diff --git a/Framework/HistogramData/test/RebinTest.h b/Framework/HistogramData/test/RebinTest.h
index 5b1d8df8e91f9fdb078fd168bede7be1bd5777e3..e3b4a7d78424ca94576a2e9dbf2c179e54be22ff 100644
--- a/Framework/HistogramData/test/RebinTest.h
+++ b/Framework/HistogramData/test/RebinTest.h
@@ -149,10 +149,10 @@ public:
     for (size_t i = 0; i < outCounts.y().size(); i++) {
       TS_ASSERT_EQUALS(outCounts.y()[i],
                        hist.y()[2 * i] + hist.y()[(2 * i) + 1]);
-      TS_ASSERT_DELTA(outCounts.e()[i], std::sqrt(outCounts.y()[i]), 1e-5);
+      TS_ASSERT_DELTA(outCounts.e()[i], std::sqrt(outCounts.y()[i]), 1e-14);
       TS_ASSERT_EQUALS(outFreq.y()[i],
                        (histFreq.y()[2 * i] + histFreq.y()[(2 * i) + 1]) / 2);
-      TS_ASSERT_DELTA(outFreq.e()[i], std::sqrt(outFreq.y()[i] / 2), 1e-5);
+      TS_ASSERT_DELTA(outFreq.e()[i], std::sqrt(outFreq.y()[i] / 2), 1e-14);
     }
   }
 
@@ -176,10 +176,10 @@ public:
     TS_ASSERT_EQUALS(outFreq.y()[2], histFreq.y()[1]);
 
     for (size_t i = 0; i < outCounts.y().size(); i++) {
-      TS_ASSERT_DELTA(outCounts.e()[i], std::sqrt(outCounts.y()[i]), 1e-5);
+      TS_ASSERT_DELTA(outCounts.e()[i], std::sqrt(outCounts.y()[i]), 1e-14);
       TS_ASSERT_DELTA(outFreq.e()[i],
                       std::sqrt(outFreq.y()[i] / (edges[i + 1] - edges[i])),
-                      1e-5);
+                      1e-14);
     }
   }
 
@@ -200,15 +200,15 @@ public:
     TS_ASSERT_EQUALS(outFreq.y()[0], (histFreq.y()[0] + histFreq.y()[1]) / 2);
     TS_ASSERT_EQUALS(outFreq.y()[1], (histFreq.y()[1] + histFreq.y()[2]) / 2);
 
-    TS_ASSERT_DELTA(outCounts.e()[0], std::sqrt(outCounts.y()[0]), 1e-5);
-    TS_ASSERT_DELTA(outCounts.e()[1], std::sqrt(outCounts.y()[1]), 1e-5);
+    TS_ASSERT_DELTA(outCounts.e()[0], std::sqrt(outCounts.y()[0]), 1e-14);
+    TS_ASSERT_DELTA(outCounts.e()[1], std::sqrt(outCounts.y()[1]), 1e-14);
 
     TS_ASSERT_DELTA(outFreq.e()[0],
                     std::sqrt(((histFreq.y()[0] / 2) + histFreq.y()[1]) / 2),
-                    1e-5);
+                    1e-14);
     TS_ASSERT_DELTA(outFreq.e()[1],
                     std::sqrt(((histFreq.y()[2] / 2) + histFreq.y()[1]) / 2),
-                    1e-5);
+                    1e-14);
   }
 
   void testSplitCombineBinsAsymmetric() {
@@ -234,10 +234,10 @@ public:
     TS_ASSERT_EQUALS(outFreq.y()[2], histFreq.y()[2]);
 
     for (size_t i = 0; i < outCounts.y().size(); i++) {
-      TS_ASSERT_DELTA(outCounts.e()[i], std::sqrt(outCounts.y()[i]), 1e-5);
+      TS_ASSERT_DELTA(outCounts.e()[i], std::sqrt(outCounts.y()[i]), 1e-14);
       TS_ASSERT_DELTA(outFreq.e()[i],
                       std::sqrt(outFreq.y()[i] / (edges[i + 1] - edges[i])),
-                      1e-5);
+                      1e-14);
     }
   }
 
@@ -260,17 +260,17 @@ public:
     TS_ASSERT_EQUALS(outFreq.y()[1], histFreq.y()[1]);
     TS_ASSERT_EQUALS(outFreq.y()[2], (histFreq.y()[1] + histFreq.y()[2]) / 2);
 
-    TS_ASSERT_DELTA(outCounts.e()[0], std::sqrt(outCounts.y()[0]), 1e-5);
-    TS_ASSERT_DELTA(outCounts.e()[1], std::sqrt(outCounts.y()[1]), 1e-5);
-    TS_ASSERT_DELTA(outCounts.e()[2], std::sqrt(outCounts.y()[2]), 1e-5);
+    TS_ASSERT_DELTA(outCounts.e()[0], std::sqrt(outCounts.y()[0]), 1e-14);
+    TS_ASSERT_DELTA(outCounts.e()[1], std::sqrt(outCounts.y()[1]), 1e-14);
+    TS_ASSERT_DELTA(outCounts.e()[2], std::sqrt(outCounts.y()[2]), 1e-14);
 
     TS_ASSERT_DELTA(
         outFreq.e()[0],
-        std::sqrt(((histFreq.y()[0] / 2) + (histFreq.y()[1] * 2)) / 2), 1e-5);
-    TS_ASSERT_DELTA(outFreq.e()[1], std::sqrt(histFreq.y()[1] * 2), 1e-5);
+        std::sqrt(((histFreq.y()[0] / 2) + (histFreq.y()[1] * 2)) / 2), 1e-14);
+    TS_ASSERT_DELTA(outFreq.e()[1], std::sqrt(histFreq.y()[1] * 2), 1e-14);
     TS_ASSERT_DELTA(
         outFreq.e()[2],
-        std::sqrt(((histFreq.y()[2] / 2) + (histFreq.y()[1] * 2)) / 2), 1e-5);
+        std::sqrt(((histFreq.y()[2] / 2) + (histFreq.y()[1] * 2)) / 2), 1e-14);
   }
 
   void testSmallerBinsAsymmetric() {
@@ -291,8 +291,8 @@ public:
     TS_ASSERT_EQUALS(outFreq.y()[1], (histFreq.y()[1] + histFreq.y()[2]) / 2);
 
     for (size_t i = 0; i < outCounts.y().size(); i++) {
-      TS_ASSERT_DELTA(outCounts.e()[i], std::sqrt(outCounts.y()[i]), 1e-5);
-      TS_ASSERT_DELTA(outFreq.e()[i], std::sqrt(outFreq.y()[i]), 1e-5);
+      TS_ASSERT_DELTA(outCounts.e()[i], std::sqrt(outCounts.y()[i]), 1e-14);
+      TS_ASSERT_DELTA(outFreq.e()[i], std::sqrt(outFreq.y()[i]), 1e-14);
     }
   }
 
@@ -315,13 +315,13 @@ public:
     TS_ASSERT_EQUALS(outFreq.y()[1], (histFreq.y()[0] + histFreq.y()[1]) / 2);
     TS_ASSERT_EQUALS(outFreq.y()[2], histFreq.y()[1] / 2);
 
-    TS_ASSERT_DELTA(outCounts.e()[0], std::sqrt(outCounts.y()[0]), 1e-5);
-    TS_ASSERT_DELTA(outCounts.e()[1], std::sqrt(outCounts.y()[1]), 1e-5);
-    TS_ASSERT_DELTA(outCounts.e()[2], std::sqrt(outCounts.y()[2]), 1e-5);
+    TS_ASSERT_DELTA(outCounts.e()[0], std::sqrt(outCounts.y()[0]), 1e-14);
+    TS_ASSERT_DELTA(outCounts.e()[1], std::sqrt(outCounts.y()[1]), 1e-14);
+    TS_ASSERT_DELTA(outCounts.e()[2], std::sqrt(outCounts.y()[2]), 1e-14);
 
-    TS_ASSERT_DELTA(outFreq.e()[0], std::sqrt(outFreq.y()[0]), 1e-5);
-    TS_ASSERT_DELTA(outFreq.e()[1], std::sqrt(outFreq.y()[1]), 1e-5);
-    TS_ASSERT_DELTA(outFreq.e()[2], outFreq.y()[2], 1e-5);
+    TS_ASSERT_DELTA(outFreq.e()[0], std::sqrt(outFreq.y()[0]), 1e-14);
+    TS_ASSERT_DELTA(outFreq.e()[1], std::sqrt(outFreq.y()[1]), 1e-14);
+    TS_ASSERT_DELTA(outFreq.e()[2], outFreq.y()[2], 1e-14);
   }
 
   void testSmallerBinsSymmetric() {
@@ -358,7 +358,7 @@ public:
     TS_ASSERT_EQUALS(outCounts.y()[2], 0);
 
     TS_ASSERT_EQUALS(outCounts.e()[0], 0);
-    TS_ASSERT_DELTA(outCounts.e()[1], std::sqrt(outCounts.y()[1]), 1e-5);
+    TS_ASSERT_DELTA(outCounts.e()[1], std::sqrt(outCounts.y()[1]), 1e-14);
     TS_ASSERT_EQUALS(outCounts.e()[2], 0);
 
     TS_ASSERT_EQUALS(outFreq.y()[0], 0);
@@ -366,7 +366,7 @@ public:
     TS_ASSERT_EQUALS(outFreq.y()[2], 0);
 
     TS_ASSERT_EQUALS(outFreq.e()[0], 0);
-    TS_ASSERT_DELTA(outFreq.e()[1], std::sqrt(outFreq.y()[1]), 1e-5);
+    TS_ASSERT_DELTA(outFreq.e()[1], std::sqrt(outFreq.y()[1]), 1e-14);
     TS_ASSERT_EQUALS(outFreq.e()[2], 0);
   }