diff --git a/paddle/fluid/operators/prim_ops/CMakeLists.txt b/paddle/fluid/operators/prim_ops/CMakeLists.txt
index 1f63d5d1721b5c2fe38586879d561b8c5db105ca..30e162a4dd2a9671d42cf9760a84f1af649220fe 100644
--- a/paddle/fluid/operators/prim_ops/CMakeLists.txt
+++ b/paddle/fluid/operators/prim_ops/CMakeLists.txt
@@ -8,7 +8,7 @@ register_operators()
 set(PRIM_OP_SRCS
     reshape_p_op.cc
     broadcast_p_op.cc
-    reduce_p_op.cc
+    reduce_sum_p_op.cc
     transpose_p_op.cc
     split_p_op.cc
     concat_p_op.cc
@@ -30,9 +30,14 @@ set(PRIM_OP_SRCS
     log_p_op.cc
     select_p_op.cc
     eq_p_op.cc
+    gt_p_op.cc
+    ge_p_op.cc
+    ne_p_op.cc
     pow_p_op.cc
     max_p_op.cc
-    erf_p_op.cc)
+    erf_p_op.cc
+    abs_p_op.cc
+    cast_p_op.cc)
 
 cc_test(
   prim_op_test
diff --git a/paddle/fluid/operators/prim_ops/abs_p_op.cc b/paddle/fluid/operators/prim_ops/abs_p_op.cc
new file mode 100644
index 0000000000000000000000000000000000000000..8ad9d131689e70e98c511608ed74504778316d43
--- /dev/null
+++ b/paddle/fluid/operators/prim_ops/abs_p_op.cc
@@ -0,0 +1,71 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "paddle/fluid/framework/op_registry.h"
+#include "paddle/fluid/framework/operator.h"
+
+namespace paddle {
+namespace operators {
+class AbsPrimOp : public framework::OperatorBase {
+ public:
+  AbsPrimOp(const std::string &type,
+            const framework::VariableNameMap &inputs,
+            const framework::VariableNameMap &outputs,
+            const framework::AttributeMap &attrs)
+      : framework::OperatorBase(type, inputs, outputs, attrs) {}
+  void RunImpl(const framework::Scope &scope,
+               const platform::Place &dev_place) const override {
+    PADDLE_THROW(platform::errors::Unimplemented(
+        "Prim operator abs_p should not be excuted directly"));
+  }
+};
+
+class AbsPrimOpMaker : public framework::OpProtoAndCheckerMaker {
+ public:
+  void Make() override {
+    AddInput("X", "(Tensor), The input tensor of abs_p op.");
+    AddOutput("Y", "(Tensor), The output tensor of abs_p op.");
+    AddComment(R"DOC(Autograd primitive abs_p operator.)DOC");
+  }
+};
+
+class AbsPrimOpShapeInference : public framework::InferShapeBase {
+ public:
+  void operator()(framework::InferShapeContext *ctx) const override {
+    framework::InferShapeVarPtr x_var_ptr = ctx->GetInputVarPtrs("X")[0];
+    framework::InferShapeVarPtr y_var_ptr = ctx->GetOutputVarPtrs("Y")[0];
+    framework::VarDesc *x_var = PADDLE_GET(framework::VarDesc *, x_var_ptr);
+    PADDLE_GET(framework::VarDesc *, y_var_ptr)->SetShape(x_var->GetShape());
+  }
+};
+
+class AbsPrimOpVarTypeInference
+    : public framework::StaticGraphVarTypeInference {
+ public:
+  void operator()(framework::InferVarTypeContext *ctx) const override {
+    auto x_name = Input(ctx, "X")[0];
+    auto y_name = Output(ctx, "Y")[0];
+    SetType(ctx, y_name, GetType(ctx, x_name));
+    SetDataType(ctx, y_name, GetDataType(ctx, x_name));
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle
+
+REGISTER_OPERATOR(abs_p,
+                  paddle::operators::AbsPrimOp,
+                  paddle::operators::AbsPrimOpMaker,
+                  paddle::operators::AbsPrimOpShapeInference,
+                  paddle::operators::AbsPrimOpVarTypeInference);
diff --git a/paddle/fluid/operators/prim_ops/cast_p_op.cc b/paddle/fluid/operators/prim_ops/cast_p_op.cc
new file mode 100644
index 0000000000000000000000000000000000000000..5c8b9ab45c6bca9a3bb44ee2ca047c0c82c86b44
--- /dev/null
+++ b/paddle/fluid/operators/prim_ops/cast_p_op.cc
@@ -0,0 +1,78 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "paddle/fluid/framework/op_registry.h"
+#include "paddle/fluid/framework/operator.h"
+
+namespace paddle {
+namespace framework {
+class InferShapeContext;
+class VarDesc;
+}  // namespace framework
+}  // namespace paddle
+
+namespace paddle {
+namespace operators {
+class CastPrimOp : public framework::OperatorBase {
+ public:
+  CastPrimOp(const std::string &type,
+             const framework::VariableNameMap &inputs,
+             const framework::VariableNameMap &outputs,
+             const framework::AttributeMap &attrs)
+      : framework::OperatorBase(type, inputs, outputs, attrs) {}
+  void RunImpl(const framework::Scope &scope,
+               const platform::Place &dev_place) const override {
+    PADDLE_THROW(platform::errors::Unimplemented(
+        "Prim operator cast_p should not be excuted directly"));
+  }
+};
+
+class CastPrimOpMaker : public framework::OpProtoAndCheckerMaker {
+ public:
+  void Make() override {
+    AddInput("X", "(Tensor), The input tensor of cast_p op.");
+    AddOutput("Y", "(Tensor), The output tensor of cast_p op.");
+    AddAttr<int>("dtype", "output data type");
+    AddComment(R"DOC(Autograd primitive cast_p operator.)DOC");
+  }
+};
+
+class CastPrimOpShapeInference : public framework::InferShapeBase {
+ public:
+  void operator()(framework::InferShapeContext *ctx) const override {
+    framework::InferShapeVarPtr x_var_ptr = ctx->GetInputVarPtrs("X")[0];
+    framework::InferShapeVarPtr y_var_ptr = ctx->GetOutputVarPtrs("Y")[0];
+    framework::VarDesc *x_var = PADDLE_GET(framework::VarDesc *, x_var_ptr);
+    PADDLE_GET(framework::VarDesc *, y_var_ptr)->SetShape(x_var->GetShape());
+  }
+};
+
+class CastPrimOpVarTypeInference
+    : public framework::StaticGraphVarTypeInference {
+ public:
+  void operator()(framework::InferVarTypeContext *ctx) const override {
+    auto out_type = static_cast<framework::proto::VarType::Type>(
+        PADDLE_GET_CONST(int, ctx->GetAttr("dtype")));
+    ctx->SetOutputDataType("Y", out_type);
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle
+
+REGISTER_OPERATOR(cast_p,
+                  paddle::operators::CastPrimOp,
+                  paddle::operators::CastPrimOpMaker,
+                  paddle::operators::CastPrimOpShapeInference,
+                  paddle::operators::CastPrimOpVarTypeInference);
diff --git a/paddle/fluid/operators/prim_ops/ge_p_op.cc b/paddle/fluid/operators/prim_ops/ge_p_op.cc
new file mode 100644
index 0000000000000000000000000000000000000000..33fbd4cd71497ff949a64abdf5a44fc1bff458b8
--- /dev/null
+++ b/paddle/fluid/operators/prim_ops/ge_p_op.cc
@@ -0,0 +1,119 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "paddle/fluid/framework/op_registry.h"
+#include "paddle/fluid/framework/operator.h"
+
+namespace paddle {
+namespace operators {
+class GePrimOp : public framework::OperatorBase {
+ public:
+  GePrimOp(const std::string &type,
+           const framework::VariableNameMap &inputs,
+           const framework::VariableNameMap &outputs,
+           const framework::AttributeMap &attrs)
+      : framework::OperatorBase(type, inputs, outputs, attrs) {}
+  void RunImpl(const framework::Scope &scope,
+               const platform::Place &dev_place) const override {
+    PADDLE_THROW(platform::errors::Unimplemented(
+        "Prim operator ge_p should not be excuted directly"));
+  }
+};
+
+class GePrimOpMaker : public framework::OpProtoAndCheckerMaker {
+ public:
+  void Make() override {
+    AddInput("X", "(Tensor), The input tensor of ge_p op.");
+    AddInput("Y", "(Tensor), The input tensor of ge_p op.");
+    AddOutput("Z", "(Tensor), The output tensor of ge_p op.");
+    AddComment(R"DOC(
+Autograd primitive ge_p operator.
+)DOC");
+  }
+};
+
+class GePrimOpShapeInference : public framework::InferShapeBase {
+ public:
+  void operator()(framework::InferShapeContext *ctx) const override {
+    framework::InferShapeVarPtr x_var_ptr = ctx->GetInputVarPtrs("X")[0];
+    framework::InferShapeVarPtr y_var_ptr = ctx->GetInputVarPtrs("Y")[0];
+    framework::InferShapeVarPtr z_var_ptr = ctx->GetOutputVarPtrs("Z")[0];
+
+    framework::VarDesc *x_var = PADDLE_GET(framework::VarDesc *, x_var_ptr);
+    framework::VarDesc *y_var = PADDLE_GET(framework::VarDesc *, y_var_ptr);
+    auto x_shape = x_var->GetShape();
+    auto y_shape = y_var->GetShape();
+    size_t x_rank = x_shape.size();
+    size_t y_rank = y_shape.size();
+    PADDLE_ENFORCE_EQ(x_rank,
+                      y_rank,
+                      platform::errors::InvalidArgument(
+                          "The dimensions of two input tensor should be same, "
+                          "but get %d and %d",
+                          x_rank,
+                          y_rank));
+    for (size_t i = 0; i < x_rank; ++i) {
+      PADDLE_ENFORCE_EQ(
+          x_shape[i],
+          y_shape[i],
+          platform::errors::InvalidArgument(
+              "The shape of two input tensor at dimension %d should be same, "
+              "but get %d and %d",
+              i,
+              x_shape[i],
+              y_shape[i]));
+    }
+
+    PADDLE_GET(framework::VarDesc *, z_var_ptr)->SetShape(x_shape);
+  }
+};
+
+class GePrimOpVarTypeInference : public framework::StaticGraphVarTypeInference {
+ public:
+  void operator()(framework::InferVarTypeContext *ctx) const override {
+    auto x_name = Input(ctx, "X")[0];
+    auto y_name = Input(ctx, "Y")[0];
+    auto z_name = Output(ctx, "Z")[0];
+    auto x_type = GetType(ctx, x_name);
+    auto y_type = GetType(ctx, y_name);
+    auto x_dtype = GetDataType(ctx, x_name);
+    auto y_dtype = GetDataType(ctx, y_name);
+    PADDLE_ENFORCE_EQ(x_type,
+                      y_type,
+                      platform::errors::InvalidArgument(
+                          "The type of two input tensor should be same, "
+                          "but get %d and %d",
+                          x_type,
+                          y_type));
+    PADDLE_ENFORCE_EQ(x_dtype,
+                      y_dtype,
+                      platform::errors::InvalidArgument(
+                          "The datatype of two input tensor should be same, "
+                          "but get %d and %d",
+                          x_dtype,
+                          y_dtype));
+
+    SetType(ctx, z_name, x_type);
+    SetDataType(ctx, z_name, framework::proto::VarType::BOOL);
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle
+
+REGISTER_OPERATOR(ge_p,
+                  paddle::operators::GePrimOp,
+                  paddle::operators::GePrimOpMaker,
+                  paddle::operators::GePrimOpShapeInference,
+                  paddle::operators::GePrimOpVarTypeInference);
diff --git a/paddle/fluid/operators/prim_ops/gt_p_op.cc b/paddle/fluid/operators/prim_ops/gt_p_op.cc
new file mode 100644
index 0000000000000000000000000000000000000000..baacab62d8c3ebfcad51819246d458002f71fd0e
--- /dev/null
+++ b/paddle/fluid/operators/prim_ops/gt_p_op.cc
@@ -0,0 +1,119 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "paddle/fluid/framework/op_registry.h"
+#include "paddle/fluid/framework/operator.h"
+
+namespace paddle {
+namespace operators {
+class GtPrimOp : public framework::OperatorBase {
+ public:
+  GtPrimOp(const std::string &type,
+           const framework::VariableNameMap &inputs,
+           const framework::VariableNameMap &outputs,
+           const framework::AttributeMap &attrs)
+      : framework::OperatorBase(type, inputs, outputs, attrs) {}
+  void RunImpl(const framework::Scope &scope,
+               const platform::Place &dev_place) const override {
+    PADDLE_THROW(platform::errors::Unimplemented(
+        "Prim operator gt_p should not be excuted directly"));
+  }
+};
+
+class GtPrimOpMaker : public framework::OpProtoAndCheckerMaker {
+ public:
+  void Make() override {
+    AddInput("X", "(Tensor), The input tensor of gt_p op.");
+    AddInput("Y", "(Tensor), The input tensor of gt_p op.");
+    AddOutput("Z", "(Tensor), The output tensor of gt_p op.");
+    AddComment(R"DOC(
+Autograd primitive gt_p operator.
+)DOC");
+  }
+};
+
+class GtPrimOpShapeInference : public framework::InferShapeBase {
+ public:
+  void operator()(framework::InferShapeContext *ctx) const override {
+    framework::InferShapeVarPtr x_var_ptr = ctx->GetInputVarPtrs("X")[0];
+    framework::InferShapeVarPtr y_var_ptr = ctx->GetInputVarPtrs("Y")[0];
+    framework::InferShapeVarPtr z_var_ptr = ctx->GetOutputVarPtrs("Z")[0];
+
+    framework::VarDesc *x_var = PADDLE_GET(framework::VarDesc *, x_var_ptr);
+    framework::VarDesc *y_var = PADDLE_GET(framework::VarDesc *, y_var_ptr);
+    auto x_shape = x_var->GetShape();
+    auto y_shape = y_var->GetShape();
+    size_t x_rank = x_shape.size();
+    size_t y_rank = y_shape.size();
+    PADDLE_ENFORCE_EQ(x_rank,
+                      y_rank,
+                      platform::errors::InvalidArgument(
+                          "The dimensions of two input tensor should be same, "
+                          "but get %d and %d",
+                          x_rank,
+                          y_rank));
+    for (size_t i = 0; i < x_rank; ++i) {
+      PADDLE_ENFORCE_EQ(
+          x_shape[i],
+          y_shape[i],
+          platform::errors::InvalidArgument(
+              "The shape of two input tensor at dimension %d should be same, "
+              "but get %d and %d",
+              i,
+              x_shape[i],
+              y_shape[i]));
+    }
+
+    PADDLE_GET(framework::VarDesc *, z_var_ptr)->SetShape(x_shape);
+  }
+};
+
+class GtPrimOpVarTypeInference : public framework::StaticGraphVarTypeInference {
+ public:
+  void operator()(framework::InferVarTypeContext *ctx) const override {
+    auto x_name = Input(ctx, "X")[0];
+    auto y_name = Input(ctx, "Y")[0];
+    auto z_name = Output(ctx, "Z")[0];
+    auto x_type = GetType(ctx, x_name);
+    auto y_type = GetType(ctx, y_name);
+    auto x_dtype = GetDataType(ctx, x_name);
+    auto y_dtype = GetDataType(ctx, y_name);
+    PADDLE_ENFORCE_EQ(x_type,
+                      y_type,
+                      platform::errors::InvalidArgument(
+                          "The type of two input tensor should be same, "
+                          "but get %d and %d",
+                          x_type,
+                          y_type));
+    PADDLE_ENFORCE_EQ(x_dtype,
+                      y_dtype,
+                      platform::errors::InvalidArgument(
+                          "The datatype of two input tensor should be same, "
+                          "but get %d and %d",
+                          x_dtype,
+                          y_dtype));
+
+    SetType(ctx, z_name, x_type);
+    SetDataType(ctx, z_name, framework::proto::VarType::BOOL);
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle
+
+REGISTER_OPERATOR(gt_p,
+                  paddle::operators::GtPrimOp,
+                  paddle::operators::GtPrimOpMaker,
+                  paddle::operators::GtPrimOpShapeInference,
+                  paddle::operators::GtPrimOpVarTypeInference);
diff --git a/paddle/fluid/operators/prim_ops/ne_p_op.cc b/paddle/fluid/operators/prim_ops/ne_p_op.cc
new file mode 100644
index 0000000000000000000000000000000000000000..fac503309de1b7c3f22497a54a424f147c84e0c4
--- /dev/null
+++ b/paddle/fluid/operators/prim_ops/ne_p_op.cc
@@ -0,0 +1,119 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "paddle/fluid/framework/op_registry.h"
+#include "paddle/fluid/framework/operator.h"
+
+namespace paddle {
+namespace operators {
+class NePrimOp : public framework::OperatorBase {
+ public:
+  NePrimOp(const std::string &type,
+           const framework::VariableNameMap &inputs,
+           const framework::VariableNameMap &outputs,
+           const framework::AttributeMap &attrs)
+      : framework::OperatorBase(type, inputs, outputs, attrs) {}
+  void RunImpl(const framework::Scope &scope,
+               const platform::Place &dev_place) const override {
+    PADDLE_THROW(platform::errors::Unimplemented(
+        "Prim operator ne_p should not be excuted directly"));
+  }
+};
+
+class NePrimOpMaker : public framework::OpProtoAndCheckerMaker {
+ public:
+  void Make() override {
+    AddInput("X", "(Tensor), The input tensor of ne_p op.");
+    AddInput("Y", "(Tensor), The input tensor of ne_p op.");
+    AddOutput("Z", "(Tensor), The output tensor of ne_p op.");
+    AddComment(R"DOC(
+Autograd primitive ne_p operator.
+)DOC");
+  }
+};
+
+class NePrimOpShapeInference : public framework::InferShapeBase {
+ public:
+  void operator()(framework::InferShapeContext *ctx) const override {
+    framework::InferShapeVarPtr x_var_ptr = ctx->GetInputVarPtrs("X")[0];
+    framework::InferShapeVarPtr y_var_ptr = ctx->GetInputVarPtrs("Y")[0];
+    framework::InferShapeVarPtr z_var_ptr = ctx->GetOutputVarPtrs("Z")[0];
+
+    framework::VarDesc *x_var = PADDLE_GET(framework::VarDesc *, x_var_ptr);
+    framework::VarDesc *y_var = PADDLE_GET(framework::VarDesc *, y_var_ptr);
+    auto x_shape = x_var->GetShape();
+    auto y_shape = y_var->GetShape();
+    size_t x_rank = x_shape.size();
+    size_t y_rank = y_shape.size();
+    PADDLE_ENFORCE_EQ(x_rank,
+                      y_rank,
+                      platform::errors::InvalidArgument(
+                          "The dimensions of two input tensor should be same, "
+                          "but get %d and %d",
+                          x_rank,
+                          y_rank));
+    for (size_t i = 0; i < x_rank; ++i) {
+      PADDLE_ENFORCE_EQ(
+          x_shape[i],
+          y_shape[i],
+          platform::errors::InvalidArgument(
+              "The shape of two input tensor at dimension %d should be same, "
+              "but get %d and %d",
+              i,
+              x_shape[i],
+              y_shape[i]));
+    }
+
+    PADDLE_GET(framework::VarDesc *, z_var_ptr)->SetShape(x_shape);
+  }
+};
+
+class NePrimOpVarTypeInference : public framework::StaticGraphVarTypeInference {
+ public:
+  void operator()(framework::InferVarTypeContext *ctx) const override {
+    auto x_name = Input(ctx, "X")[0];
+    auto y_name = Input(ctx, "Y")[0];
+    auto z_name = Output(ctx, "Z")[0];
+    auto x_type = GetType(ctx, x_name);
+    auto y_type = GetType(ctx, y_name);
+    auto x_dtype = GetDataType(ctx, x_name);
+    auto y_dtype = GetDataType(ctx, y_name);
+    PADDLE_ENFORCE_EQ(x_type,
+                      y_type,
+                      platform::errors::InvalidArgument(
+                          "The type of two input tensor should be same, "
+                          "but get %d and %d",
+                          x_type,
+                          y_type));
+    PADDLE_ENFORCE_EQ(x_dtype,
+                      y_dtype,
+                      platform::errors::InvalidArgument(
+                          "The datatype of two input tensor should be same, "
+                          "but get %d and %d",
+                          x_dtype,
+                          y_dtype));
+
+    SetType(ctx, z_name, x_type);
+    SetDataType(ctx, z_name, framework::proto::VarType::BOOL);
+  }
+};
+
+}  // namespace operators
+}  // namespace paddle
+
+REGISTER_OPERATOR(ne_p,
+                  paddle::operators::NePrimOp,
+                  paddle::operators::NePrimOpMaker,
+                  paddle::operators::NePrimOpShapeInference,
+                  paddle::operators::NePrimOpVarTypeInference);
diff --git a/paddle/fluid/operators/prim_ops/prim_op_test.cc b/paddle/fluid/operators/prim_ops/prim_op_test.cc
index 44872f9060bfe390cd62028ab58239eb53bc4c0d..153a4575463bc849796354857ad38d750e1420ee 100644
--- a/paddle/fluid/operators/prim_ops/prim_op_test.cc
+++ b/paddle/fluid/operators/prim_ops/prim_op_test.cc
@@ -18,7 +18,7 @@
 
 USE_OP_ITSELF(reshape_p);
 USE_OP_ITSELF(broadcast_p);
-USE_OP_ITSELF(reduce_p);
+USE_OP_ITSELF(reduce_sum_p);
 USE_OP_ITSELF(transpose_p);
 USE_OP_ITSELF(split_p);
 USE_OP_ITSELF(concat_p);
@@ -130,7 +130,7 @@ TEST(PrimOp, broadcast_p) {
   ASSERT_EQ(shapes[2], 5L);
 }
 
-TEST(PrimOp, reduce_p) {
+TEST(PrimOp, reduce_sum_p) {
   ProgramDesc program;
   auto *block = program.MutableBlock(0);
   std::vector<int64_t> shape{3, 4, 5};
@@ -141,7 +141,7 @@ TEST(PrimOp, reduce_p) {
 
   NewVar(block, x0, shape);
   AppendOp(block,
-           "reduce_p",
+           "reduce_sum_p",
            {{"X", {x0}}},
            {{"Y", {x1}}},
            {{"axis", std::vector<int64_t>{0, 2}}, {"keepdim", false}});
@@ -151,7 +151,7 @@ TEST(PrimOp, reduce_p) {
   ASSERT_EQ(shapes.size(), 1UL);
   ASSERT_EQ(shapes[0], 4L);
   AppendOp(block,
-           "reduce_p",
+           "reduce_sum_p",
            {{"X", {x0}}},
            {{"Y", {x2}}},
            {{"axis", std::vector<int64_t>{0, 2}}, {"keepdim", true}});
diff --git a/paddle/fluid/operators/prim_ops/reduce_p_op.cc b/paddle/fluid/operators/prim_ops/reduce_sum_p_op.cc
similarity index 74%
rename from paddle/fluid/operators/prim_ops/reduce_p_op.cc
rename to paddle/fluid/operators/prim_ops/reduce_sum_p_op.cc
index 3c18ce46f9d937969d96518b2bc6e7efb9e5505f..b31b4934706a93d5abe0a3c5d16b2b2b18ddda44 100644
--- a/paddle/fluid/operators/prim_ops/reduce_p_op.cc
+++ b/paddle/fluid/operators/prim_ops/reduce_sum_p_op.cc
@@ -24,25 +24,25 @@ class VarDesc;
 
 namespace paddle {
 namespace operators {
-class ReducePrimOp : public framework::OperatorBase {
+class ReduceSumPrimOp : public framework::OperatorBase {
  public:
-  ReducePrimOp(const std::string &type,
-               const framework::VariableNameMap &inputs,
-               const framework::VariableNameMap &outputs,
-               const framework::AttributeMap &attrs)
+  ReduceSumPrimOp(const std::string &type,
+                  const framework::VariableNameMap &inputs,
+                  const framework::VariableNameMap &outputs,
+                  const framework::AttributeMap &attrs)
       : framework::OperatorBase(type, inputs, outputs, attrs) {}
   void RunImpl(const framework::Scope &scope,
                const platform::Place &dev_place) const override {
     PADDLE_THROW(platform::errors::Unimplemented(
-        "Prim operator reduce_p should not be excuted directly"));
+        "Prim operator reduce_sum_p should not be excuted directly"));
   }
 };
 
-class ReducePrimOpMaker : public framework::OpProtoAndCheckerMaker {
+class ReduceSumPrimOpMaker : public framework::OpProtoAndCheckerMaker {
  public:
   void Make() override {
-    AddInput("X", "(Tensor), The input tensor of reduce_p op.");
-    AddOutput("Y", "(Tensor), The output tensor of reduce_p op.");
+    AddInput("X", "(Tensor), The input tensor of reduce_sum_p op.");
+    AddOutput("Y", "(Tensor), The output tensor of reduce_sum_p op.");
     AddAttr<std::vector<int64_t>>(
         "axis",
         "(std::vector<int64_t>) The axis along which to reduce on. Must be in "
@@ -53,12 +53,12 @@ class ReducePrimOpMaker : public framework::OpProtoAndCheckerMaker {
                   "If true, retain the reduced axis with length 1.")
         .SetDefault(false);
     AddComment(R"DOC(
-Autograd primitive reduce_p operator.
+Autograd primitive reduce_sum_p operator.
 )DOC");
   }
 };
 
-class ReducePrimOpShapeInference : public framework::InferShapeBase {
+class ReduceSumPrimOpShapeInference : public framework::InferShapeBase {
  public:
   void operator()(framework::InferShapeContext *ctx) const override {
     framework::InferShapeVarPtr x_var_ptr = ctx->GetInputVarPtrs("X")[0];
@@ -87,7 +87,7 @@ class ReducePrimOpShapeInference : public framework::InferShapeBase {
   }
 };
 
-class ReducePrimOpVarTypeInference
+class ReduceSumPrimOpVarTypeInference
     : public framework::StaticGraphVarTypeInference {
  public:
   void operator()(framework::InferVarTypeContext *ctx) const override {
@@ -101,8 +101,8 @@ class ReducePrimOpVarTypeInference
 }  // namespace operators
 }  // namespace paddle
 
-REGISTER_OPERATOR(reduce_p,
-                  paddle::operators::ReducePrimOp,
-                  paddle::operators::ReducePrimOpMaker,
-                  paddle::operators::ReducePrimOpShapeInference,
-                  paddle::operators::ReducePrimOpVarTypeInference);
+REGISTER_OPERATOR(reduce_sum_p,
+                  paddle::operators::ReduceSumPrimOp,
+                  paddle::operators::ReduceSumPrimOpMaker,
+                  paddle::operators::ReduceSumPrimOpShapeInference,
+                  paddle::operators::ReduceSumPrimOpVarTypeInference);
diff --git a/python/paddle/distributed/auto_parallel/operators/__init__.py b/python/paddle/distributed/auto_parallel/operators/__init__.py
index 295e3557df27d355c8aa1b86f742137b3d6c1d7d..02b5138be21467e38d6f3843c3f9d0c85e3f570c 100644
--- a/python/paddle/distributed/auto_parallel/operators/__init__.py
+++ b/python/paddle/distributed/auto_parallel/operators/__init__.py
@@ -32,4 +32,4 @@ from . import dist_pnorm
 from . import dist_slice
 from . import dist_fused_feedforward
 from . import dist_fused_attention
-from . import dist_reduce_p
+from . import dist_reduce_sum_p
diff --git a/python/paddle/distributed/auto_parallel/operators/dist_reduce_p.py b/python/paddle/distributed/auto_parallel/operators/dist_reduce_sum_p.py
similarity index 92%
rename from python/paddle/distributed/auto_parallel/operators/dist_reduce_p.py
rename to python/paddle/distributed/auto_parallel/operators/dist_reduce_sum_p.py
index bdd105ef64c30313bafdf326aba93287662507a2..6b53b2eed7ad00eb9a351a290027572dedae36e0 100644
--- a/python/paddle/distributed/auto_parallel/operators/dist_reduce_p.py
+++ b/python/paddle/distributed/auto_parallel/operators/dist_reduce_sum_p.py
@@ -33,21 +33,21 @@ from ..process_group import new_process_group
 from ..utils import _get_comm_group, _get_corresponding_rank
 
 
-class DistributedReducePrimtive(DistributedOperatorImplContainer):
+class DistributedReduceSumPrimtive(DistributedOperatorImplContainer):
 
     def __init__(self, op_type):
-        super(DistributedReducePrimtive, self).__init__(op_type)
+        super(DistributedReduceSumPrimtive, self).__init__(op_type)
 
 
 register_distributed_operator_impl_container(
-    DistributedReducePrimtive("reduce_p"))
+    DistributedReduceSumPrimtive("reduce_sum_p"))
 
 
-# Batch Dimension Reduce Primitive
-class DistributedReducePrimtiveImpl0(DistributedOperatorImpl):
+# Batch Dimension ReduceSum Primitive
+class DistributedReduceSumPrimtiveImpl0(DistributedOperatorImpl):
 
     def __init__(self, name):
-        super(DistributedReducePrimtiveImpl0, self).__init__(name)
+        super(DistributedReduceSumPrimtiveImpl0, self).__init__(name)
         self._forward_implemented = True
         self._backward_implemented = True
 
@@ -149,4 +149,5 @@ class DistributedReducePrimtiveImpl0(DistributedOperatorImpl):
 
 
 register_distributed_operator_impl(
-    "reduce_p", DistributedReducePrimtiveImpl0("batch_dimension_reduce_p"))
+    "reduce_sum_p",
+    DistributedReduceSumPrimtiveImpl0("batch_dimension_reduce_sum_p"))
diff --git a/python/paddle/fluid/tests/unittests/auto_parallel/test_prim_dist_op.py b/python/paddle/fluid/tests/unittests/auto_parallel/test_prim_dist_op.py
index 67894f6dd93df9b86dfa4c56a833b8faa53dd830..69f92012c17efbb825459218664dee01e92e059a 100644
--- a/python/paddle/fluid/tests/unittests/auto_parallel/test_prim_dist_op.py
+++ b/python/paddle/fluid/tests/unittests/auto_parallel/test_prim_dist_op.py
@@ -78,7 +78,7 @@ class TestPrimDistOp(unittest.TestCase):
                                        outputs={'Z': self.w_grad},
                                        attrs=self.attrs)
 
-        op = self.layer_help.append_op(type="reduce_p",
+        op = self.layer_help.append_op(type="reduce_sum_p",
                                        inputs={'X': self.tmp2},
                                        outputs={'Y': self.batch_reduced},
                                        attrs={"axis": [0]})
diff --git a/python/paddle/fluid/tests/unittests/autograd/test_jvp_and_transpose.py b/python/paddle/fluid/tests/unittests/autograd/test_jvp_and_transpose.py
index 51104223f954dbe5adfc0fe750e294026e6809e2..c8e1b3965228d71bbcf4a8942f7c6adfbb672f7c 100644
--- a/python/paddle/fluid/tests/unittests/autograd/test_jvp_and_transpose.py
+++ b/python/paddle/fluid/tests/unittests/autograd/test_jvp_and_transpose.py
@@ -400,6 +400,75 @@ class TestErfPJVPAndTranspose(TestAddPJVPAndTranspose):
         ]
 
 
+class TestAbsPJVPAndTranspose(TestAddPJVPAndTranspose):
+
+    def init_data(self):
+        # Set prim op
+        self.op_type = 'abs_p'
+        X = paddle.static.data(name='X', shape=[5, 6], dtype='int64')
+        self.prim_input = {
+            'X': X,
+        }
+        self.prim_output = {
+            'Y':
+            self.layer_help.create_variable_for_type_inference(dtype=X.dtype)
+        }
+        self.prim_attrs = {}
+
+        # Set JVP
+        X_DOT = paddle.static.data(name='X_DOT', shape=[5, 6], dtype='int64')
+        self.jvp_args = (X_DOT, )
+        self.jvp_out_shape_map = {0: self.prim_output['Y']}
+
+        self.all_ops = [
+            # prim op:
+            'abs_p',
+            # jvp op:
+            'select_p',
+            'ge_p',
+            'fill_constant_p',
+            'fill_constant_p',
+            'sub_p',
+            # transpose op:
+        ]
+
+
+class TestCastPJVPAndTranspose(TestAddPJVPAndTranspose):
+
+    def init_data(self):
+        # Set prim op
+        self.op_type = 'cast_p'
+        X = paddle.static.data(name='X', shape=[5, 6], dtype='int64')
+        self.prim_input = {
+            'X': X,
+        }
+        self.prim_output = {
+            'Y':
+            self.layer_help.create_variable_for_type_inference(dtype=X.dtype)
+        }
+        self.prim_attrs = {'dtype': paddle.float64}
+
+        # Set JVP
+        X_DOT = paddle.static.data(name='X_DOT', shape=[5, 6], dtype='int64')
+        self.jvp_args = (X_DOT, )
+        self.jvp_out_shape_map = {0: self.prim_output['Y']}
+
+        # Set transpose
+        check_dot = lambda v: True
+        Y_BAR = paddle.static.data(name='Y_BAR', shape=[5, 6], dtype='float')
+        self.transpose_args = (check_dot, Y_BAR)
+        self.transpose_out_shape_map = {0: X}
+
+        self.all_ops = [
+            # prim op:
+            'cast_p',
+            # jvp op:
+            'cast_p',
+            # transpose op:
+            'cast_p'
+        ]
+
+
 class TestLogPJVPAndTranspose(TestAddPJVPAndTranspose):
 
     def init_data(self):
@@ -503,7 +572,7 @@ class TestBroadcastPJVPAndTranspose(TestAddPJVPAndTranspose):
             # jvp op:
             'broadcast_p',
             # transpose op:
-            'reduce_p',
+            'reduce_sum_p',
             'reshape_p'
         ]
 
@@ -650,11 +719,11 @@ class TestConcatPJVPAndTranspose(TestAddPJVPAndTranspose):
         ]
 
 
-class TestReducePJVPAndTranspose(TestAddPJVPAndTranspose):
+class TestReduceSumPJVPAndTranspose(TestAddPJVPAndTranspose):
 
     def init_data(self):
         # Set prim op
-        self.op_type = 'reduce_p'
+        self.op_type = 'reduce_sum_p'
         X = paddle.static.data(name='X', shape=[2, 3, 4, 5], dtype='float64')
         self.prim_input = {'X': X}
         self.prim_output = {
@@ -682,9 +751,9 @@ class TestReducePJVPAndTranspose(TestAddPJVPAndTranspose):
 
         self.all_ops = [
             # prim op:
-            'reduce_p',
+            'reduce_sum_p',
             # jvp op:
-            'reduce_p',
+            'reduce_sum_p',
             # transpose op:
             'reshape_p',
             'broadcast_p',
@@ -978,6 +1047,96 @@ class TestEqPJVPAndTranspose(TestAddPJVPAndTranspose):
         ]
 
 
+class TestGtPJVPAndTranspose(TestAddPJVPAndTranspose):
+
+    def init_data(self):
+        # Set prim op
+        self.op_type = 'gt_p'
+        X = paddle.static.data(name='X', shape=[4, 5], dtype='float64')
+        Y = paddle.static.data(name='Y', shape=[4, 5], dtype='float64')
+
+        self.prim_input = {'X': X, 'Y': Y}
+        self.prim_output = {
+            'Z':
+            self.layer_help.create_variable_for_type_inference(dtype=X.dtype)
+        }
+        self.prim_attrs = {}
+
+        # Set JVP
+        X_DOT = paddle.static.data(name='X_DOT', shape=[4, 5], dtype='float64')
+        Y_DOT = paddle.static.data(name='Y_DOT', shape=[4, 5], dtype='float64')
+        self.jvp_args = (X_DOT, Y_DOT)
+        self.jvp_out_shape_map = {0: self.prim_output['Z']}
+
+        self.all_ops = [
+            # prim op:
+            'gt_p',
+            # jvp op:
+            'fill_constant_p',
+            # transpose op:
+        ]
+
+
+class TestGePJVPAndTranspose(TestAddPJVPAndTranspose):
+
+    def init_data(self):
+        # Set prim op
+        self.op_type = 'ge_p'
+        X = paddle.static.data(name='X', shape=[4, 5], dtype='float64')
+        Y = paddle.static.data(name='Y', shape=[4, 5], dtype='float64')
+
+        self.prim_input = {'X': X, 'Y': Y}
+        self.prim_output = {
+            'Z':
+            self.layer_help.create_variable_for_type_inference(dtype=X.dtype)
+        }
+        self.prim_attrs = {}
+
+        # Set JVP
+        X_DOT = paddle.static.data(name='X_DOT', shape=[4, 5], dtype='float64')
+        Y_DOT = paddle.static.data(name='Y_DOT', shape=[4, 5], dtype='float64')
+        self.jvp_args = (X_DOT, Y_DOT)
+        self.jvp_out_shape_map = {0: self.prim_output['Z']}
+
+        self.all_ops = [
+            # prim op:
+            'ge_p',
+            # jvp op:
+            'fill_constant_p',
+            # transpose op:
+        ]
+
+
+class TestNePJVPAndTranspose(TestAddPJVPAndTranspose):
+
+    def init_data(self):
+        # Set prim op
+        self.op_type = 'ne_p'
+        X = paddle.static.data(name='X', shape=[4, 5], dtype='float64')
+        Y = paddle.static.data(name='Y', shape=[4, 5], dtype='float64')
+
+        self.prim_input = {'X': X, 'Y': Y}
+        self.prim_output = {
+            'Z':
+            self.layer_help.create_variable_for_type_inference(dtype=X.dtype)
+        }
+        self.prim_attrs = {}
+
+        # Set JVP
+        X_DOT = paddle.static.data(name='X_DOT', shape=[4, 5], dtype='float64')
+        Y_DOT = paddle.static.data(name='Y_DOT', shape=[4, 5], dtype='float64')
+        self.jvp_args = (X_DOT, Y_DOT)
+        self.jvp_out_shape_map = {0: self.prim_output['Z']}
+
+        self.all_ops = [
+            # prim op:
+            'ne_p',
+            # jvp op:
+            'fill_constant_p',
+            # transpose op:
+        ]
+
+
 class TestPowPJVPAndTranspose(TestAddPJVPAndTranspose):
 
     def init_data(self):
diff --git a/python/paddle/fluid/tests/unittests/autograd/test_orig2prim.py b/python/paddle/fluid/tests/unittests/autograd/test_orig2prim.py
index 5693520ef0ace5f506f84131efc3992b4bc60ad8..e1d5ee11a13ace711db583a1772d5d5d5b94e76a 100644
--- a/python/paddle/fluid/tests/unittests/autograd/test_orig2prim.py
+++ b/python/paddle/fluid/tests/unittests/autograd/test_orig2prim.py
@@ -110,6 +110,26 @@ class TestElementWiseMulOrig2Prim(TestElementWiseAddOrig2Prim):
         self.out_map = {0: self.output['Out']}
 
 
+class TestElementWiseDivOrig2Prim(TestElementWiseAddOrig2Prim):
+
+    def init_data(self):
+        self.op_type = 'elementwise_div'
+        X = paddle.static.data(name='X', shape=[8, 8], dtype='float')
+        Y = paddle.static.data(name='Y', shape=[8, 8], dtype='float')
+
+        self.input = {'X': X, 'Y': Y}
+        self.output = {
+            'Out':
+            self.layer_help.create_variable_for_type_inference(dtype=X.dtype)
+        }
+        self.attrs = {}
+
+        self.orig2prim_args = (X, Y)
+        self.all_ops = ['elementwise_div', 'div_p']
+        # { prim_op_output_index: orig_op_output_var }
+        self.out_map = {0: self.output['Out']}
+
+
 class TestMatmulV2Orig2Prim(TestElementWiseAddOrig2Prim):
 
     def init_data(self):
@@ -229,6 +249,26 @@ class TestErfOrig2Prim(TestElementWiseAddOrig2Prim):
         self.out_map = {0: self.output['Out']}
 
 
+class TestAbsOrig2Prim(TestElementWiseAddOrig2Prim):
+
+    def init_data(self):
+        self.op_type = 'abs'
+        X = paddle.static.data(name='X', shape=[3, 4], dtype='float')
+
+        self.input = {
+            'X': X,
+        }
+        self.output = {
+            'Out':
+            self.layer_help.create_variable_for_type_inference(dtype=X.dtype)
+        }
+        self.attrs = {}
+
+        self.orig2prim_args = (X, )
+        self.all_ops = ['abs', 'abs_p']
+        self.out_map = {0: self.output['Out']}
+
+
 class TestLogOrig2Prim(TestElementWiseAddOrig2Prim):
 
     def init_data(self):
@@ -422,7 +462,9 @@ class TestPNormOrig2Prim1(TestElementWiseAddOrig2Prim):
         }
 
         self.orig2prim_args = (X, )
-        self.all_ops = ['p_norm', 'reshape_p', 'sqrt_p', 'reduce_p', 'mul_p']
+        self.all_ops = [
+            'p_norm', 'reshape_p', 'sqrt_p', 'reduce_sum_p', 'mul_p'
+        ]
         self.out_map = {0: self.output['Out']}
 
 
@@ -445,7 +487,9 @@ class TestPNormOrig2Prim2(TestElementWiseAddOrig2Prim):
         }
 
         self.orig2prim_args = (X, )
-        self.all_ops = ['p_norm', 'reshape_p', 'sqrt_p', 'reduce_p', 'mul_p']
+        self.all_ops = [
+            'p_norm', 'reshape_p', 'sqrt_p', 'reduce_sum_p', 'mul_p'
+        ]
         self.out_map = {0: self.output['Out']}
 
 
@@ -580,6 +624,63 @@ class TestEqualOrig2Prim(TestElementWiseAddOrig2Prim):
         self.out_map = {0: self.output['Out']}
 
 
+class TestNeOrig2Prim(TestElementWiseAddOrig2Prim):
+
+    def init_data(self):
+        self.op_type = 'not_equal'
+        X = paddle.static.data(name='X', shape=[5, 8], dtype='float')
+        Y = paddle.static.data(name='Y', shape=[5, 8], dtype='float')
+
+        self.input = {'X': X, 'Y': Y}
+        self.output = {
+            'Out':
+            self.layer_help.create_variable_for_type_inference(dtype='bool')
+        }
+        self.attrs = {}
+        self.orig2prim_args = (X, Y)
+        self.all_ops = ['not_equal', 'ne_p']
+        # { prim_op_output_index: orig_op_output_var }
+        self.out_map = {0: self.output['Out']}
+
+
+class TestGtOrig2Prim(TestElementWiseAddOrig2Prim):
+
+    def init_data(self):
+        self.op_type = 'greater_than'
+        X = paddle.static.data(name='X', shape=[5, 8], dtype='float')
+        Y = paddle.static.data(name='Y', shape=[5, 8], dtype='float')
+
+        self.input = {'X': X, 'Y': Y}
+        self.output = {
+            'Out':
+            self.layer_help.create_variable_for_type_inference(dtype='bool')
+        }
+        self.attrs = {}
+        self.orig2prim_args = (X, Y)
+        self.all_ops = ['greater_than', 'gt_p']
+        # { prim_op_output_index: orig_op_output_var }
+        self.out_map = {0: self.output['Out']}
+
+
+class TestGeOrig2Prim(TestElementWiseAddOrig2Prim):
+
+    def init_data(self):
+        self.op_type = 'greater_equal'
+        X = paddle.static.data(name='X', shape=[5, 8], dtype='float')
+        Y = paddle.static.data(name='Y', shape=[5, 8], dtype='float')
+
+        self.input = {'X': X, 'Y': Y}
+        self.output = {
+            'Out':
+            self.layer_help.create_variable_for_type_inference(dtype='bool')
+        }
+        self.attrs = {}
+        self.orig2prim_args = (X, Y)
+        self.all_ops = ['greater_equal', 'ge_p']
+        # { prim_op_output_index: orig_op_output_var }
+        self.out_map = {0: self.output['Out']}
+
+
 class TestPowOrig2Prim(TestElementWiseAddOrig2Prim):
 
     def init_data(self):
@@ -665,5 +766,118 @@ class TestGeluApproximateOrig2Prim(TestElementWiseAddOrig2Prim):
         self.out_map = {0: self.output['Out']}
 
 
+class TestReduceSumOrig2Prim(TestElementWiseAddOrig2Prim):
+
+    def init_data(self):
+        self.op_type = 'reduce_sum'
+        X = paddle.static.data(name='X', shape=[5, 8], dtype='float')
+
+        self.input = {'X': X}
+        self.output = {
+            'Out':
+            self.layer_help.create_variable_for_type_inference(dtype=X.dtype)
+        }
+        self.attrs = {'axis': [0, 1], 'keep_dim': False}
+
+        self.orig2prim_args = (X, )
+        self.all_ops = ['reduce_sum', 'reduce_sum_p']
+        # { prim_op_output_index: orig_op_output_var }
+        self.out_map = {0: self.output['Out']}
+
+
+class TestReduceMeanOrig2Prim(TestElementWiseAddOrig2Prim):
+
+    def init_data(self):
+        self.op_type = 'reduce_mean'
+        X = paddle.static.data(name='X', shape=[5, 8], dtype='float')
+
+        self.input = {'X': X}
+        self.output = {
+            'Out':
+            self.layer_help.create_variable_for_type_inference(dtype=X.dtype)
+        }
+        self.attrs = {'axis': [0, 1], 'keep_dim': False}
+
+        self.orig2prim_args = (X, )
+        self.all_ops = [
+            'reduce_mean', 'reduce_sum_p', 'fill_constant_p', 'div_p'
+        ]
+        # { prim_op_output_index: orig_op_output_var }
+        self.out_map = {0: self.output['Out']}
+
+
+class TestSizeOrig2Prim(TestElementWiseAddOrig2Prim):
+
+    def init_data(self):
+        self.op_type = 'size'
+        X = paddle.static.data(name='X', shape=[5, 8], dtype='float')
+
+        self.input = {'Input': X}
+        self.output = {
+            'Out':
+            self.layer_help.create_variable_for_type_inference(
+                dtype=paddle.int64)
+        }
+        self.attrs = {}
+        self.orig2prim_args = (X, )
+        self.all_ops = ['size', 'fill_constant_p']
+        # { prim_op_output_index: orig_op_output_var }
+        self.out_map = {0: self.output['Out']}
+
+
+class TestCastOrig2Prim(TestElementWiseAddOrig2Prim):
+
+    def init_data(self):
+        self.op_type = 'cast'
+        X = paddle.static.data(name='X', shape=[5, 8], dtype='float')
+
+        self.input = {'X': X}
+        self.output = {
+            'Out':
+            self.layer_help.create_variable_for_type_inference(dtype=X.dtype)
+        }
+        self.attrs = {'in_dtype': X.dtype, 'out_dtype': paddle.float64}
+        self.orig2prim_args = (X, )
+        self.all_ops = ['cast', 'cast_p']
+        # { prim_op_output_index: orig_op_output_var }
+        self.out_map = {0: self.output['Out']}
+
+
+class TestPowScalarOrig2Prim(TestElementWiseAddOrig2Prim):
+
+    def init_data(self):
+        self.op_type = 'pow'
+        X = paddle.static.data(name='X', shape=[5, 8], dtype='float')
+
+        self.input = {'X': X}
+        self.output = {
+            'Out':
+            self.layer_help.create_variable_for_type_inference(dtype=X.dtype)
+        }
+        self.attrs = {'factor': 2.}
+        self.orig2prim_args = (None, X)
+        self.all_ops = ['pow', 'pow_p', 'fill_constant_p']
+        # { prim_op_output_index: orig_op_output_var }
+        self.out_map = {0: self.output['Out']}
+
+
+class TestSquareOrig2Prim(TestElementWiseAddOrig2Prim):
+
+    def init_data(self):
+        self.op_type = 'square'
+        X = paddle.static.data(name='X', shape=[5, 8], dtype='float')
+
+        self.input = {'X': X}
+        self.output = {
+            'Out':
+            self.layer_help.create_variable_for_type_inference(dtype=X.dtype)
+        }
+        self.attrs = {}
+        self.orig2prim_args = (X, )
+        self.all_ops = ['square', 'pow_p', 'fill_constant_p']
+        # { prim_op_output_index: orig_op_output_var }
+        self.out_map = {0: self.output['Out']}
+
+
 if __name__ == '__main__':
     unittest.main()
diff --git a/python/paddle/fluid/tests/unittests/autograd/test_prim2orig.py b/python/paddle/fluid/tests/unittests/autograd/test_prim2orig.py
index 4d0f150073604f94faa5ad2f4e0f455c2d2d2d47..a89b91bdd2b64a7e28b7782a003992eb2b2e16f9 100644
--- a/python/paddle/fluid/tests/unittests/autograd/test_prim2orig.py
+++ b/python/paddle/fluid/tests/unittests/autograd/test_prim2orig.py
@@ -244,6 +244,26 @@ class TestErfPPrim2Orig(TestAddPPrim2Orig):
         self.out_map = {self.output['Y']: 0}
 
 
+class TestAbsPPrim2Orig(TestAddPPrim2Orig):
+
+    def init_data(self):
+        self.op_type = 'abs_p'
+        X = paddle.static.data(name='X', shape=[7, 8], dtype='float64')
+
+        self.input = {
+            'X': X,
+        }
+        self.output = {
+            'Y':
+            self.layer_help.create_variable_for_type_inference(dtype=X.dtype)
+        }
+        self.attrs = {}
+
+        self.prim2orig_args = (X, )
+        self.all_ops = ['abs_p', 'abs']
+        self.out_map = {self.output['Y']: 0}
+
+
 class TestLogPPrim2Orig(TestAddPPrim2Orig):
 
     def init_data(self):
@@ -375,7 +395,7 @@ class TestConcatPPrim2Orig(TestAddPPrim2Orig):
 class TestReducePPrim2Orig(TestAddPPrim2Orig):
 
     def init_data(self):
-        self.op_type = 'reduce_p'
+        self.op_type = 'reduce_sum_p'
         X = paddle.static.data(name='X', shape=[3, 9, 5], dtype='float64')
 
         self.input = {'X': X}
@@ -386,7 +406,7 @@ class TestReducePPrim2Orig(TestAddPPrim2Orig):
         self.attrs = {'axis': [1], 'keepdim': True}
 
         self.prim2orig_args = (X, )
-        self.all_ops = ['reduce_p', 'reduce_sum']
+        self.all_ops = ['reduce_sum_p', 'reduce_sum']
         self.out_map = {self.output['Y']: 0}
 
 
@@ -555,6 +575,63 @@ class TestEqPPrim2Orig(TestAddPPrim2Orig):
         self.out_map = {self.output['Z']: 0}
 
 
+class TestNePPrim2Orig(TestAddPPrim2Orig):
+
+    def init_data(self):
+        self.op_type = 'ne_p'
+        X = paddle.static.data(name='X', shape=[7, 8], dtype='float64')
+        Y = paddle.static.data(name='Y', shape=[7, 8], dtype='float64')
+
+        self.input = {'X': X, 'Y': Y}
+        self.output = {
+            'Z':
+            self.layer_help.create_variable_for_type_inference(dtype='bool')
+        }
+        self.attrs = {}
+
+        self.prim2orig_args = (X, Y)
+        self.all_ops = ['ne_p', 'not_equal']
+        self.out_map = {self.output['Z']: 0}
+
+
+class TestGtPPrim2Orig(TestAddPPrim2Orig):
+
+    def init_data(self):
+        self.op_type = 'gt_p'
+        X = paddle.static.data(name='X', shape=[7, 8], dtype='float64')
+        Y = paddle.static.data(name='Y', shape=[7, 8], dtype='float64')
+
+        self.input = {'X': X, 'Y': Y}
+        self.output = {
+            'Z':
+            self.layer_help.create_variable_for_type_inference(dtype='bool')
+        }
+        self.attrs = {}
+
+        self.prim2orig_args = (X, Y)
+        self.all_ops = ['gt_p', 'greater_than']
+        self.out_map = {self.output['Z']: 0}
+
+
+class TestGePPrim2Orig(TestAddPPrim2Orig):
+
+    def init_data(self):
+        self.op_type = 'ge_p'
+        X = paddle.static.data(name='X', shape=[7, 8], dtype='float64')
+        Y = paddle.static.data(name='Y', shape=[7, 8], dtype='float64')
+
+        self.input = {'X': X, 'Y': Y}
+        self.output = {
+            'Z':
+            self.layer_help.create_variable_for_type_inference(dtype='bool')
+        }
+        self.attrs = {}
+
+        self.prim2orig_args = (X, Y)
+        self.all_ops = ['ge_p', 'greater_equal']
+        self.out_map = {self.output['Z']: 0}
+
+
 class TestPowPPrim2Orig(TestAddPPrim2Orig):
 
     def init_data(self):
@@ -593,5 +670,25 @@ class TestMaxPPrim2Orig(TestAddPPrim2Orig):
         self.out_map = {self.output['Z']: 0}
 
 
+class TestCastPPrim2Orig(TestAddPPrim2Orig):
+
+    def init_data(self):
+        self.op_type = 'cast_p'
+        X = paddle.static.data(name='X', shape=[7, 8], dtype='float64')
+
+        self.input = {
+            'X': X,
+        }
+        self.output = {
+            'Y':
+            self.layer_help.create_variable_for_type_inference(dtype=X.dtype)
+        }
+        self.attrs = {'dtype': paddle.int64}
+
+        self.prim2orig_args = (X, )
+        self.all_ops = ['cast_p', 'cast']
+        self.out_map = {self.output['Y']: 0}
+
+
 if __name__ == '__main__':
     unittest.main()
diff --git a/python/paddle/fluid/tests/unittests/autograd/test_primapi.py b/python/paddle/fluid/tests/unittests/autograd/test_primapi.py
index 7edbb6ef77f26e7039b6da1a93969159ea00610f..bdc54563fc8d2a127670106af005ed00a1b9abf3 100644
--- a/python/paddle/fluid/tests/unittests/autograd/test_primapi.py
+++ b/python/paddle/fluid/tests/unittests/autograd/test_primapi.py
@@ -150,6 +150,8 @@ class TestWithoutProgramGuard(unittest.TestCase):
      (np.random.rand(3, 3), np.random.rand(3, 3)),
      (np.random.rand(3, 3), np.random.rand(3, 3)), 'float64'),
     ('log', paddle.log, (np.random.rand(3, 4), ), None, 'float32'),
+    ('abs', paddle.abs, (np.random.uniform(-10, 10,
+                                           (10, 10)), ), None, 'float32'),
 ))
 # paddle.where, paddle.pow, paddle.maximum has no double grad definition,
 # can not compute forward grad use double trick
@@ -255,6 +257,8 @@ where_wrap = lambda x, y: paddle.where(paddle.eye(3, 4) == 1, x, y)
          (np.random.rand(2, 3), np.random.rand(3, 2)), None, 'float32'),
         ('multiply', paddle.multiply,
          (np.random.rand(2, 3), np.random.rand(2, 3)), None, 'float64'),
+        ('div', paddle.divide,
+         (np.random.rand(2, 3), np.random.rand(2, 3)), None, 'float64'),
         ('add', paddle.add,
          (np.random.rand(2, 3), np.random.rand(2, 3)), None, 'float32'),
         ('input_not_sequence', paddle.tanh,
@@ -283,7 +287,36 @@ where_wrap = lambda x, y: paddle.where(paddle.eye(3, 4) == 1, x, y)
          (np.random.rand(200, 189), ), None, 'float32'),
         ('gelu_approximate', lambda x: paddle.nn.functional.gelu(x, True),
          (np.random.rand(200, 189), ), None, 'float32'),
-    ))
+        ('sum', paddle.sum, (np.random.rand(200, 345), ), None, 'float32'),
+        ('sum_with_axis', lambda x: paddle.sum(x, axis=1),
+         (np.random.rand(200, 345), ), None, 'float32'),
+        ('sum_with_keepdim', lambda x: paddle.sum(x, keepdim=True),
+         (np.random.rand(200, 345), ), None, 'float32'),
+        ('mean', paddle.mean, (np.random.rand(200, 345), ), None, 'float32'),
+        ('mean_with_axis', lambda x: paddle.mean(x, axis=1),
+         (np.random.rand(200, 345), ), None, 'float32'),
+        ('mean_with_keepdim', lambda x: paddle.mean(x, keepdim=True),
+         (np.random.rand(200, 345), ), None, 'float32'),
+        ('mean_with_axis_keepdim',
+         lambda x: paddle.mean(x, axis=0, keepdim=True),
+         (np.random.rand(200, 345), ), None, 'float32'),
+        ('abs', paddle.abs, (np.random.uniform(-10, 10,
+                                               (200, 345)), ), None, 'float32'),
+        ('cast_float', lambda x: paddle.cast(x, paddle.float64),
+         (np.random.rand(10, 20), ), None, 'float32'),
+        ('cast_int', lambda x: paddle.cast(x, paddle.int32),
+         (np.random.rand(10, 20), ), None, 'float32'),
+        ('square', paddle.square, (np.random.rand(100), ), None, 'float32'),
+        ('pow_scalar', lambda x: paddle.pow(x, 2),
+         (np.random.rand(20, 30), ), None, 'float32'),
+        ('var', paddle.var, (np.random.rand(200, 324), ), None, 'float32'),
+        ('var_with_axis', lambda x: paddle.var(x, axis=1),
+         (np.random.rand(10, 20, 30), ), None, 'float32'),
+        ('var_without_unbiased',
+         lambda x: paddle.var(x, axis=1, unbiased=False),
+         (np.random.rand(10, 20, 30), ), None, 'float32'),
+        ('var_with_keepdim', lambda x: paddle.var(x, axis=1, keepdim=True),
+         (np.random.rand(10, 20, 30), ), None, 'float32')))
 class TestGrad(unittest.TestCase):
 
     def setUp(self):
diff --git a/python/paddle/fluid/tests/unittests/autograd/test_primops.py b/python/paddle/fluid/tests/unittests/autograd/test_primops.py
index 25a3d9bce235a00e9ef73a72db567688606ffb48..35291432f6e8fb8da3cf070422139680066200f8 100644
--- a/python/paddle/fluid/tests/unittests/autograd/test_primops.py
+++ b/python/paddle/fluid/tests/unittests/autograd/test_primops.py
@@ -42,7 +42,11 @@ paddle.enable_static()
         ('cos', primops.cos, randn(2, 3), {}, (2, 3), 'float64'),
         ('exp', primops.exp, randn(2, 3), {}, (2, 3), 'float64'),
         ('erf', primops.erf, randn(2, 3), {}, (2, 3), 'float64'),
+        ('abs', primops.abs, randn(2, 3), {}, (2, 3), 'float64'),
         ('log', primops.log, randn(2, 3), {}, (2, 3), 'float64'),
+        ('cast', primops.cast, randn(2, 3), {
+            'dtype': paddle.int64
+        }, (2, 3), 'int64'),
         ('reshape', primops.reshape, randn(2, 3), {
             'shape': (3, 2)
         }, (3, 2), 'float64'),
@@ -58,10 +62,10 @@ paddle.enable_static()
         ('concat_axis1', primops.concat, ((randn(2, 3), randn(2, 3)), ), {
             'axis': 1
         }, (2, 6), 'float64'),
-        ('reduce_axis1', primops.reduce, randn(2, 3), {
+        ('reduce_axis1', primops.reduce_sum, randn(2, 3), {
             'axis': (1, )
         }, (2, ), 'float64'),
-        ('reduce_axis01', primops.reduce, randn(2, 3), {
+        ('reduce_axis01', primops.reduce_sum, randn(2, 3), {
             'axis': (0, 1)
         }, (1, ), 'float64'),
         ('split', primops.split, randn(2, 3), {
@@ -99,6 +103,9 @@ paddle.enable_static()
         ('select', primops.select,
          (randn(2, 3) > 0, randn(2, 3), randn(2, 3)), {}, (2, 3), 'float64'),
         ('eq', primops.eq, (randn(2, 3), randn(2, 3)), {}, (2, 3), 'bool'),
+        ('ne', primops.ne, (randn(2, 3), randn(2, 3)), {}, (2, 3), 'bool'),
+        ('gt', primops.gt, (randn(2, 3), randn(2, 3)), {}, (2, 3), 'bool'),
+        ('ge', primops.ge, (randn(2, 3), randn(2, 3)), {}, (2, 3), 'bool'),
         ('pow', primops.pow, (randn(2, 3), randn(2, 3)), {}, (2, 3), 'float64'),
         ('max', primops.max, (randn(2, 3), randn(2, 3)), {}, (2, 3), 'float64'),
     ))
diff --git a/python/paddle/fluid/tests/unittests/autograd/test_transform.py b/python/paddle/fluid/tests/unittests/autograd/test_transform.py
index f976ef729cc7a00f403e1c0f5360e9b92dd974d8..6c0aa697550bc369981408e1b7a7bd0f26ac4df2 100644
--- a/python/paddle/fluid/tests/unittests/autograd/test_transform.py
+++ b/python/paddle/fluid/tests/unittests/autograd/test_transform.py
@@ -290,8 +290,8 @@ class TestAutoGradTransformForIndexSelect(TestAutoGradTransformForAdd):
             'index_select'
         ]
         self.orig2prim_ops = [
-            'broadcast_p', 'add_p', 'reshape_p', 'mul_p', 'reduce_p', 'sqrt_p',
-            'broadcast_p', 'sub_p', 'concat_p', 'gather_p'
+            'broadcast_p', 'add_p', 'reshape_p', 'mul_p', 'reduce_sum_p',
+            'sqrt_p', 'broadcast_p', 'sub_p', 'concat_p', 'gather_p'
         ]
         self.linearize_ops = self.orig2prim_ops + [
             # call fill_const() in linearize() function
@@ -306,7 +306,7 @@ class TestAutoGradTransformForIndexSelect(TestAutoGradTransformForAdd):
             'mul_p',
             'mul_p',
             'add_p',
-            'reduce_p',
+            'reduce_sum_p',
             'fill_constant_p',  # 'sqrt_p', Will not append sqrt_p op when apply JVP for sqrt_p
             'mul_p',
             'div_p',
@@ -326,7 +326,7 @@ class TestAutoGradTransformForIndexSelect(TestAutoGradTransformForAdd):
             'fill_constant_p',
             'mul_p',
             # transposed op
-            'reduce_p',
+            'reduce_sum_p',
             'reshape_p',
             'reshape_p',
             'mul_p',
@@ -334,7 +334,7 @@ class TestAutoGradTransformForIndexSelect(TestAutoGradTransformForAdd):
             'reshape_p',
             'broadcast_p',
             'div_p',
-            'reduce_p',
+            'reduce_sum_p',
             'reshape_p',
             'fill_constant_p',
             'sub_p',
diff --git a/python/paddle/incubate/autograd/primops.py b/python/paddle/incubate/autograd/primops.py
index cb67d3f23e911d20d95feb7c055828db742f93c6..636dc8922049053daf4546823864acc483e45b02 100644
--- a/python/paddle/incubate/autograd/primops.py
+++ b/python/paddle/incubate/autograd/primops.py
@@ -137,6 +137,11 @@ def exp(x, out=None):
     return _simple_unop(LayerHelper('exp_p', **locals()))
 
 
+@REGISTER_FN('abs_p', 'X', 'Y')
+def abs(x, out=None):
+    return _simple_unop(LayerHelper('abs_p', **locals()))
+
+
 @REGISTER_FN('reshape_p', 'X', 'Y')
 def reshape(x, shape, out=None):
     return _manipulation_unop(LayerHelper('reshape_p', **locals()))
@@ -193,15 +198,17 @@ def concat(xs, axis=0, out=None):
     return out
 
 
-@REGISTER_FN('reduce_p', 'X', 'Y')
-def reduce(x, axis, keepdim=False, out=None):
+@REGISTER_FN('reduce_sum_p', 'X', 'Y')
+def reduce_sum(x, axis=None, keepdim=False, out=None):
+    axes = axis or tuple(range(0, len(x.shape)))
+    axes = (axes, ) if isinstance(axes, int) else axes
     if not isinstance(axis, (tuple, list)):
         raise TypeError(f'axis must be tuple or list, but got {type(axis)}')
     if not isinstance(keepdim, bool):
         raise TypeError(f'keepdim must be bool, but got {type(keepdim)}')
-    attrs = {'axis': axis, 'keepdim': keepdim}
 
-    helper = LayerHelper('reduce_p', **locals())
+    attrs = {'axis': axis, 'keepdim': keepdim}
+    helper = LayerHelper('reduce_sum_p', **locals())
     if out is None:
         out = helper.create_variable_for_type_inference(dtype=x.dtype)
 
@@ -347,6 +354,21 @@ def eq(x, y, out=None):
     return _simple_binop(LayerHelper('eq_p', **locals()))
 
 
+@REGISTER_FN('gt_p', 'X', 'Y', 'Z')
+def gt(x, y, out=None):
+    return _simple_binop(LayerHelper('gt_p', **locals()))
+
+
+@REGISTER_FN('ge_p', 'X', 'Y', 'Z')
+def ge(x, y, out=None):
+    return _simple_binop(LayerHelper('ge_p', **locals()))
+
+
+@REGISTER_FN('ne_p', 'X', 'Y', 'Z')
+def ne(x, y, out=None):
+    return _simple_binop(LayerHelper('ne_p', **locals()))
+
+
 @REGISTER_FN('pow_p', 'X', 'Y', 'Z')
 def pow(x, y, out=None):
     return _simple_binop(LayerHelper('pow_p', **locals()))
@@ -360,3 +382,15 @@ def max(x, y, out=None):
 @REGISTER_FN('erf_p', 'X', 'Y')
 def erf(x, out=None):
     return _simple_unop(LayerHelper('erf_p', **locals()))
+
+
+@REGISTER_FN('cast_p', 'X', 'Y')
+def cast(x, dtype, out=None):
+    helper = LayerHelper('cast_p', **locals())
+    if out is None:
+        out = helper.create_variable_for_type_inference(dtype)
+    helper.append_op(type=helper.layer_type,
+                     inputs={'X': x},
+                     outputs={'Y': out},
+                     attrs={'dtype': dtype})
+    return out
diff --git a/python/paddle/incubate/autograd/primreg.py b/python/paddle/incubate/autograd/primreg.py
index 6c3ece09a6be1ffc48fbf0b4600c250465f9e5dc..34b1c7f48334845947d81b5f3de5b4edf14b2f0a 100644
--- a/python/paddle/incubate/autograd/primreg.py
+++ b/python/paddle/incubate/autograd/primreg.py
@@ -80,7 +80,7 @@ def op_position_inputs(op):
     
     """
     args = _primop_position_argnames.lookup(op.type)
-    assert args is not None, 'args should not be None in op_position_inputs().'
+    assert args is not None, f'args of {op.type} should not be None in op_position_inputs().'
     *input_names, _ = args
 
     inputs = []
diff --git a/python/paddle/incubate/autograd/primrules.py b/python/paddle/incubate/autograd/primrules.py
index 3fe40da787d0be172b1525f9a5f7647957d3246f..4625cfd362f07030feba94c7191b178108384474 100644
--- a/python/paddle/incubate/autograd/primrules.py
+++ b/python/paddle/incubate/autograd/primrules.py
@@ -11,16 +11,19 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-import typing
+import functools
 import math
+import operator
+import typing
 
 import paddle
 
 from . import primops
-from .primops import (add, broadcast, concat, cos, div, exp, fill_const, gather,
-                      matmul, mul, neg, reduce, reshape, scatter_add, set_value,
+from .primops import (add, broadcast, concat, cos, div, eq, erf, exp,
+                      fill_const, gather, ge, gt, log, matmul, max, mul, ne,
+                      neg, reduce_sum, reshape, scatter_add, select, set_value,
                       sin, slice_assign, slice_select, split, sqrt, sub, tanh,
-                      transpose, log, select, eq, max, erf)
+                      transpose)
 from .primreg import (REGISTER_JVP, REGISTER_ORIG2PRIM, REGISTER_PRIM2ORIG,
                       REGISTER_TRANSPOSE, lookup_fn, lookup_jvp,
                       lookup_orig2prim, lookup_prim2orig, lookup_transpose,
@@ -155,6 +158,13 @@ def elementwise_mul_orig2prim(op, x, y):
     return z
 
 
+@REGISTER_ORIG2PRIM('elementwise_div')
+def elementwise_div_orig2prim(op, x, y):
+    if x.shape != y.shape:
+        y = broadcast(y, shape=x.shape)
+    return primops.div(x, y)
+
+
 @REGISTER_ORIG2PRIM('tanh')
 def tanh_orig2prim(op, x):
     return tanh(x)
@@ -180,6 +190,11 @@ def erf_orig2prim(op, x):
     return erf(x)
 
 
+@REGISTER_ORIG2PRIM('abs')
+def abs_orig2prim(op, x):
+    return primops.abs(x)
+
+
 @REGISTER_ORIG2PRIM('log')
 def log_orig2prim(op, x):
     return log(x)
@@ -307,13 +322,18 @@ def p_norm_orig2prim(op, x):
         x = reshape(x, shape=[num_el(x.shape)])
 
     if abs(op.attr('porder') - 2.0) < 1e-5:
-        return sqrt(reduce(mul(x, x), axis=[0]))
+        return sqrt(reduce_sum(mul(x, x), axis=[0]))
     elif abs(op.attr('porder') - 1.0) < 1e-5:
-        return reduce(sqrt(mul(x, x)), axis=[0])
+        return reduce_sum(sqrt(mul(x, x)), axis=[0])
     else:
         raise RuntimeError('Only support lower l2/l1 norm currently')
 
 
+@REGISTER_ORIG2PRIM('cast')
+def cast_orig2prim(op, x):
+    return primops.cast(x, paddle.dtype(op.attr('out_dtype')))
+
+
 # TODO: support broadcast
 @REGISTER_ORIG2PRIM('where')
 def select_orig2prim(op, condition, x, y):
@@ -327,15 +347,48 @@ def equal_orig2prim(op, x, y):
     return eq(x, y)
 
 
+@REGISTER_ORIG2PRIM('not_equal')
+def ne_orig2prim(op, x, y):
+    if x.shape != y.shape:
+        y = broadcast(y, shape=x.shape)
+    return ne(x, y)
+
+
+@REGISTER_ORIG2PRIM('greater_than')
+def gt_orig2prim(op, x, y):
+    if x.shape != y.shape:
+        y = broadcast(y, shape=x.shape)
+    return gt(x, y)
+
+
+@REGISTER_ORIG2PRIM('greater_equal')
+def ge_orig2prim(op, x, y):
+    if x.shape != y.shape:
+        y = broadcast(y, shape=x.shape)
+    return ge(x, y)
+
+
+# paddle.pow API use "elementwise_pow" operator when y is a Tensor.
 @REGISTER_ORIG2PRIM('elementwise_pow')
 def elementwise_pow_orig2prim(op, x, y):
     if x.shape != y.shape:
         y = broadcast(y, shape=x.shape)
-
     z = primops.pow(x, y)
     return z
 
 
+# paddle.pow API use "pow" operator when y is a scalar.
+@REGISTER_ORIG2PRIM('pow')
+def pow_orig2prim(op, x, y):
+    # x is factorTensor defined in paddle phi op. Currently it is None.
+    return primops.pow(y, fill_const(op.attr('factor'), y.shape, y.dtype))
+
+
+@REGISTER_ORIG2PRIM('square')
+def square_orig2prim(op, x):
+    return primops.pow(x, fill_const(2., x.shape, x.dtype))
+
+
 @REGISTER_ORIG2PRIM('elementwise_max')
 def elementwise_max_orig2prim(op, x, y):
     if x.shape != y.shape:
@@ -367,6 +420,31 @@ def gelu_orig2prim(op, x):
                 erf(mul(x, fill_const(1 / math.sqrt(2.), x.shape, x.dtype)))))
 
 
+@REGISTER_ORIG2PRIM('reduce_sum')
+def reduce_sum_orig2prim(op, x):
+    axes = tuple(range(0, len(
+        x.shape))) if op.attr('reduce_all') else op.attr('dim')
+    return reduce_sum(x, axis=axes, keepdim=op.attr('keep_dim'))
+
+
+@REGISTER_ORIG2PRIM('reduce_mean')
+def reduce_mean_orig2prim(op, x):
+    axes = tuple(range(0, len(
+        x.shape))) if op.attr('reduce_all') else op.attr('dim')
+    sum = reduce_sum(x, axis=axes, keepdim=op.attr('keep_dim'))
+    norm = fill_const(shape=sum.shape,
+                      value=functools.reduce(operator.mul,
+                                             [x.shape[axis] for axis in axes]),
+                      dtype=sum.dtype)
+    return div(sum, norm)
+
+
+@REGISTER_ORIG2PRIM('size')
+def size_orig2prim(op, x):
+    return fill_const(functools.reduce(operator.mul, x.shape), (1, ),
+                      paddle.int64)
+
+
 ## Register prim2orig lower rules
 @REGISTER_PRIM2ORIG('add_p')
 def add_prim2orig(op, x, y):
@@ -418,6 +496,11 @@ def erf_prim2orig(op, x):
     return paddle.erf(x)
 
 
+@REGISTER_PRIM2ORIG('abs_p')
+def abs_prim2orig(op, x):
+    return paddle.abs(x)
+
+
 @REGISTER_PRIM2ORIG('log_p')
 def log_prim2orig(op, x):
     return paddle.log(x)
@@ -453,7 +536,7 @@ def concat_prim2orig(op, xs):
     return paddle.concat(xs, axis=op.attr('axis'))
 
 
-@REGISTER_PRIM2ORIG('reduce_p')
+@REGISTER_PRIM2ORIG('reduce_sum_p')
 def reduce_prim2orig(op, x):
     return paddle.sum(x, axis=op.attr('axis'), keepdim=op.attr('keepdim'))
 
@@ -514,6 +597,21 @@ def eq_prim2orig(op, x, y):
     return paddle.equal(x, y)
 
 
+@REGISTER_PRIM2ORIG('gt_p')
+def gt_prim2orig(op, x, y):
+    return paddle.greater_than(x, y)
+
+
+@REGISTER_PRIM2ORIG('ge_p')
+def ge_prim2orig(op, x, y):
+    return paddle.greater_equal(x, y)
+
+
+@REGISTER_PRIM2ORIG('ne_p')
+def ne_prim2orig(op, x, y):
+    return paddle.not_equal(x, y)
+
+
 @REGISTER_PRIM2ORIG('pow_p')
 def pow_prim2orig(op, x, y):
     return paddle.pow(x, y)
@@ -524,6 +622,11 @@ def max_prim2orig(op, x, y):
     return paddle.maximum(x, y)
 
 
+@REGISTER_PRIM2ORIG('cast_p')
+def cast_prim2orig(op, x):
+    return paddle.cast(x, paddle.dtype(op.attr('dtype')))
+
+
 ## Register linearize rules
 @REGISTER_JVP('add_p')
 def add_jvp(op, x_dot, y_dot):
@@ -629,6 +732,14 @@ def erf_jvp(op, x_dot):
         mul(x_dot, exp(neg(primops.pow(x, fill_const(2., x.shape, x.dtype))))))
 
 
+@REGISTER_JVP('abs_p')
+def abs_jvp(op, x_dot):
+    if x_dot is None:
+        return None
+    x, = op_position_inputs(op)
+    return select(ge(x, fill_const(0., x.shape, x.dtype)), x_dot, neg(x_dot))
+
+
 @REGISTER_JVP('log_p')
 def log_jvp(op, x_dot):
     if x_dot is None:
@@ -678,8 +789,8 @@ def concat_jvp(op, xs_dot):
     return linear_jvp(op, xs_dot, axis=axis)
 
 
-@REGISTER_JVP('reduce_p')
-def reduce_jvp(op, x_dot):
+@REGISTER_JVP('reduce_sum_p')
+def reduce_sum_jvp(op, x_dot):
     if x_dot is None:
         return None
     axis = op.attr('axis')
@@ -778,6 +889,33 @@ def eq_jvp(op, x_dot, y_dot):
     return z_dot
 
 
+@REGISTER_JVP('gt_p')
+def gt_jvp(op, x_dot, y_dot):
+    if x_dot is None and y_dot is None:
+        return None
+    x, _ = op_position_inputs(op)
+    z_dot = fill_const(value=0., shape=x.shape, dtype=x.dtype)
+    return z_dot
+
+
+@REGISTER_JVP('ge_p')
+def ge_jvp(op, x_dot, y_dot):
+    if x_dot is None and y_dot is None:
+        return None
+    x, _ = op_position_inputs(op)
+    z_dot = fill_const(value=0., shape=x.shape, dtype=x.dtype)
+    return z_dot
+
+
+@REGISTER_JVP('ne_p')
+def ne_jvp(op, x_dot, y_dot):
+    if x_dot is None and y_dot is None:
+        return None
+    x, _ = op_position_inputs(op)
+    z_dot = fill_const(value=0., shape=x.shape, dtype=x.dtype)
+    return z_dot
+
+
 @REGISTER_JVP('pow_p')
 def pow_jvp(op, x_dot, y_dot):
 
@@ -825,6 +963,12 @@ def max_jvp(op, x_dot, y_dot):
         return select(eq(y, z), y_dot, x_dot)
 
 
+@REGISTER_JVP('cast_p')
+def cast_jvp(op, x_dot):
+    y = op_position_output(op)
+    return primops.cast(x_dot, y.dtype)
+
+
 ## Register transpose rules
 
 
@@ -886,7 +1030,7 @@ def broadcast_transpose(op, check_dot, y_bar):
     keepdim = [(bat + i) for i, s in enumerate(x.shape) if s == 1]
     axis += keepdim
     # TODO: Change it. keepdim boolean
-    out = reduce(y_bar, axis=axis, keepdim=False)
+    out = reduce_sum(y_bar, axis=axis, keepdim=False)
     return reshape(out, x.shape)
 
 
@@ -921,8 +1065,8 @@ def concat_transpose(op, check_dot, y_bar):
     return split(y_bar, num_or_sections=sections, axis=axis)
 
 
-@REGISTER_TRANSPOSE('reduce_p')
-def reduce_transpose(op, check_dot, y_bar):
+@REGISTER_TRANSPOSE('reduce_sum_p')
+def reduce_sum_transpose(op, check_dot, y_bar):
     x, = op_position_inputs(op)
     assert check_dot(x), 'check_dot(x) must be True'
     axes = op.attr('axis')
@@ -1029,3 +1173,9 @@ def select_transpose(op, check_dot, z_bar):
     y_bar = select(cond, zeros_y, z_bar) if check_dot(y) else None
 
     return cond_bar, x_bar, y_bar
+
+
+@REGISTER_TRANSPOSE('cast_p')
+def cast_transpose(op, check_dot, y_bar):
+    x, = op_position_inputs(op)
+    return primops.cast(y_bar, x.dtype)
diff --git a/python/paddle/incubate/autograd/primx.py b/python/paddle/incubate/autograd/primx.py
index 19f87dd9292154ca17dcca8364e76544107b2d5d..565fcb0b4ed836670db1ae23290820d36a52581b 100644
--- a/python/paddle/incubate/autograd/primx.py
+++ b/python/paddle/incubate/autograd/primx.py
@@ -12,18 +12,21 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
+from collections import OrderedDict
+
 import paddle
-from paddle.fluid import framework as framework
-from paddle.fluid.framework import default_main_program
-from paddle.fluid.framework import Operator
 from paddle import compat as cpt
-from .primops import fill_const, add
-from .primreg import op_position_inputs, op_position_output, lookup_orig2prim, lookup_prim2orig
-from .primrules import _orig2prim, _prim2orig, _jvp, _transpose
-from .utils import get_input_var_list, get_output_var_list, flatten, flatten_and_remove_none
-from collections import OrderedDict
+from paddle.fluid import framework as framework
+from paddle.fluid.framework import Operator, default_main_program
 from paddle.incubate.autograd.utils import as_tensors
 
+from .primops import add, fill_const
+from .primreg import (lookup_orig2prim, lookup_prim2orig, op_position_inputs,
+                      op_position_output)
+from .primrules import _jvp, _orig2prim, _prim2orig, _transpose
+from .utils import (flatten, flatten_and_remove_none, get_input_var_list,
+                    get_output_var_list)
+
 
 def topo_path(xs, ys, block=None):
     """ Returns the list of ops on the path from `xs` to `ys` in topological