Follow-up Comment #16, bug #39713 (project gsl):

I can confirm that my examples work with 4848
revision (2013-10-03 08:58:48) of roots/secant.c.

On the other hand I am in doubt if the form
  df_new = df * (1 - f_new / f);
may lead to a problem with some functions
(slowly converging third order root or something
else).

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