diff --git a/gemma/ops_test.cc b/gemma/ops_test.cc
index 604190f..abb7dae 100644
--- a/gemma/ops_test.cc
+++ b/gemma/ops_test.cc
@@ -510,11 +510,14 @@ template <typename MatT>
 void AssertClose(const MatT* HWY_RESTRICT expected,
                  const MatT* HWY_RESTRICT actual, size_t num) {
   for (size_t idx = 0; idx < num; idx++) {
-    double expected_value = hwy::ConvertScalarTo<double>(expected[idx]);
-    double actual_value = hwy::ConvertScalarTo<double>(actual[idx]);
+    const double expected_value = hwy::ConvertScalarTo<double>(expected[idx]);
+    const double actual_value = hwy::ConvertScalarTo<double>(actual[idx]);
+
+    const double magnitude = std::abs(expected_value);
 
     const double tolerance =
-        expected_value * 21 * 1.0 / (1ULL << hwy::MantissaBits<MatT>());
+        64.0 * hwy::ConvertScalarTo<double>(hwy::Epsilon<MatT>()) *
+        HWY_MAX(magnitude, 1.0);
 
     if (!(expected_value - tolerance <= actual_value &&
           actual_value <= expected_value + tolerance)) {
@@ -559,7 +562,7 @@ void TestAllTiledMatMul() {
 
   // large-scale test
   // TODO(philculliton): investigate rounding issues with large matrices
-  // TestTiledMatMul<512, 24576, 3072, float>();
+  TestTiledMatMul<512, 24576, 3072, float>();
 
   // TODO(janwas): SFP
 }