diff --git a/nnvm/include/nnvm/node.h b/nnvm/include/nnvm/node.h
index 0e46e23f25e9..603ff3d05fb2 100644
--- a/nnvm/include/nnvm/node.h
+++ b/nnvm/include/nnvm/node.h
@@ -128,6 +128,33 @@ class Node {
   static NodePtr Create();
 };
 
+/*!
+ * \brief Quick utilities make node.
+ * \param op_name The name of operator
+ * \param node_name The name of the node
+ * \param inputs The input entries
+ * \param attrs The attributes
+ * \return The created node entry.
+ */
+inline NodeEntry MakeNode(
+    const char* op_name,
+    std::string node_name,
+    std::vector<NodeEntry> inputs,
+    std::unordered_map<std::string, std::string> attrs =
+    std::unordered_map<std::string, std::string>()) {
+  NodePtr p = Node::Create();
+  p->attrs.op = nnvm::Op::Get(op_name);
+  p->attrs.name = std::move(node_name);
+  if (attrs.size() != 0) {
+    p->attrs.dict = attrs;
+    if (p->attrs.op->attr_parser) {
+      p->attrs.op->attr_parser(&(p->attrs));
+    }
+  }
+  p->inputs = std::move(inputs);
+  return NodeEntry{p, 0, 0};
+}
+
 // implementation of functions.
 inline const Op* Node::op() const {
   return this->attrs.op;
diff --git a/nnvm/python/nnvm/compiler/graph_attr.py b/nnvm/python/nnvm/compiler/graph_attr.py
index 0b5d19898221..3787eca68707 100644
--- a/nnvm/python/nnvm/compiler/graph_attr.py
+++ b/nnvm/python/nnvm/compiler/graph_attr.py
@@ -83,6 +83,5 @@ def set_layout_inputs(g, layout):
     g._set_json_attr("layout_inputs", list_shape, 'list_str')
     return g
 
-
-_move_out_module = tvm.get_global_func("nnvm.graph_attr._move_module")
-_move_out_graph = tvm.get_global_func("nnvm.graph_attr._move_graph")
+_move_out_module = tvm.get_global_func("nnvm.graph._move_module")
+_move_out_graph = tvm.get_global_func("nnvm.graph._move_graph")
diff --git a/nnvm/python/nnvm/compiler/graph_pass.py b/nnvm/python/nnvm/compiler/graph_pass.py
index 7d25a055777d..3e98615d8ff2 100644
--- a/nnvm/python/nnvm/compiler/graph_pass.py
+++ b/nnvm/python/nnvm/compiler/graph_pass.py
@@ -7,6 +7,7 @@
 """
 from __future__ import absolute_import as _abs
 
+import tvm
 from . import graph_attr
 
 
@@ -60,3 +61,26 @@ def infer_dtype(graph, **dtype):
     output_dtype = [graph_attr.TCODE_TO_DTYPE[dtype[index.entry_id(x)]]
                     for x in index.output_entries]
     return input_dtype, output_dtype
+
+
+_deep_compare = tvm.get_global_func("nnvm.graph.DeepCompare")
+
+def check_graph_equal(grapha, graphb):
+    """Check if two graphs have equal structure.
+
+    Parameters
+    ----------
+    grapha : Graph
+        The first graph
+
+    graphb : Graph
+        The second graph
+
+    Raises
+    ------
+    ValueError
+        ValueError is raised with error message when graph not equal
+    """
+    err = _deep_compare(grapha, graphb)
+    if err:
+        raise ValueError("Graph compare error: " + err)
diff --git a/nnvm/python/nnvm/graph.py b/nnvm/python/nnvm/graph.py
index 309603d06264..b8cb655c9b65 100644
--- a/nnvm/python/nnvm/graph.py
+++ b/nnvm/python/nnvm/graph.py
@@ -177,6 +177,10 @@ def index(self):
             self._index = GraphIndex(self)
         return self._index
 
+    def graphir(self):
+        """Get text form of graph ir."""
+        return self.apply("PrintGraphIR").json_attr("graphir")
+
     def apply(self, passes):
         """Apply passes to the graph
 
diff --git a/nnvm/python/nnvm/top/nn.py b/nnvm/python/nnvm/top/nn.py
index 69ca49e6603e..b4c0c44f0edc 100644
--- a/nnvm/python/nnvm/top/nn.py
+++ b/nnvm/python/nnvm/top/nn.py
@@ -10,7 +10,7 @@
 
 # relu
 @reg.register_compute("relu")
-def compute_relu(attrs, inputs):
+def compute_relu(_, inputs):
     """Compute definition of relu"""
     return topi.nn.relu(inputs[0])
 
@@ -72,8 +72,7 @@ def schedule_conv2d(attrs, outs, target):
     if target == "cuda":
         if groups == 1:
             return topi.cuda.schedule_conv2d_nchw(outs)
-        else:
-            return topi.cuda.schedule_depthwise_conv2d_nchw(outs)
+        return topi.cuda.schedule_depthwise_conv2d_nchw(outs)
     # naive schedule
     return tvm.create_schedule([x.op for x in outs])
 
diff --git a/nnvm/src/compiler/graph_deep_compare.cc b/nnvm/src/compiler/graph_deep_compare.cc
new file mode 100644
index 000000000000..dd64f0e3b062
--- /dev/null
+++ b/nnvm/src/compiler/graph_deep_compare.cc
@@ -0,0 +1,113 @@
+/*!
+ *  Copyright (c) 2017 by Contributors
+ * \file graph_deep_compare.cc
+ * \brief Deep compare two graph structure
+ */
+#include <nnvm/graph.h>
+#include <nnvm/op_attr_types.h>
+#include <nnvm/compiler/packed_func_ext.h>
+#include <tvm/runtime/packed_func.h>
+#include "./node_attr.h"
+
+namespace nnvm {
+namespace compiler {
+
+// deep compare the graph structure
+// not considering the graph attributes
+// return non-empty error message if the graph mismatch.
+// the comparator won't match name of intermediate node.
+std::string DeepCompare(Graph a, Graph b) {
+  const IndexedGraph& idxa = a.indexed_graph();
+  const IndexedGraph& idxb = b.indexed_graph();
+  std::ostringstream err;
+  if (idxa.num_nodes() != idxb.num_nodes()) {
+    err << "Number of nodes mismatch";
+    return err.str();
+  }
+  if (idxa.num_node_entries() != idxb.num_node_entries()) {
+    err << "Number of node entry mismatch";
+    return err.str();
+  }
+  if (idxa.outputs().size() != idxb.outputs().size()) {
+    err << "Number of outputs mismatch";
+    return err.str();
+  }
+  for (size_t i = 0; i < idxa.outputs().size(); ++i) {
+    if (idxa.outputs()[i].node_id != idxb.outputs()[i].node_id ||
+        idxa.outputs()[i].index != idxb.outputs()[i].index) {
+      err << "Output entry mismatch";
+      return err.str();
+    }
+  }
+  if (idxa.input_nodes().size() != idxb.input_nodes().size()) {
+    err << "Number of inputs mismatch";
+    return err.str();
+  }
+
+  for (uint32_t nid = 0; nid < idxa.num_nodes(); ++nid) {
+    const IndexedGraph::Node& anode = idxa[nid];
+    const IndexedGraph::Node& bnode = idxb[nid];
+    if (anode.source->op() != bnode.source->op()) {
+      err << "Node mismatch ";
+      return err.str();
+    }
+    AttrDict adict = GetAttrDict(anode.source->attrs);
+    AttrDict bdict = GetAttrDict(bnode.source->attrs);
+
+    auto fmatch = [&err, &anode](const AttrDict& adict, const AttrDict& bdict) {
+      for (const auto& kv : adict) {
+        auto it = bdict.find(kv.first);
+        if (it != bdict.end()) {
+          if (it->second != kv.second) {
+            err << "Node attr mismatch, op=" << anode.source->attrs.name
+                << " attr_key=" << kv.first << " " << it->second
+                << " v.s. " << kv.second;
+            return false;
+          }
+        } else {
+          err << "One attr_key=" << kv.first << " is missing in another "
+               << "op=" << anode.source->attrs.name;
+          return false;
+        }
+      }
+      return true;
+    };
+    if (!fmatch(adict, bdict)) return err.str();
+    if (adict.size() != bdict.size()) {
+      CHECK(!fmatch(bdict, adict));
+      return err.str();
+    }
+    if (anode.inputs.size() != bnode.inputs.size()) {
+      err << "Node input mismatch, op=" << anode.source->attrs.name;
+      return err.str();
+    }
+    if (anode.control_deps.size() != bnode.control_deps.size()) {
+      err << "Node control_deps mistach, op=" << anode.source->attrs.name;
+      return err.str();
+    }
+    for (size_t i = 0; i < anode.inputs.size(); ++i) {
+      const IndexedGraph::NodeEntry& ae = anode.inputs[i];
+      const IndexedGraph::NodeEntry& be = bnode.inputs[i];
+      if (ae.node_id != be.node_id ||
+          ae.index != be.index ||
+          ae.version != be.version) {
+        err << "Node input mismatch on, op=" << anode.source->attrs.name;
+        return err.str();
+      }
+    }
+    for (size_t i = 0; i < anode.control_deps.size(); ++i) {
+      if (anode.control_deps[i] != bnode.control_deps[i]) {
+        err << "Node control_dep mismatch on, op=" << anode.source->attrs.name;
+        return err.str();
+      }
+    }
+  }
+  return "";
+}
+
+TVM_REGISTER_GLOBAL("nnvm.graph.DeepCompare")
+.set_body([](tvm::runtime::TVMArgs args, tvm::runtime::TVMRetValue *rv) {
+    *rv = DeepCompare(args[0], args[1]);
+  });
+}  // namespace compiler
+}  // namespace nnvm
diff --git a/nnvm/src/compiler/pass/graph_fuse.cc b/nnvm/src/compiler/graph_fuse.cc
similarity index 99%
rename from nnvm/src/compiler/pass/graph_fuse.cc
rename to nnvm/src/compiler/graph_fuse.cc
index 0880a90b9dad..9496e110ba64 100644
--- a/nnvm/src/compiler/pass/graph_fuse.cc
+++ b/nnvm/src/compiler/graph_fuse.cc
@@ -13,7 +13,7 @@
 #include <tvm/runtime/packed_func.h>
 #include <tvm/operation.h>
 #include <tvm/lowered_func.h>
-#include "../../runtime/graph_executor.h"
+#include "../runtime/graph_executor.h"
 
 namespace nnvm {
 namespace compiler {
diff --git a/nnvm/src/compiler/graph_transform.h b/nnvm/src/compiler/graph_transform.h
new file mode 100644
index 000000000000..2099809115aa
--- /dev/null
+++ b/nnvm/src/compiler/graph_transform.h
@@ -0,0 +1,125 @@
+/*!
+ * Copyright (c) 2017 by Contributors
+ * \file graph_transform.h
+ * \brief A mutator class that does local pattern matching and mutates a node.
+*/
+#ifndef NNVM_COMPILER_GRAPH_TRANSFORM_H_
+#define NNVM_COMPILER_GRAPH_TRANSFORM_H_
+
+#include <nnvm/graph.h>
+#include <vector>
+
+namespace nnvm {
+namespace compiler {
+
+/*!
+ * \brief Transform the graph to build a new Graph, in post DFS order.
+ *
+ *  Automatically copies node when some of its children or control_deps changed.
+ *  This function won't be called in Variable.
+ *
+ * \param graph The original graph
+ *
+ * \param ftransform Function of (int nid, const Node* node, std::vector<NodeEntry>* out) -> bool
+ *
+ *      If empty vector is returned, it means original entries should be kept.
+ *
+ * \tparam FTransform The transformation function.
+ */
+template<typename FTransform>
+Graph GraphTransform(Graph graph, FTransform ftransform) {
+  const IndexedGraph& idx = graph.indexed_graph();
+  // new nodes
+  std::vector<NodeEntry> new_entry_map(idx.num_node_entries());
+  std::vector<bool> updated(idx.num_node_entries(), false);
+
+  // setup inputs and placeholder.
+  for (uint32_t nid = 0; nid < idx.num_nodes(); ++nid) {
+    const auto& inode = idx[nid];
+    if (inode.source->is_variable()) continue;
+    bool need_copy = false;
+    for (const IndexedGraph::NodeEntry& e : inode.inputs) {
+      if (updated[idx.entry_id(e)]) {
+        need_copy = true; break;
+      }
+    }
+    if (!need_copy) {
+      for (const uint32_t cid : inode.control_deps) {
+        const auto& cnode = idx[cid];
+        for (uint32_t i = 0 ; i < cnode.source->num_outputs(); ++i) {
+          if (updated[idx.entry_id(cid, i)]) {
+            need_copy = true;
+          }
+        }
+        if (need_copy) break;
+      }
+    }
+
+    if (!need_copy) {
+      std::vector<NodeEntry> ret;
+      if (ftransform(nid, inode.source, &ret)) {
+        CHECK_EQ(ret.size(), static_cast<size_t>(inode.source->num_outputs()));
+        for (uint32_t i = 0 ; i < inode.source->num_outputs(); ++i) {
+          updated[idx.entry_id(nid, i)] = true;
+          new_entry_map[idx.entry_id(nid, i)] = ret[i];
+        }
+      }
+    } else {
+      NodePtr node = Node::Create();
+      node->attrs = inode.source->attrs;
+      for (size_t i = 0; i < inode.inputs.size(); ++i) {
+        const IndexedGraph::NodeEntry& e = inode.inputs[i];
+        if (updated[idx.entry_id(e)]) {
+          node->inputs.push_back(new_entry_map[idx.entry_id(e)]);
+        } else {
+          node->inputs.push_back(inode.source->inputs[i]);
+        }
+      }
+      for (size_t i = 0; i < inode.control_deps.size(); ++i) {
+        const uint32_t cid = inode.control_deps[i];
+        const auto& cnode = idx[cid];
+        CHECK_NE(cnode.source->num_outputs(), 0U);
+        NodePtr selected_ptr;
+        for (uint32_t j = 0 ; j < cnode.source->num_outputs(); ++j) {
+          NodePtr cptr = updated[idx.entry_id(cid, j)] ?
+              new_entry_map[idx.entry_id(cid, j)].node : inode.source->control_deps[i];
+          if (selected_ptr == nullptr) {
+            selected_ptr = std::move(cptr);
+          } else {
+            CHECK(selected_ptr.get() == cptr.get())
+                << "Control dependency node changed to more than one node";
+          }
+        }
+        node->control_deps.push_back(selected_ptr);
+      }
+      std::vector<NodeEntry> ret;
+      if (ftransform(nid, node.get(), &ret)) {
+        CHECK_EQ(ret.size(), static_cast<size_t>(inode.source->num_outputs()));
+        for (uint32_t i = 0 ; i < inode.source->num_outputs(); ++i) {
+          updated[idx.entry_id(nid, i)] = true;
+          new_entry_map[idx.entry_id(nid, i)] = ret[i];
+        }
+      } else {
+        for (uint32_t i = 0 ; i < inode.source->num_outputs(); ++i) {
+          updated[idx.entry_id(nid, i)] = true;
+          new_entry_map[idx.entry_id(nid, i)] = NodeEntry{node, i, 0};
+        }
+      }
+    }
+  }
+  Graph ret;
+  for (size_t i = 0; i < idx.outputs().size(); ++i) {
+    const IndexedGraph::NodeEntry& e = idx.outputs()[i];
+    if (updated[idx.entry_id(e)]) {
+      ret.outputs.push_back(new_entry_map[idx.entry_id(e)]);
+    } else {
+      ret.outputs.push_back(graph.outputs[i]);
+    }
+  }
+  return ret;
+}
+
+}  // namespace compiler
+}  // namespace nnvm
+
+#endif  // NNVM_COMPILER_GRAPH_TRANSFORM_H_
diff --git a/nnvm/src/compiler/pass/layout_transform.cc b/nnvm/src/compiler/layout_transform.cc
similarity index 100%
rename from nnvm/src/compiler/pass/layout_transform.cc
rename to nnvm/src/compiler/layout_transform.cc
diff --git a/nnvm/src/compiler/node_attr.h b/nnvm/src/compiler/node_attr.h
new file mode 100644
index 000000000000..c4395ad98b69
--- /dev/null
+++ b/nnvm/src/compiler/node_attr.h
@@ -0,0 +1,34 @@
+/*!
+ * Copyright (c) 2017 by Contributors
+ * \file node_attr.h
+ * \brief utility to access node attributes
+*/
+#ifndef NNVM_COMPILER_NODE_ATTR_H_
+#define NNVM_COMPILER_NODE_ATTR_H_
+
+#include <nnvm/op.h>
+#include <nnvm/compiler/op_attr_types.h>
+#include <unordered_map>
+#include <string>
+
+namespace nnvm {
+namespace compiler {
+
+using AttrDict = std::unordered_map<std::string, std::string>;
+/*!
+ * \brief Get canonicalized attr dict from node
+ * \param attrs The node attrs
+ * \return The attribute dict
+ */
+inline AttrDict GetAttrDict(const NodeAttrs& attrs) {
+  static auto& fgetdict = nnvm::Op::GetAttr<FGetAttrDict>("FGetAttrDict");
+  if (fgetdict.count(attrs.op)) {
+    return fgetdict[attrs.op](attrs);
+  } else {
+    return attrs.dict;
+  }
+}
+
+}  // namespace compiler
+}  // namespace nnvm
+#endif  // NNVM_COMPILER_NODE_ATTR_H_
diff --git a/nnvm/src/compiler/packed_func_ext.cc b/nnvm/src/compiler/packed_func_ext.cc
index 54d0f627c7a5..5444ece9c110 100644
--- a/nnvm/src/compiler/packed_func_ext.cc
+++ b/nnvm/src/compiler/packed_func_ext.cc
@@ -8,6 +8,7 @@
 #include <nnvm/op.h>
 #include <nnvm/compiler/packed_func_ext.h>
 #include <nnvm/compiler/op_attr_types.h>
+#include "./node_attr.h"
 
 namespace tvm {
 namespace runtime {
@@ -19,7 +20,6 @@ TVM_REGISTER_EXT_TYPE(nnvm::compiler::AttrDict);
 }  // namespace runtime
 }  // namespace tvm
 
-
 namespace nnvm {
 namespace compiler {
 
@@ -58,17 +58,6 @@ TVM_REGISTER_GLOBAL("nnvm.compiler._dict_keys")
   });
 
 // custom version of TVM compute
-inline std::unordered_map<std::string, std::string>
-GetAttrDict(const NodeAttrs& attrs) {
-  static auto& fgetdict = nnvm::Op::GetAttr<FGetAttrDict>("FGetAttrDict");
-  if (fgetdict.count(attrs.op)) {
-    return fgetdict[attrs.op](attrs);
-  } else {
-    return attrs.dict;
-  }
-}
-
-
 TVM_REGISTER_GLOBAL("nnvm._register_compute")
 .set_body([](TVMArgs args, TVMRetValue *rv) {
     // Intentionally copy and not de-allocate it, to avoid free pyobject during shutdown
@@ -105,14 +94,14 @@ TVM_REGISTER_GLOBAL("nnvm._register_pattern")
     op.set_attr<TOpPattern>("TOpPattern", args[1].operator int(), args[2]);
   });
 
-TVM_REGISTER_GLOBAL("nnvm.graph_attr._move_module")
+TVM_REGISTER_GLOBAL("nnvm.graph._move_module")
 .set_body([](TVMArgs args, TVMRetValue *rv) {
     const nnvm::Graph& g = args[0].AsExtension<Graph>();
     *rv = const_cast<nnvm::Graph*>(&g)->
         MoveCopyAttr<tvm::runtime::Module>(args[1]);
   });
 
-TVM_REGISTER_GLOBAL("nnvm.graph_attr._move_graph")
+TVM_REGISTER_GLOBAL("nnvm.graph._move_graph")
 .set_body([](TVMArgs args, TVMRetValue *rv) {
     const nnvm::Graph& g = args[0].AsExtension<Graph>();
     *rv = const_cast<nnvm::Graph*>(&g)->
diff --git a/nnvm/src/compiler/pass/precompute_prune.cc b/nnvm/src/compiler/precompute_prune.cc
similarity index 100%
rename from nnvm/src/compiler/pass/precompute_prune.cc
rename to nnvm/src/compiler/precompute_prune.cc
diff --git a/nnvm/src/compiler/simplify_batch_norm.cc b/nnvm/src/compiler/simplify_batch_norm.cc
new file mode 100644
index 000000000000..16d7557f29a5
--- /dev/null
+++ b/nnvm/src/compiler/simplify_batch_norm.cc
@@ -0,0 +1,114 @@
+/*!
+ * Copyright (c) 2017 by Contributors
+ * \file simplify_batch_norm.cc
+ * \author Ziheng Jiang
+*/
+#include <nnvm/graph.h>
+#include <nnvm/op_attr_types.h>
+#include <nnvm/graph_attr_types.h>
+#include <nnvm/pass.h>
+#include <nnvm/compiler/op_attr_types.h>
+#include <nnvm/top/nn.h>
+#include "./graph_transform.h"
+
+namespace nnvm {
+namespace compiler {
+
+std::vector<NodeEntry>
+BatchNormToInferUnpack(const nnvm::NodeAttrs& attrs,
+                       nnvm::NodeEntry data,
+                       nnvm::NodeEntry gamma,
+                       nnvm::NodeEntry beta,
+                       nnvm::NodeEntry moving_mean,
+                       nnvm::NodeEntry moving_var,
+                       int data_dim) {
+  CHECK(attrs.op);
+  static const  Op* bn_op = Op::Get("batch_norm");
+  CHECK(attrs.op == bn_op);
+  const auto& param = nnvm::get<top::BatchNormParam>(attrs.parsed);
+  std::string bn_name = attrs.name;
+
+  // transform batch_norm(data) to scale * data + shift
+  NodeEntry var_add_eps = MakeNode(
+      "__add_scalar__", bn_name + "_add_eps",
+      {moving_var}, {{"scalar", std::to_string(param.epsilon)}});
+
+  NodeEntry sqrt = MakeNode(
+      "sqrt", bn_name + "_sqrt", {var_add_eps});
+
+  NodeEntry scale = MakeNode(
+      "__rdiv_scalar__", bn_name + "_div",
+      {sqrt}, {{"scalar", "1"}});
+
+  if (param.scale) {
+    scale = MakeNode(
+        "elemwise_mul", bn_name + "_gamma_mul_div",
+        {scale, gamma});
+  }
+
+  NodeEntry neg_mean = MakeNode(
+      "negative", bn_name + "_neg_mean", {moving_mean});
+
+  NodeEntry shift = MakeNode(
+      "elemwise_mul", bn_name + "_neg_mean_mul_a",
+      {neg_mean, scale});
+
+  if (param.center) {
+    shift = MakeNode(
+        "elemwise_add", bn_name + "_add_beta", {shift, beta});
+  }
+  // reshape to nhwc
+  std::ostringstream oshape;
+  oshape << "(";
+  for (int i = 0; i < data_dim; ++i) {
+    if (i != 0) oshape << ", ";
+    if (i == param.axis) {
+      oshape << "-1";
+    } else {
+      oshape << "1";
+    }
+  }
+  oshape << ")";
+
+  scale = MakeNode("reshape", bn_name + "_sc_reshape",
+                   {scale}, {{"shape", oshape.str()}});
+  shift = MakeNode("reshape", bn_name + "_sh_reshape",
+                   {shift}, {{"shape", oshape.str()}});
+  NodeEntry out = MakeNode("broadcast_mul", bn_name + "_a_mul_data",
+                           {data, scale});
+  out = MakeNode("broadcast_add", bn_name + "_out",
+                 {out, shift});
+  // It is invalid to ref the other values of BN after infernece transform.
+  NodeEntry undef = MakeNode("__undef__", "undef", {});
+  return {out, undef, undef};
+}
+
+Graph SimplifyBatchNormInference(nnvm::Graph src) {
+  // Get attributes from the graph
+  const IndexedGraph& idx = src.indexed_graph();
+  const ShapeVector& shape_vec = src.GetAttr<ShapeVector>("shape");
+  auto transform = [&](uint32_t nid, const Node* n, std::vector<NodeEntry>* ret) {
+    if (n->is_variable()) return false;
+    static const Op* bn_op = Op::Get("batch_norm");
+    if (n->op() == bn_op) {
+      *ret = BatchNormToInferUnpack(
+          n->attrs,
+          n->inputs[0],
+          n->inputs[1],
+          n->inputs[2],
+          n->inputs[3],
+          n->inputs[4],
+          shape_vec[idx.entry_id(nid, 0)].ndim());
+      return true;
+    } else {
+      return false;
+    }
+  };
+  return GraphTransform(src, transform);
+}
+
+NNVM_REGISTER_PASS(SimplifyBatchNormInference)
+.set_body(SimplifyBatchNormInference);
+
+}  // namespace compiler
+}  // namespace nnvm
diff --git a/nnvm/src/pass/print_graph_ir.cc b/nnvm/src/pass/print_graph_ir.cc
new file mode 100644
index 000000000000..a29ee922b644
--- /dev/null
+++ b/nnvm/src/pass/print_graph_ir.cc
@@ -0,0 +1,127 @@
+/*!
+ *  Copyright (c) 2017 by Contributors
+ * \file print_graph_ir.cc
+ * \brief Print the graph IR in LLVM style human readable format.
+ */
+#include <nnvm/graph.h>
+#include <nnvm/pass.h>
+#include <iostream>
+
+namespace nnvm {
+namespace pass {
+
+// print the graph ir in readable format
+void PrintGraphIR_(Graph src, std::ostream& os) { // NOLINT(*)
+  const IndexedGraph& idx = src.indexed_graph();
+  os << "Graph(";
+  if (idx.input_nodes().size() < 4) {
+    for (size_t i = 0; i < idx.input_nodes().size(); ++i) {
+      uint32_t nid = idx.input_nodes()[i];
+      if (i != 0)  {
+        os << ", ";
+      }
+      os << '%' << idx[nid].source->attrs.name;
+    }
+  } else {
+    for (size_t i = 0; i < idx.input_nodes().size(); ++i) {
+      uint32_t nid = idx.input_nodes()[i];
+      if (i != 0)  {
+        os << ",\n      ";
+      }
+      os << '%' << idx[nid].source->attrs.name;
+    }
+  }
+  os << ") {\n";
+
+  auto print_entry = [&](const IndexedGraph::NodeEntry& e) {
+    if (idx[e.node_id].source->is_variable()) {
+      os << '%' << idx[e.node_id].source->attrs.name;
+    } else if (idx[e.node_id].source->num_outputs() == 1) {
+      os << '%' << e.node_id;
+    } else {
+      os << '%' << e.node_id << "." << e.index;
+    }
+  };
+
+  for (uint32_t nid = 0; nid < idx.num_nodes(); ++nid) {
+    const auto& inode = idx[nid];
+    if (inode.source->is_variable()) continue;
+    os << "  " << "%" << nid << " = "
+       << inode.source->op()->name << "(";
+    bool first = true;
+    for (const IndexedGraph::NodeEntry& e : inode.inputs) {
+      if (first) {
+        first = false;
+      } else {
+        os << ", ";
+      }
+      print_entry(e);
+    }
+    for (const auto& kv : inode.source->attrs.dict) {
+      if (first) {
+        first = false;
+      } else {
+        os << ", ";
+      }
+      os << kv.first << "=\'" << kv.second << "\'";
+    }
+    os << ")";
+    if (inode.control_deps.size() != 0) {
+      os << ", control_deps=[";
+      for (size_t i = 0; i < inode.control_deps.size(); ++i) {
+        if (i != 0) os << ", ";
+        uint32_t cid = inode.control_deps[i];
+        if (idx[cid].source->is_variable()) {
+          os << '%' << idx[cid].source->attrs.name;
+        } else {
+          os << '%' << cid;
+        }
+      }
+      os << "]";
+    }
+    os << "\n";
+  }
+  os << "  ret ";
+  {
+    bool first = true;
+    for (const IndexedGraph::NodeEntry& e : idx.outputs()) {
+      if (first) {
+        first = false;
+      } else {
+        os << ", ";
+      }
+      print_entry(e);
+    }
+  }
+  os << "\n}";
+  if (src.attrs.size() != 0) {
+    os << "\ngraph_attr_keys = [";
+    bool first = true;
+    for (const auto& kv : src.attrs) {
+      if (first) {
+        first = false;
+      } else {
+        os << ", ";
+      }
+      os << kv.first;
+    }
+    os << "]\n";
+  }
+}
+
+// save a graph to json
+Graph PrintGraphIR(Graph src) {
+  std::ostringstream os;
+  PrintGraphIR_(src, os);
+  Graph ret;
+  ret.attrs["graphir"] = std::make_shared<any>(os.str());
+  return ret;
+}
+
+// register pass
+NNVM_REGISTER_PASS(PrintGraphIR)
+.describe("Return a empty Graph, save ir to ret.attrs[\"graphir\"]")
+.set_body(PrintGraphIR);
+
+}  // namespace pass
+}  // namespace nnvm
diff --git a/nnvm/src/top/nn/nn_common.h b/nnvm/src/top/nn/nn_common.h
index a4ce6b1b78d0..a75077b87ca4 100644
--- a/nnvm/src/top/nn/nn_common.h
+++ b/nnvm/src/top/nn/nn_common.h
@@ -11,6 +11,7 @@
 #include <nnvm/top/nn.h>
 #include <string>
 #include <vector>
+#include <utility>
 #include <algorithm>
 
 namespace nnvm {
diff --git a/nnvm/src/top/tensor/elemwise.cc b/nnvm/src/top/tensor/elemwise.cc
index 825b01b018e2..17e457e56b3c 100644
--- a/nnvm/src/top/tensor/elemwise.cc
+++ b/nnvm/src/top/tensor/elemwise.cc
@@ -12,6 +12,16 @@
 
 namespace nnvm {
 namespace top {
+// undefined op
+NNVM_REGISTER_ELEMWISE_UNARY_OP(__undef__)
+.describe(R"code(undefined op.
+
+Used to produce invalide node during optimization.
+
+)code" NNVM_ADD_FILELINE)
+.set_num_outputs(1)
+.set_num_inputs(0);
+
 // sigmoid
 NNVM_REGISTER_ELEMWISE_UNARY_OP(sigmoid)
 .describe(R"code(Computes sigmoid.
@@ -52,6 +62,16 @@ NNVM_REGISTER_ELEMWISE_UNARY_OP(log)
 )code" NNVM_ADD_FILELINE)
 .set_support_level(1);
 
+// sqrt
+NNVM_REGISTER_ELEMWISE_UNARY_OP(sqrt)
+.describe(R"code(Returns the sqrt input array, computed element-wise.
+
+.. math::
+   \sqrt(x)
+
+)code" NNVM_ADD_FILELINE)
+.set_support_level(1);
+
 // binary ops
 
 NNVM_REGISTER_ELEMWISE_BINARY_OP(elemwise_add)
diff --git a/nnvm/tests/python/compiler/test_graph_pass.py b/nnvm/tests/python/compiler/test_graph_pass.py
index 110184c8f07c..9f2c36a1d3f9 100644
--- a/nnvm/tests/python/compiler/test_graph_pass.py
+++ b/nnvm/tests/python/compiler/test_graph_pass.py
@@ -1,10 +1,11 @@
 """Unittest cases for graph pass"""
 import nnvm
 import nnvm.compiler
-from nnvm.compiler import graph_pass
+from nnvm import symbol as sym
+from nnvm.compiler import graph_pass, graph_attr
 
 def test_infer_attr():
-    x = nnvm.symbol.Variable("x")
+    x = sym.Variable("x")
     y = x * 2
     g = nnvm.graph.create(y)
     ishape, oshape = graph_pass.infer_shape(g, x=(10,20))
@@ -13,6 +14,5 @@ def test_infer_attr():
     itype, otype = graph_pass.infer_dtype(g, x="float32")
     assert otype[0] == "float32"
 
-
 if __name__ == "__main__":
     test_infer_attr()
diff --git a/nnvm/tests/python/compiler/test_simplify_batchnorm.py b/nnvm/tests/python/compiler/test_simplify_batchnorm.py
new file mode 100644
index 000000000000..54cb8bc0bc57
--- /dev/null
+++ b/nnvm/tests/python/compiler/test_simplify_batchnorm.py
@@ -0,0 +1,49 @@
+"""Unittest cases for simplify batch_norm"""
+import nnvm
+from nnvm import symbol as sym
+from nnvm.compiler import graph_pass, graph_attr
+
+def test_simplify_batchnorm():
+    def simple_bn(x, gamma, beta, moving_mean, moving_var,
+                  axis=1, epsilon=1e-5, dim=2):
+        # expect = (x - moving_mean) / sym.sqrt(moving_var + eps) * gamma + beta
+        scale = sym.elemwise_mul(1 / sym.sqrt(moving_var + epsilon), gamma)
+        shift = sym.elemwise_add(
+            sym.elemwise_mul(sym.negative(moving_mean), scale), beta)
+        # for 2D
+        shape = tuple(1 if i != axis else -1 for i in range(dim))
+        scale = sym.reshape(scale, shape=shape)
+        shift = sym.reshape(shift, shape=shape)
+        return x * scale + shift
+
+
+    # Before simplify
+    def check(dim, axis, nstep):
+        eps = 0.01
+        x = sym.Variable("x") + 1
+        beta = sym.Variable("beta")
+        gamma = sym.Variable("gamma")
+        moving_var = sym.Variable("moving_var")
+        moving_mean = sym.Variable("moving_mean")
+        y1, y2 = x, x
+
+        for i in range(nstep):
+            y1 = sym.batch_norm(
+                y1 + 1, gamma, beta, moving_mean, moving_var, epsilon=eps, axis=axis)
+            y2 = simple_bn(y2 + 1, gamma, beta, moving_mean, moving_var,
+                           epsilon=eps, axis=axis, dim=dim)
+        g = nnvm.graph.create(y1)
+        g2 = nnvm.graph.create(y2)
+        ishape = {"x": tuple(10 for i in range(dim))}
+        graph_attr.set_shape_inputs(g, ishape)
+        g1 = g.apply("InferShape").apply("SimplifyBatchNormInference")
+        # Some prints for debug
+        # print(g1.graphir())
+        # assert graph equals as expected
+        graph_pass.check_graph_equal(g1, g2)
+
+    check(2, 1, 1)
+    check(4, 0, 3)
+
+if __name__ == "__main__":
+    test_simplify_batchnorm()
diff --git a/nnvm/tests/python/unittest/test_top_level1.py b/nnvm/tests/python/unittest/test_top_level1.py
index 4c5c28005f88..6b75cf1d83f1 100644
--- a/nnvm/tests/python/unittest/test_top_level1.py
+++ b/nnvm/tests/python/unittest/test_top_level1.py
@@ -1,4 +1,5 @@
 import nnvm.symbol as sym
+import nnvm.graph as graph
 
 def test_dense():
     x = sym.Variable('x')