Toy dataset 1 (1D)

See >>notebook<< for the complete procedure.

This fit generates 44 candidate functions in total! The output files can be found here (feel free to download them and look at what a typical fit will produce).

Lets look at the output file candidates_reduced.csv, which is a csv table storing all candidate functions and their evaluations:

Unnamed: 0	Parameterized equation, unscaled	Parameters: (best-fit, +1, -1)	Covariance	Correlation	RMSE	R2	NDF	Chi2	Chi2/NDF	p-value
0	164.796*(a1)	{'a1': (0.217, 0, 0)}	{}	{}	251.4	-0.3575	20	2617	130.9	0
1	164.796*(a1)	{'a1': (0.214, 0, 0)}	{}	{}	251.7	-0.3603	20	2616	130.8	0
2	164.796*(a1)	{'a1': (0.207, 0, 0)}	{}	{}	252.3	-0.3667	20	2615	130.8	0
3	164.796(a1gauss(((x0 - 12.5) * 0.00210526)))	{'a1': (0.281, 0, 0)}	{}	{}	247.1	-0.3115	20	2442	122.1	0
4	164.796(a1gauss(((x0 - 12.5) * 0.00210526)))	{'a1': (0.364, 0, 0)}	{}	{}	240.5	-0.2418	20	2391	119.5	0
5	164.796(a1 + gauss(a2((x0 - 12.5) * 0.00210526)))	{'a1': (-0.580262, 0.0879, -0.0879), 'a2': (0.664, 0, 0)}	{}	{}	236.2	-0.1981	19	2341	123.2	0
6	164.796(a1((x0 - 12.5) * 0.00210526)**2 + a2)	{'a1': (-0.373, 0, 0), 'a2': (0.42, 0, 0)}	{}	{}	235.9	-0.195	20	2332	116.6	0
7	164.796(a2((x0 - 12.5) * 0.00210526)gauss(a1((x0 - 12.5) * 0.00210526)))	{'a1': (3.59295, 0.209, -0.209), 'a2': (23.0598, 3.58, -3.58)}	{'a1, a2': 0.566709136164767, 'a1, a1': 0.04388603536666481, 'a2, a2': 12.80292001370725}	{'a1, a2': 0.7574}	101.1	0.7806	18	516.1	28.67	4.309e-98
8	164.796(a2gauss(a1((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)))	{'a1': (3.54742, 0.212, -0.212), 'a2': (23.0587, 3.57, -3.57)}	{'a1, a2': 0.5720814049618776, 'a1, a1': 0.04482502637342434, 'a2, a2': 12.77891143029013}	{'a1, a2': 0.7559}	101.1	0.7805	18	515.6	28.64	5.579e-98
9	164.796(a1 + a3((x0 - 12.5) * 0.00210526)gauss(a2((x0 - 12.5) * 0.00210526)))	{'a1': (0.101, 0, 0), 'a2': (3.74294, 0.201, -0.201), 'a3': (23.3141, 3.23, -3.23)}	{'a2, a3': 0.48251182272739823, 'a2, a2': 0.040211012455602, 'a3, a3': 10.462590199359195}	{'a2, a3': 0.7432}	98.01	0.7937	18	374.3	20.79	2.066e-68
10	164.796(a1 + a3gauss(a2((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)))	{'a1': (0.101, 0, 0), 'a2': (3.69972, 0.203, -0.203), 'a3': (23.3188, 3.23, -3.23)}	{'a2, a3': 0.4872585724370911, 'a2, a2': 0.04105411260081572, 'a3, a3': 10.455540369032775}	{'a2, a3': 0.7431}	98.02	0.7937	18	374.1	20.78	2.255e-68
11	164.796(a2 + a3((x0 - 12.5) * 0.00210526)gauss(((x0 - 12.5) * 0.00210526)(a1 + ((x0 - 12.5) * 0.00210526))))	{'a1': (-4.14994, 0.171, -0.171), 'a2': (0.0872, 0, 0), 'a3': (24.3991, 3.21, -3.21)}	{'a1, a3': -0.4011883357672433, 'a1, a1': 0.02935889720666659, 'a3, a3': 10.28912788954329}	{'a1, a3': -0.7309}	99.26	0.7884	18	360.7	20.04	1.367e-65
12	164.796(a2 + a3gauss(((x0 - 12.5) * 0.00210526)(a1 + ((x0 - 12.5) * 0.00210526)))tanh(((x0 - 12.5) * 0.00210526)))	{'a1': (-4.1065, 0.173, -0.173), 'a2': (0.0871, 0, 0), 'a3': (24.3929, 3.21, -3.21)}	{'a1, a3': -0.40626319063172056, 'a1, a1': 0.030082893812041454, 'a3, a3': 10.289660354170426}	{'a1, a3': -0.7316}	99.26	0.7885	18	360.7	20.04	1.389e-65
13	164.796(a1 + a3((x0 - 12.5) * 0.00210526)2gauss(a2((x0 - 12.5) * 0.00210526)))	{'a1': (0.129, 0, 0), 'a2': (5.24767, 0.216, -0.216), 'a3': (266.419, 39.4, -39.4)}	{'a2, a3': 6.963559580470911, 'a2, a2': 0.046632482818286546, 'a3, a3': 1551.6445788927706}	{'a2, a3': 0.8182}	67.97	0.9008	18	311.4	17.3	2.143e-55
14	164.796(a2 + a4((x0 - 12.5) * 0.00210526)gauss(a1((x0 - 12.5) * 0.00210526))tanh(a3((x0 - 12.5) * 0.00210526)))	{'a1': (-4.21353, 0.192, -0.192), 'a2': (0.115, 0, 0), 'a3': (9.58, 0, 0), 'a4': (34.2102, 4.27, -4.27)}	{'a1, a4': -0.6416464471766923, 'a1, a1': 0.03678536292764734, 'a4, a4': 18.21270324041777}	{'a1, a4': -0.7826}	74.04	0.8823	18	267.9	14.88	1.825e-46
15	164.796(a2 + a4((x0 - 12.5) * 0.00210526)gauss(((x0 - 12.5) * 0.00210526)(a1 + ((x0 - 12.5) * 0.00210526)))tanh(a3((x0 - 12.5) * 0.00210526)))	{'a1': (-4.57364, 0.164, -0.164), 'a2': (0.107, 0, 0), 'a3': (9.55, 0, 0), 'a4': (35.5794, 4.09, -4.09)}	{'a1, a4': -0.5197029357615864, 'a1, a1': 0.026806771817266546, 'a4, a4': 16.73751870683508}	{'a1, a4': -0.7748}	74.51	0.8808	18	240	13.33	8.772e-41
16	164.796((a2 + a4((x0 - 12.5) * 0.00210526)2)gauss(a1((x0 - 12.5) * 0.00210526)) + gauss(a3*((x0 - 12.5) * 0.00210526)))	{'a1': (-5.88415, 0.2, -0.2), 'a2': (-0.951513, 0.0517, -0.0517), 'a3': (1.72352, 0.0815, -0.0815), 'a4': (296.816, 31.8, -31.8)}	{'a1, a2': 0.001358738686085326, 'a1, a3': 0.002392240533753859, 'a1, a4': -4.821726365958421, 'a2, a3': 4.184992307981176e-05, 'a2, a4': -0.3430854341608032, 'a3, a4': -0.14611265771480253, 'a1, a1': 0.039852692178434554, 'a2, a2': 0.0026721348659727185, 'a3, a3': 0.0066353130493951576, 'a4, a4': 1009.314739792375}	{'a1, a2': 0.1314, 'a1, a3': 0.1468, 'a1, a4': -0.7581, 'a2, a3': 0.009932, 'a2, a4': -0.2087, 'a3, a4': -0.05638}	56.46	0.9315	16	117.7	7.354	1.546e-17
17	164.796((a3 + ((x0 - 12.5) * 0.00210526)(a2 + a5((x0 - 12.5) * 0.00210526)))gauss(a1((x0 - 12.5) * 0.00210526)) + gauss(a4((x0 - 12.5) * 0.00210526)))	{'a1': (-5.93305, 0.193, -0.193), 'a2': (-1.74, 0, 0), 'a3': (-0.949194, 0.0506, -0.0506), 'a4': (1.72226, 0.0795, -0.0795), 'a5': (315.024, 31.4, -31.4)}	{'a1, a3': 0.0012720509708813409, 'a1, a4': 0.0022015376507341497, 'a1, a5': -4.554023119646412, 'a3, a4': 3.863236767342754e-05, 'a3, a5': -0.33180893448387044, 'a4, a5': -0.13504295742916245, 'a1, a1': 0.037061431174509975, 'a3, a3': 0.0025572210830953654, 'a4, a4': 0.006315394091461188, 'a5, a5': 984.7532882618256}	{'a1, a3': 0.1303, 'a1, a4': 0.1435, 'a1, a5': -0.7515, 'a3, a4': 0.009604, 'a3, a5': -0.2088, 'a4, a5': -0.0541}	55.05	0.9349	16	112.5	7.034	1.471e-16
18	164.796((a3 + ((x0 - 12.5) * 0.00210526)(a2 + a5((x0 - 12.5) * 0.00210526)))gauss(((x0 - 12.5) * 0.00210526)(a4 + ((x0 - 12.5) * 0.00210526))) + gauss(a1((x0 - 12.5) * 0.00210526)))	{'a1': (-1.71724, 0.0777, -0.0777), 'a2': (-1.62, 0, 0), 'a3': (-0.948158, 0.0499, -0.0499), 'a4': (5.63102, 0.196, -0.196), 'a5': (306.791, 30.3, -30.3)}	{'a1, a3': -3.307949862370362e-05, 'a1, a4': 0.001965653103544322, 'a1, a5': 0.11017239570788573, 'a3, a4': -0.0012919869183709034, 'a3, a5': -0.3189537669434852, 'a4, a5': 4.493143296107543, 'a1, a1': 0.006042028320034161, 'a3, a3': 0.002492102085339699, 'a4, a4': 0.03848694720921967, 'a5, a5': 915.3872876282832}	{'a1, a3': -0.008532, 'a1, a4': 0.1291, 'a1, a5': 0.0468, 'a3, a4': -0.1321, 'a3, a5': -0.211, 'a4, a5': 0.7566}	53.45	0.9387	16	109.8	6.861	4.952e-16
19	164.796(a2 + a4gauss(a1((x0 - 12.5) * 0.00210526) + a3) + a5((x0 - 12.5) * 0.00210526)gauss(3((x0 - 12.5) * 0.00210526)))	{'a1': (-15.7101, 0.729, -0.729), 'a2': (0.0818629, 0.00943, -0.00943), 'a3': (2.73635, 0.125, -0.125), 'a4': (3.62418, 0.181, -0.181), 'a5': (9.97479, 0.438, -0.438)}	{'a1, a2': 0.0002580687983396584, 'a1, a3': -0.08796670217153323, 'a1, a4': -0.05971170602055764, 'a1, a5': -0.13332902930119728, 'a2, a3': -2.6378046240731032e-05, 'a2, a4': 0.00010988057298370571, 'a2, a5': -0.0014687048926676296, 'a3, a4': 0.010272927590888221, 'a3, a5': 0.020936898697029853, 'a4, a5': -0.01551298712857567, 'a1, a1': 0.5317979337001922, 'a2, a2': 8.892791923303169e-05, 'a3, a3': 0.015619281642037316, 'a4, a4': 0.03270606723490801, 'a5, a5': 0.1916348232599745}	{'a1, a2': 0.03754, 'a1, a3': -0.9653, 'a1, a4': -0.4525, 'a1, a5': -0.4176, 'a2, a3': -0.02238, 'a2, a4': 0.06438, 'a2, a5': -0.3556, 'a3, a4': 0.4541, 'a3, a5': 0.3824, 'a4, a5': -0.1957}	13.09	0.9963	15	18.06	1.204	0.2597
20	164.796(a2 + a4gauss(a1((x0 - 12.5) * 0.00210526) + a3) + a5((x0 - 12.5) * 0.00210526)gauss(3((x0 - 12.5) * 0.00210526)))	{'a1': (-15.7101, 0.729, -0.729), 'a2': (0.0818629, 0.00943, -0.00943), 'a3': (2.73635, 0.125, -0.125), 'a4': (3.62418, 0.181, -0.181), 'a5': (9.97479, 0.438, -0.438)}	{'a1, a2': 0.00025806879745395646, 'a1, a3': -0.08796670204936519, 'a1, a4': -0.05971170593667058, 'a1, a5': -0.13332902926009663, 'a2, a3': -2.6378046071006507e-05, 'a2, a4': 0.00010988057311525785, 'a2, a5': -0.0014687048927142705, 'a3, a4': 0.01027292757740066, 'a3, a5': 0.020936898689562666, 'a4, a5': -0.015512987140457749, 'a1, a1': 0.5317979329381102, 'a2, a2': 8.89279192350535e-05, 'a3, a3': 0.015619281622074634, 'a4, a4': 0.03270606721340964, 'a5, a5': 0.1916348233227214}	{'a1, a2': 0.03754, 'a1, a3': -0.9653, 'a1, a4': -0.4525, 'a1, a5': -0.4176, 'a2, a3': -0.02238, 'a2, a4': 0.06438, 'a2, a5': -0.3556, 'a3, a4': 0.4541, 'a3, a5': 0.3824, 'a4, a5': -0.1957}	13.09	0.9963	15	18.06	1.204	0.2597
21	164.796(a2 + a4gauss(3((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)) + a5((x0 - 12.5) * 0.00210526)gauss(a1*((x0 - 12.5) * 0.00210526) + a3))	{'a1': (-15.422, 0.789, -0.789), 'a2': (0.0847897, 0.00919, -0.00919), 'a3': (2.49001, 0.146, -0.146), 'a4': (10.5105, 0.45, -0.45), 'a5': (21.3584, 1.07, -1.07)}	{'a1, a2': 0.0005034362218010011, 'a1, a3': -0.11176638509268574, 'a1, a4': -0.15491335947282706, 'a1, a5': -0.3478035947729082, 'a2, a3': -7.71366181413733e-05, 'a2, a4': -0.001484046672751355, 'a2, a5': 0.0004236620031573899, 'a3, a4': 0.02661383948716382, 'a3, a5': 0.05512457033987832, 'a4, a5': -0.09067798078770183, 'a1, a1': 0.6223571138655177, 'a2, a2': 8.453748909705521e-05, 'a3, a3': 0.021244075955464597, 'a4, a4': 0.20279562127904655, 'a5, a5': 1.15062011938191}	{'a1, a2': 0.06943, 'a1, a3': -0.9702, 'a1, a4': -0.4363, 'a1, a5': -0.412, 'a2, a3': -0.05749, 'a2, a4': -0.3589, 'a2, a5': 0.04308, 'a3, a4': 0.4051, 'a3, a5': 0.3529, 'a4, a5': -0.1883}	11.62	0.9971	15	17.26	1.151	0.3035
22	164.796(a3 + a5((x0 - 12.5) * 0.00210526)gauss(a2 + 3((x0 - 12.5) * 0.00210526)) + a6((x0 - 12.5) * 0.00210526)gauss(a1*((x0 - 12.5) * 0.00210526) + a4))	{'a1': (-15.3006, 0.769, -0.769), 'a2': (0.0224, 0, 0), 'a3': (0.0834143, 0.00914, -0.00914), 'a4': (2.47001, 0.142, -0.142), 'a5': (10.5191, 0.449, -0.449), 'a6': (21.4103, 1.06, -1.06)}	{'a1, a3': 0.0004972005534260852, 'a1, a4': -0.10641718524968845, 'a1, a5': -0.1498686299884518, 'a1, a6': -0.33518490313816723, 'a3, a4': -7.629183317514878e-05, 'a3, a5': -0.0014928949935860479, 'a3, a6': 0.0004207287772246051, 'a4, a5': 0.02577417933903252, 'a4, a6': 0.053109368677595185, 'a5, a6': -0.08863852757720175, 'a1, a1': 0.5915205912477756, 'a3, a3': 8.357418723538808e-05, 'a4, a4': 0.02027869261288221, 'a5, a5': 0.2013132916929035, 'a6, a6': 1.1199041228547506}	{'a1, a3': 0.07074, 'a1, a4': -0.9745, 'a1, a5': -0.434, 'a1, a6': -0.4112, 'a3, a4': -0.05878, 'a3, a5': -0.3638, 'a3, a6': 0.04343, 'a4, a5': 0.4043, 'a4, a6': 0.3528, 'a5, a6': -0.1862}	12.03	0.9969	15	16.98	1.132	0.32
23	164.796(a3 + a5((x0 - 12.5) * 0.00210526)gauss(a2 + 3((x0 - 12.5) * 0.00210526)) + a6((x0 - 12.5) * 0.00210526)gauss(a1*((x0 - 12.5) * 0.00210526) + a4))	{'a1': (-15.3006, 0.769, -0.769), 'a2': (0.0224, 0, 0), 'a3': (0.0834143, 0.00914, -0.00914), 'a4': (2.47001, 0.142, -0.142), 'a5': (10.5191, 0.449, -0.449), 'a6': (21.4103, 1.06, -1.06)}	{'a1, a3': 0.0004972005531937404, 'a1, a4': -0.10641718524783202, 'a1, a5': -0.14986862998055342, 'a1, a6': -0.3351849031510033, 'a3, a4': -7.629183313871982e-05, 'a3, a5': -0.001492894993455817, 'a3, a6': 0.0004207287776063034, 'a4, a5': 0.02577417933780345, 'a4, a6': 0.053109368679266494, 'a5, a6': -0.08863852758420511, 'a1, a1': 0.5915205912382033, 'a3, a3': 8.35741872352503e-05, 'a4, a4': 0.020278692612509364, 'a5, a5': 0.20131329168529624, 'a6, a6': 1.1199041229162134}	{'a1, a3': 0.07074, 'a1, a4': -0.9745, 'a1, a5': -0.434, 'a1, a6': -0.4112, 'a3, a4': -0.05878, 'a3, a5': -0.3638, 'a3, a6': 0.04343, 'a4, a5': 0.4043, 'a4, a6': 0.3528, 'a5, a6': -0.1862}	12.03	0.9969	15	16.98	1.132	0.32
24	164.796(a3 + a5((x0 - 12.5) * 0.00210526)gauss(a2 + 3((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526)(a6 + ((x0 - 12.5) * 0.00210526))gauss(a1*((x0 - 12.5) * 0.00210526) + a4))	{'a1': (-15.3006, 0.769, -0.769), 'a2': (0.0224, 0, 0), 'a3': (0.0834143, 0.00914, -0.00914), 'a4': (2.46848, 0.143, -0.143), 'a5': (10.5191, 0.449, -0.449), 'a6': (21.2489, 1.06, -1.06)}	{'a1, a3': 0.0004972002389246601, 'a1, a4': -0.1065008527034714, 'a1, a5': -0.14986865686295975, 'a1, a6': -0.3344705808498065, 'a3, a4': -7.631139796191702e-05, 'a3, a5': -0.001492894980273963, 'a3, a6': 0.00042047142267889775, 'a4, a5': 0.025782811249843204, 'a4, a6': 0.053019900900367, 'a5, a6': -0.08874260408765743, 'a1, a1': 0.5915253689638038, 'a3, a3': 8.357418585321686e-05, 'a4, a4': 0.020307628627637974, 'a5, a5': 0.20131329062457767, 'a6, a6': 1.1200310220873257}	{'a1, a3': 0.07074, 'a1, a4': -0.9685, 'a1, a5': -0.434, 'a1, a6': -0.4103, 'a3, a4': -0.05839, 'a3, a5': -0.3638, 'a3, a6': 0.0434, 'a4, a5': 0.4016, 'a4, a6': 0.3498, 'a5, a6': -0.1865}	12.03	0.9969	15	16.98	1.132	0.32
25	164.796(a3 + a4gauss((a1 + a5((x0 - 12.5) * 0.00210526))(a2 + 2((x0 - 12.5) * 0.00210526))) + a6gauss(3((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)))	{'a1': (-9.32526, 0.339, -0.339), 'a2': (-0.341645, 0.00377, -0.00377), 'a3': (0.0854909, 0.00849, -0.00849), 'a4': (3.61539, 0.163, -0.163), 'a5': (7.51, 0, 0), 'a6': (10.3924, 0.429, -0.429)}	{'a1, a2': -6.66619806897634e-05, 'a1, a3': 0.00015090024884515456, 'a1, a4': -0.022721986056464902, 'a1, a6': -0.0692675420354921, 'a2, a3': -1.5016196879198127e-06, 'a2, a4': -1.9101081159580943e-05, 'a2, a6': 0.00018740217730194765, 'a3, a4': 9.110362187432428e-05, 'a3, a6': -0.0012616953396642938, 'a4, a6': -0.013977349948602847, 'a1, a1': 0.11522081080849536, 'a2, a2': 1.4181128560835926e-05, 'a3, a3': 7.204754163608026e-05, 'a4, a4': 0.026717267774596695, 'a6, a6': 0.18388886553969228}	{'a1, a2': -0.05216, 'a1, a3': 0.05243, 'a1, a4': -0.4112, 'a1, a6': -0.4763, 'a2, a3': -0.04691, 'a2, a4': -0.03108, 'a2, a6': 0.1159, 'a3, a4': 0.06583, 'a3, a6': -0.3464, 'a4, a6': -0.1999}	7.747	0.9987	15	14.73	0.982	0.471
26	164.796(a2 + a5((x0 - 12.5) * 0.00210526)gauss(a1((x0 - 12.5) * 0.00210526) + a3) + (a4((x0 - 12.5) * 0.00210526)gauss(3((x0 - 12.5) * 0.00210526))exp(((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526))gauss(2((x0 - 12.5) * 0.00210526)))	{'a1': (-16.2404, 0.606, -0.606), 'a2': (0.0606542, 0.00591, -0.00591), 'a3': (2.62806, 0.111, -0.111), 'a4': (10.0408, 0.344, -0.344), 'a5': (20.7786, 0.738, -0.738)}	{'a1, a2': 0.00022743109844358943, 'a1, a3': -0.06552280132472307, 'a1, a4': -0.10404615360476874, 'a1, a5': -0.15750527322341726, 'a2, a3': -3.5839514366765815e-05, 'a2, a4': -0.0005939723115673539, 'a2, a5': 0.0002000091932983482, 'a3, a4': 0.018001330792777805, 'a3, a5': 0.024756727927048455, 'a4, a5': -0.06072461368614437, 'a1, a1': 0.3677154210719365, 'a2, a2': 3.494243079857677e-05, 'a3, a3': 0.012257232974891548, 'a4, a4': 0.11864611765506987, 'a5, a5': 0.5448397024093972}	{'a1, a2': 0.0635, 'a1, a3': -0.9741, 'a1, a4': -0.4991, 'a1, a5': -0.3522, 'a2, a3': -0.05463, 'a2, a4': -0.2922, 'a2, a5': 0.04586, 'a3, a4': 0.4714, 'a3, a5': 0.3022, 'a4, a5': -0.2392}	8.418	0.9985	15	7.504	0.5003	0.9421
27	164.796(a2 + a5((x0 - 12.5) * 0.00210526)gauss(a1((x0 - 12.5) * 0.00210526) + a3) + (a4gauss(3((x0 - 12.5) * 0.00210526))exp(((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526))gauss(2((x0 - 12.5) * 0.00210526)))	{'a1': (-16.5784, 0.62, -0.62), 'a2': (0.0615655, 0.00575, -0.00575), 'a3': (2.69036, 0.113, -0.113), 'a4': (10.5069, 0.347, -0.347), 'a5': (20.5662, 0.728, -0.728)}	{'a1, a2': 0.00022883809806944092, 'a1, a3': -0.06861022183017443, 'a1, a4': -0.10823057093468892, 'a1, a5': -0.1560842900056618, 'a2, a3': -3.6680582783394054e-05, 'a2, a4': -0.0005736741201581841, 'a2, a5': 0.00019486680179378282, 'a3, a4': 0.01882342323914207, 'a3, a5': 0.024565377193946608, 'a4, a5': -0.06171766009264407, 'a1, a1': 0.38459644563714085, 'a2, a2': 3.3115216218152016e-05, 'a3, a3': 0.012820464098046245, 'a4, a4': 0.12052921084234806, 'a5, a5': 0.5305000561070429}	{'a1, a2': 0.06419, 'a1, a3': -0.9793, 'a1, a4': -0.5031, 'a1, a5': -0.3458, 'a2, a3': -0.05645, 'a2, a4': -0.2875, 'a2, a5': 0.04655, 'a3, a4': 0.4801, 'a3, a5': 0.2986, 'a4, a5': -0.2443}	7.762	0.9987	15	7.137	0.4758	0.9537
28	164.796(a2 + a5gauss(a1((x0 - 12.5) * 0.00210526) + a3)tanh(((x0 - 12.5) * 0.00210526)) + (a4gauss(3((x0 - 12.5) * 0.00210526))exp(((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526))gauss(2((x0 - 12.5) * 0.00210526)))	{'a1': (-16.5688, 0.621, -0.621), 'a2': (0.0615655, 0.00575, -0.00575), 'a3': (2.69201, 0.113, -0.113), 'a4': (10.5069, 0.347, -0.347), 'a5': (20.7467, 0.735, -0.735)}	{'a1, a2': 0.00022896826762918267, 'a1, a3': -0.06861242569767433, 'a1, a4': -0.10829040964182425, 'a1, a5': -0.15835448144717928, 'a2, a3': -3.665704308033626e-05, 'a2, a4': -0.000573655719635049, 'a2, a5': 0.00019663689931506852, 'a3, a4': 0.01881278200486112, 'a3, a5': 0.024986832975003963, 'a4, a5': -0.062091827381001025, 'a1, a1': 0.38502740555356313, 'a2, a2': 3.311397195756671e-05, 'a3, a3': 0.012808204057245986, 'a4, a4': 0.1205255275755125, 'a5, a5': 0.5396252180995603}	{'a1, a2': 0.06412, 'a1, a3': -0.9778, 'a1, a4': -0.5025, 'a1, a5': -0.3469, 'a2, a3': -0.05642, 'a2, a4': -0.2875, 'a2, a5': 0.04653, 'a3, a4': 0.4798, 'a3, a5': 0.3008, 'a4, a5': -0.2435}	7.761	0.9987	15	7.137	0.4758	0.9537
29	164.796(a3 + a6((x0 - 12.5) * 0.00210526)gauss(a1((x0 - 12.5) * 0.00210526) + a4) + (((x0 - 12.5) * 0.00210526) + (a2 + a5exp(((x0 - 12.5) * 0.00210526)))gauss(3((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)))gauss(2((x0 - 12.5) * 0.00210526)))	{'a1': (-16.535, 0.619, -0.619), 'a2': (-0.324, 0, 0), 'a3': (0.0615135, 0.00577, -0.00577), 'a4': (2.68188, 0.113, -0.113), 'a5': (10.7346, 0.349, -0.349), 'a6': (20.5949, 0.73, -0.73)}	{'a1, a3': 0.00022937515065732579, 'a1, a4': -0.06835062151302758, 'a1, a5': -0.10872324380011698, 'a1, a6': -0.15585464357954168, 'a3, a4': -3.671875541332764e-05, 'a3, a5': -0.000578243617000947, 'a3, a6': 0.00019662263972379494, 'a4, a5': 0.018899085707333754, 'a4, a6': 0.02450973454332286, 'a5, a6': -0.0623378876637221, 'a1, a1': 0.38327054060245785, 'a3, a3': 3.3347989273451166e-05, 'a4, a4': 0.012770514459068554, 'a5, a5': 0.12167372248569391, 'a6, a6': 0.5331176288576749}	{'a1, a3': 0.06422, 'a1, a4': -0.9772, 'a1, a5': -0.5033, 'a1, a6': -0.3449, 'a3, a4': -0.05632, 'a3, a5': -0.2872, 'a3, a6': 0.04668, 'a4, a5': 0.4792, 'a4, a6': 0.2971, 'a5, a6': -0.2447}	7.815	0.9987	15	7.187	0.4791	0.9523
30	164.796(a2 + a5((x0 - 12.5) * 0.00210526)gauss(a1((x0 - 12.5) * 0.00210526) + a3) + ((x0 - 12.5) * 0.00210526)(a4gauss(3((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526))gauss(((x0 - 12.5) * 0.00210526)**2 + ((x0 - 12.5) * 0.00210526)))	{'a1': (-16.4076, 0.538, -0.538), 'a2': (0.052737, 0.00515, -0.00515), 'a3': (2.66548, 0.0986, -0.0986), 'a4': (12.1953, 0.323, -0.323), 'a5': (20.6961, 0.645, -0.645)}	{'a1, a2': 0.00017430129176483503, 'a1, a3': -0.051857901939350685, 'a1, a4': -0.08604957868916507, 'a1, a5': -0.12411930172412508, 'a2, a3': -2.7989415161140623e-05, 'a2, a4': -0.0004852634261827058, 'a2, a5': 0.0001457726495690921, 'a3, a4': 0.01501630242137658, 'a3, a5': 0.019563074209685265, 'a4, a5': -0.04823904616525749, 'a1, a1': 0.28980041701361037, 'a2, a2': 2.6559948537245677e-05, 'a3, a3': 0.009729851072180872, 'a4, a4': 0.10437291847051594, 'a5, a5': 0.41581205029836155}	{'a1, a2': 0.06291, 'a1, a3': -0.9776, 'a1, a4': -0.4952, 'a1, a5': -0.3577, 'a2, a3': -0.05512, 'a2, a4': -0.2917, 'a2, a5': 0.04388, 'a3, a4': 0.4715, 'a3, a5': 0.3076, 'a4, a5': -0.2315}	8.305	0.9985	15	5.707	0.3804	0.9843
31	164.796(a2 + a5((x0 - 12.5) * 0.00210526)gauss(a1((x0 - 12.5) * 0.00210526) + a3) + ((x0 - 12.5) * 0.00210526)(a4gauss(3((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526))gauss(((x0 - 12.5) * 0.00210526)**2 + ((x0 - 12.5) * 0.00210526)))	{'a1': (-16.4075, 0.538, -0.538), 'a2': (0.052737, 0.00515, -0.00515), 'a3': (2.66548, 0.0986, -0.0986), 'a4': (12.1952, 0.323, -0.323), 'a5': (20.6961, 0.645, -0.645)}	{'a1, a2': 0.00017430125398469693, 'a1, a3': -0.05185769027624358, 'a1, a4': -0.0860496448299757, 'a1, a5': -0.12411862550391575, 'a2, a3': -2.7989404342492505e-05, 'a2, a4': -0.00048526393337538023, 'a2, a5': 0.00014577286888793576, 'a3, a4': 0.015016315600592089, 'a3, a5': 0.01956295986605688, 'a4, a5': -0.048239145755498786, 'a1, a1': 0.28979916625765856, 'a2, a2': 2.6559949708841196e-05, 'a3, a3': 0.009729814695230406, 'a4, a4': 0.10437316153002757, 'a5, a5': 0.4158111062071607}	{'a1, a2': 0.06291, 'a1, a3': -0.9776, 'a1, a4': -0.4952, 'a1, a5': -0.3577, 'a2, a3': -0.05512, 'a2, a4': -0.2917, 'a2, a5': 0.04388, 'a3, a4': 0.4715, 'a3, a5': 0.3076, 'a4, a5': -0.2315}	8.306	0.9985	15	5.707	0.3804	0.9843
32	164.796(a2 + a5gauss(a1((x0 - 12.5) * 0.00210526) + a3)tanh(((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526)(a4gauss(3((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526))gauss(((x0 - 12.5) * 0.00210526)**2 + ((x0 - 12.5) * 0.00210526)))	{'a1': (-16.3978, 0.539, -0.539), 'a2': (0.0527371, 0.00515, -0.00515), 'a3': (2.66715, 0.0986, -0.0986), 'a4': (12.1952, 0.323, -0.323), 'a5': (20.8781, 0.65, -0.65)}	{'a1, a2': 0.00017439888513519458, 'a1, a3': -0.051858264414066005, 'a1, a4': -0.08609651911638688, 'a1, a5': -0.12591612891339446, 'a2, a3': -2.797051288003611e-05, 'a2, a4': -0.00048523887014328217, 'a2, a5': 0.00014709613914205832, 'a3, a4': 0.015007394879763502, 'a3, a5': 0.019896307209920805, 'a4, a5': -0.048522251406970744, 'a1, a1': 0.29012365230072723, 'a2, a2': 2.655841416835728e-05, 'a3, a3': 0.009720149568592004, 'a4, a4': 0.10436804553341239, 'a5, a5': 0.422966474944266}	{'a1, a2': 0.06283, 'a1, a3': -0.9758, 'a1, a4': -0.4945, 'a1, a5': -0.3594, 'a2, a3': -0.05508, 'a2, a4': -0.2917, 'a2, a5': 0.04394, 'a3, a4': 0.4712, 'a3, a5': 0.3104, 'a4, a5': -0.2311}	8.305	0.9985	15	5.706	0.3804	0.9843
33	164.796(a3 + a6((x0 - 12.5) * 0.00210526)gauss((a1 + ((x0 - 12.5) * 0.00210526))(a2 + 2((x0 - 12.5) * 0.00210526))) + (a4 + a5gauss(3((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526))gauss(((x0 - 12.5) * 0.00210526)*2 + ((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)))	{'a1': (-8.47959, 0.256, -0.256), 'a2': (-0.324911, 0.00263, -0.00263), 'a3': (0.0570331, 0.0048, -0.0048), 'a4': (0.0899, 0, 0), 'a5': (12.404, 0.314, -0.314), 'a6': (20.5868, 0.605, -0.605)}	{'a1, a2': 0.0002692310591035809, 'a1, a3': 8.114722723227641e-05, 'a1, a5': -0.040756269532480356, 'a1, a6': -0.052638538873972546, 'a2, a3': 1.6547448147694097e-08, 'a2, a5': -0.00012673051872765618, 'a2, a6': 7.116088645956187e-05, 'a3, a5': -0.0004329458812418076, 'a3, a6': 0.0001317575464453444, 'a5, a6': -0.04598293495682237, 'a1, a1': 0.06575336300971724, 'a2, a2': 6.937801896652358e-06, 'a3, a3': 2.3007223302015217e-05, 'a5, a5': 0.09848922732566012, 'a6, a6': 0.36550931532474945}	{'a1, a2': 0.3999, 'a1, a3': 0.06604, 'a1, a5': -0.507, 'a1, a6': -0.3399, 'a2, a3': 0.001311, 'a2, a5': -0.1535, 'a2, a6': 0.04472, 'a3, a5': -0.2873, 'a3, a6': 0.04537, 'a5, a6': -0.2421}	7.484	0.9988	15	4.958	0.3305	0.9925
34	164.796(a3 + a6((x0 - 12.5) * 0.00210526)gauss((a1 + ((x0 - 12.5) * 0.00210526))(a2 + 2((x0 - 12.5) * 0.00210526))) + (a4 + a5gauss(3((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526))gauss(((x0 - 12.5) * 0.00210526)*2 + ((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)))	{'a1': (-8.47959, 0.256, -0.256), 'a2': (-0.324911, 0.00263, -0.00263), 'a3': (0.0570331, 0.0048, -0.0048), 'a4': (0.0899, 0, 0), 'a5': (12.404, 0.314, -0.314), 'a6': (20.5868, 0.605, -0.605)}	{'a1, a2': 0.0002692310602117791, 'a1, a3': 8.114722728247085e-05, 'a1, a5': -0.0407562709503126, 'a1, a6': -0.052638527474456576, 'a2, a3': 1.654743920186623e-08, 'a2, a5': -0.00012673054067015727, 'a2, a6': 7.1160914399137e-05, 'a3, a5': -0.00043294590048648243, 'a3, a6': 0.00013175755468551188, 'a5, a6': -0.045982938727037896, 'a1, a1': 0.06575335212286335, 'a2, a2': 6.937802646445262e-06, 'a3, a3': 2.3007223344169516e-05, 'a5, a5': 0.09848923674508434, 'a6, a6': 0.36550928427567053}	{'a1, a2': 0.3999, 'a1, a3': 0.06604, 'a1, a5': -0.507, 'a1, a6': -0.3399, 'a2, a3': 0.001311, 'a2, a5': -0.1535, 'a2, a6': 0.04472, 'a3, a5': -0.2873, 'a3, a6': 0.04537, 'a5, a6': -0.2421}	7.484	0.9988	15	4.958	0.3305	0.9925
35	164.796(a3 + a6((x0 - 12.5) * 0.00210526)gauss((a1 + ((x0 - 12.5) * 0.00210526))(a2 + 2((x0 - 12.5) * 0.00210526))) + (a4 + a5gauss(3((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526))gauss(((x0 - 12.5) * 0.00210526)*2 + ((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)))	{'a1': (-8.47983, 0.256, -0.256), 'a2': (-0.324912, 0.00263, -0.00263), 'a3': (0.057044, 0.0048, -0.0048), 'a4': (0.0897, 0, 0), 'a5': (12.4047, 0.314, -0.314), 'a6': (20.5866, 0.605, -0.605)}	{'a1, a2': 0.0002692970297857357, 'a1, a3': 8.116556847173629e-05, 'a1, a5': -0.04076474867775151, 'a1, a6': -0.052653587871259545, 'a2, a3': 1.656493346763856e-08, 'a2, a5': -0.0001267521208568937, 'a2, a6': 7.116908788427582e-05, 'a3, a5': -0.00043302213382133246, 'a3, a6': 0.00013177933969027374, 'a5, a6': -0.045990102421631734, 'a1, a1': 0.06577297946392865, 'a2, a2': 6.939160650215462e-06, 'a3, a3': 2.3011565368419392e-05, 'a5, a5': 0.09850485920411665, 'a6, a6': 0.36558794866286004}	{'a1, a2': 0.4, 'a1, a3': 0.06605, 'a1, a5': -0.5071, 'a1, a6': -0.34, 'a2, a3': 0.001312, 'a2, a5': -0.1535, 'a2, a6': 0.04473, 'a3, a5': -0.2873, 'a3, a6': 0.04538, 'a5, a6': -0.2421}	7.483	0.9988	15	4.959	0.3306	0.9925
36	164.796(a3 + a5((x0 - 12.5) * 0.00210526)gauss((a1 + 4((x0 - 12.5) * 0.00210526))(a2 + 2((x0 - 12.5) * 0.00210526))) + (((x0 - 12.5) * 0.00210526)(a4gauss(3((x0 - 12.5) * 0.00210526)) + gauss(((x0 - 12.5) * 0.00210526))) + tanh(((x0 - 12.5) * 0.00210526)))gauss(2*((x0 - 12.5) * 0.00210526)))	{'a1': (-9.00491, 0.257, -0.257), 'a2': (-0.324444, 0.0027, -0.0027), 'a3': (0.04774, 0.00474, -0.00474), 'a4': (11.2583, 0.395, -0.395), 'a5': (20.4687, 0.604, -0.604)}	{'a1, a2': 0.00031633099815270744, 'a1, a3': 0.00010264155250825059, 'a1, a4': -0.058311916428906534, 'a1, a5': -0.03680442169355027, 'a2, a3': 2.8091744930848306e-07, 'a2, a4': -0.00024568431480607213, 'a2, a5': 0.00013594734291605786, 'a3, a4': -0.0005212839719633228, 'a3, a5': 0.00017424797100111929, 'a4, a5': -0.07415699382968759, 'a1, a1': 0.06628477021936333, 'a2, a2': 7.266542660241084e-06, 'a3, a3': 2.242047165086606e-05, 'a4, a4': 0.15569252523040913, 'a5, a5': 0.3643257246903647}	{'a1, a2': 0.4559, 'a1, a3': 0.08426, 'a1, a4': -0.5744, 'a1, a5': -0.2371, 'a2, a3': 0.02195, 'a2, a4': -0.2304, 'a2, a5': 0.08336, 'a3, a4': -0.2784, 'a3, a5': 0.06086, 'a4, a5': -0.3108}	7.139	0.9989	15	4.857	0.3238	0.9933
37	164.796(a3 + a7((x0 - 12.5) * 0.00210526)gauss(a1 + a6((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526)(a5gauss(a2 + 4((x0 - 12.5) * 0.00210526)) + 2((x0 - 12.5) * 0.00210526) + tanh(((x0 - 12.5) * 0.00210526)))gauss(a4((x0 - 12.5) * 0.00210526)**2 + ((x0 - 12.5) * 0.00210526)))	{'a1': (-2.91196, 0.125, -0.125), 'a2': (-0.302525, 0.0273, -0.0273), 'a3': (0.0678991, 0.00587, -0.00587), 'a4': (1.6513, 0.0522, -0.0522), 'a5': (12.3724, 0.682, -0.682), 'a6': (17.874, 0.667, -0.667), 'a7': (19.5316, 0.63, -0.63)}	{'a1, a2': -0.0018732939051410908, 'a1, a3': 3.340921292963213e-05, 'a1, a4': 0.0003485664933282089, 'a1, a5': -0.059753884544025075, 'a1, a6': -0.08246929771682666, 'a1, a7': 0.005314583059855831, 'a2, a3': -2.8757645487266857e-05, 'a2, a4': -0.00043701192808579757, 'a2, a5': 0.016459141159571578, 'a2, a6': 0.009154981376001837, 'a2, a7': -0.007086715362658406, 'a3, a4': 0.00021444789112320186, 'a3, a5': -0.0007081497592436802, 'a3, a6': -0.0001632906881783371, 'a3, a7': 0.00018914752126542733, 'a4, a5': -0.0068435979360445525, 'a4, a6': -0.0013853492995834424, 'a4, a7': 0.0016849098472664942, 'a5, a6': 0.3065130196882292, 'a5, a7': -0.21529058570708037, 'a6, a7': -0.0060446641283122705, 'a1, a1': 0.015733890090984942, 'a2, a2': 0.0007461537493960946, 'a3, a3': 3.4464147953107814e-05, 'a4, a4': 0.002724756998084846, 'a5, a5': 0.4645494826174772, 'a6, a6': 0.44505807497886096, 'a7, a7': 0.3967536139035305}	{'a1, a2': -0.549, 'a1, a3': 0.04553, 'a1, a4': 0.05342, 'a1, a5': -0.7009, 'a1, a6': -0.9891, 'a1, a7': 0.06749, 'a2, a3': -0.1795, 'a2, a4': -0.3067, 'a2, a5': 0.884, 'a2, a6': 0.5028, 'a2, a7': -0.412, 'a3, a4': 0.6999, 'a3, a5': -0.1769, 'a3, a6': -0.04171, 'a3, a7': 0.05115, 'a4, a5': -0.1922, 'a4, a6': -0.03979, 'a4, a7': 0.05123, 'a5, a6': 0.6738, 'a5, a7': -0.5011, 'a6, a7': -0.01438}	4.132	0.9996	13	3.395	0.2612	0.9961
38	164.796(a3 + ((x0 - 12.5) * 0.00210526)(a8 + gauss(((x0 - 12.5) * 0.00210526)))gauss(a1 + a7((x0 - 12.5) * 0.00210526)) + (a4 + a6gauss(a2 + 4((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526))gauss(a5((x0 - 12.5) * 0.00210526)*2 + ((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)))	{'a1': (-2.8971, 0.119, -0.119), 'a2': (-0.310465, 0.0309, -0.0309), 'a3': (0.062877, 0.00663, -0.00663), 'a4': (0.872472, 0.15, -0.15), 'a5': (1.34992, 0.104, -0.104), 'a6': (11.6705, 0.656, -0.656), 'a7': (17.7835, 0.632, -0.632), 'a8': (18.6433, 0.602, -0.602)}	{'a1, a2': -0.0018492199566506138, 'a1, a3': 3.154244675020045e-05, 'a1, a4': -0.00041210816737061797, 'a1, a5': 0.00015616281192992564, 'a1, a6': -0.05403003950723993, 'a1, a7': -0.07391193168674091, 'a1, a8': 0.005123655381863374, 'a2, a3': -3.6779716399995225e-06, 'a2, a4': 0.0020981582125823815, 'a2, a5': 0.0007357086334955846, 'a2, a6': 0.01490711029828145, 'a2, a7': 0.008775826411887776, 'a2, a8': -0.007017744928607174, 'a3, a4': 0.00034053613496275214, 'a3, a5': 0.00046429037271923, 'a3, a6': -0.0009691652637514007, 'a3, a7': -0.00019994556929166875, 'a3, a8': 0.00020627918325656934, 'a4, a5': 0.013079473264303282, 'a4, a6': -0.011032267779577545, 'a4, a7': -0.0010732859328118924, 'a4, a8': -0.0006710568691077966, 'a5, a6': -0.014125680250430588, 'a5, a7': -0.0022805435271651014, 'a5, a8': 0.001609664253560598, 'a6, a7': 0.2789858121501957, 'a6, a8': -0.1977398884993664, 'a7, a8': -0.006931412901477568, 'a1, a1': 0.014111288149978899, 'a2, a2': 0.0009551883890544028, 'a3, a3': 4.3987794936383135e-05, 'a4, a4': 0.022467073255408695, 'a5, a5': 0.010730603495694904, 'a6, a6': 0.429977796488108, 'a7, a7': 0.3990791141591075, 'a8, a8': 0.36255903028857966}	{'a1, a2': -0.5029, 'a1, a3': 0.03998, 'a1, a4': -0.02309, 'a1, a5': 0.01262, 'a1, a6': -0.6921, 'a1, a7': -0.9828, 'a1, a8': 0.07152, 'a2, a3': -0.01795, 'a2, a4': 0.4527, 'a2, a5': 0.2289, 'a2, a6': 0.7354, 'a2, a7': 0.4494, 'a2, a8': -0.3773, 'a3, a4': 0.3424, 'a3, a5': 0.6734, 'a3, a6': -0.2228, 'a3, a7': -0.04772, 'a3, a8': 0.05168, 'a4, a5': 0.8384, 'a4, a6': -0.1121, 'a4, a7': -0.01132, 'a4, a8': -0.007431, 'a5, a6': -0.207, 'a5, a7': -0.0347, 'a5, a8': 0.02571, 'a6, a7': 0.6729, 'a6, a8': -0.5007, 'a7, a8': -0.01822}	4.306	0.9996	12	2.864	0.2387	0.9964
39	164.796(a3 + (a8 + gauss(((x0 - 12.5) * 0.00210526)))gauss(a1 + a7((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)) + (a4 + a6gauss(a2 + 4((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526))gauss(a5((x0 - 12.5) * 0.00210526)*2 + ((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)))	{'a1': (-2.89864, 0.119, -0.119), 'a2': (-0.310463, 0.0309, -0.0309), 'a3': (0.0628771, 0.00663, -0.00663), 'a4': (0.872479, 0.15, -0.15), 'a5': (1.34992, 0.104, -0.104), 'a6': (11.6705, 0.656, -0.656), 'a7': (17.7745, 0.632, -0.632), 'a8': (18.8168, 0.607, -0.607)}	{'a1, a2': -0.0018485356089360122, 'a1, a3': 3.152494850257226e-05, 'a1, a4': -0.0004123227836734884, 'a1, a5': 0.00015592086060009752, 'a1, a6': -0.054007289635291715, 'a1, a7': -0.07391502937117672, 'a1, a8': 0.0049250925608261, 'a2, a3': -3.67769578985483e-06, 'a2, a4': 0.0020980761527911356, 'a2, a5': 0.0007356802417864339, 'a2, a6': 0.014906303979068804, 'a2, a7': 0.008779601069595185, 'a2, a8': -0.0070296412792102934, 'a3, a4': 0.00034052324260898137, 'a3, a5': 0.0004642701575835755, 'a3, a6': -0.0009691327953109968, 'a3, a7': -0.00020004827440727596, 'a3, a8': 0.0002082240222854791, 'a4, a5': 0.0130790049820171, 'a4, a6': -0.011032615902750866, 'a4, a7': -0.0010746757974125652, 'a4, a8': -0.0006067365166881823, 'a5, a6': -0.01412544930328174, 'a5, a7': -0.00228200601940539, 'a5, a8': 0.0016496582620897859, 'a6, a7': 0.2791126642391832, 'a6, a8': -0.1984634783764149, 'a7, a8': -0.005944438529703581, 'a1, a1': 0.014099756041612947, 'a2, a2': 0.0009551435261630502, 'a3, a3': 4.398585448311773e-05, 'a4, a4': 0.022466335505436794, 'a5, a5': 0.010730172182709025, 'a6, a6': 0.42995934746740244, 'a7, a7': 0.39946093215820483, 'a8, a8': 0.3680304022999112}	{'a1, a2': -0.5027, 'a1, a3': 0.03996, 'a1, a4': -0.0231, 'a1, a5': 0.0126, 'a1, a6': -0.6918, 'a1, a7': -0.9828, 'a1, a8': 0.06818, 'a2, a3': -0.01795, 'a2, a4': 0.4527, 'a2, a5': 0.2289, 'a2, a6': 0.7354, 'a2, a7': 0.4496, 'a2, a8': -0.3748, 'a3, a4': 0.3424, 'a3, a5': 0.6733, 'a3, a6': -0.2228, 'a3, a7': -0.04774, 'a3, a8': 0.05174, 'a4, a5': 0.8384, 'a4, a6': -0.1121, 'a4, a7': -0.01134, 'a4, a8': -0.006664, 'a5, a6': -0.207, 'a5, a7': -0.03472, 'a5, a8': 0.02613, 'a6, a7': 0.6732, 'a6, a8': -0.4984, 'a7, a8': -0.0155}	4.306	0.9996	12	2.864	0.2387	0.9964
40	164.796(a3 + a7((x0 - 12.5) * 0.00210526)gauss(a1 + a6((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526)(a5gauss(a2 + 4((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526) + 2tanh(((x0 - 12.5) * 0.00210526)))gauss(a4((x0 - 12.5) * 0.00210526)**2 + ((x0 - 12.5) * 0.00210526)))	{'a1': (-2.91086, 0.124, -0.124), 'a2': (-0.301998, 0.0269, -0.0269), 'a3': (0.0673338, 0.00586, -0.00586), 'a4': (1.61383, 0.0522, -0.0522), 'a5': (12.3694, 0.673, -0.673), 'a6': (17.8686, 0.658, -0.658), 'a7': (19.5378, 0.622, -0.622)}	{'a1, a2': -0.0018255706921989814, 'a1, a3': 3.331432725989808e-05, 'a1, a4': 0.0003495576071717213, 'a1, a5': -0.058234753589675455, 'a1, a6': -0.08028635510801947, 'a1, a7': 0.005174682254938723, 'a2, a3': -2.8753806869979282e-05, 'a2, a4': -0.0004321058806633029, 'a2, a5': 0.016048318061667077, 'a2, a6': 0.008928018504700725, 'a2, a7': -0.006912446673940403, 'a3, a4': 0.00021624403481625777, 'a3, a5': -0.0007067064867885562, 'a3, a6': -0.0001627956517248418, 'a3, a7': 0.00018860937411999533, 'a4, a5': -0.006842099659779191, 'a4, a6': -0.0014008613288632344, 'a4, a7': 0.0016943954870457226, 'a5, a6': 0.29878643543540007, 'a5, a7': -0.21002419017850613, 'a6, a7': -0.005871333914417173, 'a1, a1': 0.015316101251836706, 'a2, a2': 0.0007253239456903507, 'a3, a3': 3.434365422366215e-05, 'a4, a4': 0.00272136587848256, 'a5, a5': 0.4533482106454874, 'a6, a6': 0.4333164560642867, 'a7, a7': 0.38689386251843993}	{'a1, a2': -0.5473, 'a1, a3': 0.04585, 'a1, a4': 0.054, 'a1, a5': -0.6978, 'a1, a6': -0.984, 'a1, a7': 0.06709, 'a2, a3': -0.1824, 'a2, a4': -0.3077, 'a2, a5': 0.8865, 'a2, a6': 0.5044, 'a2, a7': -0.4131, 'a3, a4': 0.7069, 'a3, a5': -0.1792, 'a3, a6': -0.04222, 'a3, a7': 0.05175, 'a4, a5': -0.1948, 'a4, a6': -0.04078, 'a4, a7': 0.05219, 'a5, a6': 0.6747, 'a5, a7': -0.5017, 'a6, a7': -0.01435}	4.134	0.9996	13	3.312	0.2547	0.9966
41	164.796(a3 + (a8 + gauss(a2))gauss(a1 + a7((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)) + (a4 + a6gauss(a2 + 4((x0 - 12.5) * 0.00210526)) + ((x0 - 12.5) * 0.00210526))gauss(a5((x0 - 12.5) * 0.00210526)*2 + ((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)))	{'a1': (-2.89841, 0.119, -0.119), 'a2': (-0.310464, 0.0309, -0.0309), 'a3': (0.0628771, 0.00663, -0.00663), 'a4': (0.872477, 0.15, -0.15), 'a5': (1.34992, 0.104, -0.104), 'a6': (11.6705, 0.656, -0.656), 'a7': (17.7758, 0.632, -0.632), 'a8': (18.8824, 0.614, -0.614)}	{'a1, a2': -0.0018485784676407417, 'a1, a3': 3.152507942599029e-05, 'a1, a4': -0.00041231079155755495, 'a1, a5': 0.0001559279165952253, 'a1, a6': -0.05400887288720797, 'a1, a7': -0.07391578549959243, 'a1, a8': 0.005999334423343717, 'a2, a3': -3.677771075435309e-06, 'a2, a4': 0.0020981024647896123, 'a2, a5': 0.0007356893796909785, 'a2, a6': 0.014906545837243023, 'a2, a7': 0.008779628016314534, 'a2, a8': -0.007575740855325165, 'a3, a4': 0.0003405273294581627, 'a3, a5': 0.0004642762704976658, 'a3, a6': -0.000969142813325969, 'a3, a7': -0.0002000469217445581, 'a3, a8': 0.00021028039978098991, 'a4, a5': 0.013079159924989325, 'a4, a6': -0.01103254525051356, 'a4, a7': -0.0010742999243689075, 'a4, a8': -0.001800307438853524, 'a5, a6': -0.014125536842527556, 'a5, a7': -0.0022818548496061053, 'a5, a8': 0.0012309757745423181, 'a6, a7': 0.27910975062995, 'a6, a8': -0.2070224400377824, 'a7, a8': -0.01107511828050803, 'a1, a1': 0.014101543859008314, 'a2, a2': 0.0009551572126901864, 'a3, a3': 4.398642841867241e-05, 'a4, a4': 0.022466585619691122, 'a5, a5': 0.010730309405809348, 'a6, a6': 0.42996499987728504, 'a7, a7': 0.39940983413459, 'a8, a8': 0.3764160460698961}	{'a1, a2': -0.5027, 'a1, a3': 0.03996, 'a1, a4': -0.0231, 'a1, a5': 0.0126, 'a1, a6': -0.6919, 'a1, a7': -0.9828, 'a1, a8': 0.08211, 'a2, a3': -0.01795, 'a2, a4': 0.4527, 'a2, a5': 0.2289, 'a2, a6': 0.7354, 'a2, a7': 0.4496, 'a2, a8': -0.3993, 'a3, a4': 0.3424, 'a3, a5': 0.6733, 'a3, a6': -0.2228, 'a3, a7': -0.04774, 'a3, a8': 0.05166, 'a4, a5': 0.8384, 'a4, a6': -0.1121, 'a4, a7': -0.01133, 'a4, a8': -0.01955, 'a5, a6': -0.207, 'a5, a7': -0.03472, 'a5, a8': 0.01928, 'a6, a7': 0.6732, 'a6, a8': -0.514, 'a7, a8': -0.02854}	4.306	0.9996	12	2.864	0.2387	0.9964
42	164.796(a3 + ((x0 - 12.5) * 0.00210526)(a8 + ((x0 - 12.5) * 0.00210526))gauss(a1((x0 - 12.5) * 0.00210526) + a6) + (a4 + a7gauss(a2 + 4((x0 - 12.5) * 0.00210526)) + tanh(((x0 - 12.5) * 0.00210526)))gauss(a5((x0 - 12.5) * 0.00210526)*2 + ((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)))	{'a1': (-17.7747, 0.628, -0.628), 'a2': (-0.307739, 0.0307, -0.0307), 'a3': (0.0625018, 0.00668, -0.00668), 'a4': (0.88682, 0.149, -0.149), 'a5': (1.30996, 0.107, -0.107), 'a6': (2.89406, 0.118, -0.118), 'a7': (11.6623, 0.654, -0.654), 'a8': (19.4612, 0.599, -0.599)}	{'a1, a2': -0.008680882973610513, 'a1, a3': 0.00020071541225058517, 'a1, a4': 0.0010131824443871042, 'a1, a5': 0.00230400320757737, 'a1, a6': -0.07306244772497582, 'a1, a7': -0.2764811214665746, 'a1, a8': 0.007289797767018418, 'a2, a3': -3.907297290516338e-06, 'a2, a4': 0.002034885144012566, 'a2, a5': 0.0007572071778591571, 'a2, a6': 0.0018282747100596204, 'a2, a7': 0.014828511041536999, 'a2, a8': -0.006970204011101957, 'a3, a4': 0.0003483722810579555, 'a3, a5': 0.00048615325136724426, 'a3, a6': -3.165954286853486e-05, 'a3, a7': -0.0009849141326324744, 'a3, a8': 0.00020690917565038846, 'a4, a5': 0.013573205874384027, 'a4, a6': 0.00040722953339787546, 'a4, a7': -0.01094536257104187, 'a4, a8': -0.0007355887922884244, 'a5, a6': -0.0001516012675503622, 'a5, a7': -0.014600777064255667, 'a5, a8': 0.001590076008108117, 'a6, a7': 0.05357534797481512, 'a6, a8': -0.0051487006134417306, 'a7, a8': -0.19658069112571727, 'a1, a1': 0.3941908722585038, 'a2, a2': 0.0009399817510334554, 'a3, a3': 4.4624955126715984e-05, 'a4, a4': 0.022083502216275357, 'a5, a5': 0.011537086318474018, 'a6, a6': 0.013958280784745196, 'a7, a7': 0.4280936016242561, 'a8, a8': 0.35918410261429234}	{'a1, a2': -0.4503, 'a1, a3': 0.04785, 'a1, a4': 0.01083, 'a1, a5': 0.03429, 'a1, a6': -0.9859, 'a1, a7': -0.6732, 'a1, a8': 0.01938, 'a2, a3': -0.01905, 'a2, a4': 0.4449, 'a2, a5': 0.2305, 'a2, a6': 0.5047, 'a2, a7': 0.7386, 'a2, a8': -0.379, 'a3, a4': 0.35, 'a3, a5': 0.6802, 'a3, a6': -0.04016, 'a3, a7': -0.2254, 'a3, a8': 0.05171, 'a4, a5': 0.8514, 'a4, a6': 0.02316, 'a4, a7': -0.1123, 'a4, a8': -0.008242, 'a5, a6': -0.01201, 'a5, a7': -0.2086, 'a5, a8': 0.02481, 'a6, a7': 0.6942, 'a6, a8': -0.07284, 'a7, a8': -0.5018}	4.34	0.9996	12	2.837	0.2364	0.9966
43	164.796(a3 + ((x0 - 12.5) * 0.00210526)(a8 + 2((x0 - 12.5) * 0.00210526) + gauss(((x0 - 12.5) * 0.00210526)))gauss(a1((x0 - 12.5) * 0.00210526) + a6) + (a4 + a7gauss(a2 + 4((x0 - 12.5) * 0.00210526)) + tanh(((x0 - 12.5) * 0.00210526)))gauss(a5((x0 - 12.5) * 0.00210526)2 + ((x0 - 12.5) * 0.00210526))tanh(((x0 - 12.5) * 0.00210526)))	{'a1': (-17.7733, 0.628, -0.628), 'a2': (-0.307739, 0.0307, -0.0307), 'a3': (0.0625018, 0.00668, -0.00668), 'a4': (0.886819, 0.149, -0.149), 'a5': (1.30996, 0.107, -0.107), 'a6': (2.89285, 0.118, -0.118), 'a7': (11.6623, 0.654, -0.654), 'a8': (18.3245, 0.6, -0.6)}	{'a1, a2': -0.008680705106722735, 'a1, a3': 0.0002007169585245231, 'a1, a4': 0.0010132003515236237, 'a1, a5': 0.002303994952291726, 'a1, a6': -0.07309411782490632, 'a1, a7': -0.27648004519105945, 'a1, a8': 0.007603501541076403, 'a2, a3': -3.9078981330186764e-06, 'a2, a4': 0.0020347415345037204, 'a2, a5': 0.000757152205992997, 'a2, a6': 0.0018283875313100536, 'a2, a7': 0.01482787554962086, 'a2, a8': -0.006985838680406736, 'a3, a4': 0.00034836076254927305, 'a3, a5': 0.0004861513776551137, 'a3, a6': -3.1660581854734646e-05, 'a3, a7': -0.0009849062050628055, 'a3, a8': 0.00020686734033669503, 'a4, a5': 0.013572431916179968, 'a4, a6': 0.0004071423443432247, 'a4, a7': -0.010944393194259475, 'a4, a8': -0.0007576184581350992, 'a5, a6': -0.00015164293034062413, 'a5, a7': -0.014600159755155242, 'a5, a8': 0.0015814106374113868, 'a6, a7': 0.053580945608055285, 'a6, a8': -0.005206076269383371, 'a7, a8': -0.19690283434444888, 'a1, a1': 0.3942481052999607, 'a2, a2': 0.0009399284561672959, 'a3, a3': 4.462537344855556e-05, 'a4, a4': 0.02208195381909836, 'a5, a5': 0.011536685881377618, 'a6, a6': 0.013967745597430064, 'a7, a7': 0.4280774910932677, 'a8, a8': 0.3594826802864236}	{'a1, a2': -0.4503, 'a1, a3': 0.04785, 'a1, a4': 0.01083, 'a1, a5': 0.03429, 'a1, a6': -0.9864, 'a1, a7': -0.6732, 'a1, a8': 0.02018, 'a2, a3': -0.01906, 'a2, a4': 0.4448, 'a2, a5': 0.2305, 'a2, a6': 0.5047, 'a2, a7': 0.7385, 'a2, a8': -0.3793, 'a3, a4': 0.35, 'a3, a5': 0.6802, 'a3, a6': -0.04017, 'a3, a7': -0.2254, 'a3, a8': 0.05161, 'a4, a5': 0.8513, 'a4, a6': 0.02316, 'a4, a7': -0.1123, 'a4, a8': -0.008474, 'a5, a6': -0.01201, 'a5, a7': -0.2086, 'a5, a8': 0.02463, 'a6, a7': 0.6943, 'a6, a8': -0.07353, 'a7, a8': -0.5018}	4.34	0.9996	12	2.837	0.2364	0.9966

The goodness-of-fit scores are plotted in candidates_gof.pdf, such as the chi2/ndf:

For other goodness-of-fit scores:

Click to expand

^ p-value

^ Root-mean-square error

^ Coefficient of determination R2

Now, lets take a look at one of the candidate functions, say candidate #43. The functional form can be found in the corresponding plots from the PDF files and in the csv table above, which is:

164.796*(a3 + ((x0 - 12.5) * 0.00210526)*(a8 + ((x0 - 12.5) * 0.00210526))*gauss(a1*((x0 - 12.5) * 0.00210526) + a6) + (a4 + a7*gauss(a2 + 4*((x0 - 12.5) * 0.00210526)) + tanh(((x0 - 12.5) * 0.00210526)))*gauss(a5*((x0 - 12.5) * 0.00210526)**2 + ((x0 - 12.5) * 0.00210526))*tanh(((x0 - 12.5) * 0.00210526))).

Here, the function has 164.796*(...), this is the result of scale_y_by = 'mean' as the input y was scaled by its mean for when performing the fits (to avoid numerical overflow), so this factor is to unscale it after the fits are done so that the final function describes the original input dataset. Also, there is (x0 - 12.5) * 0.00210526 appearing everywhere, this is the result of input_rescale = True as the input x was scaled to [0,1] when performing the fits and then unscaled afterward.

This candidate function has 8 parameters: a1, a2, a3, a4, a5, a6, a7, a8. Their best-fit values and +/-1 sigma uncertainties can be found in the corresponding PDF files and in the csv table above. The individual variations of each parameter in each candidate function are all plotted in candidates.pdf.

To see how this candidate function behaves when each of these 8 parameters is varied to its +/-1 sigma value:

Click to expand

^ +/-1 sigma variations of parameter a1

^ +/-1 sigma variations of parameter a2

^ +/-1 sigma variations of parameter a3

^ +/-1 sigma variations of parameter a4

^ +/-1 sigma variations of parameter a5

^ +/-1 sigma variations of parameter a6

^ +/-1 sigma variations of parameter a7

^ +/-1 sigma variations of parameter a8

^ Correlation matrix

As shown in the correlation matrix, these parameters are not all independent to each other, so it will be nice to see the actual uncertainty coverage considering uncertainties from all parameters in a candidate function. These are plotted in candidates_sampling.pdf. Here, what it does is to generate an ensemble of functions for a candidate function by sampling its parameters, where the sampling is done by sampling from a multidimensional normal distribution for the parameters, with the best-fit parameter values being the mean location and the covariance matrix for the parameters being the covarience. In this way, the total uncertainty is obtained by considering uncertainties from all parameters simultaneously. Then the 68% quantile range of this function ensemble as green bands in the plots and compared with the input data.

Note the 95% quantile range can also be added by sampling_95quantile = True.