Failure of a spline curve

Hi:

This is my first post, so forgive me if this is not the right forum. Please direct to correct forum, if necessary

I've done many spline calculations but the data below yields some strange results.

Table 1 represents the x,y data that is used to create the spline.

Table 2 represents the spline coefficients.

To determine x for a certain value of y I use the Newton-Raphson method.

The question is why for the value of y = 0.16721 does the value of x calculate to 770.35 when clearly it should be around 500.

Yet, when y = 0.16740, x = 500.58. That makes sense.

Also, why for a value of y = 0.14788 does the value of x calculate to -238.97. Based on the x,y data, x should be around 375, not a negative number.

Doesn't make sense to me.

Table 1

x y

1E-20 0.09215762

100 0.098262815

500 0.167314111

750 0.187933238

1000 0.198293337

Table 2

ai bi ci di

1.57803E-09 0 4.52716E-05 0.09215762

-6.83425E-10 4.73409E-07 9.26125E-05 0.098262815

4.1369E-10 -3.467E-07 0.000143296 0.167314111

4.85776E-11 -3.64332E-08 4.75126E-05 0.187933238

0 0 0 0

Thanks for any help in this matter.