Send both standardOutput and errorOutput to a single file

When defining an Exec task, is it possible to redirect both standardOutput and errorOutput to the same file, so they are interleaved as they happen? I tried this:

def logFile = file("${temporaryDir}/output.txt")
standardOutput = logFile.newOutputStream()
errorOutput = standardOutput

This sometimes seems to work and sometimes fails with java.io.IOException: Stream Closed. For now I’m sending the two streams to two separate files, but is there any (simple) way to use only one?