least_square_fit.c fit 1.0 + 2.0*a + 3.0*b + 4.0*c + 5.0*d + 6.0*a*a + 7.0*a*b + 8.0*a*c + 9.0*a*d + 10.0*b*b + 11.0*b*c + 12.0*b*d + 13.0*c*c + 14.0*c*d + 15.0*d*d + 16.0*a*a*a + 17.0*a*a*b + 18.0*a*a*c + 19.0*a*a*d + 20.0*a*b*b + 21.0*a*b*c + 22.0*a*b*d + 23.0*a*c*c + 24.0*a*c*d + 25.0*a*d*d + 26.0*b*b*b + 27.0*b*b*c + 28.0*b*b*d + 29.0*b*c*c + 30.0*b*c*d + 31.0*c*c*c + 32.0*c*c*d + 33.0*c*d*d + 34.0*d*d*d + 35.0*a*a*a*a + 36.0*a*a*a*b + 37.0*a*a*a*c + 38.0*a*a*a*d + 39.0*a*a*b*b + 40.0*a*a*b*c + 41.0*a*a*b*d + 42.0*a*a*c*c + 43.0*a*a*c*d + 44.0*a*a*d*d + 45.0*a*b*b*b + 46.0*a*b*b*c + 47.0*a*b*b*d + 48.0*a*c*c*c + 49.0*a*c*c*d + 50.0*a*c*d*d + 51.0*a*d*d*d + 52.0*b*b*b*b + 53.0*b*b*b*c + 54.0*b*b*b*d + 55.0*b*b*c*c + 56.0*b*b*c*d + 57.0*b*b*d*d + 58.0*b*c*c*c + 59.0*b*c*c*d + 60.0*b*c*d*d + 61.0*b*d*d*d + 62.0*c*c*c*c + 63.0*c*c*c*d + 64.0*c*c*d*d + 65.0*c*d*d*d + 66.0*d*d*d*d; 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 fit with 4 variables to 1 power using 5 terms check_4d k=624, amin=0, amax=4, bmin=0, bmax=4 cmin=0, cmax=4, dmin=0, dmax=4, umin=60, umax=445833 Least Square Fit is u = -102150 * a^0 * b^0 * c^0 *d^0 17250.6 * a^1 * b^0 * c^0 *d^0 21102.8 * a^0 * b^1 * c^0 *d^0 23310.4 * a^0 * b^0 * c^1 *d^0 23782.8 * a^0 * b^0 * c^0 *d^1 rms_err=28582.1, avg_err=20391, max_err=206196 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 fit with 4 variables to 2 power using 15 terms check_4d k=624, amin=0, amax=4, bmin=0, bmax=4 cmin=0, cmax=4, dmin=0, dmax=4, umin=60, umax=445833 Least Square Fit is u = 49745 * a^0 * b^0 * c^0 * d^0 -21587.3 * a^1 * b^0 * c^0 * d^0 -26593.9 * a^0 * b^1 * c^0 * d^0 -28669 * a^0 * b^0 * c^1 * d^0 -29285.9 * a^0 * b^0 * c^0 * d^1 3839.85 * a^2 * b^0 * c^0 * d^0 3583.99 * a^1 * b^1 * c^0 * d^0 3954.59 * a^1 * b^0 * c^1 * d^0 4079.19 * a^1 * b^0 * c^0 * d^1 5177.14 * a^0 * b^2 * c^0 * d^0 4893.99 * a^0 * b^1 * c^1 * d^0 4894.59 * a^0 * b^1 * c^0 * d^1 5612.42 * a^0 * b^0 * c^2 * d^0 5794.79 * a^0 * b^0 * c^1 * d^1 5822.14 * a^0 * b^0 * c^0 * d^2 rms_err=6796.88, avg_err=4595.39, max_err=58189.5 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 15 a^3 * b^0 * c^0 *d^0 16 a^2 * b^1 * c^0 *d^0 17 a^2 * b^0 * c^1 *d^0 18 a^2 * b^0 * c^0 *d^1 19 a^1 * b^2 * c^0 *d^0 20 a^1 * b^1 * c^1 *d^0 21 a^1 * b^1 * c^0 *d^1 22 a^1 * b^0 * c^2 *d^0 23 a^1 * b^0 * c^1 *d^1 24 a^1 * b^0 * c^0 *d^2 25 a^0 * b^3 * c^0 *d^0 26 a^0 * b^2 * c^1 *d^0 27 a^0 * b^2 * c^0 *d^1 28 a^0 * b^1 * c^2 *d^0 29 a^0 * b^1 * c^1 *d^1 30 a^0 * b^0 * c^3 *d^0 31 a^0 * b^0 * c^2 *d^1 32 a^0 * b^0 * c^1 *d^2 33 a^0 * b^0 * c^0 *d^3 fit with 4 variables to 3 power using 34 terms check_4d k=624, amin=0, amax=4, bmin=0, bmax=4 cmin=0, cmax=4, dmin=0, dmax=4, umin=60, umax=445833 Least Square Fit is u = -4572.37 * a^0 * b^0 * c^0 * d^0 6678.96 * a^1 * b^0 * c^0 * d^0 6842.76 * a^0 * b^1 * c^0 * d^0 8521.47 * a^0 * b^0 * c^1 * d^0 3027.4 * a^0 * b^0 * c^0 * d^1 -2811.88 * a^2 * b^0 * c^0 * d^0 -2784 * a^1 * b^1 * c^0 * d^0 -2721.4 * a^1 * b^0 * c^1 * d^0 -2802.8 * a^1 * b^0 * c^0 * d^1 -3784.59 * a^0 * b^2 * c^0 * d^0 -3390 * a^0 * b^1 * c^1 * d^0 -594.494 * a^0 * b^1 * c^0 * d^1 -4037.31 * a^0 * b^0 * c^2 * d^0 -4131.2 * a^0 * b^0 * c^1 * d^1 -2787.14 * a^0 * b^0 * c^0 * d^2 521.049 * a^3 * b^0 * c^0 * d^0 556.227 * a^2 * b^1 * c^0 * d^0 579.227 * a^2 * b^0 * c^1 * d^0 596.227 * a^2 * b^0 * c^0 * d^1 637.227 * a^1 * b^2 * c^0 * d^0 372.317 * a^1 * b^1 * c^1 * d^0 381.317 * a^1 * b^1 * c^0 * d^1 582.227 * a^1 * b^0 * c^2 * d^0 599.317 * a^1 * b^0 * c^1 * d^1 612.227 * a^1 * b^0 * c^0 * d^2 749.049 * a^0 * b^3 * c^0 * d^0 774.227 * a^0 * b^2 * c^1 * d^0 791.227 * a^0 * b^2 * c^0 * d^1 720.227 * a^0 * b^1 * c^2 * d^0 737.317 * a^0 * b^1 * c^1 * d^1 868.049 * a^0 * b^0 * c^3 * d^0 887.227 * a^0 * b^0 * c^2 * d^1 904.227 * a^0 * b^0 * c^1 * d^2 919.049 * a^0 * b^0 * c^0 * d^3 rms_err=1853.23, avg_err=1514.88, max_err=9210.76 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 15 a^3 * b^0 * c^0 *d^0 16 a^2 * b^1 * c^0 *d^0 17 a^2 * b^0 * c^1 *d^0 18 a^2 * b^0 * c^0 *d^1 19 a^1 * b^2 * c^0 *d^0 20 a^1 * b^1 * c^1 *d^0 21 a^1 * b^1 * c^0 *d^1 22 a^1 * b^0 * c^2 *d^0 23 a^1 * b^0 * c^1 *d^1 24 a^1 * b^0 * c^0 *d^2 25 a^0 * b^3 * c^0 *d^0 26 a^0 * b^2 * c^1 *d^0 27 a^0 * b^2 * c^0 *d^1 28 a^0 * b^1 * c^2 *d^0 29 a^0 * b^1 * c^1 *d^1 30 a^0 * b^0 * c^3 *d^0 31 a^0 * b^0 * c^2 *d^1 32 a^0 * b^0 * c^1 *d^2 33 a^0 * b^0 * c^0 *d^3 34 a^4 * b^0 * c^0 *d^0 35 a^3 * b^1 * c^0 *d^0 36 a^3 * b^0 * c^1 *d^0 37 a^3 * b^0 * c^0 *d^1 38 a^2 * b^2 * c^0 *d^0 39 a^2 * b^1 * c^1 *d^0 40 a^2 * b^1 * c^0 *d^1 41 a^2 * b^0 * c^2 *d^0 42 a^2 * b^0 * c^1 *d^1 43 a^2 * b^0 * c^0 *d^2 44 a^1 * b^3 * c^0 *d^0 45 a^1 * b^2 * c^1 *d^0 46 a^1 * b^2 * c^0 *d^1 47 a^1 * b^0 * c^3 *d^0 48 a^1 * b^0 * c^2 *d^1 49 a^1 * b^0 * c^1 *d^2 50 a^1 * b^0 * c^0 *d^3 51 a^0 * b^4 * c^0 *d^0 52 a^0 * b^3 * c^1 *d^0 53 a^0 * b^3 * c^0 *d^1 54 a^0 * b^2 * c^2 *d^0 55 a^0 * b^2 * c^1 *d^1 56 a^0 * b^2 * c^0 *d^2 57 a^0 * b^1 * c^3 *d^0 58 a^0 * b^1 * c^2 *d^1 59 a^0 * b^1 * c^1 *d^2 60 a^0 * b^1 * c^0 *d^3 61 a^0 * b^0 * c^4 *d^0 62 a^0 * b^0 * c^3 *d^1 63 a^0 * b^0 * c^2 *d^2 64 a^0 * b^0 * c^1 *d^3 65 a^0 * b^0 * c^0 *d^4 fit with 4 variables to 4 power using 66 terms check_4d k=624, amin=0, amax=4, bmin=0, bmax=4 cmin=0, cmax=4, dmin=0, dmax=4, umin=60, umax=445833 Least Square Fit is u = 1 * a^0 * b^0 * c^0 * d^0 2 * a^1 * b^0 * c^0 * d^0 3 * a^0 * b^1 * c^0 * d^0 4 * a^0 * b^0 * c^1 * d^0 5 * a^0 * b^0 * c^0 * d^1 6 * a^2 * b^0 * c^0 * d^0 7 * a^1 * b^1 * c^0 * d^0 8 * a^1 * b^0 * c^1 * d^0 9 * a^1 * b^0 * c^0 * d^1 10 * a^0 * b^2 * c^0 * d^0 11 * a^0 * b^1 * c^1 * d^0 12 * a^0 * b^1 * c^0 * d^1 13 * a^0 * b^0 * c^2 * d^0 14 * a^0 * b^0 * c^1 * d^1 15 * a^0 * b^0 * c^0 * d^2 16 * a^3 * b^0 * c^0 * d^0 17 * a^2 * b^1 * c^0 * d^0 18 * a^2 * b^0 * c^1 * d^0 19 * a^2 * b^0 * c^0 * d^1 20 * a^1 * b^2 * c^0 * d^0 21 * a^1 * b^1 * c^1 * d^0 22 * a^1 * b^1 * c^0 * d^1 23 * a^1 * b^0 * c^2 * d^0 24 * a^1 * b^0 * c^1 * d^1 25 * a^1 * b^0 * c^0 * d^2 26 * a^0 * b^3 * c^0 * d^0 27 * a^0 * b^2 * c^1 * d^0 28 * a^0 * b^2 * c^0 * d^1 29 * a^0 * b^1 * c^2 * d^0 30 * a^0 * b^1 * c^1 * d^1 31 * a^0 * b^0 * c^3 * d^0 32 * a^0 * b^0 * c^2 * d^1 33 * a^0 * b^0 * c^1 * d^2 34 * a^0 * b^0 * c^0 * d^3 35 * a^4 * b^0 * c^0 * d^0 36 * a^3 * b^1 * c^0 * d^0 37 * a^3 * b^0 * c^1 * d^0 38 * a^3 * b^0 * c^0 * d^1 39 * a^2 * b^2 * c^0 * d^0 40 * a^2 * b^1 * c^1 * d^0 41 * a^2 * b^1 * c^0 * d^1 42 * a^2 * b^0 * c^2 * d^0 43 * a^2 * b^0 * c^1 * d^1 44 * a^2 * b^0 * c^0 * d^2 45 * a^1 * b^3 * c^0 * d^0 46 * a^1 * b^2 * c^1 * d^0 47 * a^1 * b^2 * c^0 * d^1 48 * a^1 * b^0 * c^3 * d^0 49 * a^1 * b^0 * c^2 * d^1 50 * a^1 * b^0 * c^1 * d^2 51 * a^1 * b^0 * c^0 * d^3 52 * a^0 * b^4 * c^0 * d^0 53 * a^0 * b^3 * c^1 * d^0 54 * a^0 * b^3 * c^0 * d^1 55 * a^0 * b^2 * c^2 * d^0 56 * a^0 * b^2 * c^1 * d^1 57 * a^0 * b^2 * c^0 * d^2 58 * a^0 * b^1 * c^3 * d^0 59 * a^0 * b^1 * c^2 * d^1 60 * a^0 * b^1 * c^1 * d^2 61 * a^0 * b^1 * c^0 * d^3 62 * a^0 * b^0 * c^4 * d^0 63 * a^0 * b^0 * c^3 * d^1 64 * a^0 * b^0 * c^2 * d^2 65 * a^0 * b^0 * c^1 * d^3 66 * a^0 * b^0 * c^0 * d^4 rms_err=8.85853e-10, avg_err=7.01943e-10, max_err=3.20142e-09