diff --git a/pyomo/repn/tests/ampl/test_nlv2.py b/pyomo/repn/tests/ampl/test_nlv2.py
index 35030caeb52..43327dd9ae7 100644
--- a/pyomo/repn/tests/ampl/test_nlv2.py
+++ b/pyomo/repn/tests/ampl/test_nlv2.py
@@ -48,7 +48,7 @@
 )
 import pyomo.environ as pyo
 
-_invalid_1j = r'InvalidNumber\((\([-+0-9.e]+\+)?1j\)?\)'
+nan = float('nan')
 
 
 class INFO(object):
@@ -171,7 +171,7 @@ def test_errors_divide_by_0(self):
         )
         self.assertEqual(repn.nl, None)
         self.assertEqual(repn.mult, 1)
-        self.assertEqual(str(repn.const), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.const, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -186,7 +186,7 @@ def test_errors_divide_by_0(self):
         )
         self.assertEqual(repn.nl, None)
         self.assertEqual(repn.mult, 1)
-        self.assertEqual(str(repn.const), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.const, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -201,7 +201,7 @@ def test_errors_divide_by_0(self):
         )
         self.assertEqual(repn.nl, None)
         self.assertEqual(repn.mult, 1)
-        self.assertEqual(str(repn.const), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.const, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -216,7 +216,7 @@ def test_errors_divide_by_0(self):
         )
         self.assertEqual(repn.nl, None)
         self.assertEqual(repn.mult, 1)
-        self.assertEqual(str(repn.const), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.const, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -231,7 +231,7 @@ def test_errors_divide_by_0(self):
         )
         self.assertEqual(repn.nl, None)
         self.assertEqual(repn.mult, 1)
-        self.assertEqual(str(repn.const), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.const, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -424,7 +424,7 @@ def test_errors_negative_frac_pow(self):
         )
         self.assertEqual(repn.nl, None)
         self.assertEqual(repn.mult, 1)
-        self.assertRegex(str(repn.const), _invalid_1j)
+        self.assertStructuredAlmostEqual(repn.const, InvalidNumber(1j))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -440,7 +440,7 @@ def test_errors_negative_frac_pow(self):
         )
         self.assertEqual(repn.nl, None)
         self.assertEqual(repn.mult, 1)
-        self.assertRegex(str(repn.const), _invalid_1j)
+        self.assertStructuredAlmostEqual(repn.const, InvalidNumber(1j))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -460,7 +460,7 @@ def test_errors_unary_func(self):
         )
         self.assertEqual(repn.nl, None)
         self.assertEqual(repn.mult, 1)
-        self.assertEqual(str(repn.const), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.const, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -484,7 +484,7 @@ def test_errors_propagate_nan(self):
         )
         self.assertEqual(repn.nl, None)
         self.assertEqual(repn.mult, 1)
-        self.assertEqual(str(repn.const), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.const, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -494,7 +494,7 @@ def test_errors_propagate_nan(self):
             repn = info.visitor.walk_expression((expr, None, None, 1))
         self.assertEqual(repn.nl, None)
         self.assertEqual(repn.mult, 1)
-        self.assertEqual(str(repn.const), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.const, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
diff --git a/pyomo/repn/tests/test_linear.py b/pyomo/repn/tests/test_linear.py
index d88ddf96baa..3d5048ce653 100644
--- a/pyomo/repn/tests/test_linear.py
+++ b/pyomo/repn/tests/test_linear.py
@@ -149,7 +149,7 @@ def test_scalars(self):
         self.assertEqual(cfg.var_map, {})
         self.assertEqual(cfg.var_order, {})
         self.assertEqual(repn.multiplier, 1)
-        self.assertEqual(str(repn.constant), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.constant, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -203,7 +203,7 @@ def test_scalars(self):
         self.assertEqual(cfg.var_map, {})
         self.assertEqual(cfg.var_order, {})
         self.assertEqual(repn.multiplier, 1)
-        self.assertEqual(str(repn.constant), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.constant, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -214,7 +214,7 @@ def test_scalars(self):
         self.assertEqual(cfg.var_map, {})
         self.assertEqual(cfg.var_order, {})
         self.assertEqual(repn.multiplier, 1)
-        self.assertEqual(str(repn.constant), 'InvalidNumber(1j)')
+        self.assertEqual(repn.constant, InvalidNumber(1j))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -253,7 +253,7 @@ def test_npv(self):
         self.assertEqual(cfg.var_map, {})
         self.assertEqual(cfg.var_order, {})
         self.assertEqual(repn.multiplier, 1)
-        self.assertEqual(str(repn.constant), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.constant, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -488,7 +488,7 @@ def test_monomial(self):
         self.assertEqual(cfg.var_map, {})
         self.assertEqual(cfg.var_order, {})
         self.assertEqual(repn.multiplier, 1)
-        self.assertEqual(str(repn.constant), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.constant, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -498,7 +498,7 @@ def test_monomial(self):
         self.assertEqual(cfg.var_map, {})
         self.assertEqual(cfg.var_order, {})
         self.assertEqual(repn.multiplier, 1)
-        self.assertEqual(str(repn.constant), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.constant, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -508,7 +508,7 @@ def test_monomial(self):
         self.assertEqual(cfg.var_map, {})
         self.assertEqual(cfg.var_order, {})
         self.assertEqual(repn.multiplier, 1)
-        self.assertEqual(str(repn.constant), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.constant, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -551,7 +551,7 @@ def test_monomial(self):
         self.assertEqual(cfg.var_map, {})
         self.assertEqual(cfg.var_order, {})
         self.assertEqual(repn.multiplier, 1)
-        self.assertEqual(str(repn.constant), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.constant, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -765,7 +765,8 @@ def test_linear(self):
         with LoggingIntercept() as LOG:
             repn = LinearRepnVisitor(*cfg).walk_expression(e)
         self.assertIn(
-            "DEPRECATED: Encountered 0*nan in expression tree.", LOG.getvalue()
+            "DEPRECATED: Encountered 0*InvalidNumber(nan) in expression tree.",
+            LOG.getvalue(),
         )
 
         self.assertEqual(cfg.subexpr, {})
@@ -1447,9 +1448,8 @@ def test_errors_propagate_nan(self):
             "\texpression: (x + 1)/p\n",
         )
         self.assertEqual(repn.multiplier, 1)
-        self.assertEqual(str(repn.constant), 'InvalidNumber(nan)')
-        self.assertEqual(len(repn.linear), 1)
-        self.assertEqual(str(repn.linear[id(m.x)]), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.constant, InvalidNumber(nan))
+        self.assertStructuredAlmostEqual(repn.linear, {id(m.x): InvalidNumber(nan)})
         self.assertEqual(repn.nonlinear, None)
 
         expr = m.y + m.x + m.z + ((3 * m.x) / m.p) / m.y
@@ -1464,16 +1464,16 @@ def test_errors_propagate_nan(self):
         )
         self.assertEqual(repn.multiplier, 1)
         self.assertEqual(repn.constant, 1)
-        self.assertEqual(len(repn.linear), 2)
-        self.assertEqual(repn.linear[id(m.z)], 1)
-        self.assertEqual(str(repn.linear[id(m.x)]), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(
+            repn.linear, {id(m.z): 1, id(m.x): InvalidNumber(nan)}
+        )
         self.assertEqual(repn.nonlinear, None)
 
         m.y.fix(None)
         expr = log(m.y) + 3
         repn = LinearRepnVisitor(*cfg).walk_expression(expr)
         self.assertEqual(repn.multiplier, 1)
-        self.assertEqual(str(repn.constant), 'InvalidNumber(nan)')
+        self.assertStructuredAlmostEqual(repn.constant, InvalidNumber(nan))
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
@@ -1631,7 +1631,9 @@ def test_nonnumeric(self):
         self.assertEqual(cfg.var_map, {})
         self.assertEqual(cfg.var_order, {})
         self.assertEqual(repn.multiplier, 1)
-        self.assertEqual(str(repn.constant), 'InvalidNumber(array([3, 4]))')
+        self.assertStructuredAlmostEqual(
+            repn.constant, InvalidNumber(numpy.array([3, 4]))
+        )
         self.assertEqual(repn.linear, {})
         self.assertEqual(repn.nonlinear, None)
 
diff --git a/pyomo/repn/tests/test_util.py b/pyomo/repn/tests/test_util.py
index e0fea0fb45c..fc9d86f966f 100644
--- a/pyomo/repn/tests/test_util.py
+++ b/pyomo/repn/tests/test_util.py
@@ -242,7 +242,7 @@ def test_apply_operation(self):
             pyomo.repn.util.HALT_ON_EVALUATION_ERROR = False
             with LoggingIntercept() as LOG:
                 val = apply_node_operation(div, [1, 0])
-                self.assertEqual(str(val), "InvalidNumber(nan)")
+                self.assertStructuredAlmostEqual(val, InvalidNumber(float('nan')))
             self.assertEqual(
                 LOG.getvalue(),
                 "Exception encountered evaluating expression 'div(1, 0)'\n"
@@ -293,7 +293,7 @@ class Visitor(object):
             pyomo.repn.util.HALT_ON_EVALUATION_ERROR = False
             with LoggingIntercept() as LOG:
                 val = complex_number_error(1j, visitor, exp)
-                self.assertEqual(str(val), "InvalidNumber(1j)")
+                self.assertEqual(val, InvalidNumber(1j))
             self.assertEqual(
                 LOG.getvalue(),
                 "Complex number returned from expression\n"