Generation of interpolation tables
... y=1/(1+x^2)    -5<x<5
How many entries go in these tables?
100
       x           f(x)    interpolated   error
1   -5.000000    0.038462-3.24084085002874949E51    -.2186E+52
2   -4.900990    0.039968-7.29536258823079249E50    -.5395E+51
3   -4.801980    0.041564-3.77867784005347708E50    -.2534E+51
4   -4.702970    0.043256-8.1924556442085577E49    -.6056E+50
5   -4.603960    0.045052-4.18652226397050322E49    -.2769E+50
6   -4.504950    0.046960-8.23291961762470959E48    -.6142E+49
7   -4.405941    0.048990-6.58358445391221616E48    -.4004E+49
8   -4.306931    0.051152-1.90738476061210822E48    -.1260E+49
9   -4.207921    0.053457-6.45176043673584333E47    -.3893E+48
10   -4.108911    0.055919-1.8168363456903492E47    -.1189E+48
11   -4.009901    0.058550-5.8613578616343183E46    -.3505E+47
12   -3.910891    0.061368-5.69342832906784261E45    -.4504E+46
13   -3.811881    0.064390-1.18211978644468884E46    -.6850E+46
14   -3.712871    0.067634-1.13865424210585384E45    -.7063E+45
15   -3.613861    0.071124-3.16383634907206582E44    -.1956E+45
16   -3.514851    0.074883-8.47117170938396546E43    -.5203E+44
17   -3.415842    0.078939-2.19145411128649905E43    -.1341E+44
18   -3.316832    0.083324-6.04813932733313754E42    -.3682E+43
19   -3.217822    0.088072-1.54825150073769119E42    -.1109E+43
20   -3.118812    0.0932231.13174068858635128E42    .6992E+42
21   -3.019802    0.098822-3.83827903035603783E41    -.2412E+42
22   -2.920792    0.1049206.59167327295199982E40    .4036E+41
23   -2.821782    0.111577-2.11314238555017605E40    -.1316E+41
24   -2.722772    0.118857-8.81887094160868136E38    -.5571E+39
25   -2.623762    0.126837-2.09499583110668559E38    -.1313E+39
26   -2.524752    0.135605-4.2899871056227394E37    -.2679E+38
27   -2.425743    0.145260-8.83082355177673694E36    -.5503E+37
28   -2.326733    0.155917-1.78905224704407561E36    -.1106E+37
29   -2.227723    0.167708-8.62975178549457144E35    -.5245E+36
30   -2.128713    0.180785-3.18110099939633109E34    -.1145E+35
31   -2.029703    0.195324-2.25658738938058115E34    -.1323E+35
32   -1.930693    0.211525-2.82291366541823555E33    -.1545E+34
33   -1.831683    0.229618-3.16802942000229612E32    -.1899E+33
34   -1.732673    0.249865-5.07789741462604654E31    -.3038E+32
35   -1.633663    0.272565-7.58986121030401962E30    -.4509E+31
36   -1.534653    0.298048-1.59255898613432958E30    -.8720E+30
37   -1.435644    0.326683-2.14491300681297688E29    -.1167E+30
38   -1.336634    0.358862-2.9618851129798261E28    -.1619E+29
39   -1.237624    0.394990-3.53725382349783876E27    -.1916E+28
40   -1.138614    0.435456-4.03238261134504138E26    -.2165E+27
41   -1.039604    0.480590-2.33261675930186236E25    -.1409E+26
42   -0.940594    0.530584-2.24444817675638089E24    -.1349E+25
43   -0.841584    0.585390-2.49068552579937888E23    -.1396E+24
44   -0.742574    0.644572-2.03781367922139469E22    -.1134E+23
45   -0.643564    0.707126-1.45634594180082408E21    -.8038E+21
46   -0.544554    0.771284-1.08000526444374344E20    -.5959E+20
47   -0.445545    0.834369-8.2034205194673111E18    -.4106E+19
48   -0.346535    0.892788-359247643289844032.000000    -.1782E+18
49   -0.247525    0.942269-12395637436594604.000000    -.6156E+16
50   -0.148515    0.978419-341315308418765.062000    -.1642E+15
51   -0.049505    0.997555-4264803917879.197750    -.2141E+13
52    0.049505    0.997555-21926722714.010651    -.1088E+11
53    0.148515    0.978419120693671.200726    .5932E+08
54    0.247525    0.942269-1478698.193716    -.7564E+06
55    0.346535    0.89278821191.723693    .1218E+05
56    0.445545    0.834369-3066.918701    -.1388E+04
57    0.544554    0.771284  140.027344    .6123E+02
58    0.643564    0.707126   -0.061168    -.5303E+00
59    0.742574    0.644572    1.144913    .2206E+00
60    0.841584    0.585390    0.552474    -.1490E-01
61    0.940594    0.530584    0.533673    .1382E-02
62    1.039604    0.480590    0.480257    -.1464E-03
63    1.138614    0.435456    0.435489    .1498E-04
64    1.237624    0.394990    0.394985    -.1950E-05
65    1.336634    0.358862    0.358862    .2807E-06
66    1.435644    0.326683    0.326683    -.6561E-07
67    1.534653    0.298048    0.298048    .2725E-08
68    1.633663    0.272565    0.272565    -.1948E-08
69    1.732673    0.249865    0.249865    .4152E-09
70    1.831683    0.229618    0.229618    -.8056E-10
71    1.930693    0.211525    0.211525    .1503E-10
72    2.029703    0.195324    0.195324    -.3643E-11
73    2.128713    0.180785    0.180785    .9428E-12
74    2.227723    0.167708    0.167708    -.2551E-12
75    2.326733    0.155917    0.155917    .7132E-13
76    2.425743    0.145260    0.145260    -.1940E-13
77    2.524752    0.135605    0.135605    .6928E-14
78    2.623762    0.126837    0.126837    -.2320E-14
79    2.722772    0.118857    0.118857    .8490E-15
80    2.821782    0.111577    0.111577    -.2951E-15
81    2.920792    0.104920    0.104920    .1141E-15
82    3.019802    0.098822    0.098822    -.4746E-16
83    3.118812    0.093223    0.093223    .1994E-16
84    3.217822    0.088072    0.088072    -.8866E-17
85    3.316832    0.083324    0.083324    .3906E-17
86    3.415842    0.078939    0.078939    -.1984E-17
87    3.514851    0.074883    0.074883    .9793E-18
88    3.613861    0.071124    0.071124    -.5226E-18
89    3.712871    0.067634    0.067634    .2618E-18
90    3.811881    0.064390    0.064390    -.1443E-18
91    3.910891    0.061368    0.061368    .8431E-19
92    4.009901    0.058550    0.058550    -.5161E-19
93    4.108911    0.055919    0.055919    .3327E-19
94    4.207921    0.053457    0.053457    -.2023E-19
95    4.306931    0.051152    0.051152    .1344E-19
96    4.405941    0.048990    0.048990    -.8702E-20
97    4.504950    0.046960    0.046960    .6025E-20
98    4.603960    0.045052    0.045052    -.3797E-20
99    4.702970    0.043256    0.043256    .2455E-20
100    4.801980    0.041564    0.041564    -.1557E-20