diff --git a/test/test_proxy_tensor.py b/test/test_proxy_tensor.py
index 30baf1fdae01..abcd12fc3b18 100644
--- a/test/test_proxy_tensor.py
+++ b/test/test_proxy_tensor.py
@@ -1344,6 +1344,28 @@ def f(a):
         tensor = make_fx(f, tracing_mode="symbolic")(torch.randn(15))
         self.assertExpectedInline(show_guards(tensor), """L['a'].size()[0] < 20""")
 
+    def test_guard_upperbound_range_refinement_multivariate(self):
+        def f(a):
+            assert a.shape[0] > 5 and a.shape[0] > 12
+            assert a.shape[1] > 5 and a.shape[1] > a.shape[0]
+            return a.cos()
+        tensor = make_fx(f, tracing_mode="symbolic")(torch.randn((15, 20)))
+        self.assertExpectedInline(show_guards(tensor), """\
+L['a'].size()[1] > L['a'].size()[0]
+L['a'].size()[0] > 12""")
+
+    def test_guard_lowerbound_range_refinement_multivariate(self):
+        def f(a):
+            assert a.shape[0] < 20 and a.shape[0] < 30
+            assert a.shape[1] < 30 and a.shape[1] < a.shape[0]
+            return a.cos()
+        tensor = make_fx(f, tracing_mode="symbolic")(torch.randn((15, 5)))
+        self.assertExpectedInline(
+            show_guards(tensor),
+            """\
+L['a'].size()[1] < L['a'].size()[0]
+L['a'].size()[0] < 20""")
+
     def test_sym_storage_offset(self):
         def f(x, y):
             return x + y
diff --git a/torch/fx/experimental/symbolic_shapes.py b/torch/fx/experimental/symbolic_shapes.py
index 3a6548875952..10a8a6616efe 100644
--- a/torch/fx/experimental/symbolic_shapes.py
+++ b/torch/fx/experimental/symbolic_shapes.py
@@ -34,7 +34,7 @@
 )
 from torch._guards import ShapeGuard, Source, TracingContext, detect_fake_mode
 from torch.utils._sympy.interp import sympy_interp
-from torch.utils._sympy.value_ranges import ValueRangeAnalysis, ValueRanges, ValueRangeError
+from torch.utils._sympy.value_ranges import PythonValueRangeAnalysis, ValueRangeAnalysis, ValueRanges, ValueRangeError
 from torch.utils._traceback import format_frame
 from torch._utils_internal import signpost_event
 
@@ -3434,10 +3434,6 @@ def simplify_until(expr: sympy.Expr, max_iterations: int = 10) -> sympy.Expr:
             ):
                 continue
 
-            # Use only univariate functions.
-            if len(expr.rhs.free_symbols) > 0:
-                continue
-
             # Update the value range of the left-hand side, if the
             # right-hand side provides a better range.
             symbol = expr.lhs
@@ -3445,7 +3441,7 @@ def simplify_until(expr: sympy.Expr, max_iterations: int = 10) -> sympy.Expr:
             vr = self.var_to_range[symbol]
             lower, upper = vr.lower, vr.upper
 
-            rhs_vr = sympy_interp(ValueRangeAnalysis, self.var_to_range, expr.rhs)  # type: ignore[arg-type]
+            rhs_vr = sympy_interp(PythonValueRangeAnalysis, self.var_to_range, expr.rhs)  # type: ignore[arg-type]
             lower_guard, upper_guard = self.var_to_guards.get(symbol, (None, None))
 
             # Let's suppose that we have a preexisting range for x [0, 100].
diff --git a/torch/utils/_sympy/value_ranges.py b/torch/utils/_sympy/value_ranges.py
index f3500b4d5940..565967cf3a4c 100644
--- a/torch/utils/_sympy/value_ranges.py
+++ b/torch/utils/_sympy/value_ranges.py
@@ -469,3 +469,15 @@ def floor_ceil(x, fn):
     def __getattr__(self, name):
         log.warning("unhandled ValueRange op %s", name)
         return self.default_handler
+
+
+# Implements Python semantics for 'ValueRangeAnalysis'.
+# Reasoning about guards relies on Python operator semantics.
+class PythonValueRangeAnalysis(ValueRangeAnalysis):
+    def __init__(self):
+        super().__init__()
+        self.name = "PythonValueRangeAnalysis"
+
+    @staticmethod
+    def div(a, b):
+        return PythonValueRangeAnalysis.floordiv(a, b)