diff --git a/tensorflow/compiler/jit/kernels/xla_ops.cc b/tensorflow/compiler/jit/kernels/xla_ops.cc
index 782ac342fc8991..8629635a0536f2 100644
--- a/tensorflow/compiler/jit/kernels/xla_ops.cc
+++ b/tensorflow/compiler/jit/kernels/xla_ops.cc
@@ -691,6 +691,9 @@ absl::Status CompileToLocalExecutable(
             int64_t old = shp.dim_size(j);
             old_vars.push_back({i, j, old});
             xla::DExpr padded_expr = xla::DExpr::Const(filled_batch);
+            // TODO: If fractional expressions are allowed to
+            // survive until padding substitution, validate integrality before
+            // calling get_val() here instead of assuming simplify() is exact.
             xla::DExpr subst_expr = e.substitute(1, padded_expr).simplify();
             int64_t new_dim = subst_expr->get_val();
             if (new_dim >= 0) {
diff --git a/tensorflow/compiler/jit/xla_launch_util.cc b/tensorflow/compiler/jit/xla_launch_util.cc
index ccf97cb24d75f8..5ea00a8a585909 100644
--- a/tensorflow/compiler/jit/xla_launch_util.cc
+++ b/tensorflow/compiler/jit/xla_launch_util.cc
@@ -447,6 +447,9 @@ absl::Status XlaComputationLaunchContext::PopulateOutputs(
           VLOG(1) << "Current expression is " << expr;
           if (run_options) {
             xla::DExpr batch_size = xla::DExpr::Const(run_options->batch_size());
+            // TODO: If fractional expressions are allowed to
+            // survive until runtime substitution, validate integrality before
+            // calling get_val() here instead of assuming simplify() is exact.
             xla::DExpr subst_expr = expr.substitute(1, batch_size).simplify();
             shape.set_dim(dim, subst_expr->get_val());
           } else {
@@ -458,6 +461,9 @@ absl::Status XlaComputationLaunchContext::PopulateOutputs(
                           ctx->resource_manager(), BatchSizeResourceName, &bsr));
             xla::DExpr batch_size = xla::DExpr::Const(bsr->GetBatchSize());
             // Just substitute Var(1) for now.
+            // TODO: If fractional expressions are allowed to
+            // survive until runtime substitution, validate integrality before
+            // calling get_val() here instead of assuming simplify() is exact.
             xla::DExpr subst_expr = expr.substitute(1, batch_size).simplify();
             shape.set_dim(dim, subst_expr->get_val());
             bsr->Unref();
diff --git a/third_party/xla/xla/shape.cc b/third_party/xla/xla/shape.cc
index 5e256a6303d6b1..bbb46add7d7af2 100644
--- a/third_party/xla/xla/shape.cc
+++ b/third_party/xla/xla/shape.cc
@@ -17,6 +17,8 @@ limitations under the License.
 
 #include <algorithm>
 #include <cstdint>
+#include <cstdlib>
+#include <numeric>
 #include <optional>
 #include <ostream>
 #include <string>
@@ -41,6 +43,38 @@ limitations under the License.
 
 namespace xla {
 
+namespace {
+
+Constant* AsConstant(DynExpr* expr) {
+  return expr != nullptr && expr->kind() == DExpr::Kind::kConstant
+             ? static_cast<Constant*>(expr)
+             : nullptr;
+}
+
+void NormalizeFraction(int64_t* numerator, int64_t* denominator) {
+  CHECK(denominator != nullptr);
+  CHECK(*denominator != 0);
+  int64_t divisor = std::gcd(std::llabs(*numerator), std::llabs(*denominator));
+  if (divisor > 1) {
+    *numerator /= divisor;
+    *denominator /= divisor;
+  }
+  if (*denominator < 0) {
+    *numerator = -*numerator;
+    *denominator = -*denominator;
+  }
+}
+
+std::unique_ptr<DynExpr> MultiplyByConstant(int64_t factor, DynExpr* expr) {
+  CHECK(expr != nullptr);
+  if (factor == 1) {
+    return expr->clone();
+  }
+  return std::make_unique<Mul>(DynExpr::_(factor), expr->clone().release());
+}
+
+}  // namespace
+
 const DExpr& Shape::MissingExpression() {
   static const DExpr missing = DExpr::Unknown();
   return missing;
@@ -180,6 +214,43 @@ DynExpr* Mul::s() {
     auto reordered = std::unique_ptr<DynExpr>(r->get_val() * *s_lhs);
     return reordered->s();
   }
+  // (c / d) * X = (c * X) / d, but keep the reduced fraction symbolic.
+  if (s_lhs->kind() == DExpr::Kind::kDiv &&
+      s_rhs->kind() != DExpr::Kind::kDiv) {
+    auto* div = static_cast<Div*>(s_lhs.get());
+    Constant* numerator = AsConstant(div->get_lhs());
+    Constant* denominator = AsConstant(div->get_rhs());
+    if (numerator != nullptr && denominator != nullptr) {
+      int64_t reduced_numerator = numerator->get_val();
+      int64_t reduced_denominator = denominator->get_val();
+      NormalizeFraction(&reduced_numerator, &reduced_denominator);
+      auto scaled_rhs = MultiplyByConstant(reduced_numerator, s_rhs.get());
+      if (reduced_denominator == 1) {
+        return scaled_rhs->s();
+      }
+      auto rewritten =
+          std::make_unique<Div>(scaled_rhs->s(), DynExpr::_(reduced_denominator));
+      return rewritten->s();
+    }
+  }
+  if (s_rhs->kind() == DExpr::Kind::kDiv &&
+      s_lhs->kind() != DExpr::Kind::kDiv) {
+    auto* div = static_cast<Div*>(s_rhs.get());
+    Constant* numerator = AsConstant(div->get_lhs());
+    Constant* denominator = AsConstant(div->get_rhs());
+    if (numerator != nullptr && denominator != nullptr) {
+      int64_t reduced_numerator = numerator->get_val();
+      int64_t reduced_denominator = denominator->get_val();
+      NormalizeFraction(&reduced_numerator, &reduced_denominator);
+      auto scaled_lhs = MultiplyByConstant(reduced_numerator, s_lhs.get());
+      if (reduced_denominator == 1) {
+        return scaled_lhs->s();
+      }
+      auto rewritten =
+          std::make_unique<Div>(scaled_lhs->s(), DynExpr::_(reduced_denominator));
+      return rewritten->s();
+    }
+  }
   // m * (nX) = (m*n) * X
   if (s_rhs->kind() == DExpr::Kind::kMul) {
     auto* nX = static_cast<Mul*>(s_rhs.get());
@@ -349,14 +420,21 @@ DynExpr* Div::s() {
       s_rhs->kind() == DExpr::Kind::kUnknown) {
     return DExpr::Unknown().release();
   }
-  Constant* l = s_lhs->kind() == DExpr::Kind::kConstant
-                    ? static_cast<Constant*>(s_lhs.get())
-                    : nullptr;
-  Constant* r = s_rhs->kind() == DExpr::Kind::kConstant
-                    ? static_cast<Constant*>(s_rhs.get())
-                    : nullptr;
+  Constant* l = AsConstant(s_lhs.get());
+  Constant* r = AsConstant(s_rhs.get());
+  if (l && l->get_val() == 0) return DynExpr::_(0);
   // constant / constant
-  if (l && r) return DynExpr::_(l->get_val() / r->get_val());
+  if (l && r) {
+    int64_t numerator = l->get_val();
+    int64_t denominator = r->get_val();
+    NormalizeFraction(&numerator, &denominator);
+    if (denominator == 1) {
+      return DynExpr::_(numerator);
+    }
+    return std::make_unique<Div>(DynExpr::_(numerator),
+                                 DynExpr::_(denominator))
+        .release();
+  }
   // X / 1 = X
   if (r && r->get_val() == 1) return s_lhs.release();
   // (X + Y) / Z = (X/Z) + (Y/Z)
@@ -369,14 +447,36 @@ DynExpr* Div::s() {
     auto distributed = std::unique_ptr<DynExpr>(*left + *right);
     return distributed->s();
   }
-  // (X * Y) / Z = (X/Z) * Y
-  if (s_lhs->kind() == DExpr::Kind::kMul) {
+  // (c * X) / d = (c/g * X) / (d/g), keeping any non-integral division
+  // symbolic instead of truncating c / d to zero.
+  if (r && s_lhs->kind() == DExpr::Kind::kMul) {
     auto* XY = static_cast<Mul*>(s_lhs.get());
     DynExpr* X = XY->get_lhs();
     DynExpr* Y = XY->get_rhs();
-    auto left = std::unique_ptr<DynExpr>(*X / *s_rhs);
-    auto distributed = std::unique_ptr<DynExpr>(*left * (*Y));
-    return distributed->s();
+    if (Constant* c = AsConstant(X)) {
+      int64_t numerator = c->get_val();
+      int64_t denominator = r->get_val();
+      NormalizeFraction(&numerator, &denominator);
+      auto scaled = MultiplyByConstant(numerator, Y);
+      if (denominator == 1) {
+        return scaled->s();
+      }
+      auto rewritten =
+          std::make_unique<Div>(scaled->s(), DynExpr::_(denominator));
+      return rewritten->s();
+    }
+    if (Constant* c = AsConstant(Y)) {
+      int64_t numerator = c->get_val();
+      int64_t denominator = r->get_val();
+      NormalizeFraction(&numerator, &denominator);
+      auto scaled = MultiplyByConstant(numerator, X);
+      if (denominator == 1) {
+        return scaled->s();
+      }
+      auto rewritten =
+          std::make_unique<Div>(scaled->s(), DynExpr::_(denominator));
+      return rewritten->s();
+    }
   }
   // (X / Y) / Z = X / (Y*Z)
   if (s_lhs->kind() == DExpr::Kind::kDiv) {
diff --git a/third_party/xla/xla/shape_dynexpr.h b/third_party/xla/xla/shape_dynexpr.h
index a5713d92fbfc2b..97d8ee5a7fb4c5 100644
--- a/third_party/xla/xla/shape_dynexpr.h
+++ b/third_party/xla/xla/shape_dynexpr.h
@@ -293,11 +293,11 @@ class Add : public DynExpr {
   std::optional<int64_t> solve(int64_t x) {
     // Cannot solve if both lhs and rhs are dynamic...
     if (lhs->is_dynamic() && rhs->is_dynamic()) return std::nullopt;
-    if (lhs->get_all_ids().size() == 1) {
+    if (lhs->get_all_ids().size() == 1 && rhs->is_constant()) {
       // (A + c) = x <=> A = x - c => solve A = y with y = x - c
       return lhs->solve(x - rhs->get_val());
     }
-    if (rhs->get_all_ids().size() == 1) {
+    if (rhs->get_all_ids().size() == 1 && lhs->is_constant()) {
       // (c + A) = x <=> A = x - c => solve A = y with y = x - c
       return rhs->solve(x - lhs->get_val());
     }
@@ -357,11 +357,11 @@ class Sub : public DynExpr {
   std::optional<int64_t> solve(int64_t x) {
     // Cannot solve if both lhs and rhs are dynamic...
     if (lhs->is_dynamic() && rhs->is_dynamic()) return std::nullopt;
-    if (lhs->get_all_ids().size() == 1) {
+    if (lhs->get_all_ids().size() == 1 && rhs->is_constant()) {
       // (A - c) = x <=> A = x + c => solve A = y with y = x + c
       return lhs->solve(x + rhs->get_val());
     }
-    if (rhs->get_all_ids().size() == 1) {
+    if (rhs->get_all_ids().size() == 1 && lhs->is_constant()) {
       // (c - A) = x <=> A = c - x => solve A = y with y = c - x
       return rhs->solve(lhs->get_val() - x);
     }
@@ -421,14 +421,14 @@ class Mul : public DynExpr {
   std::optional<int64_t> solve(int64_t x) {
     // Cannot solve if both lhs and rhs are dynamic...
     if (lhs->is_dynamic() && rhs->is_dynamic()) return std::nullopt;
-    if (lhs->get_all_ids().size() == 1) {
+    if (lhs->get_all_ids().size() == 1 && rhs->is_constant()) {
       // (A * c) = x <=> A = x / c => solve A = y with y = x / c
       int64_t c = rhs->get_val();
       if (c == 0) return x == 0 ? lhs->solve(0) : std::nullopt;
       if (x % c != 0) return std::nullopt;
       return lhs->solve(x / c);
     }
-    if (rhs->get_all_ids().size() == 1) {
+    if (rhs->get_all_ids().size() == 1 && lhs->is_constant()) {
       // (c * A) = x <=> A = x / c => solve A = y with y = x / c
       int64_t c = lhs->get_val();
       if (c == 0) return x == 0 ? rhs->solve(0) : std::nullopt;
@@ -473,10 +473,15 @@ class Div : public DynExpr {
   }
 
   bool is_constant() const override {
-    return lhs->is_constant() && rhs->is_constant();
+    return lhs->is_constant() && rhs->is_constant() && rhs->get_val() != 0 &&
+           lhs->get_val() % rhs->get_val() == 0;
   }
 
-  int64_t get_val() const override { return lhs->get_val() / rhs->get_val(); }
+  int64_t get_val() const override {
+    CHECK(is_constant()) << "Attempted to get integer value of non-integral "
+                         << "division expression";
+    return lhs->get_val() / rhs->get_val();
+  }
 
   DynExpr* substitute(int id, DynExpr* v) {
     return new Div(lhs->substitute(id, v), rhs->substitute(id, v));
@@ -493,11 +498,11 @@ class Div : public DynExpr {
   std::optional<int64_t> solve(int64_t x) {
     // Cannot solve if both lhs and rhs are dynamic...
     if (lhs->is_dynamic() && rhs->is_dynamic()) return std::nullopt;
-    if (lhs->get_all_ids().size() == 1) {
+    if (lhs->get_all_ids().size() == 1 && rhs->is_constant()) {
       // (A / c) = x <=> A = x * c => solve A = y with y = x * c
       return lhs->solve(x * rhs->get_val());
     }
-    if (rhs->get_all_ids().size() == 1) {
+    if (rhs->get_all_ids().size() == 1 && lhs->is_constant()) {
       // (c / A) = x <=> A = c / x => solve A = y with y = c / x
       int64_t c = lhs->get_val();
       if (x == 0) return std::nullopt;