input: from typing import List
  
  
  def compare_heuristics_performance(data: List[float], algorithm1: str, algorithm2: str) -> str:
      """Compares the performance of two heuristics algorithms based on the time taken to process the input data.
      Returns a string indicating which algorithm is faster, or if both have the same performance time.
      >>> compare_heuristics_performance([1.0, 2.0, 3.0], 'heuristics_algorithm1', 'heuristics_algorithm2')
      "Algorithm 1 is faster than algorithm 2"
      >>> compare_heuristics_performance([5.0, 4.0, 3.0, 2.0, 1.0], 'heuristics_algorithm1', 'heuristics_algorithm2')
      "Algorithm 2 is faster than algorithm 1"
      """
output:     import time
  
      def heuristics_algorithm1(data):
          time.sleep(0.1)  # Simulate processing time
  
      def heuristics_algorithm2(data):
          time.sleep(0.05)  # Simulate processing time
  
      start_time1 = time.time()
      heuristics_algorithm1(data)
      end_time1 = time.time()
      time1 = end_time1 - start_time1
  
      start_time2 = time.time()
      heuristics_algorithm2(data)
      end_time2 = time.time()
      time2 = end_time2 - start_time2
  
      if time1 < time2:
          return "Algorithm 1 is faster than algorithm 2"
      elif time1 > time2:
          return "Algorithm 2 is faster than algorithm 1"
      else:
          return "Both algorithms have the same performance time"