diff --git a/neural_compressor/torch/algorithms/smooth_quant/utility.py b/neural_compressor/torch/algorithms/smooth_quant/utility.py
index 7dc647dbc95..e2ce9c97f5b 100644
--- a/neural_compressor/torch/algorithms/smooth_quant/utility.py
+++ b/neural_compressor/torch/algorithms/smooth_quant/utility.py
@@ -26,8 +26,8 @@
 
 from neural_compressor.torch.algorithms.static_quant import (
     CpuInfo,
+    Statistics,
     TransformerBasedModelBlockPatternDetector,
-    dump_model_op_stats,
     generate_activation_observer,
     get_quantizable_ops_from_cfgs,
     ipex_config_path,
@@ -251,6 +251,59 @@ def cfg_to_qconfig(
     return None
 
 
+def dump_model_op_stats(user_cfg):
+    """This is a function to dump quantizable ops of model to user.
+
+    Args:
+        user_cfg (dict): quantization config
+    Returns:
+        None
+    """
+    res = dict()
+    for k, v in user_cfg.items():
+        op_type_list = k[-1].split("><")
+        op_type = ""
+        for op in op_type_list:
+            if "class" in op:
+                op_type = (
+                    op[op.rfind(".") + 1 : op.rfind("'")]
+                    if op_type == ""
+                    else op_type + "&" + op[op.rfind(".") + 1 : op.rfind("'")]
+                )
+            elif "method" in op:
+                start = op.find("'") + 1
+                if start > 1:
+                    op_type = (
+                        op[start : op.find("'", start)]
+                        if op_type == ""
+                        else op_type + "&" + op[start : op.find("'", start)]
+                    )
+                else:
+                    start = op.find("method") + 7
+                    op_type = (
+                        op[start : op.find(" ", start)]
+                        if op_type == ""
+                        else op_type + "&" + op[start : op.find(" ", start)]
+                    )
+            else:
+                op_type = op if op_type == "" else op_type + "&" + op
+        if op_type not in res.keys():
+            res[op_type] = {"INT8": 0, "BF16": 0, "FP32": 0}
+        if v["weight"]["dtype"] == "int8":
+            res[op_type]["INT8"] += 1
+        elif v["weight"]["dtype"] == "fp32":
+            res[op_type]["FP32"] += 1
+
+    output_data = [
+        [op_type, sum(res[op_type].values()), res[op_type]["INT8"], res[op_type]["BF16"], res[op_type]["FP32"]]
+        for op_type in res.keys()
+    ]
+
+    Statistics(
+        output_data, header="Mixed Precision Statistics", field_names=["Op Type", "Total", "INT8", "BF16", "FP32"]
+    ).print_stat()
+
+
 def get_parent(node, all_parents=False):  # pragma: no cover
     if node.inputs() is None:
         return None
diff --git a/neural_compressor/torch/algorithms/static_quant/utility.py b/neural_compressor/torch/algorithms/static_quant/utility.py
index f90471539fd..81133557b3e 100644
--- a/neural_compressor/torch/algorithms/static_quant/utility.py
+++ b/neural_compressor/torch/algorithms/static_quant/utility.py
@@ -43,13 +43,19 @@
     "<class 'torch.nn.modules.conv.Conv2d'>": "Conv2d",
     "<class 'torch.nn.modules.conv.Conv3d'>": "Conv3d",
     "<class 'torch.nn.modules.activation.ReLU'>": "ReLU",
+    "<class 'torch.nn.modules.sparse.EmbeddingBag'>": "EmbeddingBag",
     "<method 'add' of 'torch._C._TensorBase' objects>": "add",  # for IPEX < 2.2
     "<method 'add' of 'torch._C.TensorBase' objects>": "add",  # for IPEX >= 2.2
     "<class 'torch.nn.modules.pooling.AdaptiveAvgPool2d'>": "AdaptiveAvgPool2d",
     "Linear_Relu": "Linear",
+    "Linear_add": "Linear",
     "<class 'torch.nn.modules.linear.Linear'>": "Linear",
     "<class 'torch.nn.modules.pooling.MaxPool2d'>": "MaxPool2d",
-    "re": {"<built-in method matmul of type object at": "matmul"},
+    "re": {
+        "<built-in method matmul of type object at": "matmul",
+        "<built-in method add of type object at": "add",
+        "<built-in method bmm of type object at": "bmm",
+    },
 }
 
 BLOCK_PATTERNS = [
@@ -85,6 +91,7 @@ def check_cfg_and_qconfig(user_cfg, cfgs, op_infos_from_cfgs, output_tensor_ids_
     Returns:
         cfgs (dict): updated configs.
     """
+    ori_user_cfg = copy.deepcopy(user_cfg)
     tmp_user_cfg = OrderedDict()
     for op in user_cfg:  # map ipex op_name to pt op_name
         for i, op_name in enumerate(op):
@@ -94,9 +101,9 @@ def check_cfg_and_qconfig(user_cfg, cfgs, op_infos_from_cfgs, output_tensor_ids_
                         ori_op = (tuple(ops), unify_op_type_mapping_ipex[op_infos_from_cfgs[ops]["op_type"]])
                         tmp_user_cfg[((ori_op[0],), ori_op[1])] = user_cfg[op]
                         break
-    user_cfg = tmp_user_cfg
-    for op_name in user_cfg:
-        inc_op_cfg = user_cfg[op_name]
+
+    for op_name in tmp_user_cfg:
+        inc_op_cfg = tmp_user_cfg[op_name]
         for i, name in enumerate(op_name[0]):
             # to int8
             ipex_op_cfg = op_infos_from_cfgs[name]
@@ -154,7 +161,7 @@ def check_cfg_and_qconfig(user_cfg, cfgs, op_infos_from_cfgs, output_tensor_ids_
                         else:
                             pass
             cfgs[name[0]][name[1]][name[2]] = ipex_op_cfg
-    return cfgs, user_cfg
+    return cfgs, ori_user_cfg
 
 
 def generate_activation_observer(scheme, algorithm, smooth_quant=False, smooth_quant_enable=False):  # pragma: no cover
@@ -333,8 +340,8 @@ def get_quantizable_ops_recursively(model, example_inputs):  # pragma: no cover
                     elif "method" in ipex_op_type:  # "<method 'add' of 'torch._C._TensorBase' objects>"
                         method = ipex_op_type.split("'")[1]
                         op_name_info.append((module_fqn, method))
-                    elif "Convolution" in ipex_op_type:  # "Convolution_Relu"
-                        op_name_info.append((module_fqn, "Conv2d"))
+                    elif "_" in ipex_op_type:  # "Convolution_Relu", "Linear_Relu"
+                        op_name_info.append((module_fqn, ipex_op_type.split("_")[0]))
                 else:
                     re_flag = False
                     for pattern, unify_op_type in unify_op_type_mapping_ipex["re"].items():
@@ -394,32 +401,7 @@ def dump_model_op_stats(user_cfg):
     """
     res = dict()
     for k, v in user_cfg.items():
-        op_type_list = k[-1].split("><")
-        op_type = ""
-        for op in op_type_list:
-            if "class" in op:
-                op_type = (
-                    op[op.rfind(".") + 1 : op.rfind("'")]
-                    if op_type == ""
-                    else op_type + "&" + op[op.rfind(".") + 1 : op.rfind("'")]
-                )
-            elif "method" in op:
-                start = op.find("'") + 1
-                if start > 1:
-                    op_type = (
-                        op[start : op.find("'", start)]
-                        if op_type == ""
-                        else op_type + "&" + op[start : op.find("'", start)]
-                    )
-                else:
-                    start = op.find("method") + 7
-                    op_type = (
-                        op[start : op.find(" ", start)]
-                        if op_type == ""
-                        else op_type + "&" + op[start : op.find(" ", start)]
-                    )
-            else:
-                op_type = op if op_type == "" else op_type + "&" + op
+        op_type = k[1]
         if op_type not in res.keys():
             res[op_type] = {"INT8": 0, "BF16": 0, "FP32": 0}
         if v["weight"]["dtype"] == "int8":
diff --git a/test/3x/torch/quantization/test_static_quant.py b/test/3x/torch/quantization/test_static_quant.py
index 60d0b205371..46e791aa52f 100644
--- a/test/3x/torch/quantization/test_static_quant.py
+++ b/test/3x/torch/quantization/test_static_quant.py
@@ -22,13 +22,18 @@ class Model(torch.nn.Module):
         def __init__(self):
             super(Model, self).__init__()
             self.fc1 = torch.nn.Linear(30, 50)
-            self.fc2 = torch.nn.Linear(50, 30)
-            self.fc3 = torch.nn.Linear(30, 5)
+            self.fc2 = torch.nn.Linear(50, 50)
+            self.fc3 = torch.nn.Linear(50, 30)
+            self.fc4 = torch.nn.Linear(30, 5)
+            self.relu = torch.nn.ReLU()
 
         def forward(self, x):
             out = self.fc1(x)
             out = self.fc2(out)
+            out = self.relu(out)
             out = self.fc3(out)
+            out = out + x
+            out = self.fc4(out)
             return out
 
     model = Model()
@@ -78,21 +83,22 @@ def test_static_quant_fallback(self):
         assert q_model is not None, "Quantization failed!"
 
         for op, op_info in q_model.tune_cfg[" "]["q_op_infos"].items():
-            if op_info["op_type"] == "<class 'torch.nn.modules.linear.Linear'>":
+            if op_info["op_type"] == "Linear":
                 dtype = q_model.tune_cfg[" "]["q_op_infos"][op]["input_tensor_infos"][0]["force_dtype"]
                 assert dtype == "torch.float32", "Failed to fallback linear op, please check!"
 
         # fallback by op_name
-        quant_config.set_local("fc1", StaticQuantConfig(w_dtype="fp32", act_dtype="fp32"))
+        quant_config = get_default_static_config()
+        quant_config.set_local("fc2", StaticQuantConfig(w_dtype="fp32", act_dtype="fp32"))
         prepared_model = prepare(fp32_model, quant_config=quant_config, example_inputs=example_inputs)
         run_fn(prepared_model)
         q_model = convert(prepared_model)
         assert q_model is not None, "Quantization failed!"
 
         for op, op_info in q_model.tune_cfg[" "]["q_op_infos"].items():
-            if op_info["fqn"] == "fc1":
+            if op_info["fqn"] == "fc2":
                 dtype = q_model.tune_cfg[" "]["q_op_infos"][op]["input_tensor_infos"][0]["force_dtype"]
-                assert dtype == "torch.float32", "Failed to fallback fc1 layer, please check!"
+                assert dtype == "torch.float32", "Failed to fallback fc2 layer, please check!"
 
     @pytest.mark.skipif(not is_ipex_available(), reason="Requires IPEX")
     @pytest.mark.parametrize(