code: def _call_1993(s, k, t, r, b, sigma):
      """Calculates the approximate value of an American call option."""
      # (4) in reference [1].
  
      # The naming convention will align variables with the variables named in
      # reference [1], but with X = _boundary_1993().
      # [1] https://core.ac.uk/download/pdf/30824897.pdf
  
      beta = (0.5 - b / sigma**2) + tf.math.sqrt(
          (b / sigma**2 - 0.5) ** 2 + 2 * r / sigma**2
      )
      alpha = (
          _boundary_1993(k, t, r, b, sigma, beta) - k
      ) * _boundary_1993(k, t, r, b, sigma, beta) ** (-beta)
  
      return tf.where(
          s >= _boundary_1993(k, t, r, b, sigma, beta),
          s - k,
          alpha * s**beta
          - alpha
          * _phi_1993(
              s,
              t,
              beta,
              _boundary_1993(k, t, r, b, sigma, beta),
              _boundary_1993(k, t, r, b, sigma, beta),
              r,
              b,
              sigma,
          )
          + _phi_1993(
              s,
              t,
              1,
              _boundary_1993(k, t, r, b, sigma, beta),
              _boundary_1993(k, t, r, b, sigma, beta),
              r,
              b,
              sigma,
          )
          - _phi_1993(
              s,
              t,
              1,
              k,
              _boundary_1993(k, t, r, b, sigma, beta),
              r,
              b,
              sigma,
          )
          - k
          * _phi_1993(
              s,
              t,
              0,
              _boundary_1993(k, t, r, b, sigma, beta),
              _boundary_1993(k, t, r, b, sigma, beta),
              r,
              b,
              sigma,
          )
          + k
          * _phi_1993(
              s,
              t,
              0,
              k,
              _boundary_1993(k, t, r, b, sigma, beta),
              r,
              b,
              sigma,
          ),
      )
  
imports: from typing import Tuple
  import numpy
  import tensorflow.compat.v2
  from tf_quant_finance import types
  from tf_quant_finance.black_scholes import vanilla_prices
  from tf_quant_finance.math import gradient
  from tf_quant_finance.math import integration
  from tf_quant_finance.math.root_search import newton
label_desc: Use image node_id 11 for calling a global function with example usage: _call_1993(s, k, t, r, b, sigma) and returns: tf