This example illustrates the dangers of picking a poor starting point, one relatively far from the root. Note that iterating from 0 is impossible (division by zero). Iterating from -1 also gives wonky behaviour. Iterating from 1, -2, -3 or -4 gives quick convergence. 2.000000000000000000 1.169815477487221478 .357149517115751899 -1.835679335890070815 -4.505093832444827674 <<< relatively far from root and f' close to zero -.043640880622785036 <<< very close to problem point 0 23.930484215614439965 the grand tour continues 22.930484215562109153 21.930484215538255219 20.930484215854862270 19.930484216961118040 18.930484217871193078 17.930484212370250497 16.930484189487252676 15.930484162917787555 14.930484253956713380 13.930484717696496547 12.930485407189078200 11.930484005897337486 10.930474795005322990 9.930458093473765801 8.930477095311892615 7.930656296571728588 6.931042321320887568 5.930852736960792660 4.927434541434775579 3.918796960235235254 2.919023936049257771 1.980365443023475471 1.152470976239139932 .336377137744136832 <<< not far from 2nd iteration -2.010131876587732107 but by luck a better outcome this time -3.867790320137767698 -3.031049197542676763 -3.183217037259705302 -3.183063010987051498 -3.183063011933363592 << 36th iteration after a grand tour -3.183063011933363592