Merge pull request #1549 from ethereum/optimizeOptimizer

Optimize optimizer

12 files changed, 646 insertions, 461 deletions

diff --git a/Changelog.md b/Changelog.md
index 7676b5be..3e999d13 100644
--- a/Changelog.md
+++ b/Changelog.md
@@ -1,9 +1,10 @@
 ### 0.4.8 (unreleased)
 
 Features:
+ * Optimiser: Performance improvements.
  * Output: Print assembly in new standardized Solidity assembly format.
 
-BugFixes:
+Bugfixes:
  * Remappings: Prefer longer context over longer prefix.
  * Type checker, code generator: enable access to events of base contracts' names.
  * Imports: ``import ".dir/a"`` is not a relative path.  Relative paths begin with directory ``.`` or ``..``.
diff --git a/libdevcore/Assertions.h b/libdevcore/Assertions.h
index 05e0b0e5..0fb5837c 100644
--- a/libdevcore/Assertions.h
+++ b/libdevcore/Assertions.h
@@ -73,27 +73,19 @@ inline bool assertEqualAux(A const& _a, B const& _b, char const* _aStr, char con
 /// Use it as assertThrow(1 == 1, ExceptionType, "Mathematics is wrong.");
 /// Do NOT supply an exception object as the second parameter.
 #define assertThrow(_condition, _ExceptionType, _description) \
-	::dev::assertThrowAux<_ExceptionType>(!!(_condition), _description, __LINE__, __FILE__, ETH_FUNC)
+	do \
+	{ \
+		if (!(_condition)) \
+			::boost::throw_exception( \
+				_ExceptionType() << \
+				::dev::errinfo_comment(_description) << \
+				::boost::throw_function(ETH_FUNC) << \
+				::boost::throw_file(__FILE__) << \
+				::boost::throw_line(__LINE__) \
+			); \
+	} \
+	while (false)
 
 using errinfo_comment = boost::error_info<struct tag_comment, std::string>;
 
-template <class _ExceptionType>
-inline void assertThrowAux(
-	bool _condition,
-	::std::string const& _errorDescription,
-	unsigned _line,
-	char const* _file,
-	char const* _function
-)
-{
-	if (!_condition)
-		::boost::throw_exception(
-			_ExceptionType() <<
-			::dev::errinfo_comment(_errorDescription) <<
-			::boost::throw_function(_function) <<
-			::boost::throw_file(_file) <<
-			::boost::throw_line(_line)
-		);
-}
-
 }
diff --git a/libevmasm/Assembly.cpp b/libevmasm/Assembly.cpp
index f50a38a6..845abfd4 100644
--- a/libevmasm/Assembly.cpp
+++ b/libevmasm/Assembly.cpp
@@ -416,7 +416,7 @@ LinkerObject const& Assembly::assemble() const
 		switch (i.type())
 		{
 		case Operation:
-			ret.bytecode.push_back((byte)i.data());
+			ret.bytecode.push_back((byte)i.instruction());
 			break;
 		case PushString:
 		{
diff --git a/libevmasm/AssemblyItem.cpp b/libevmasm/AssemblyItem.cpp
index b790e094..6c7d5425 100644
--- a/libevmasm/AssemblyItem.cpp
+++ b/libevmasm/AssemblyItem.cpp
@@ -29,19 +29,19 @@ using namespace dev::eth;
 
 AssemblyItem AssemblyItem::toSubAssemblyTag(size_t _subId) const
 {
-	assertThrow(m_data < (u256(1) << 64), Exception, "Tag already has subassembly set.");
+	assertThrow(data() < (u256(1) << 64), Exception, "Tag already has subassembly set.");
 
 	assertThrow(m_type == PushTag || m_type == Tag, Exception, "");
 	AssemblyItem r = *this;
 	r.m_type = PushTag;
-	r.setPushTagSubIdAndTag(_subId, size_t(m_data));
+	r.setPushTagSubIdAndTag(_subId, size_t(data()));
 	return r;
 }
 
 pair<size_t, size_t> AssemblyItem::splitForeignPushTag() const
 {
 	assertThrow(m_type == PushTag || m_type == Tag, Exception, "");
-	return make_pair(size_t(m_data / (u256(1) << 64)) - 1, size_t(m_data));
+	return make_pair(size_t((data()) / (u256(1) << 64)) - 1, size_t(data()));
 }
 
 void AssemblyItem::setPushTagSubIdAndTag(size_t _subId, size_t _tag)
@@ -60,7 +60,7 @@ unsigned AssemblyItem::bytesRequired(unsigned _addressLength) const
 	case PushString:
 		return 33;
 	case Push:
-		return 1 + max<unsigned>(1, dev::bytesRequired(m_data));
+		return 1 + max<unsigned>(1, dev::bytesRequired(data()));
 	case PushSubSize:
 	case PushProgramSize:
 		return 4;		// worst case: a 16MB program
diff --git a/libevmasm/AssemblyItem.h b/libevmasm/AssemblyItem.h
index cddfb17c..002b3c87 100644
--- a/libevmasm/AssemblyItem.h
+++ b/libevmasm/AssemblyItem.h
@@ -59,16 +59,22 @@ public:
 	AssemblyItem(u256 _push, SourceLocation const& _location = SourceLocation()):
 		AssemblyItem(Push, _push, _location) { }
 	AssemblyItem(solidity::Instruction _i, SourceLocation const& _location = SourceLocation()):
-		AssemblyItem(Operation, byte(_i), _location) { }
+		m_type(Operation),
+		m_instruction(_i),
+		m_location(_location)
+	{}
 	AssemblyItem(AssemblyItemType _type, u256 _data = 0, SourceLocation const& _location = SourceLocation()):
 		m_type(_type),
-		m_data(_data),
 		m_location(_location)
 	{
+		if (m_type == Operation)
+			m_instruction = Instruction(byte(_data));
+		else
+			m_data = std::make_shared<u256>(_data);
 	}
 
-	AssemblyItem tag() const { assertThrow(m_type == PushTag || m_type == Tag, Exception, ""); return AssemblyItem(Tag, m_data); }
-	AssemblyItem pushTag() const { assertThrow(m_type == PushTag || m_type == Tag, Exception, ""); return AssemblyItem(PushTag, m_data); }
+	AssemblyItem tag() const { assertThrow(m_type == PushTag || m_type == Tag, Exception, ""); return AssemblyItem(Tag, data()); }
+	AssemblyItem pushTag() const { assertThrow(m_type == PushTag || m_type == Tag, Exception, ""); return AssemblyItem(PushTag, data()); }
 	/// Converts the tag to a subassembly tag. This has to be called in order to move a tag across assemblies.
 	/// @param _subId the identifier of the subassembly the tag is taken from.
 	AssemblyItem toSubAssemblyTag(size_t _subId) const;
@@ -79,18 +85,33 @@ public:
 	void setPushTagSubIdAndTag(size_t _subId, size_t _tag);
 
 	AssemblyItemType type() const { return m_type; }
-	u256 const& data() const { return m_data; }
-	void setType(AssemblyItemType const _type) { m_type = _type; }
-	void setData(u256 const& _data) { m_data = _data; }
+	u256 const& data() const { assertThrow(m_type != Operation, Exception, ""); return *m_data; }
+	void setData(u256 const& _data) { assertThrow(m_type != Operation, Exception, ""); m_data = std::make_shared<u256>(_data); }
 
 	/// @returns the instruction of this item (only valid if type() == Operation)
-	Instruction instruction() const { return Instruction(byte(m_data)); }
+	Instruction instruction() const { assertThrow(m_type == Operation, Exception, ""); return m_instruction; }
 
 	/// @returns true if the type and data of the items are equal.
-	bool operator==(AssemblyItem const& _other) const { return m_type == _other.m_type && m_data == _other.m_data; }
+	bool operator==(AssemblyItem const& _other) const
+	{
+		if (type() != _other.type())
+			return false;
+		if (type() == Operation)
+			return instruction() == _other.instruction();
+		else
+			return data() == _other.data();
+	}
 	bool operator!=(AssemblyItem const& _other) const { return !operator==(_other); }
 	/// Less-than operator compatible with operator==.
-	bool operator<(AssemblyItem const& _other) const { return std::tie(m_type, m_data) < std::tie(_other.m_type, _other.m_data); }
+	bool operator<(AssemblyItem const& _other) const
+	{
+		if (type() != _other.type())
+			return type() < _other.type();
+		else if (type() == Operation)
+			return instruction() < _other.instruction();
+		else
+			return data() < _other.data();
+	}
 
 	/// @returns an upper bound for the number of bytes required by this item, assuming that
 	/// the value of a jump tag takes @a _addressLength bytes.
@@ -100,7 +121,6 @@ public:
 	/// @returns true if the assembly item can be used in a functional context.
 	bool canBeFunctional() const;
 
-	bool match(AssemblyItem const& _i) const { return _i.m_type == UndefinedItem || (m_type == _i.m_type && (m_type != Operation || m_data == _i.m_data)); }
 	void setLocation(SourceLocation const& _location) { m_location = _location; }
 	SourceLocation const& location() const { return m_location; }
 
@@ -115,7 +135,8 @@ public:
 
 private:
 	AssemblyItemType m_type;
-	u256 m_data;
+	Instruction m_instruction; ///< Only valid if m_type == Operation
+	std::shared_ptr<u256> m_data; ///< Only valid if m_type != Operation
 	SourceLocation m_location;
 	JumpType m_jumpType = JumpType::Ordinary;
 	/// Pushed value for operations with data to be determined during assembly stage,
diff --git a/libevmasm/CommonSubexpressionEliminator.cpp b/libevmasm/CommonSubexpressionEliminator.cpp
index 6294e579..fd4fffa6 100644
--- a/libevmasm/CommonSubexpressionEliminator.cpp
+++ b/libevmasm/CommonSubexpressionEliminator.cpp
@@ -303,7 +303,9 @@ void CSECodeGenerator::generateClassElement(Id _c, bool _allowSequenced)
 	for (auto it: m_classPositions)
 		for (auto p: it.second)
 			if (p > m_stackHeight)
+			{
 				assertThrow(false, OptimizerException, "");
+			}
 	// do some cleanup
 	removeStackTopIfPossible();
 
diff --git a/libevmasm/ConstantOptimiser.cpp b/libevmasm/ConstantOptimiser.cpp
index f4a50c2d..86244e17 100644
--- a/libevmasm/ConstantOptimiser.cpp
+++ b/libevmasm/ConstantOptimiser.cpp
@@ -38,6 +38,7 @@ unsigned ConstantOptimisationMethod::optimiseConstants(
 	for (AssemblyItem const& item: _items)
 		if (item.type() == Push)
 			pushes[item]++;
+	map<u256, AssemblyItems> pendingReplacements;
 	for (auto it: pushes)
 	{
 		AssemblyItem const& item = it.first;
@@ -53,17 +54,22 @@ unsigned ConstantOptimisationMethod::optimiseConstants(
 		bigint copyGas = copy.gasNeeded();
 		ComputeMethod compute(params, item.data());
 		bigint computeGas = compute.gasNeeded();
+		AssemblyItems replacement;
 		if (copyGas < literalGas && copyGas < computeGas)
 		{
-			copy.execute(_assembly, _items);
+			replacement = copy.execute(_assembly);
 			optimisations++;
 		}
-		else if (computeGas < literalGas && computeGas < copyGas)
+		else if (computeGas < literalGas && computeGas <= copyGas)
 		{
-			compute.execute(_assembly, _items);
+			replacement = compute.execute(_assembly);
 			optimisations++;
 		}
+		if (!replacement.empty())
+			pendingReplacements[item.data()] = replacement;
 	}
+	if (!pendingReplacements.empty())
+		replaceConstants(_items, pendingReplacements);
 	return optimisations;
 }
 
@@ -101,18 +107,24 @@ size_t ConstantOptimisationMethod::bytesRequired(AssemblyItems const& _items)
 
 void ConstantOptimisationMethod::replaceConstants(
 	AssemblyItems& _items,
-	AssemblyItems const& _replacement
-) const
+	map<u256, AssemblyItems> const& _replacements
+)
 {
-	assertThrow(_items.size() > 0, OptimizerException, "");
-	for (size_t i = 0; i < _items.size(); ++i)
+	AssemblyItems replaced;
+	for (AssemblyItem const& item: _items)
 	{
-		if (_items.at(i) != AssemblyItem(m_value))
-			continue;
-		_items[i] = _replacement[0];
-		_items.insert(_items.begin() + i + 1, _replacement.begin() + 1, _replacement.end());
-		i += _replacement.size() - 1;
+		if (item.type() == Push)
+		{
+			auto it = _replacements.find(item.data());
+			if (it != _replacements.end())
+			{
+				replaced += it->second;
+				continue;
+			}
+		}
+		replaced.push_back(item);
 	}
+	_items = std::move(replaced);
 }
 
 bigint LiteralMethod::gasNeeded()
@@ -128,38 +140,44 @@ bigint LiteralMethod::gasNeeded()
 CodeCopyMethod::CodeCopyMethod(Params const& _params, u256 const& _value):
 	ConstantOptimisationMethod(_params, _value)
 {
-	m_copyRoutine = AssemblyItems{
-		u256(0),
-		Instruction::DUP1,
-		Instruction::MLOAD, // back up memory
-		u256(32),
-		AssemblyItem(PushData, u256(1) << 16), // has to be replaced
-		Instruction::DUP4,
-		Instruction::CODECOPY,
-		Instruction::DUP2,
-		Instruction::MLOAD,
-		Instruction::SWAP2,
-		Instruction::MSTORE
-	};
 }
 
 bigint CodeCopyMethod::gasNeeded()
 {
 	return combineGas(
 		// Run gas: we ignore memory increase costs
-		simpleRunGas(m_copyRoutine) + GasCosts::copyGas,
+		simpleRunGas(copyRoutine()) + GasCosts::copyGas,
 		// Data gas for copy routines: Some bytes are zero, but we ignore them.
-		bytesRequired(m_copyRoutine) * (m_params.isCreation ? GasCosts::txDataNonZeroGas : GasCosts::createDataGas),
+		bytesRequired(copyRoutine()) * (m_params.isCreation ? GasCosts::txDataNonZeroGas : GasCosts::createDataGas),
 		// Data gas for data itself
 		dataGas(toBigEndian(m_value))
 	);
 }
 
-void CodeCopyMethod::execute(Assembly& _assembly, AssemblyItems& _items)
+AssemblyItems CodeCopyMethod::execute(Assembly& _assembly)
 {
 	bytes data = toBigEndian(m_value);
-	m_copyRoutine[4] = _assembly.newData(data);
-	replaceConstants(_items, m_copyRoutine);
+	AssemblyItems actualCopyRoutine = copyRoutine();
+	actualCopyRoutine[4] = _assembly.newData(data);
+	return actualCopyRoutine;
+}
+
+AssemblyItems const& CodeCopyMethod::copyRoutine() const
+{
+	AssemblyItems static copyRoutine{
+		u256(0),
+		Instruction::DUP1,
+		Instruction::MLOAD, // back up memory
+		u256(32),
+		AssemblyItem(PushData, u256(1) << 16), // has to be replaced
+		Instruction::DUP4,
+		Instruction::CODECOPY,
+		Instruction::DUP2,
+		Instruction::MLOAD,
+		Instruction::SWAP2,
+		Instruction::MSTORE
+	};
+	return copyRoutine;
 }
 
 AssemblyItems ComputeMethod::findRepresentation(u256 const& _value)
diff --git a/libevmasm/ConstantOptimiser.h b/libevmasm/ConstantOptimiser.h
index b35b2a69..dfa2fbf8 100644
--- a/libevmasm/ConstantOptimiser.h
+++ b/libevmasm/ConstantOptimiser.h
@@ -60,7 +60,10 @@ public:
 	explicit ConstantOptimisationMethod(Params const& _params, u256 const& _value):
 		m_params(_params), m_value(_value) {}
 	virtual bigint gasNeeded() = 0;
-	virtual void execute(Assembly& _assembly, AssemblyItems& _items) = 0;
+	/// Executes the method, potentially appending to the assembly and returns a vector of
+	/// assembly items the constant should be relpaced with in one sweep.
+	/// If the vector is empty, the constants will not be deleted.
+	virtual AssemblyItems execute(Assembly& _assembly) = 0;
 
 protected:
 	size_t dataSize() const { return std::max<size_t>(1, dev::bytesRequired(m_value)); }
@@ -83,8 +86,8 @@ protected:
 		return m_params.runs * _runGas + m_params.multiplicity * _repeatedDataGas + _uniqueDataGas;
 	}
 
-	/// Replaces the constant by the code given in @a _replacement.
-	void replaceConstants(AssemblyItems& _items, AssemblyItems const& _replacement) const;
+	/// Replaces all constants i by the code given in @a _replacement[i].
+	static void replaceConstants(AssemblyItems& _items, std::map<u256, AssemblyItems> const& _replacement);
 
 	Params m_params;
 	u256 const& m_value;
@@ -100,7 +103,7 @@ public:
 	explicit LiteralMethod(Params const& _params, u256 const& _value):
 		ConstantOptimisationMethod(_params, _value) {}
 	virtual bigint gasNeeded() override;
-	virtual void execute(Assembly&, AssemblyItems&) override {}
+	virtual AssemblyItems execute(Assembly&) override { return AssemblyItems{}; }
 };
 
 /**
@@ -111,10 +114,10 @@ class CodeCopyMethod: public ConstantOptimisationMethod
 public:
 	explicit CodeCopyMethod(Params const& _params, u256 const& _value);
 	virtual bigint gasNeeded() override;
-	virtual void execute(Assembly& _assembly, AssemblyItems& _items) override;
+	virtual AssemblyItems execute(Assembly& _assembly) override;
 
 protected:
-	AssemblyItems m_copyRoutine;
+	AssemblyItems const& copyRoutine() const;
 };
 
 /**
@@ -130,9 +133,9 @@ public:
 	}
 
 	virtual bigint gasNeeded() override { return gasNeeded(m_routine); }
-	virtual void execute(Assembly&, AssemblyItems& _items) override
+	virtual AssemblyItems execute(Assembly&) override
 	{
-		replaceConstants(_items, m_routine);
+		return m_routine;
 	}
 
 protected:
diff --git a/libevmasm/ExpressionClasses.cpp b/libevmasm/ExpressionClasses.cpp
index d5ccd7e3..fc283b0b 100644
--- a/libevmasm/ExpressionClasses.cpp
+++ b/libevmasm/ExpressionClasses.cpp
@@ -29,6 +29,7 @@
 #include <boost/noncopyable.hpp>
 #include <libevmasm/Assembly.h>
 #include <libevmasm/CommonSubexpressionEliminator.h>
+#include <libevmasm/SimplificationRules.h>
 
 using namespace std;
 using namespace dev;
@@ -40,8 +41,18 @@ bool ExpressionClasses::Expression::operator<(ExpressionClasses::Expression cons
 	assertThrow(!!item && !!_other.item, OptimizerException, "");
 	auto type = item->type();
 	auto otherType = _other.item->type();
-	return std::tie(type, item->data(), arguments, sequenceNumber) <
-		std::tie(otherType, _other.item->data(), _other.arguments, _other.sequenceNumber);
+	if (type != otherType)
+		return type < otherType;
+	else if (type == Operation)
+	{
+		auto instr = item->instruction();
+		auto otherInstr = _other.item->instruction();
+		return std::tie(instr, arguments, sequenceNumber) <
+			std::tie(otherInstr, _other.arguments, _other.sequenceNumber);
+	}
+	else
+		return std::tie(item->data(), arguments, sequenceNumber) <
+			std::tie(_other.item->data(), _other.arguments, _other.sequenceNumber);
 }
 
 ExpressionClasses::Id ExpressionClasses::find(
@@ -170,191 +181,6 @@ string ExpressionClasses::fullDAGToString(ExpressionClasses::Id _id) const
 	return str.str();
 }
 
-class Rules: public boost::noncopyable
-{
-public:
-	Rules();
-	void resetMatchGroups() { m_matchGroups.clear(); }
-	vector<pair<Pattern, function<Pattern()>>> rules() const { return m_rules; }
-
-private:
-	using Expression = ExpressionClasses::Expression;
-	map<unsigned, Expression const*> m_matchGroups;
-	vector<pair<Pattern, function<Pattern()>>> m_rules;
-};
-
-template <class S> S divWorkaround(S const& _a, S const& _b)
-{
-	return (S)(bigint(_a) / bigint(_b));
-}
-
-template <class S> S modWorkaround(S const& _a, S const& _b)
-{
-	return (S)(bigint(_a) % bigint(_b));
-}
-
-Rules::Rules()
-{
-	// Multiple occurences of one of these inside one rule must match the same equivalence class.
-	// Constants.
-	Pattern A(Push);
-	Pattern B(Push);
-	Pattern C(Push);
-	// Anything.
-	Pattern X;
-	Pattern Y;
-	Pattern Z;
-	A.setMatchGroup(1, m_matchGroups);
-	B.setMatchGroup(2, m_matchGroups);
-	C.setMatchGroup(3, m_matchGroups);
-	X.setMatchGroup(4, m_matchGroups);
-	Y.setMatchGroup(5, m_matchGroups);
-	Z.setMatchGroup(6, m_matchGroups);
-
-	m_rules = vector<pair<Pattern, function<Pattern()>>>{
-		// arithmetics on constants
-		{{Instruction::ADD, {A, B}}, [=]{ return A.d() + B.d(); }},
-		{{Instruction::MUL, {A, B}}, [=]{ return A.d() * B.d(); }},
-		{{Instruction::SUB, {A, B}}, [=]{ return A.d() - B.d(); }},
-		{{Instruction::DIV, {A, B}}, [=]{ return B.d() == 0 ? 0 : divWorkaround(A.d(), B.d()); }},
-		{{Instruction::SDIV, {A, B}}, [=]{ return B.d() == 0 ? 0 : s2u(divWorkaround(u2s(A.d()), u2s(B.d()))); }},
-		{{Instruction::MOD, {A, B}}, [=]{ return B.d() == 0 ? 0 : modWorkaround(A.d(), B.d()); }},
-		{{Instruction::SMOD, {A, B}}, [=]{ return B.d() == 0 ? 0 : s2u(modWorkaround(u2s(A.d()), u2s(B.d()))); }},
-		{{Instruction::EXP, {A, B}}, [=]{ return u256(boost::multiprecision::powm(bigint(A.d()), bigint(B.d()), bigint(1) << 256)); }},
-		{{Instruction::NOT, {A}}, [=]{ return ~A.d(); }},
-		{{Instruction::LT, {A, B}}, [=]() { return A.d() < B.d() ? u256(1) : 0; }},
-		{{Instruction::GT, {A, B}}, [=]() -> u256 { return A.d() > B.d() ? 1 : 0; }},
-		{{Instruction::SLT, {A, B}}, [=]() -> u256 { return u2s(A.d()) < u2s(B.d()) ? 1 : 0; }},
-		{{Instruction::SGT, {A, B}}, [=]() -> u256 { return u2s(A.d()) > u2s(B.d()) ? 1 : 0; }},
-		{{Instruction::EQ, {A, B}}, [=]() -> u256 { return A.d() == B.d() ? 1 : 0; }},
-		{{Instruction::ISZERO, {A}}, [=]() -> u256 { return A.d() == 0 ? 1 : 0; }},
-		{{Instruction::AND, {A, B}}, [=]{ return A.d() & B.d(); }},
-		{{Instruction::OR, {A, B}}, [=]{ return A.d() | B.d(); }},
-		{{Instruction::XOR, {A, B}}, [=]{ return A.d() ^ B.d(); }},
-		{{Instruction::BYTE, {A, B}}, [=]{ return A.d() >= 32 ? 0 : (B.d() >> unsigned(8 * (31 - A.d()))) & 0xff; }},
-		{{Instruction::ADDMOD, {A, B, C}}, [=]{ return C.d() == 0 ? 0 : u256((bigint(A.d()) + bigint(B.d())) % C.d()); }},
-		{{Instruction::MULMOD, {A, B, C}}, [=]{ return C.d() == 0 ? 0 : u256((bigint(A.d()) * bigint(B.d())) % C.d()); }},
-		{{Instruction::MULMOD, {A, B, C}}, [=]{ return A.d() * B.d(); }},
-		{{Instruction::SIGNEXTEND, {A, B}}, [=]() -> u256 {
-			if (A.d() >= 31)
-				return B.d();
-			unsigned testBit = unsigned(A.d()) * 8 + 7;
-			u256 mask = (u256(1) << testBit) - 1;
-			return u256(boost::multiprecision::bit_test(B.d(), testBit) ? B.d() | ~mask : B.d() & mask);
-		}},
-
-		// invariants involving known constants
-		{{Instruction::ADD, {X, 0}}, [=]{ return X; }},
-		{{Instruction::SUB, {X, 0}}, [=]{ return X; }},
-		{{Instruction::MUL, {X, 1}}, [=]{ return X; }},
-		{{Instruction::DIV, {X, 1}}, [=]{ return X; }},
-		{{Instruction::SDIV, {X, 1}}, [=]{ return X; }},
-		{{Instruction::OR, {X, 0}}, [=]{ return X; }},
-		{{Instruction::XOR, {X, 0}}, [=]{ return X; }},
-		{{Instruction::AND, {X, ~u256(0)}}, [=]{ return X; }},
-		{{Instruction::AND, {X, 0}}, [=]{ return u256(0); }},
-		{{Instruction::MUL, {X, 0}}, [=]{ return u256(0); }},
-		{{Instruction::DIV, {X, 0}}, [=]{ return u256(0); }},
-		{{Instruction::DIV, {0, X}}, [=]{ return u256(0); }},
-		{{Instruction::MOD, {X, 0}}, [=]{ return u256(0); }},
-		{{Instruction::MOD, {0, X}}, [=]{ return u256(0); }},
-		{{Instruction::OR, {X, ~u256(0)}}, [=]{ return ~u256(0); }},
-		{{Instruction::EQ, {X, 0}}, [=]() -> Pattern { return {Instruction::ISZERO, {X}}; } },
-		// operations involving an expression and itself
-		{{Instruction::AND, {X, X}}, [=]{ return X; }},
-		{{Instruction::OR, {X, X}}, [=]{ return X; }},
-		{{Instruction::XOR, {X, X}}, [=]{ return u256(0); }},
-		{{Instruction::SUB, {X, X}}, [=]{ return u256(0); }},
-		{{Instruction::EQ, {X, X}}, [=]{ return u256(1); }},
-		{{Instruction::LT, {X, X}}, [=]{ return u256(0); }},
-		{{Instruction::SLT, {X, X}}, [=]{ return u256(0); }},
-		{{Instruction::GT, {X, X}}, [=]{ return u256(0); }},
-		{{Instruction::SGT, {X, X}}, [=]{ return u256(0); }},
-		{{Instruction::MOD, {X, X}}, [=]{ return u256(0); }},
-
-		{{Instruction::NOT, {{Instruction::NOT, {X}}}}, [=]{ return X; }},
-		{{Instruction::XOR, {{{X}, {Instruction::XOR, {X, Y}}}}}, [=]{ return Y; }},
-		{{Instruction::OR, {{{X}, {Instruction::AND, {X, Y}}}}}, [=]{ return X; }},
-		{{Instruction::AND, {{{X}, {Instruction::OR, {X, Y}}}}}, [=]{ return X; }},
-		{{Instruction::AND, {{{X}, {Instruction::NOT, {X}}}}}, [=]{ return u256(0); }},
-		{{Instruction::OR, {{{X}, {Instruction::NOT, {X}}}}}, [=]{ return ~u256(0); }},
-	};
-	// Double negation of opcodes with binary result
-	for (auto const& op: vector<Instruction>{
-		Instruction::EQ,
-		Instruction::LT,
-		Instruction::SLT,
-		Instruction::GT,
-		Instruction::SGT
-	})
-		m_rules.push_back({
-			{Instruction::ISZERO, {{Instruction::ISZERO, {{op, {X, Y}}}}}},
-			[=]() -> Pattern { return {op, {X, Y}}; }
-		});
-	m_rules.push_back({
-		{Instruction::ISZERO, {{Instruction::ISZERO, {{Instruction::ISZERO, {X}}}}}},
-		[=]() -> Pattern { return {Instruction::ISZERO, {X}}; }
-	});
-	m_rules.push_back({
-		{Instruction::ISZERO, {{Instruction::XOR, {X, Y}}}},
-		[=]() -> Pattern { return { Instruction::EQ, {X, Y} }; }
-	});
-	// Associative operations
-	for (auto const& opFun: vector<pair<Instruction,function<u256(u256 const&,u256 const&)>>>{
-		{Instruction::ADD, plus<u256>()},
-		{Instruction::MUL, multiplies<u256>()},
-		{Instruction::AND, bit_and<u256>()},
-		{Instruction::OR, bit_or<u256>()},
-		{Instruction::XOR, bit_xor<u256>()}
-	})
-	{
-		auto op = opFun.first;
-		auto fun = opFun.second;
-		// Moving constants to the outside, order matters here!
-		// we need actions that return expressions (or patterns?) here, and we need also reversed rules
-		// (X+A)+B -> X+(A+B)
-		m_rules += vector<pair<Pattern, function<Pattern()>>>{{
-			{op, {{op, {X, A}}, B}},
-			[=]() -> Pattern { return {op, {X, fun(A.d(), B.d())}}; }
-		}, {
-		// X+(Y+A) -> (X+Y)+A
-			{op, {{op, {X, A}}, Y}},
-			[=]() -> Pattern { return {op, {{op, {X, Y}}, A}}; }
-		}, {
-		// For now, we still need explicit commutativity for the inner pattern
-			{op, {{op, {A, X}}, B}},
-			[=]() -> Pattern { return {op, {X, fun(A.d(), B.d())}}; }
-		}, {
-			{op, {{op, {A, X}}, Y}},
-			[=]() -> Pattern { return {op, {{op, {X, Y}}, A}}; }
-		}};
-	}
-	// move constants across subtractions
-	m_rules += vector<pair<Pattern, function<Pattern()>>>{
-		{
-			// X - A -> X + (-A)
-			{Instruction::SUB, {X, A}},
-			[=]() -> Pattern { return {Instruction::ADD, {X, 0 - A.d()}}; }
-		}, {
-			// (X + A) - Y -> (X - Y) + A
-			{Instruction::SUB, {{Instruction::ADD, {X, A}}, Y}},
-			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, A}}; }
-		}, {
-			// (A + X) - Y -> (X - Y) + A
-			{Instruction::SUB, {{Instruction::ADD, {A, X}}, Y}},
-			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, A}}; }
-		}, {
-			// X - (Y + A) -> (X - Y) + (-A)
-			{Instruction::SUB, {X, {Instruction::ADD, {Y, A}}}},
-			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, 0 - A.d()}}; }
-		}, {
-			// X - (A + Y) -> (X - Y) + (-A)
-			{Instruction::SUB, {X, {Instruction::ADD, {A, Y}}}},
-			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, 0 - A.d()}}; }
-		}
-	};
-}
-
 ExpressionClasses::Id ExpressionClasses::tryToSimplify(Expression const& _expr, bool _secondRun)
 {
 	static Rules rules;
@@ -366,21 +192,17 @@ ExpressionClasses::Id ExpressionClasses::tryToSimplify(Expression const& _expr,
 	)
 		return -1;
 
-	for (auto const& rule: rules.rules())
+	if (auto match = rules.findFirstMatch(_expr, *this))
 	{
-		rules.resetMatchGroups();
-		if (rule.first.matches(_expr, *this))
-		{
-			// Debug info
-			//cout << "Simplifying " << *_expr.item << "(";
-			//for (Id arg: _expr.arguments)
-			//	cout << fullDAGToString(arg) << ", ";
-			//cout << ")" << endl;
-			//cout << "with rule " << rule.first.toString() << endl;
-			//ExpressionTemplate t(rule.second());
-			//cout << "to " << rule.second().toString() << endl;
-			return rebuildExpression(ExpressionTemplate(rule.second(), _expr.item->location()));
-		}
+		// Debug info
+		//cout << "Simplifying " << *_expr.item << "(";
+		//for (Id arg: _expr.arguments)
+		//	cout << fullDAGToString(arg) << ", ";
+		//cout << ")" << endl;
+		//cout << "with rule " << match->first.toString() << endl;
+		//ExpressionTemplate t(match->second());
+		//cout << "to " << match->second().toString() << endl;
+		return rebuildExpression(ExpressionTemplate(match->second(), _expr.item->location()));
 	}
 
 	if (!_secondRun && _expr.arguments.size() == 2 && SemanticInformation::isCommutativeOperation(*_expr.item))
@@ -403,122 +225,3 @@ ExpressionClasses::Id ExpressionClasses::rebuildExpression(ExpressionTemplate co
 		arguments.push_back(rebuildExpression(t));
 	return find(_template.item, arguments);
 }
-
-
-Pattern::Pattern(Instruction _instruction, std::vector<Pattern> const& _arguments):
-	m_type(Operation),
-	m_requireDataMatch(true),
-	m_data(_instruction),
-	m_arguments(_arguments)
-{
-}
-
-void Pattern::setMatchGroup(unsigned _group, map<unsigned, Expression const*>& _matchGroups)
-{
-	m_matchGroup = _group;
-	m_matchGroups = &_matchGroups;
-}
-
-bool Pattern::matches(Expression const& _expr, ExpressionClasses const& _classes) const
-{
-	if (!matchesBaseItem(_expr.item))
-		return false;
-	if (m_matchGroup)
-	{
-		if (!m_matchGroups->count(m_matchGroup))
-			(*m_matchGroups)[m_matchGroup] = &_expr;
-		else if ((*m_matchGroups)[m_matchGroup]->id != _expr.id)
-			return false;
-	}
-	assertThrow(m_arguments.size() == 0 || _expr.arguments.size() == m_arguments.size(), OptimizerException, "");
-	for (size_t i = 0; i < m_arguments.size(); ++i)
-		if (!m_arguments[i].matches(_classes.representative(_expr.arguments[i]), _classes))
-			return false;
-	return true;
-}
-
-AssemblyItem Pattern::toAssemblyItem(SourceLocation const& _location) const
-{
-	return AssemblyItem(m_type, m_data, _location);
-}
-
-string Pattern::toString() const
-{
-	stringstream s;
-	switch (m_type)
-	{
-	case Operation:
-		s << instructionInfo(Instruction(unsigned(m_data))).name;
-		break;
-	case Push:
-		s << "PUSH " << hex << m_data;
-		break;
-	case UndefinedItem:
-		s << "ANY";
-		break;
-	default:
-		s << "t=" << dec << m_type << " d=" << hex << m_data;
-		break;
-	}
-	if (!m_requireDataMatch)
-		s << " ~";
-	if (m_matchGroup)
-		s << "[" << dec << m_matchGroup << "]";
-	s << "(";
-	for (Pattern const& p: m_arguments)
-		s << p.toString() << ", ";
-	s << ")";
-	return s.str();
-}
-
-bool Pattern::matchesBaseItem(AssemblyItem const* _item) const
-{
-	if (m_type == UndefinedItem)
-		return true;
-	if (!_item)
-		return false;
-	if (m_type != _item->type())
-		return false;
-	if (m_requireDataMatch && m_data != _item->data())
-		return false;
-	return true;
-}
-
-Pattern::Expression const& Pattern::matchGroupValue() const
-{
-	assertThrow(m_matchGroup > 0, OptimizerException, "");
-	assertThrow(!!m_matchGroups, OptimizerException, "");
-	assertThrow((*m_matchGroups)[m_matchGroup], OptimizerException, "");
-	return *(*m_matchGroups)[m_matchGroup];
-}
-
-
-ExpressionTemplate::ExpressionTemplate(Pattern const& _pattern, SourceLocation const& _location)
-{
-	if (_pattern.matchGroup())
-	{
-		hasId = true;
-		id = _pattern.id();
-	}
-	else
-	{
-		hasId = false;
-		item = _pattern.toAssemblyItem(_location);
-	}
-	for (auto const& arg: _pattern.arguments())
-		arguments.push_back(ExpressionTemplate(arg, _location));
-}
-
-string ExpressionTemplate::toString() const
-{
-	stringstream s;
-	if (hasId)
-		s << id;
-	else
-		s << item;
-	s << "(";
-	for (auto const& arg: arguments)
-		s << arg.toString();
-	s << ")";
-	return s.str();
-}
diff --git a/libevmasm/ExpressionClasses.h b/libevmasm/ExpressionClasses.h
index 11a698dd..5d53b292 100644
--- a/libevmasm/ExpressionClasses.h
+++ b/libevmasm/ExpressionClasses.h
@@ -121,70 +121,5 @@ private:
 	std::vector<std::shared_ptr<AssemblyItem>> m_spareAssemblyItems;
 };
 
-/**
- * Pattern to match against an expression.
- * Also stores matched expressions to retrieve them later, for constructing new expressions using
- * ExpressionTemplate.
- */
-class Pattern
-{
-public:
-	using Expression = ExpressionClasses::Expression;
-	using Id = ExpressionClasses::Id;
-
-	// Matches a specific constant value.
-	Pattern(unsigned _value): Pattern(u256(_value)) {}
-	// Matches a specific constant value.
-	Pattern(u256 const& _value): m_type(Push), m_requireDataMatch(true), m_data(_value) {}
-	// Matches a specific assembly item type or anything if not given.
-	Pattern(AssemblyItemType _type = UndefinedItem): m_type(_type) {}
-	// Matches a given instruction with given arguments
-	Pattern(Instruction _instruction, std::vector<Pattern> const& _arguments = {});
-	/// Sets this pattern to be part of the match group with the identifier @a _group.
-	/// Inside one rule, all patterns in the same match group have to match expressions from the
-	/// same expression equivalence class.
-	void setMatchGroup(unsigned _group, std::map<unsigned, Expression const*>& _matchGroups);
-	unsigned matchGroup() const { return m_matchGroup; }
-	bool matches(Expression const& _expr, ExpressionClasses const& _classes) const;
-
-	AssemblyItem toAssemblyItem(SourceLocation const& _location) const;
-	std::vector<Pattern> arguments() const { return m_arguments; }
-
-	/// @returns the id of the matched expression if this pattern is part of a match group.
-	Id id() const { return matchGroupValue().id; }
-	/// @returns the data of the matched expression if this pattern is part of a match group.
-	u256 const& d() const { return matchGroupValue().item->data(); }
-
-	std::string toString() const;
-
-private:
-	bool matchesBaseItem(AssemblyItem const* _item) const;
-	Expression const& matchGroupValue() const;
-
-	AssemblyItemType m_type;
-	bool m_requireDataMatch = false;
-	u256 m_data = 0;
-	std::vector<Pattern> m_arguments;
-	unsigned m_matchGroup = 0;
-	std::map<unsigned, Expression const*>* m_matchGroups = nullptr;
-};
-
-/**
- * Template for a new expression that can be built from matched patterns.
- */
-struct ExpressionTemplate
-{
-	using Expression = ExpressionClasses::Expression;
-	using Id = ExpressionClasses::Id;
-	explicit ExpressionTemplate(Pattern const& _pattern, SourceLocation const& _location);
-	std::string toString() const;
-	bool hasId = false;
-	/// Id of the matched expression, if available.
-	Id id = Id(-1);
-	// Otherwise, assembly item.
-	AssemblyItem item = UndefinedItem;
-	std::vector<ExpressionTemplate> arguments;
-};
-
 }
 }
diff --git a/libevmasm/SimplificationRules.cpp b/libevmasm/SimplificationRules.cpp
new file mode 100644
index 00000000..2976d95f
--- /dev/null
+++ b/libevmasm/SimplificationRules.cpp
@@ -0,0 +1,370 @@
+/*
+	This file is part of solidity.
+
+	solidity is free software: you can redistribute it and/or modify
+	it under the terms of the GNU General Public License as published by
+	the Free Software Foundation, either version 3 of the License, or
+	(at your option) any later version.
+
+	solidity is distributed in the hope that it will be useful,
+	but WITHOUT ANY WARRANTY; without even the implied warranty of
+	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+	GNU General Public License for more details.
+
+	You should have received a copy of the GNU General Public License
+	along with solidity.  If not, see <http://www.gnu.org/licenses/>.
+*/
+/**
+ * @file ExpressionClasses.cpp
+ * @author Christian <c@ethdev.com>
+ * @date 2015
+ * Container for equivalence classes of expressions for use in common subexpression elimination.
+ */
+
+#include <libevmasm/ExpressionClasses.h>
+#include <utility>
+#include <tuple>
+#include <functional>
+#include <boost/range/adaptor/reversed.hpp>
+#include <boost/noncopyable.hpp>
+#include <libevmasm/Assembly.h>
+#include <libevmasm/CommonSubexpressionEliminator.h>
+#include <libevmasm/SimplificationRules.h>
+
+using namespace std;
+using namespace dev;
+using namespace dev::eth;
+
+
+pair<Pattern, function<Pattern()> > const* Rules::findFirstMatch(
+	Expression const& _expr,
+	ExpressionClasses const& _classes
+)
+{
+	resetMatchGroups();
+
+	assertThrow(_expr.item, OptimizerException, "");
+	for (auto const& rule: m_rules[byte(_expr.item->instruction())])
+	{
+		if (rule.first.matches(_expr, _classes))
+			return &rule;
+		resetMatchGroups();
+	}
+	return nullptr;
+}
+
+void Rules::addRules(std::vector<std::pair<Pattern, std::function<Pattern ()> > > const& _rules)
+{
+	for (auto const& r: _rules)
+		addRule(r);
+}
+
+void Rules::addRule(std::pair<Pattern, std::function<Pattern()> > const& _rule)
+{
+	m_rules[byte(_rule.first.instruction())].push_back(_rule);
+}
+
+template <class S> S divWorkaround(S const& _a, S const& _b)
+{
+	return (S)(bigint(_a) / bigint(_b));
+}
+
+template <class S> S modWorkaround(S const& _a, S const& _b)
+{
+	return (S)(bigint(_a) % bigint(_b));
+}
+
+Rules::Rules()
+{
+	// Multiple occurences of one of these inside one rule must match the same equivalence class.
+	// Constants.
+	Pattern A(Push);
+	Pattern B(Push);
+	Pattern C(Push);
+	// Anything.
+	Pattern X;
+	Pattern Y;
+	Pattern Z;
+	A.setMatchGroup(1, m_matchGroups);
+	B.setMatchGroup(2, m_matchGroups);
+	C.setMatchGroup(3, m_matchGroups);
+	X.setMatchGroup(4, m_matchGroups);
+	Y.setMatchGroup(5, m_matchGroups);
+	Z.setMatchGroup(6, m_matchGroups);
+
+	addRules(vector<pair<Pattern, function<Pattern()>>>{
+		// arithmetics on constants
+		{{Instruction::ADD, {A, B}}, [=]{ return A.d() + B.d(); }},
+		{{Instruction::MUL, {A, B}}, [=]{ return A.d() * B.d(); }},
+		{{Instruction::SUB, {A, B}}, [=]{ return A.d() - B.d(); }},
+		{{Instruction::DIV, {A, B}}, [=]{ return B.d() == 0 ? 0 : divWorkaround(A.d(), B.d()); }},
+		{{Instruction::SDIV, {A, B}}, [=]{ return B.d() == 0 ? 0 : s2u(divWorkaround(u2s(A.d()), u2s(B.d()))); }},
+		{{Instruction::MOD, {A, B}}, [=]{ return B.d() == 0 ? 0 : modWorkaround(A.d(), B.d()); }},
+		{{Instruction::SMOD, {A, B}}, [=]{ return B.d() == 0 ? 0 : s2u(modWorkaround(u2s(A.d()), u2s(B.d()))); }},
+		{{Instruction::EXP, {A, B}}, [=]{ return u256(boost::multiprecision::powm(bigint(A.d()), bigint(B.d()), bigint(1) << 256)); }},
+		{{Instruction::NOT, {A}}, [=]{ return ~A.d(); }},
+		{{Instruction::LT, {A, B}}, [=]() { return A.d() < B.d() ? u256(1) : 0; }},
+		{{Instruction::GT, {A, B}}, [=]() -> u256 { return A.d() > B.d() ? 1 : 0; }},
+		{{Instruction::SLT, {A, B}}, [=]() -> u256 { return u2s(A.d()) < u2s(B.d()) ? 1 : 0; }},
+		{{Instruction::SGT, {A, B}}, [=]() -> u256 { return u2s(A.d()) > u2s(B.d()) ? 1 : 0; }},
+		{{Instruction::EQ, {A, B}}, [=]() -> u256 { return A.d() == B.d() ? 1 : 0; }},
+		{{Instruction::ISZERO, {A}}, [=]() -> u256 { return A.d() == 0 ? 1 : 0; }},
+		{{Instruction::AND, {A, B}}, [=]{ return A.d() & B.d(); }},
+		{{Instruction::OR, {A, B}}, [=]{ return A.d() | B.d(); }},
+		{{Instruction::XOR, {A, B}}, [=]{ return A.d() ^ B.d(); }},
+		{{Instruction::BYTE, {A, B}}, [=]{ return A.d() >= 32 ? 0 : (B.d() >> unsigned(8 * (31 - A.d()))) & 0xff; }},
+		{{Instruction::ADDMOD, {A, B, C}}, [=]{ return C.d() == 0 ? 0 : u256((bigint(A.d()) + bigint(B.d())) % C.d()); }},
+		{{Instruction::MULMOD, {A, B, C}}, [=]{ return C.d() == 0 ? 0 : u256((bigint(A.d()) * bigint(B.d())) % C.d()); }},
+		{{Instruction::MULMOD, {A, B, C}}, [=]{ return A.d() * B.d(); }},
+		{{Instruction::SIGNEXTEND, {A, B}}, [=]() -> u256 {
+			if (A.d() >= 31)
+				return B.d();
+			unsigned testBit = unsigned(A.d()) * 8 + 7;
+			u256 mask = (u256(1) << testBit) - 1;
+			return u256(boost::multiprecision::bit_test(B.d(), testBit) ? B.d() | ~mask : B.d() & mask);
+		}},
+
+		// invariants involving known constants
+		{{Instruction::ADD, {X, 0}}, [=]{ return X; }},
+		{{Instruction::SUB, {X, 0}}, [=]{ return X; }},
+		{{Instruction::MUL, {X, 1}}, [=]{ return X; }},
+		{{Instruction::DIV, {X, 1}}, [=]{ return X; }},
+		{{Instruction::SDIV, {X, 1}}, [=]{ return X; }},
+		{{Instruction::OR, {X, 0}}, [=]{ return X; }},
+		{{Instruction::XOR, {X, 0}}, [=]{ return X; }},
+		{{Instruction::AND, {X, ~u256(0)}}, [=]{ return X; }},
+		{{Instruction::AND, {X, 0}}, [=]{ return u256(0); }},
+		{{Instruction::MUL, {X, 0}}, [=]{ return u256(0); }},
+		{{Instruction::DIV, {X, 0}}, [=]{ return u256(0); }},
+		{{Instruction::DIV, {0, X}}, [=]{ return u256(0); }},
+		{{Instruction::MOD, {X, 0}}, [=]{ return u256(0); }},
+		{{Instruction::MOD, {0, X}}, [=]{ return u256(0); }},
+		{{Instruction::OR, {X, ~u256(0)}}, [=]{ return ~u256(0); }},
+		{{Instruction::EQ, {X, 0}}, [=]() -> Pattern { return {Instruction::ISZERO, {X}}; } },
+		// operations involving an expression and itself
+		{{Instruction::AND, {X, X}}, [=]{ return X; }},
+		{{Instruction::OR, {X, X}}, [=]{ return X; }},
+		{{Instruction::XOR, {X, X}}, [=]{ return u256(0); }},
+		{{Instruction::SUB, {X, X}}, [=]{ return u256(0); }},
+		{{Instruction::EQ, {X, X}}, [=]{ return u256(1); }},
+		{{Instruction::LT, {X, X}}, [=]{ return u256(0); }},
+		{{Instruction::SLT, {X, X}}, [=]{ return u256(0); }},
+		{{Instruction::GT, {X, X}}, [=]{ return u256(0); }},
+		{{Instruction::SGT, {X, X}}, [=]{ return u256(0); }},
+		{{Instruction::MOD, {X, X}}, [=]{ return u256(0); }},
+
+		{{Instruction::NOT, {{Instruction::NOT, {X}}}}, [=]{ return X; }},
+		{{Instruction::XOR, {{{X}, {Instruction::XOR, {X, Y}}}}}, [=]{ return Y; }},
+		{{Instruction::OR, {{{X}, {Instruction::AND, {X, Y}}}}}, [=]{ return X; }},
+		{{Instruction::AND, {{{X}, {Instruction::OR, {X, Y}}}}}, [=]{ return X; }},
+		{{Instruction::AND, {{{X}, {Instruction::NOT, {X}}}}}, [=]{ return u256(0); }},
+		{{Instruction::OR, {{{X}, {Instruction::NOT, {X}}}}}, [=]{ return ~u256(0); }},
+	});
+	// Double negation of opcodes with binary result
+	for (auto const& op: vector<Instruction>{
+		Instruction::EQ,
+		Instruction::LT,
+		Instruction::SLT,
+		Instruction::GT,
+		Instruction::SGT
+	})
+		addRule({
+			{Instruction::ISZERO, {{Instruction::ISZERO, {{op, {X, Y}}}}}},
+			[=]() -> Pattern { return {op, {X, Y}}; }
+		});
+	addRule({
+		{Instruction::ISZERO, {{Instruction::ISZERO, {{Instruction::ISZERO, {X}}}}}},
+		[=]() -> Pattern { return {Instruction::ISZERO, {X}}; }
+	});
+	addRule({
+		{Instruction::ISZERO, {{Instruction::XOR, {X, Y}}}},
+		[=]() -> Pattern { return { Instruction::EQ, {X, Y} }; }
+	});
+	// Associative operations
+	for (auto const& opFun: vector<pair<Instruction,function<u256(u256 const&,u256 const&)>>>{
+		{Instruction::ADD, plus<u256>()},
+		{Instruction::MUL, multiplies<u256>()},
+		{Instruction::AND, bit_and<u256>()},
+		{Instruction::OR, bit_or<u256>()},
+		{Instruction::XOR, bit_xor<u256>()}
+	})
+	{
+		auto op = opFun.first;
+		auto fun = opFun.second;
+		// Moving constants to the outside, order matters here!
+		// we need actions that return expressions (or patterns?) here, and we need also reversed rules
+		// (X+A)+B -> X+(A+B)
+		addRules(vector<pair<Pattern, function<Pattern()>>>{{
+			{op, {{op, {X, A}}, B}},
+			[=]() -> Pattern { return {op, {X, fun(A.d(), B.d())}}; }
+		}, {
+		// X+(Y+A) -> (X+Y)+A
+			{op, {{op, {X, A}}, Y}},
+			[=]() -> Pattern { return {op, {{op, {X, Y}}, A}}; }
+		}, {
+		// For now, we still need explicit commutativity for the inner pattern
+			{op, {{op, {A, X}}, B}},
+			[=]() -> Pattern { return {op, {X, fun(A.d(), B.d())}}; }
+		}, {
+			{op, {{op, {A, X}}, Y}},
+			[=]() -> Pattern { return {op, {{op, {X, Y}}, A}}; }
+		}});
+	}
+	// move constants across subtractions
+	addRules(vector<pair<Pattern, function<Pattern()>>>{
+		{
+			// X - A -> X + (-A)
+			{Instruction::SUB, {X, A}},
+			[=]() -> Pattern { return {Instruction::ADD, {X, 0 - A.d()}}; }
+		}, {
+			// (X + A) - Y -> (X - Y) + A
+			{Instruction::SUB, {{Instruction::ADD, {X, A}}, Y}},
+			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, A}}; }
+		}, {
+			// (A + X) - Y -> (X - Y) + A
+			{Instruction::SUB, {{Instruction::ADD, {A, X}}, Y}},
+			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, A}}; }
+		}, {
+			// X - (Y + A) -> (X - Y) + (-A)
+			{Instruction::SUB, {X, {Instruction::ADD, {Y, A}}}},
+			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, 0 - A.d()}}; }
+		}, {
+			// X - (A + Y) -> (X - Y) + (-A)
+			{Instruction::SUB, {X, {Instruction::ADD, {A, Y}}}},
+			[=]() -> Pattern { return {Instruction::ADD, {{Instruction::SUB, {X, Y}}, 0 - A.d()}}; }
+		}
+	});
+}
+
+Pattern::Pattern(Instruction _instruction, std::vector<Pattern> const& _arguments):
+	m_type(Operation),
+	m_instruction(_instruction),
+	m_arguments(_arguments)
+{
+}
+
+void Pattern::setMatchGroup(unsigned _group, map<unsigned, Expression const*>& _matchGroups)
+{
+	m_matchGroup = _group;
+	m_matchGroups = &_matchGroups;
+}
+
+bool Pattern::matches(Expression const& _expr, ExpressionClasses const& _classes) const
+{
+	if (!matchesBaseItem(_expr.item))
+		return false;
+	if (m_matchGroup)
+	{
+		if (!m_matchGroups->count(m_matchGroup))
+			(*m_matchGroups)[m_matchGroup] = &_expr;
+		else if ((*m_matchGroups)[m_matchGroup]->id != _expr.id)
+			return false;
+	}
+	assertThrow(m_arguments.size() == 0 || _expr.arguments.size() == m_arguments.size(), OptimizerException, "");
+	for (size_t i = 0; i < m_arguments.size(); ++i)
+		if (!m_arguments[i].matches(_classes.representative(_expr.arguments[i]), _classes))
+			return false;
+	return true;
+}
+
+AssemblyItem Pattern::toAssemblyItem(SourceLocation const& _location) const
+{
+	if (m_type == Operation)
+		return AssemblyItem(m_instruction, _location);
+	else
+		return AssemblyItem(m_type, data(), _location);
+}
+
+string Pattern::toString() const
+{
+	stringstream s;
+	switch (m_type)
+	{
+	case Operation:
+		s << instructionInfo(m_instruction).name;
+		break;
+	case Push:
+		if (m_data)
+			s << "PUSH " << hex << data();
+		else
+			s << "PUSH ";
+		break;
+	case UndefinedItem:
+		s << "ANY";
+		break;
+	default:
+		if (m_data)
+			s << "t=" << dec << m_type << " d=" << hex << data();
+		else
+			s << "t=" << dec << m_type << " d: nullptr";
+		break;
+	}
+	if (!m_requireDataMatch)
+		s << " ~";
+	if (m_matchGroup)
+		s << "[" << dec << m_matchGroup << "]";
+	s << "(";
+	for (Pattern const& p: m_arguments)
+		s << p.toString() << ", ";
+	s << ")";
+	return s.str();
+}
+
+bool Pattern::matchesBaseItem(AssemblyItem const* _item) const
+{
+	if (m_type == UndefinedItem)
+		return true;
+	if (!_item)
+		return false;
+	if (m_type != _item->type())
+		return false;
+	else if (m_type == Operation)
+		return m_instruction == _item->instruction();
+	else if (m_requireDataMatch)
+		return data() == _item->data();
+	return true;
+}
+
+Pattern::Expression const& Pattern::matchGroupValue() const
+{
+	assertThrow(m_matchGroup > 0, OptimizerException, "");
+	assertThrow(!!m_matchGroups, OptimizerException, "");
+	assertThrow((*m_matchGroups)[m_matchGroup], OptimizerException, "");
+	return *(*m_matchGroups)[m_matchGroup];
+}
+
+u256 const& Pattern::data() const
+{
+	assertThrow(m_data, OptimizerException, "");
+	return *m_data;
+}
+
+ExpressionTemplate::ExpressionTemplate(Pattern const& _pattern, SourceLocation const& _location)
+{
+	if (_pattern.matchGroup())
+	{
+		hasId = true;
+		id = _pattern.id();
+	}
+	else
+	{
+		hasId = false;
+		item = _pattern.toAssemblyItem(_location);
+	}
+	for (auto const& arg: _pattern.arguments())
+		arguments.push_back(ExpressionTemplate(arg, _location));
+}
+
+string ExpressionTemplate::toString() const
+{
+	stringstream s;
+	if (hasId)
+		s << id;
+	else
+		s << item;
+	s << "(";
+	for (auto const& arg: arguments)
+		s << arg.toString();
+	s << ")";
+	return s.str();
+}
diff --git a/libevmasm/SimplificationRules.h b/libevmasm/SimplificationRules.h
new file mode 100644
index 00000000..a4da5849
--- /dev/null
+++ b/libevmasm/SimplificationRules.h
@@ -0,0 +1,140 @@
+/*
+	This file is part of solidity.
+
+	solidity is free software: you can redistribute it and/or modify
+	it under the terms of the GNU General Public License as published by
+	the Free Software Foundation, either version 3 of the License, or
+	(at your option) any later version.
+
+	solidity is distributed in the hope that it will be useful,
+	but WITHOUT ANY WARRANTY; without even the implied warranty of
+	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+	GNU General Public License for more details.
+
+	You should have received a copy of the GNU General Public License
+	along with solidity.  If not, see <http://www.gnu.org/licenses/>.
+*/
+/**
+ * @file SimplificationRules
+ * @author Christian <chris@ethereum.org>
+ * @date 2017
+ * Module for applying replacement rules against Expressions.
+ */
+
+#pragma once
+
+#include <libevmasm/ExpressionClasses.h>
+
+#include <functional>
+#include <vector>
+
+namespace dev
+{
+namespace eth
+{
+
+class Pattern;
+
+/**
+ * Container for all simplification rules.
+ */
+class Rules: public boost::noncopyable
+{
+public:
+	using Expression = ExpressionClasses::Expression;
+
+	Rules();
+
+	/// @returns a pointer to the first matching pattern and sets the match
+	/// groups accordingly.
+	std::pair<Pattern, std::function<Pattern()>> const* findFirstMatch(
+		Expression const& _expr,
+		ExpressionClasses const& _classes
+	);
+
+private:
+	void addRules(std::vector<std::pair<Pattern, std::function<Pattern()>>> const& _rules);
+	void addRule(std::pair<Pattern, std::function<Pattern()>> const& _rule);
+
+	void resetMatchGroups() { m_matchGroups.clear(); }
+
+	std::map<unsigned, Expression const*> m_matchGroups;
+	std::vector<std::pair<Pattern, std::function<Pattern()>>> m_rules[256];
+};
+
+/**
+ * Pattern to match against an expression.
+ * Also stores matched expressions to retrieve them later, for constructing new expressions using
+ * ExpressionTemplate.
+ */
+class Pattern
+{
+public:
+	using Expression = ExpressionClasses::Expression;
+	using Id = ExpressionClasses::Id;
+
+	// Matches a specific constant value.
+	Pattern(unsigned _value): Pattern(u256(_value)) {}
+	// Matches a specific constant value.
+	Pattern(u256 const& _value): m_type(Push), m_requireDataMatch(true), m_data(std::make_shared<u256>(_value)) {}
+	// Matches a specific assembly item type or anything if not given.
+	Pattern(AssemblyItemType _type = UndefinedItem): m_type(_type) {}
+	// Matches a given instruction with given arguments
+	Pattern(Instruction _instruction, std::vector<Pattern> const& _arguments = {});
+	/// Sets this pattern to be part of the match group with the identifier @a _group.
+	/// Inside one rule, all patterns in the same match group have to match expressions from the
+	/// same expression equivalence class.
+	void setMatchGroup(unsigned _group, std::map<unsigned, Expression const*>& _matchGroups);
+	unsigned matchGroup() const { return m_matchGroup; }
+	bool matches(Expression const& _expr, ExpressionClasses const& _classes) const;
+
+	AssemblyItem toAssemblyItem(SourceLocation const& _location) const;
+	std::vector<Pattern> arguments() const { return m_arguments; }
+
+	/// @returns the id of the matched expression if this pattern is part of a match group.
+	Id id() const { return matchGroupValue().id; }
+	/// @returns the data of the matched expression if this pattern is part of a match group.
+	u256 const& d() const { return matchGroupValue().item->data(); }
+
+	std::string toString() const;
+
+	AssemblyItemType type() const { return m_type; }
+	Instruction instruction() const
+	{
+		assertThrow(type() == Operation, OptimizerException, "");
+		return m_instruction;
+	}
+
+private:
+	bool matchesBaseItem(AssemblyItem const* _item) const;
+	Expression const& matchGroupValue() const;
+	u256 const& data() const;
+
+	AssemblyItemType m_type;
+	bool m_requireDataMatch = false;
+	Instruction m_instruction; ///< Only valid if m_type is Operation
+	std::shared_ptr<u256> m_data; ///< Only valid if m_type is not Operation
+	std::vector<Pattern> m_arguments;
+	unsigned m_matchGroup = 0;
+	std::map<unsigned, Expression const*>* m_matchGroups = nullptr;
+};
+
+/**
+ * Template for a new expression that can be built from matched patterns.
+ */
+struct ExpressionTemplate
+{
+	using Expression = ExpressionClasses::Expression;
+	using Id = ExpressionClasses::Id;
+	explicit ExpressionTemplate(Pattern const& _pattern, SourceLocation const& _location);
+	std::string toString() const;
+	bool hasId = false;
+	/// Id of the matched expression, if available.
+	Id id = Id(-1);
+	// Otherwise, assembly item.
+	AssemblyItem item = UndefinedItem;
+	std::vector<ExpressionTemplate> arguments;
+};
+
+}
+}