from decimal import *
d = Decimal
getcontext().prec = 256
#e = d(e) #this is inaccurate
pi = d(pi)  #we actually don't need a fully accurate estimate of e, the entire thing converges even
#with just an aproximation

e=d('2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274274663919320030599218174135966290435729003342952605956307381323286279434907632338298807531')
#should write an override of d, that takes in a space separated string, or even a comma delimited version,
#or an underscore delimited version, and simply detects and removes the delimiters, before returning
#a relevant Decimal() instance with that value.

def est_e(limit = 20, F=None, E=None):
  x = d('1.391925581569705')

  if F == None:
    _f = d('596.25') #596.25
  else:
    _f = F

  if E == None:
    _e = (((1/(((((1/(x.ln() / (pi-d('0.5')).ln()))-1))-1)*(x-1)))-(1/((((1/_f)*17)+17)**2))))
  else:
    _e = E

  i = 0
  while i < limit:
    v = (1/((_e).ln()-1)).ln()
    _e = ((((1/(((((1/(x.ln() / (pi-d('0.5')).ln()))-1))-1)*(x-1)))-(1/((((1/_f)*17)+17)**2)))) - (1/(_e**v)))
    _f = 1/((((1/((1/(((((1/(x.ln() / (pi-d('0.5')).ln()))-1))-1)*(x-1)))-_e)).sqrt())/17)-1)
    i = i + 1

  print("done!")
  print(f"estimate e: {_e},  actual: {e},  ratio: {_e/e}, F: {F}")
  return _f, _e


#Edited slightly for those who want to do something like...

F, E = est_e(1, d(1))
#and then

i = 0
somelimit = 10000
while i < somelimit:
  F, E = est_e(1, F, E)
  i = i + 1