human
Solve the following python programming problem given the following code:
# Our original implementation of `huber_loss` is not compatible with non-scalar
# data. Your task is to fix that. For your convenience, the original
# implementation is reproduced below.
#
#   def huber_loss(y, y_hat, m=1.0):
#     delta = tf.abs(y - y_hat)
#     return delta ** 2 if delta <= m else m * (2 * delta - m)
#
def batched_huber_loss(y, y_hat, m=1.0):
  # TODO: Uncomment out the below code and replace `...` with your solution.
  # Hint: Tensors are immutable.
  # Hint: `tf.where` might be useful.
  delta = tf.abs(y - y_hat)
  # ...
  # ...
  # return ...
  
regression = Regression(batched_huber_loss)

num_epochs = 4
batch_sizes = [1, 10, 20, 100, 200, 500, 1000]
times = []

X, Y = gen_regression_data(num_examples=1000)
dataset = tf.data.Dataset.from_tensor_slices((X, Y))
optimizer = tf.train.GradientDescentOptimizer(learning_rate=0.0001)
for size in batch_sizes:
  batched_dataset = dataset.batch(size)
  start = time.time()
  regress(model=regression, optimizer=optimizer, dataset=batched_dataset,
          epochs=num_epochs, log_every=None)
  end = time.time()
  times.append((end - start) / num_epochs)
  regression.w.assign(0.0)
  regression.b.assign(0.0)
  
plt.figure()
plt.plot(batch_sizes, times, "bo")
plt.xlabel("batch size")
plt.ylabel("time (seconds)")
plt.semilogx()
plt.semilogy()
plt.title("Time per Epoch vs. Batch Size")
plt.show()
Given the above code, generate some markdown instructions for it.
assistant
#Here is Python program to fix that.

4. Exercises
Exercise 1: Batching
Executing operations eagerly incurs small overheads; these overheads become neglible when amortized over batched operations. In this exercise, we explore the relationship between batching and performance by revisiting our Huber regression example.