code: def init_pysr_lut_functions(
      init_defaults=False, function_definitions=None
  ):
      """Register LUT-based approximations with PySR.
  
      Functions should be in the form of::
  
          <func_name>(x) = math_lut(<func>, x, N=<table_size>, range_start=<start>, range_end=<end>)
  
      where ``<func_name>`` is a given name that can be used with PySR, ``<func>`` is the math function to approximate
      (`sin`, `cos`, `log`,...), ``<table_size>`` is the size of the lookup table, and ``<start>`` and ``<end>`` are the
      ranges in which the function will be approximated. It is **strongly** recommended to use a power-of-two as a range.
  
      Registered functions can be passed by name to ``PySRRegressor`` (as ``unary_operators``).
  
      Args:
          init_defaults (bool, optional): Register the most frequently used functions (sin, cos, tan, log, exp).
              Defaults to False.
          function_definitions (list, optional): List of strings with function definitions to register with PySR.
              Defaults to None.
      """
      from pysr.julia_helpers import init_julia
  
      Main = init_julia()
      Main.eval(math_lut_julia)
  
      if init_defaults:
          Main.eval(
              "sin_lut(x) = math_lut(sin, x, N=1024, range_start=-4, range_end=4)"
          )
          Main.eval(
              "cos_lut(x) = math_lut(cos, x, N=1024, range_start=-4, range_end=4)"
          )
          Main.eval(
              "tan_lut(x) = math_lut(tan, x, N=1024, range_start=-4, range_end=4)"
          )
  
          Main.eval(
              "log_lut(x) = math_lut(log, x, N=1024, range_start=0, range_end=8)"
          )
          Main.eval(
              "exp_lut(x) = math_lut(exp, x, N=1024, range_start=0, range_end=16)"
          )
  
      for func in function_definitions or []:
          register_pysr_lut_function(func, Main)
  
imports: import subprocess
  import tempfile
label_desc: Use image node_id 1 for calling a global function with example usage: init_pysr_lut_functions(init_defaults, function_definitions) without return types