HI Don,
When I'm on the course, I have a simple set of numbers I keep in my head to calculate whether I should bear off or not.
In other words, I ask myself is "will pinching more, or bearing away more, increase my VMG?"
I used your example, which was a wind speed of 8 knots, a boat speed of 3 knots ,and I used a normal close hauled course of 45 deg. This is expressed in blue, and becomes the reference. This gives you a VMG of 2.12 knots.

I added in a 5 and 10 degree variation of the TWA, pinching up to 35 TWA, and bearing down to 55 TWA.
The % change from reference shows you how much more boat speed, or less, you need to maintain the same VMG for each TWA change.
As you can see, if you bear away 5 degrees you need a minimum of a 10% increase in boat speed
to maintain the same VMG.So, when I'm on the course I can do a quick check without getting all techo, and that is :
- I'm at 45TWA. Check my boat speed.
- Bear away 5 degrees. Check my boat speed again.
- If my new boat speed is greater than 10% increase, it's a faster angle. Stay on this angle.
- If my new boat speed is less than 10% increase, its slower. go back to your 45 TWA.
- If the result is exactly 10%, then pick either 45 or 50 deg TWA. It doesn't matter which as your VMG is the same.
It's also a sobering reminder if you're lazy and inattentive and you end up sailing down to 55 or 60TWA, you need a BIG lift in boat speed to keep the same VMG (which in the real world you won't ever get!).
The cool part is the % change in boat speed does not change regardless of the wind strength.
See the following table where I used a higher wind speed (16 knots) and a higher boat speed (6 knots) to calculate the same thing.

The percentage increase in boat speed that you are looking for
never changes regardless of the wind strength. A bear away from 45 to 50 deg TWA will always require a 10% increase in boat speed just to maintain the same VMG.
I've memorised the % numbers from 35 to 55 degrees, so when I'm helming I only need to calculate this % change to my current boat speed to ensure I'm not going slower.
35 TWA means a reduction in boat speed of no more than 14%.
40 TWA means a reduction in boat speed of no more than 8%.
45 TWA is my reference.
50 TWA means an increase in boat speed of no less than 10%. (This is the one I use most often as I'm normally playing in this range)
55 TWA means an increase in boat speed of no less than 23%
I've always found getting fixated and pinching to lay a mark means I get flogged. If I sail the boat to optimal VMG, even if that means throwing in a tack, I always get there quicker.
Important note: None of the above allows for tide and sea state as a factor. Or if you really suck at tacking!
Hope this helps mate,
SB