from math import *

f = lambda x: 13* sin(x)-12
driv_f = lambda x: 13*cos(x)
starting_point = -4

_loop_limits = 8
_loop_snap_shot = 5

_ans = starting_point - ( f(starting_point) / driv_f(starting_point))

for loop in range(_loop_limits):
	_ans = _ans - ( f(_ans) / driv_f(_ans) )
	if (_loop_snap_shot == loop):
		print("loop snap",loop,'\n',_ans)

print("final loop",'\n',_ans)