GUI with automatic scaling does not resize proportionally

The bug

When you resize the game vertically the GUI is not proportional to the window size. The attached screenshots show the GUI with automatically scaling where "GUI size after window resize (1.11).png" shows the GUI after the window height was reduced by maybe 10 pixels.

How to reproduce

1. Start Minecraft
2. Set Options... → Video Settings... → GUI Scale: Auto
3. Decrease the game window height slightly vertically (continue decreasing the height in case the issue does not occur directly)
   The GUI size changes drastically