code: def simulate_easy_propensity_difficult_baseline(
      n=1000, p=5, sigma=1.0, adj=0.0
  ):
      """Synthetic data with easy propensity and a difficult baseline
          From Setup C in Nie X. and Wager S. (2018) 'Quasi-Oracle Estimation of Heterogeneous Treatment Effects'
      Args:
          n (int, optional): number of observations
          p (int optional): number of covariates (>=3)
          sigma (float): standard deviation of the error term
          adj (float): no effect. added for consistency
      Returns:
          (tuple): Synthetically generated samples with the following outputs:
              - y ((n,)-array): outcome variable.
              - X ((n,p)-ndarray): independent variables.
              - w ((n,)-array): treatment flag with value 0 or 1.
              - tau ((n,)-array): individual treatment effect.
              - b ((n,)-array): expected outcome.
              - e ((n,)-array): propensity of receiving treatment.
      """
  
      X = np.random.normal(size=n * p).reshape((n, -1))
      b = 2 * np.log1p(np.exp(X[:, 0] + X[:, 1] + X[:, 2]))
      e = 1 / (1 + np.exp(X[:, 1] + X[:, 2]))
      tau = np.repeat(1.0, n)
  
      w = np.random.binomial(1, e, size=n)
      y = b + (w - 0.5) * tau + sigma * np.random.normal(size=n)
  
      return y, X, w, tau, b, e
  
file_path: causalml/causalml/dataset/regression.py
imports: import logging
  import numpy
  from scipy.special import expit, logit
label_desc: Use image node_id 4 for calling a global function with example usage: simulate_easy_propensity_difficult_baseline(n, p, sigma, adj) and returns: y,  X,  w,  tau,  b,  e