code: def test_variance_prop_with_covar():
      x, y, z = symbols("x y z")
      phi, t = consts = symbols("phi t")
      a = RandomSymbol(x)
      var_x = Variance(a)
      b = RandomSymbol(y)
      var_y = Variance(b)
      c = RandomSymbol(z)
      var_z = Variance(c)
      covar_x_y = Covariance(a, b)
      covar_x_z = Covariance(a, c)
      covar_y_z = Covariance(b, c)
      cases = {
          x + y: var_x + var_y + 2 * covar_x_y,
          a + y: var_x + var_y + 2 * covar_x_y,
          x
          + y
          + z: var_x
          + var_y
          + var_z
          + 2 * covar_x_y
          + 2 * covar_x_z
          + 2 * covar_y_z,
          2 * x: 4 * var_x,
          x * y: var_x * y**2
          + var_y * x**2
          + 2 * covar_x_y / (x * y),
          1 / x: var_x / x**4,
          exp(x): var_x * exp(2 * x),
          exp(2 * x): 4 * var_x * exp(4 * x),
          exp(-x * t): t**2 * var_x * exp(-2 * t * x),
      }
      for inp, out in cases.items():
          obs = variance_prop(inp, consts=consts, include_covar=True)
          assert out == obs
  
imports: from sympy.core.function import Function
  from sympy.core.symbol import symbols
  from sympy.functions.elementary.exponential import exp
  from sympy.stats.error_prop import variance_prop
  from sympy.stats.symbolic_probability import RandomSymbol, Variance, Covariance
label_desc: Use image node_id 2 for calling a global function with example usage: test_variance_prop_with_covar() without return types