<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def _embedding_dim(vocab_size):
 """Calculate a reasonable embedding size for a vocabulary. Rule of thumb is 6 * 4th root of vocab_size. Args: vocab_size: Size of the input vocabulary. Returns: The embedding size to use. Raises: ValueError: if `vocab_size` is invalid. """

  if not vocab_size or (vocab_size <= 0):
    raise ValueError("Invalid vocab_size %g." % vocab_size)
  return int(round(6.0 * math.sqrt(math.sqrt(vocab_size))))