fit_data_file.java
fit to 2 degree polynomial in 4 variables
terms used to find fit 
0   a^0 * b^0 * c^0 * d^0
 
1   a^1 * b^0 * c^0 * d^0
2   a^0 * b^1 * c^0 * d^0
3   a^0 * b^0 * c^1 * d^0
4   a^0 * b^0 * c^0 * d^1
 
5   a^2 * b^0 * c^0 * d^0
6   a^1 * b^1 * c^0 * d^0
7   a^1 * b^0 * c^1 * d^0
8   a^1 * b^0 * c^0 * d^1
9   a^0 * b^2 * c^0 * d^0
10   a^0 * b^1 * c^1 * d^0
11   a^0 * b^1 * c^0 * d^1
12   a^0 * b^0 * c^2 * d^0
13   a^0 * b^0 * c^1 * d^1
14   a^0 * b^0 * c^0 * d^2
 
trying 15 terms
16 lines read
Polynomial Coefficients
0.9999999999999998 * a^0 * b^0 * c^0 * d^0
-0.10000000000000009 * a^1 * b^0 * c^0 * d^0
0.10000000000000009 * a^0 * b^1 * c^0 * d^0
0.1999999999999993 * a^0 * b^0 * c^1 * d^1
16 lines read
check_4d k=16, amin=0.0, amax=1.0, bmin=0.0, bmax=1.0
         cmin=0.0, cmax=1.0, dmin=0.0, dmax=1.0, umin=0.9, umax=1.3
rms_err=1.9821445675202305E-16, avg_err=1.734723475976807E-16, max_err=3.3306690738754696E-16