[XLA:GPU] Add the fallback to F32 for dot algorithms bf16_x3 and bf16…

…_x6 and f32 output.

We do not have the lowering to multiply version of the algorithm at the moment.
The default f32_f32_f32 version is way faster. Let's use it as the fallback now and do the lowering for these algorithms in the follow up cls.

PiperOrigin-RevId: 695351871

xla/hlo/transforms/simplifiers/algebraic_simplifier.cc

@@ -3964,6 +3964,10 @@ absl::Status AlgebraicSimplifierVisitor::HandleDot(HloInstruction* dot) {
                             PrecisionConfig::PACKED_NIBBLE);
   const bool can_rewrite_dot_with_precision_config_algorithm =
       dot->precision_config().algorithm() == PrecisionConfig::ALG_UNSET ||
+      dot->precision_config().algorithm() ==
+          PrecisionConfig::ALG_DOT_BF16_BF16_F32_X3 ||
+      dot->precision_config().algorithm() ==
+          PrecisionConfig::ALG_DOT_BF16_BF16_F32_X6 ||
       dot->precision_config().algorithm() ==
           PrecisionConfig::ALG_DOT_F32_F32_F32;
   // If there are no contracting dimensions, a dot can be rewritten as

xla/hlo/transforms/simplifiers/algebraic_simplifier_test.cc

@@ -9499,6 +9499,36 @@ TEST_F(AlgebraicSimplifierTest,
   ASSERT_TRUE(AlgebraicSimplifier(default_options_).Run(m.get()).value());
 }
 
+TEST_F(AlgebraicSimplifierTest,
+       DotToMultiplyRewriteWith_BF16_BF16_F32_X3_Algorithm) {
+  constexpr char kModuleStr[] = R"(
+    HloModule test
+    ENTRY dot {
+      a = f32[128]{0} parameter(0)
+      b = f32[128]{0} parameter(1)
+      ROOT dot = f32[128,128]{1,0} dot(a, b),
+        algorithm=dot_bf16_bf16_f32_x3
+    }
+  )";
+  TF_ASSERT_OK_AND_ASSIGN(auto m, ParseAndReturnVerifiedModule(kModuleStr));
+  ASSERT_TRUE(AlgebraicSimplifier(default_options_).Run(m.get()).value());
+}
+
+TEST_F(AlgebraicSimplifierTest,
+       DotToMultiplyRewriteWith_BF16_BF16_F32_X6_Algorithm) {
+  constexpr char kModuleStr[] = R"(
+    HloModule test
+    ENTRY dot {
+      a = f32[128]{0} parameter(0)
+      b = f32[128]{0} parameter(1)
+      ROOT dot = f32[128,128]{1,0} dot(a, b),
+        algorithm=dot_bf16_bf16_f32_x6
+    }
+  )";
+  TF_ASSERT_OK_AND_ASSIGN(auto m, ParseAndReturnVerifiedModule(kModuleStr));
+  ASSERT_TRUE(AlgebraicSimplifier(default_options_).Run(m.get()).value());
+}
+
 TEST_F(AlgebraicSimplifierTest, RemainderOfIota) {
   const char* kModuleStr = R"(
     HloModule m