code: def _preprocessing_fn_for_common_optimize_traversal(inputs):
      _ = tft.vocabulary(inputs["s"])
      x = inputs["x"]
      x_mean = tft.mean(x, name="x")
      x_square_deviations = tf.square(x - x_mean)
  
      # 2nd analysis phase defined here.
      x_var = tft.mean(x_square_deviations, name="x_square_deviations")
      x_normalized = (x - x_mean) / tf.sqrt(x_var)
      return {"x_normalized": x_normalized}
  
imports: import functools
  import os
  import struct
  from typing import Callable, Mapping, List
  import uuid
  import apache_beam
  from apache_beam.testing import util
  import numpy
  import tensorflow
  import tensorflow_transform
  from tensorflow_transform import analyzer_nodes
  from tensorflow_transform import common_types
  from tensorflow_transform import impl_helper
  from tensorflow_transform import nodes
  import tensorflow_transform.beam
  from tensorflow_transform.beam import analysis_graph_builder
  from tensorflow_transform.beam import analyzer_cache
  from tensorflow_transform.beam import tft_unit
  from tensorflow_transform.tf_metadata import dataset_metadata
  from tfx_bsl.types import tfx_namedtuple
label_desc: Use image node_id 3 for calling a global function with example usage: _preprocessing_fn_for_common_optimize_traversal(inputs) and returns: dict