isSimpleFunction(e.first) &&
-        ExpressionUtil::isSimpleFunction(e.second) &&
-        copy.find(e.second) != copy.end()) {
+    if (!ExpressionUtil::isSimpleFunction(e.first, true) ||
+        !ExpressionUtil::isSimpleFunction(e.second, false) ||
+        e.first.name == main) {
+      continue;
+    }
+    auto r = ExpressionUtil::newFunction(e.second.name);
+    if (copy.find(r) != copy.end()) {
+      std::cout << "candidate " << e.first.toString() << " = "
+                << e.second.toString() << std::endl;
       entries.erase(e.first);
-      replaceName(e.second.name, e.first.name);
+
+      substituteFunction(e.first.name, e.second);
     }
   }
 }
diff --git a/src/form/formula.hpp b/src/form/formula.hpp
index 41ca38b7..ac6f1112 100644
--- a/src/form/formula.hpp
+++ b/src/form/formula.hpp
@@ -24,11 +24,13 @@ class Formula {
 
   void replaceName(const std::string& from, const std::string& to);
 
+  void substituteFunction(const std::string& from, const Expression& to);
+
   void collectEntries(const std::string& name, Formula& target);
 
   void collectEntries(const Expression& e, Formula& target);
 
-  void resolveIdentities();
+  void resolveIdentities(const std::string& main);
 
   void resolveSimpleFunctions();
 
diff --git a/src/form/formula_gen.cpp b/src/form/formula_gen.cpp
index 1b773558..5d3f6b6f 100644
--- a/src/form/formula_gen.cpp
+++ b/src/form/formula_gen.cpp
@@ -420,16 +420,16 @@ bool FormulaGenerator::generateSingle(const Program& p) {
   formula.resolveSimpleFunctions();
   Log::get().debug("Resolved simple functions: " + formula.toString());
 
+  // resolve identities
+  formula.resolveIdentities(getCellName(Program::OUTPUT_CELL));
+  Log::get().debug("Resolved identities: " + formula.toString());
+
   // extract main formula (filter out irrelant memory cells)
   Formula tmp;
   formula.collectEntries(getCellName(Program::OUTPUT_CELL), tmp);
   formula = tmp;
   Log::get().debug("Pruned formula: " + formula.toString());
 
-  // resolve identities
-  formula.resolveIdentities();
-  Log::get().debug("Resolved identities: " + formula.toString());
-
   // success
   return true;
 }