diff --git a/src/Pure/General/timing.scala b/src/Pure/General/timing.scala
--- a/src/Pure/General/timing.scala
+++ b/src/Pure/General/timing.scala
@@ -1,61 +1,66 @@
 /*  Title:      Pure/General/timing.scala
-    Module:     PIDE
     Author:     Makarius
 
 Basic support for time measurement.
 */
 
 package isabelle
 
 
 import java.util.Locale
 
 
 object Timing
 {
   val zero = Timing(Time.zero, Time.zero, Time.zero)
 
   def timeit[A](message: String, enabled: Boolean = true)(e: => A) =
     if (enabled) {
       val start = Time.now()
       val result = Exn.capture(e)
       val stop = Time.now()
 
       val timing = stop - start
       if (timing.is_relevant)
         Output.warning(
           (if (message == null || message.isEmpty) "" else message + ": ") +
             timing.message + " elapsed time")
 
       Exn.release(result)
     }
     else e
 }
 
 sealed case class Timing(elapsed: Time, cpu: Time, gc: Time)
 {
   def is_relevant: Boolean = elapsed.is_relevant || cpu.is_relevant || gc.is_relevant
 
+  def resources: Time = cpu + gc
+
+  def factor: Option[Double] =
+  {
+    val t1 = elapsed.seconds
+    val t2 = resources.seconds
+    if (t1 >= 3.0 && t2 >= 3.0) Some(t2 / t1) else None
+  }
+
   def + (t: Timing): Timing = Timing(elapsed + t.elapsed, cpu + t.cpu, gc + t.gc)
 
   def message: String =
     elapsed.message + " elapsed time, " + cpu.message + " cpu time, " + gc.message + " GC time"
 
-  def resources: Time = cpu + gc
   def message_resources: String =
   {
-    val resources = cpu + gc
-    val t1 = elapsed.seconds
-    val t2 = resources.seconds
-    val factor =
-      if (t1 >= 3.0 && t2 >= 3.0)
-        String.format(Locale.ROOT, ", factor %.2f", new java.lang.Double(t2 / t1))
-      else ""
-    if (t2 >= 3.0)
-      elapsed.message_hms + " elapsed time, " + resources.message_hms + " cpu time" + factor
+    val factor_text =
+      factor match {
+        case Some(f) => String.format(Locale.ROOT, ", factor %.2f", new java.lang.Double(f))
+        case None => ""
+      }
+    if (resources.seconds >= 3.0)
+      elapsed.message_hms + " elapsed time, " + resources.message_hms + " cpu time" + factor_text
     else
-      elapsed.message_hms + " elapsed time" + factor
+      elapsed.message_hms + " elapsed time" + factor_text
   }
 
   override def toString: String = message
 }