diff --git a/include/ir/PassManager.h b/include/ir/PassManager.h
index 062c197..a8e565d 100644
--- a/include/ir/PassManager.h
+++ b/include/ir/PassManager.h
@@ -36,6 +36,7 @@ class DominatorTree {
 bool RunMem2Reg(Function* func, Context& ctx);
 bool RunConstProp(Function* func, Context& ctx);
 bool RunConstFold(Function* func, Context& ctx);
+bool RunAlgebraicSimplify(Function* func, Context& ctx);
 bool RunDCE(Function* func);
 bool RunCFGSimplify(Function* func);
 bool RunCSE(Function* func);
diff --git a/src/ir/passes/AlgebraicSimplify.cpp b/src/ir/passes/AlgebraicSimplify.cpp
new file mode 100644
index 0000000..2e3fa23
--- /dev/null
+++ b/src/ir/passes/AlgebraicSimplify.cpp
@@ -0,0 +1,112 @@
+#include "ir/PassManager.h"
+
+#include <vector>
+
+namespace ir {
+namespace {
+
+bool IsConstInt(Value* value, int expected) {
+  auto* constant = dynamic_cast<ConstantInt*>(value);
+  return constant && constant->GetValue() == expected;
+}
+
+bool IsConstFloat(Value* value, float expected) {
+  auto* constant = dynamic_cast<ConstantFloat*>(value);
+  return constant && constant->GetValue() == expected;
+}
+
+bool IsSameValue(Value* lhs, Value* rhs) {
+  return lhs == rhs;
+}
+
+Value* SimplifyBinary(BinaryInst* bin, Context& ctx) {
+  auto* lhs = bin->GetLhs();
+  auto* rhs = bin->GetRhs();
+
+  switch (bin->GetOpcode()) {
+    case Opcode::Add:
+      if (IsConstInt(rhs, 0)) return lhs;
+      if (IsConstInt(lhs, 0)) return rhs;
+      break;
+    case Opcode::Sub:
+      if (IsConstInt(rhs, 0)) return lhs;
+      if (IsSameValue(lhs, rhs)) return ctx.GetConstInt(0);
+      break;
+    case Opcode::Mul:
+      if (IsConstInt(rhs, 1)) return lhs;
+      if (IsConstInt(lhs, 1)) return rhs;
+      if (IsConstInt(rhs, 0) || IsConstInt(lhs, 0)) return ctx.GetConstInt(0);
+      break;
+    case Opcode::Div:
+      if (IsConstInt(rhs, 1)) return lhs;
+      if (IsConstInt(lhs, 0)) return ctx.GetConstInt(0);
+      break;
+    case Opcode::Mod:
+      if (IsConstInt(rhs, 1) || IsConstInt(lhs, 0)) return ctx.GetConstInt(0);
+      break;
+    case Opcode::FAdd:
+      if (IsConstFloat(rhs, 0.0f)) return lhs;
+      if (IsConstFloat(lhs, 0.0f)) return rhs;
+      break;
+    case Opcode::FSub:
+      if (IsConstFloat(rhs, 0.0f)) return lhs;
+      break;
+    case Opcode::FMul:
+      if (IsConstFloat(rhs, 1.0f)) return lhs;
+      if (IsConstFloat(lhs, 1.0f)) return rhs;
+      if (IsConstFloat(rhs, 0.0f) || IsConstFloat(lhs, 0.0f)) {
+        return ctx.GetConstFloat(0.0f);
+      }
+      break;
+    case Opcode::FDiv:
+      if (IsConstFloat(rhs, 1.0f)) return lhs;
+      break;
+    case Opcode::ICmpEQ:
+      if (IsSameValue(lhs, rhs)) return ctx.GetConstInt(1);
+      break;
+    case Opcode::ICmpNE:
+      if (IsSameValue(lhs, rhs)) return ctx.GetConstInt(0);
+      break;
+    case Opcode::ICmpLE:
+    case Opcode::ICmpGE:
+      if (IsSameValue(lhs, rhs)) return ctx.GetConstInt(1);
+      break;
+    case Opcode::ICmpLT:
+    case Opcode::ICmpGT:
+      if (IsSameValue(lhs, rhs)) return ctx.GetConstInt(0);
+      break;
+    default:
+      break;
+  }
+
+  return nullptr;
+}
+
+}  // namespace
+
+bool RunAlgebraicSimplify(Function* func, Context& ctx) {
+  bool changed = false;
+  std::vector<Instruction*> to_erase;
+
+  for (const auto& bbPtr : func->GetBlocks()) {
+    for (const auto& instPtr : bbPtr->GetInstructions()) {
+      auto* bin = dynamic_cast<BinaryInst*>(instPtr.get());
+      if (!bin) {
+        continue;
+      }
+      if (auto* replacement = SimplifyBinary(bin, ctx)) {
+        bin->ReplaceAllUsesWith(replacement);
+        to_erase.push_back(bin);
+        changed = true;
+      }
+    }
+  }
+
+  for (auto* inst : to_erase) {
+    inst->GetParent()->EraseInstruction(inst);
+  }
+
+  return changed;
+}
+
+}  // namespace ir
diff --git a/src/ir/passes/CMakeLists.txt b/src/ir/passes/CMakeLists.txt
index d3ece9d..0a533d6 100644
--- a/src/ir/passes/CMakeLists.txt
+++ b/src/ir/passes/CMakeLists.txt
@@ -3,6 +3,7 @@ add_library(ir_passes STATIC
   Mem2Reg.cpp
   ConstFold.cpp
   ConstProp.cpp
+  AlgebraicSimplify.cpp
   CSE.cpp
   DCE.cpp
   CFGSimplify.cpp
diff --git a/src/ir/passes/PassManager.cpp b/src/ir/passes/PassManager.cpp
index d4d46fb..8f3009f 100644
--- a/src/ir/passes/PassManager.cpp
+++ b/src/ir/passes/PassManager.cpp
@@ -16,6 +16,7 @@ void RunFunctionOptimizationPasses(Function* func, Context& ctx) {
 
     changed |= RunConstProp(func, ctx);
     changed |= RunConstFold(func, ctx);
+    changed |= RunAlgebraicSimplify(func, ctx);
     changed |= RunCSE(func);
     changed |= RunLICM(func);
     changed |= RunDCE(func);