If you are using Python 2.x, be careful with an expression such as U/60. If U is an integer, or a numpy array of integers, then this operation is integer division (i.e. 45/60 is 0, 65/60 is 1, 123/60 ...

The functions in scipy.optimize fsolve and root both return a wrong number function evaluations in the information they return. So this two extra function evaluations should be counted (or at least ...