gimp - How can I get this HDR or painted blur effect from a photo?

How can I get this HDR or painted blur effect from a photo in Photoshop, Gimp, Inkscape or some other software?

Answer

To create a similar effect as can be seen from HDR photos we can increase overall image details by a fake contrast enhancement by a dynamic range increase.

There is quite a cool effect "Freaky Details" from the G'MIC plugin to Gimp which tremendously helps us to do so.

1. 
   

   Source image:

   
   

   

   
   


2. 
   

   "Freaky Details" with ridicoulous high settings:

   
   

   

   
   


3. 
   
   

   Heavy Gaussian blurring:

   
   

   

   
   


4. 
   

   The blurred image 3. with 50% opacity as a layer on top of the detailed image 2. gives the desired effect: