code: def evalf(x: "Expr", prec: int, options: OPT_DICT) -> TMP_RES:
      """
      Evaluate the ``Expr`` instance, ``x``
      to a binary precision of ``prec``. This
      function is supposed to be used internally.
  
      Parameters
      ==========
  
      x : Expr
          The formula to evaluate to a float.
      prec : int
          The binary precision that the output should have.
      options : dict
          A dictionary with the same entries as
          ``EvalfMixin.evalf`` and in addition,
          ``maxprec`` which is the maximum working precision.
  
      Returns
      =======
  
      An optional tuple, ``(re, im, re_acc, im_acc)``
      which are the real, imaginary, real accuracy
      and imaginary accuracy respectively. ``re`` is
      an mpf value tuple and so is ``im``. ``re_acc``
      and ``im_acc`` are ints.
  
      NB: all these return values can be ``None``.
      If all values are ``None``, then that represents 0.
      Note that 0 is also represented as ``fzero = (0, 0, 0, 0)``.
      """
      from sympy.functions.elementary.complexes import (
          re as re_,
          im as im_,
      )
  
      try:
          rf = evalf_table[type(x)]
          r = rf(x, prec, options)
      except KeyError:
          # Fall back to ordinary evalf if possible
          if "subs" in options:
              x = x.subs(evalf_subs(prec, options["subs"]))
          xe = x._eval_evalf(prec)
          if xe is None:
              raise NotImplementedError
          as_real_imag = getattr(xe, "as_real_imag", None)
          if as_real_imag is None:
              raise NotImplementedError  # e.g. FiniteSet(-1.0, 1.0).evalf()
          re, im = as_real_imag()
          if re.has(re_) or im.has(im_):
              raise NotImplementedError
          if re == 0.0:
              re = None
              reprec = None
          elif re.is_number:
              re = re._to_mpmath(prec, allow_ints=False)._mpf_
              reprec = prec
          else:
              raise NotImplementedError
          if im == 0.0:
              im = None
              imprec = None
          elif im.is_number:
              im = im._to_mpmath(prec, allow_ints=False)._mpf_
              imprec = prec
          else:
              raise NotImplementedError
          r = re, im, reprec, imprec
  
      if options.get("verbose"):
          print("### input", x)
          print(
              "### output",
              to_str(r[0] or fzero, 50) if isinstance(r, tuple) else r,
          )
          print("### raw", r)  # r[0], r[2]
          print()
      chop = options.get("chop", False)
      if chop:
          if chop is True:
              chop_prec = prec
          else:
              # convert (approximately) from given tolerance;
              # the formula here will will make 1e-i rounds to 0 for
              # i in the range +/-27 while 2e-i will not be chopped
              chop_prec = int(round(-3.321 * math.log10(chop) + 2.5))
              if chop_prec == 3:
                  chop_prec -= 1
          r = chop_parts(r, chop_prec)
      if options.get("strict"):
          check_target(x, r, prec)
      return r
  
imports: from __future__ import annotations
  from typing import Tuple, Optional, Union, Callable, List, Dict, Type, TYPE_CHECKING, Any, overload
  import math
  import mpmath.libmp
  from mpmath import make_mpc, make_mpf, mp, mpc, mpf, nsum, quadts, quadosc, workprec
  from mpmath import inf
  from mpmath.libmp import from_int, from_man_exp, from_rational, fhalf, fnan, finf, fninf, fnone, fone, fzero, mpf_abs, mpf_add, mpf_atan, mpf_atan2, mpf_cmp, mpf_cos, mpf_e, mpf_exp, mpf_log, mpf_lt, mpf_mul, mpf_neg, mpf_pi, mpf_pow, mpf_pow_int, mpf_shift, mpf_sin, mpf_sqrt, normalize, round_nearest, to_int, to_str
  from mpmath.libmp import bitcount
  from mpmath.libmp.backend import MPZ
  from mpmath.libmp.libmpc import _infs_nan
  from mpmath.libmp.libmpf import dps_to_prec, prec_to_dps
  from .sympify import sympify
  from .singleton import S
  from sympy.external.gmpy import SYMPY_INTS
  from sympy.utilities.iterables import is_sequence
  from sympy.utilities.lambdify import lambdify
  from sympy.utilities.misc import as_int
label_desc: Use image node_id 43 for calling a global function with example usage: evalf(x, prec, options) and returns: r