code: def product_simplify(s, **kwargs):
      """Main function for Product simplification"""
      terms = Mul.make_args(s)
      p_t = []  # Product Terms
      o_t = []  # Other Terms
  
      deep = kwargs.get("deep", True)
      for term in terms:
          if isinstance(term, Product):
              if deep:
                  p_t.append(
                      Product(
                          term.function.simplify(**kwargs), *term.limits
                      )
                  )
              else:
                  p_t.append(term)
          else:
              o_t.append(term)
  
      used = [False] * len(p_t)
  
      for method in range(2):
          for i, p_term1 in enumerate(p_t):
              if not used[i]:
                  for j, p_term2 in enumerate(p_t):
                      if not used[j] and i != j:
                          tmp_prod = product_mul(
                              p_term1, p_term2, method
                          )
                          if isinstance(tmp_prod, Product):
                              p_t[i] = tmp_prod
                              used[j] = True
  
      result = Mul(*o_t)
  
      for i, p_term in enumerate(p_t):
          if not used[i]:
              result = Mul(result, p_term)
  
      return result
  
imports: from collections import defaultdict
  from sympy.concrete.products import Product
  from sympy.concrete.summations import Sum
  from sympy.core import Basic, S, Add, Mul, Pow, Symbol, sympify, expand_func, Function, Dummy, Expr, factor_terms, expand_power_exp, Eq
  from sympy.core.exprtools import factor_nc
  from sympy.core.parameters import global_parameters
  from sympy.core.function import expand_log, count_ops, _mexpand, nfloat, expand_mul, expand
  from sympy.core.numbers import Float, I, pi, Rational
  from sympy.core.relational import Relational
  from sympy.core.rules import Transform
  from sympy.core.sorting import ordered
  from sympy.core.sympify import _sympify
  from sympy.core.traversal import bottom_up, walk
  from sympy.functions import gamma, exp, sqrt, log, exp_polar, re
  from sympy.functions.combinatorial.factorials import CombinatorialFunction
  from sympy.functions.elementary.complexes import unpolarify, Abs, sign
  from sympy.functions.elementary.exponential import ExpBase
  from sympy.functions.elementary.hyperbolic import HyperbolicFunction
  from sympy.functions.elementary.integers import ceiling
  from sympy.functions.elementary.piecewise import Piecewise, piecewise_fold, piecewise_simplify
  from sympy.functions.elementary.trigonometric import TrigonometricFunction
  from sympy.functions.special.bessel import BesselBase, besselj, besseli, besselk, bessely, jn
  from sympy.functions.special.tensor_functions import KroneckerDelta
  from sympy.integrals.integrals import Integral
  from sympy.matrices.expressions import MatrixExpr, MatAdd, MatMul, MatPow, MatrixSymbol
  from sympy.polys import together, cancel, factor
  from sympy.polys.numberfields.minpoly import _is_sum_surds, _minimal_polynomial_sq
  from sympy.simplify.combsimp import combsimp
  from sympy.simplify.cse_opts import sub_pre, sub_post
  from sympy.simplify.hyperexpand import hyperexpand
  from sympy.simplify.powsimp import powsimp
  from sympy.simplify.radsimp import radsimp, fraction, collect_abs
  from sympy.simplify.sqrtdenest import sqrtdenest
  from sympy.simplify.trigsimp import trigsimp, exptrigsimp
  from sympy.utilities.decorator import deprecated
  from sympy.utilities.iterables import has_variety, sift, subsets, iterable
  from sympy.utilities.misc import as_int
  import mpmath
label_desc: Use image node_id 13 for calling a global function with example usage: product_simplify(s) and returns: result