windows - output both stderr and stdout to file, and only stderr to command prompt

When my batch script runs, I want any errors to show up on the command prompt, so the user sees it straight away, while suppressing all the standard output that shows up.

But I want everything to be outputted to a log file. How do I do this?

In other words,

+---------+
|         | --- stderr ---------> Console
| Program |
|         | --- stdout/err -----> Log file
+---------+