code: def _lambertw_approx_hybrid(z, k):
      imag_sign = 0
      if hasattr(z, "imag"):
          x = float(z.real)
          y = z.imag
          if y:
              imag_sign = (-1) ** (y < 0)
          y = float(y)
      else:
          x = float(z)
          y = 0.0
          imag_sign = 0
      # hack to work regardless of whether Python supports -0.0
      if not y:
          y = 0.0
      z = complex(x, y)
      if k == 0:
          if -4.0 < y < 4.0 and -1.0 < x < 2.5:
              if imag_sign:
                  # Taylor series in upper/lower half-plane
                  if y > 1.00:
                      return (0.876 + 0.645j) + (0.118 - 0.174j) * (
                          z - (0.75 + 2.5j)
                      )
                  if y > 0.25:
                      return (0.505 + 0.204j) + (0.375 - 0.132j) * (
                          z - (0.75 + 0.5j)
                      )
                  if y < -1.00:
                      return (0.876 - 0.645j) + (0.118 + 0.174j) * (
                          z - (0.75 - 2.5j)
                      )
                  if y < -0.25:
                      return (0.505 - 0.204j) + (0.375 + 0.132j) * (
                          z - (0.75 - 0.5j)
                      )
              # Taylor series near -1
              if x < -0.5:
                  if imag_sign >= 0:
                      return (-0.318 + 1.34j) + (-0.697 - 0.593j) * (
                          z + 1
                      )
                  else:
                      return (-0.318 - 1.34j) + (-0.697 + 0.593j) * (
                          z + 1
                      )
              # return real type
              r = -0.367879441171442
              if (not imag_sign) and x > r:
                  z = x
              # Singularity near -1/e
              if x < -0.2:
                  return (
                      -1
                      + 2.33164398159712 * (z - r) ** 0.5
                      - 1.81218788563936 * (z - r)
                  )
              # Taylor series near 0
              if x < 0.5:
                  return z
              # Simple linear approximation
              return 0.2 + 0.3 * z
          if (not imag_sign) and x > 0.0:
              L1 = math.log(x)
              L2 = math.log(L1)
          else:
              L1 = cmath.log(z)
              L2 = cmath.log(L1)
      elif k == -1:
          # return real type
          r = -0.367879441171442
          if (not imag_sign) and r < x < 0.0:
              z = x
          if (imag_sign >= 0) and y < 0.1 and -0.6 < x < -0.2:
              return (
                  -1
                  - 2.33164398159712 * (z - r) ** 0.5
                  - 1.81218788563936 * (z - r)
              )
          if (not imag_sign) and -0.2 <= x < 0.0:
              L1 = math.log(-x)
              return L1 - math.log(-L1)
          else:
              if imag_sign == -1 and (not y) and x < 0.0:
                  L1 = cmath.log(z) - 3.1415926535897932j
              else:
                  L1 = cmath.log(z) - 6.2831853071795865j
              L2 = cmath.log(L1)
      return L1 - L2 + L2 / L1 + L2 * (L2 - 2) / (2 * L1**2)
  
imports: from ..libmp.backend import xrange
  import math
  import cmath
label_desc: Use image node_id 39 for calling a global function with example usage: _lambertw_approx_hybrid(z, k) and returns: unknown, unknown, unknown, z, unknown, unknown, unknown, unknown, unknown, unknown, unknown, unknown