Newton Root Work

newton_root.rb

def newton_root(n)
	puts "\nvalue   : #{n}"
	guess = Math.sqrt(n)-4
	puts "start   : #{guess}"
	for i in 1..9
		guess = (n/guess + guess)/2
		puts "guess #{i} : #{guess}"
	end
	puts "result  : #{guess}"
	return guess
end

newton_root(250)
newton_root(25)
newton_root(173889)
newton_root(8100)
newton_root(2**53+1)
newton_root(5*(8670007398507948658051921 **2)+4)
newton_root(5*(8670007398507948658051921 **2)-4)


# value   : 250
# start   : 11.811388300841896
# guess 1 : 16.4887007213835
# guess 2 : 15.825299406476343
# guess 3 : 15.811394415066184
# guess 4 : 15.811388300843078
# guess 5 : 15.811388300841896
# guess 6 : 15.811388300841896
# guess 7 : 15.811388300841896
# guess 8 : 15.811388300841896
# guess 9 : 15.811388300841896
# result  : 15.811388300841896

# value   : 25
# start   : 1.0
# guess 1 : 13.0
# guess 2 : 7.461538461538462
# guess 3 : 5.406026962727994
# guess 4 : 5.015247601944898
# guess 5 : 5.000023178253949
# guess 6 : 5.000000000053722
# guess 7 : 5.0
# guess 8 : 5.0
# guess 9 : 5.0
# result  : 5.0

# value   : 173889
# start   : 413.0
# guess 1 : 417.01937046004844
# guess 2 : 417.0000004498769
# guess 3 : 417.0
# guess 4 : 417.0
# guess 5 : 417.0
# guess 6 : 417.0
# guess 7 : 417.0
# guess 8 : 417.0
# guess 9 : 417.0
# result  : 417.0

# value   : 8100
# start   : 86.0
# guess 1 : 90.09302325581396
# guess 2 : 90.00004802439639
# guess 3 : 90.00000000001282
# guess 4 : 90.0
# guess 5 : 90.0
# guess 6 : 90.0
# guess 7 : 90.0
# guess 8 : 90.0
# guess 9 : 90.0
# result  : 90.0

# value   : 9007199254740993
# start   : 94906261.62425156
# guess 1 : 94906265.62425163
# guess 2 : 94906265.62425154
# guess 3 : 94906265.62425154
# guess 4 : 94906265.62425154
# guess 5 : 94906265.62425154
# guess 6 : 94906265.62425154
# guess 7 : 94906265.62425154
# guess 8 : 94906265.62425154
# guess 9 : 94906265.62425154
# result  : 94906265.62425154

# value   : 375845141450912838252433332577199316842733658951209
# start   : 19386725908489880000000000.0
# guess 1 : 19386725908489883000000000.0
# guess 2 : 19386725908489883000000000.0
# guess 3 : 19386725908489883000000000.0
# guess 4 : 19386725908489883000000000.0
# guess 5 : 19386725908489883000000000.0
# guess 6 : 19386725908489883000000000.0
# guess 7 : 19386725908489883000000000.0
# guess 8 : 19386725908489883000000000.0
# guess 9 : 19386725908489883000000000.0
# result  : 19386725908489883000000000.0

# value   : 375845141450912838252433332577199316842733658951201
# start   : 19386725908489880000000000.0
# guess 1 : 19386725908489883000000000.0
# guess 2 : 19386725908489883000000000.0
# guess 3 : 19386725908489883000000000.0
# guess 4 : 19386725908489883000000000.0
# guess 5 : 19386725908489883000000000.0
# guess 6 : 19386725908489883000000000.0
# guess 7 : 19386725908489883000000000.0
# guess 8 : 19386725908489883000000000.0
# guess 9 : 19386725908489883000000000.0
# result  : 19386725908489883000000000.0