Quantifying chromatic adaptations made by the brain What are the ways one can use to measure the kind of adaptations done by the brain to provide colour constancy? Has this been done before?
You have specifically asked about the &quot;adaptations done by the brain&quot; in your initial question and an interest in &quot;what has been done towards finding the formula and what it was replaced with for the time being?&quot; By formula, I'm assuming that you meant a perceptual algorithm that can be useful in machine learning and the attempt to reverse-engineer human's perceptual systems.
Yes, there has been extensive work done on this. I cannot give you an extensive answer on this platform, but hopefully point you towards the right direction. I have mentioned two papers and their abstracts, the former is more accessible, and the later in case you want a sneak-peak of the mathematical methods involved in making a computational model of color constancy and chromatic adaptations.
On the other hand, if you're new to this or you want to simply refresh your memory - I have attached my ex-Professor's notes from a Perception class I took a few years ago to give a clearer idea. It might just be best to first read through those first, in which case you should skip the first two papers I have mentioned.

Sensory, computational and cognitive components of human colour constancy. 
Smithson H. 
Philosophical Transactions of the Royal Society, Biological Sciences. 2005; 360(1458): 1329-1346.

Abstract  
When the illumination on a scene changes, so do the visual signals
elicited by that scene. In spite of these changes, the objects within
a scene tend to remain constant in their apparent colour. We start
this review by discussing the psychophysical procedures that have been
used to quantify colour constancy. The transformation imposed on the
visual signals by a change in illumination dictates what the visual
system must ‘undo’ to achieve constancy. The problem is mathematically
underdetermined, and can be solved only by exploiting regularities of
the visual world. The last decade has seen a substantial increase in
our knowledge of such regularities as technical advances have made it
possible to make empirical measurements of large numbers of
environmental scenes and illuminants. This review provides a taxonomy
of models of human colour constancy based first on the assumptions
they make about how the inverse transformation might be simplified,
and second, on how the parameters of the inverse transformation might
be set by elements of a complex scene. Candidate algorithms for human
colour constancy are represented graphically and pictorially, and the
availability and utility of an accurate estimate of the illuminant is
discussed. Throughout this review, we consider both the information
that is, in principle, available and empirical assessments of what
information the visual system actually uses. In the final section we
discuss where in our visual systems these computations might be
implemented.


Color constancy using natural image statistics and scene semantics. 
A. Gijsenij and T.Gevers. 
IEEE PAMI, 33(4):687–698, 2011.

Abstract  
To achieve selection and combining of color constancy algorithms, in
this paper natural image statistics are used to identify the most
important characteristics of color images. Then, based on these image
characteristics, the proper color constancy algorithm (or best
combination of algorithms) is selected for a specific image. To
capture the image characteristics, the Weibull parameterization (e.g.,
grain size and contrast) is used. It is shown that the Weibull
parameterization is related to the image attributes to which the used
color constancy methods are sensitive. An MoG-classifier is used to
learn the correlation and weighting between the Weibull-parameters and
the image attributes (number of edges, amount of texture, and SNR).
The output of the classifier is the selection of the best performing
color constancy method for a certain image. Experimental results show
a large improvement over state-of-the-art single algorithms. On a data
set consisting of more than 11,000 images, an increase in color
constancy performance up to 20 percent (median angular error) can be
obtained compared to the best-performing single algorithm. Further, it
is shown that for certain scene categories, one specific color
constancy algorithm can be used instead of the classifier considering
several algorithms.



Below are examples of a few experiments that can be played out from behind your computer screen:
From Jonathon Winawer's notes on Perception:

Color Constancy and Chromatic Adaption  
Take a photograph under fluorescent light, and compare it to the same picture under daylight. The colors come out totally differently - greenish under the fluorescent light and reddish under daylight - unless you do some &quot;color correction&quot; while developing the film.

But  you wouldn't  see  it  that  way if  you were  in the  room.  To  you the  colors  would  look  pretty much the  same  under both  illuminants.  This  phenomenon  is  called  color  constancy,  analogous  to  brightness  constancy that  we  discussed earlier.  The  eye  does  not  act  like  a  camera,  simply recording  the  image.  Rather,  the  eye  adapts  to  compensate  for the  color  (SPD)  of  the  light  source.

Above  is  another  example  of  a  pair  of  photographs  taken under  different  lighting  conditions  without  color  correction. The  physical  characteristics  of  the  light  reaching  the  camera  is  very different  depending  on  the  color  of  the  illuminant. This  results  in  dramatically  different  photographs.  But  if  you  were  there  when  the  pictures  were  taken,  this  object would  look  pretty  much the  same  to  you under  both illuminants.

Glance  at  the  penguin and  dragon pictures  above  by fixated  on the  dot  between them.  The  penguin picture  looks very  blueish  and  the  dragon looks  very yellowish.  Next,  you will  hold  your  gaze  on the  dot  between the  blue  and  yellow fields.  Continue  staring  at  that  dot  for  30  secs  or  so.  Then look  back  at  the  penguin and  dragon by fixating  the  dot between them.  What  do  you see?  Why? The  change  in percept  following  adaptation is  due  to  chromatic  adaptation.  Chromatic  adaptation is  like  light  and dark  adaptation  but  instead  of  adapting  just  to  light  and  dark,  it  adapts  to  whatever  the  color  is  of  the  ambient illumination.

Each cone  type  adapts  independently.  For  example,  a  given L  cone  adapts  according  to  local  average  L  cone excitation.  Likewise  for  the  M  cones.  Thus,  the  retinal  image  adjusts  to  compensate  not  only for  the  overall  intensity of  the  light  source,  but  also  to  compensate  for  the  color  of  the  light  source.

Chromatic  adaptation,  like  light  adaptation,  can  give  rise  to  dramatic  aftereffects.  For  example,  adapt  to  this  green, black,  and  yellow  flag  for  60  secs,  then look  at  a  white  field  and  you will  see  an afterimage  of  a  red,  white,  and  blue flag.  Red/green,  blue/yellow,  black/white  are  complementary colors.  Normally,  when  you look  at  a  white  field,  L  and  M cones  give  about  the  same  response  so  the  red/green opponnent  colors  mechanism  does  not  respond  at  all.  If  you adapt  to  green,  the  M  cone  sensitivity is  reduced.  Then,  when you look  at  a  white  field,  the  L:M  cones  are  out  of balance;  the  L  cones  are  now  more  sensitive  than the  M  cones  so  the  red/green mechanism  gives  a  positive response  and  you see  red  instead  of  white.  This  only lasts  for  a  couple  of  seconds  because  the  M  cone  sensitivity starts  to  readjust  right  away. The  visual  system  is  designed  to  try to  achieve  a  perceptual  constancy.  But,  as  with the  various  brightness  illusions  I showed  earlier,  color  adaptation  also  results  in  some  misperceptions.  The  colored  afterimage  is  an undesirable consequence  of  chromatic  adaptation coupled  with color  opponency.  Usually chromatic  adaptation does  the  right thing,  it  compensates  for  the  color  of  the  illuminant.