Integrals 101 to 200

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2.2.2 Integrals 101 to 200

Detailed conclusion table per each integral is given by table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given just an F.

In this table,the column N.S. in the table below, which stands for normalized size is deﬁned as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table ﬁt, Mathematica was abbreviated to MMA.


Problem 101	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	94	94	91	77	94	328	194	80	92
N.S.	1	1.00	0.97	0.82	1.00	3.49	2.06	0.85	0.98
time (sec)	N/A	0.059	0.055	0.086	0.510	0.836	0.594	0.952	0.079


Problem 102	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	89	89	83	76	92	301	155	78	82
N.S.	1	1.00	0.93	0.85	1.03	3.38	1.74	0.88	0.92
time (sec)	N/A	0.045	0.062	0.093	0.541	0.703	0.393	1.201	0.079


Problem 103	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	92	92	84	77	92	300	150	78	82
N.S.	1	1.00	0.91	0.84	1.00	3.26	1.63	0.85	0.89
time (sec)	N/A	0.024	0.047	0.101	0.537	0.581	0.386	1.471	0.079


Problem 104	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	97	97	96	82	96	324	194	82	113
N.S.	1	1.00	0.99	0.85	0.99	3.34	2.00	0.85	1.16
time (sec)	N/A	0.069	0.043	0.077	0.500	0.686	0.368	1.228	0.096


Problem 105	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	117	117	116	98	128	368	226	108	114
N.S.	1	1.00	0.99	0.84	1.09	3.15	1.93	0.92	0.97
time (sec)	N/A	0.115	0.067	0.088	0.506	0.575	0.478	0.930	0.102


Problem 106	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	142	142	139	119	154	426	260	135	135
N.S.	1	1.00	0.98	0.84	1.08	3.00	1.83	0.95	0.95
time (sec)	N/A	0.224	0.073	0.099	0.507	0.997	0.468	0.948	0.105


Problem 107	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	C	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	12	12	12	13	12	12	26	12	12
N.S.	1	1.00	1.00	1.08	1.00	1.00	2.17	1.00	1.00
time (sec)	N/A	0.005	0.005	0.085	0.498	1.154	0.065	0.801	0.042


Problem 108	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	B	B	B	B	B	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	11	11	28	32	23	23	22	25	11
N.S.	1	1.00	2.55	2.91	2.09	2.09	2.00	2.27	1.00
time (sec)	N/A	0.005	0.008	0.082	0.277	1.062	0.084	1.418	0.062


Problem 109	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	11	11	10	16	10	10	7	11	10
N.S.	1	1.00	0.91	1.45	0.91	0.91	0.64	1.00	0.91
time (sec)	N/A	0.002	0.004	0.084	0.304	1.107	0.025	1.197	0.041


Problem 110	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	9	9	9	10	9	9	5	7	9
N.S.	1	1.00	1.00	1.11	1.00	1.00	0.56	0.78	1.00
time (sec)	N/A	0.002	0.004	0.067	0.279	1.031	0.022	1.507	0.043


Problem 111	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	19	19	19	16	15	20	14	15	16
N.S.	1	1.00	1.00	0.84	0.79	1.05	0.74	0.79	0.84
time (sec)	N/A	0.003	0.006	0.067	0.492	0.889	0.041	1.134	0.042


Problem 112	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	19	19	19	16	15	21	15	15	17
N.S.	1	1.00	1.00	0.84	0.79	1.11	0.79	0.79	0.89
time (sec)	N/A	0.003	0.006	0.070	0.490	0.632	0.032	1.259	0.039


Problem 113	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	14	14	14	15	14	19	10	14	14
N.S.	1	1.00	1.00	1.07	1.00	1.36	0.71	1.00	1.00
time (sec)	N/A	0.003	0.005	0.070	0.493	1.183	0.028	1.198	0.013


Problem 114	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	12	12	14	13	14	14	8	14	12
N.S.	1	1.00	1.17	1.08	1.17	1.17	0.67	1.17	1.00
time (sec)	N/A	0.003	0.005	0.061	0.276	1.116	0.077	1.176	0.024


Problem 115	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	12	12	14	13	14	14	8	14	12
N.S.	1	1.00	1.17	1.08	1.17	1.17	0.67	1.17	1.00
time (sec)	N/A	0.003	0.004	0.069	0.289	1.295	0.076	1.526	0.001


Problem 116	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	39	39	39	37	49	98	75	36	31
N.S.	1	1.00	1.00	0.95	1.26	2.51	1.92	0.92	0.79
time (sec)	N/A	0.013	0.017	0.085	0.501	0.792	0.146	1.031	0.077


Problem 117	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	35	35	35	25	30	39	27	25	30
N.S.	1	1.00	1.00	0.71	0.86	1.11	0.77	0.71	0.86
time (sec)	N/A	0.005	0.008	0.085	0.503	0.705	0.045	1.058	0.043


Problem 118	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	B	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	14	14	14	30	16	16	17	11	20
N.S.	1	1.00	1.00	2.14	1.14	1.14	1.21	0.79	1.43
time (sec)	N/A	0.006	0.005	0.112	0.276	0.894	0.037	1.682	0.020


Problem 119	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	1	1	1	2	1	1	0	1	1
N.S.	1	1.00	1.00	2.00	1.00	1.00	0.00	1.00	1.00
time (sec)	N/A	0.000	0.000	0.097	0.292	0.842	0.010	1.319	0.001


Problem 120	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	8	8	8	7	6	6	5	6	6
N.S.	1	1.00	1.00	0.88	0.75	0.75	0.62	0.75	0.75
time (sec)	N/A	0.001	0.000	0.059	0.294	0.804	0.012	1.324	0.012


Problem 121	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	8	8	8	7	6	6	5	6	6
N.S.	1	1.00	1.00	0.88	0.75	0.75	0.62	0.75	0.75
time (sec)	N/A	0.001	0.000	0.062	0.292	1.247	0.012	1.266	0.006


Problem 122	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	8	8	8	7	6	6	5	6	6
N.S.	1	1.00	1.00	0.88	0.75	0.75	0.62	0.75	0.75
time (sec)	N/A	0.001	0.000	0.059	0.315	0.911	0.012	1.071	0.007


Problem 123	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	3	3	3	4	3	3	2	3	3
N.S.	1	1.00	1.00	1.33	1.00	1.00	0.67	1.00	1.00
time (sec)	N/A	0.001	0.000	0.062	0.287	1.265	0.009	1.377	0.003


Problem 124	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	4	4	4	5	7	4	3	5	4
N.S.	1	1.00	1.00	1.25	1.75	1.00	0.75	1.25	1.00
time (sec)	N/A	0.001	0.000	0.073	0.277	1.081	0.013	1.492	0.007


Problem 125	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	6	6	6	7	6	6	3	6	6
N.S.	1	1.00	1.00	1.17	1.00	1.00	0.50	1.00	1.00
time (sec)	N/A	0.001	0.000	0.060	0.301	1.060	0.012	1.255	0.008


Problem 126	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	8	8	8	7	6	6	7	6	6
N.S.	1	1.00	1.00	0.88	0.75	0.75	0.88	0.75	0.75
time (sec)	N/A	0.001	0.000	0.069	0.317	1.047	0.018	1.360	0.010


Problem 127	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	29	29	29	26	25	24	22	47	23
N.S.	1	1.00	1.00	0.90	0.86	0.83	0.76	1.62	0.79
time (sec)	N/A	0.014	0.004	0.064	0.282	0.965	0.053	1.685	0.022


Problem 128	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	33	33	33	29	28	86	58	28	25
N.S.	1	1.00	1.00	0.88	0.85	2.61	1.76	0.85	0.76
time (sec)	N/A	0.011	0.007	0.083	0.630	1.108	0.067	1.100	0.023


Problem 129	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	16	16	16	15	14	14	12	63	14
N.S.	1	1.00	1.00	0.94	0.88	0.88	0.75	3.94	0.88
time (sec)	N/A	0.003	0.003	0.066	0.289	0.965	0.039	1.141	0.017


Problem 130	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	25	25	25	17	16	69	54	16	17
N.S.	1	1.00	1.00	0.68	0.64	2.76	2.16	0.64	0.68
time (sec)	N/A	0.006	0.004	0.080	0.505	0.930	0.094	1.301	0.025


Problem 131	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	24	24	24	23	25	21	17	26	19
N.S.	1	1.00	1.00	0.96	1.04	0.88	0.71	1.08	0.79
time (sec)	N/A	0.010	0.005	0.067	0.316	1.185	0.098	1.248	0.055


Problem 132	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	36	36	36	32	31	86	66	31	28
N.S.	1	1.00	1.00	0.89	0.86	2.39	1.83	0.86	0.78
time (sec)	N/A	0.010	0.010	0.071	0.570	1.044	0.073	0.955	0.052


Problem 133	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	38	38	37	34	36	36	32	47	34
N.S.	1	1.00	0.97	0.89	0.95	0.95	0.84	1.24	0.89
time (sec)	N/A	0.018	0.006	0.074	0.278	0.775	0.148	0.871	0.057


Problem 134	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	35	35	28	32	34	40	31	32	31
N.S.	1	1.00	0.80	0.91	0.97	1.14	0.89	0.91	0.89
time (sec)	N/A	0.021	0.008	0.064	0.283	1.118	0.085	0.787	0.051


Problem 135	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	47	47	47	38	38	128	80	37	35
N.S.	1	1.00	1.00	0.81	0.81	2.72	1.70	0.79	0.74
time (sec)	N/A	0.011	0.016	0.087	0.518	0.955	0.099	1.286	0.023


Problem 136	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	17	17	17	16	16	16	15	15	15
N.S.	1	1.00	1.00	0.94	0.94	0.94	0.88	0.88	0.88
time (sec)	N/A	0.003	0.002	0.064	0.294	0.829	0.087	0.900	0.017


Problem 137	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	47	47	47	38	37	128	80	37	35
N.S.	1	1.00	1.00	0.81	0.79	2.72	1.70	0.79	0.74
time (sec)	N/A	0.010	0.018	0.084	0.550	0.791	0.132	0.968	0.022


Problem 138	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	41	41	34	44	40	54	36	51	37
N.S.	1	1.00	0.83	1.07	0.98	1.32	0.88	1.24	0.90
time (sec)	N/A	0.020	0.013	0.074	0.287	0.958	0.148	0.874	0.051


Problem 139	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	60	60	56	47	52	144	94	50	48
N.S.	1	1.00	0.93	0.78	0.87	2.40	1.57	0.83	0.80
time (sec)	N/A	0.015	0.028	0.083	0.506	0.925	0.185	1.109	0.037


Problem 140	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	53	53	42	57	57	80	53	56	55
N.S.	1	1.00	0.79	1.08	1.08	1.51	1.00	1.06	1.04
time (sec)	N/A	0.031	0.027	0.076	0.270	0.954	0.176	0.860	0.061


Problem 141	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	55	55	55	52	51	51	56	53	51
N.S.	1	1.00	1.00	0.95	0.93	0.93	1.02	0.96	0.93
time (sec)	N/A	0.025	0.007	0.096	0.266	0.730	0.011	0.950	0.052


Problem 142	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	55	55	55	52	51	51	53	53	51
N.S.	1	1.00	1.00	0.95	0.93	0.93	0.96	0.96	0.93
time (sec)	N/A	0.043	0.007	0.082	0.291	0.873	0.017	0.782	0.025


Problem 143	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	55	55	55	52	51	51	56	53	51
N.S.	1	1.00	1.00	0.95	0.93	0.93	1.02	0.96	0.93
time (sec)	N/A	0.022	0.006	0.096	0.271	0.887	0.011	1.158	0.054


Problem 144	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	42	42	51	52	51	51	53	53	51
N.S.	1	1.00	1.21	1.24	1.21	1.21	1.26	1.26	1.21
time (sec)	N/A	0.042	0.010	0.085	0.305	0.810	0.013	0.754	0.025


Problem 145	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	50	50	50	49	48	48	53	50	48
N.S.	1	1.00	1.00	0.98	0.96	0.96	1.06	1.00	0.96
time (sec)	N/A	0.016	0.007	0.059	0.307	0.668	0.012	1.289	0.030


Problem 146	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	43	43	51	51	52	49	49	53	48
N.S.	1	1.00	1.19	1.19	1.21	1.14	1.14	1.23	1.12
time (sec)	N/A	0.022	0.012	0.069	0.366	0.971	0.048	0.922	0.021


Problem 147	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	48	48	48	49	48	53	48	48	48
N.S.	1	1.00	1.00	1.02	1.00	1.10	1.00	1.00	1.00
time (sec)	N/A	0.018	0.013	0.061	0.272	1.201	0.046	0.945	0.025


Problem 148	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	51	51	49	48	52	54	48	70	48
N.S.	1	1.00	0.96	0.94	1.02	1.06	0.94	1.37	0.94
time (sec)	N/A	0.031	0.018	0.085	0.286	0.977	0.103	0.803	0.048


Problem 149	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	48	48	50	46	50	52	51	50	50
N.S.	1	1.00	1.04	0.96	1.04	1.08	1.06	1.04	1.04
time (sec)	N/A	0.020	0.015	0.068	0.265	1.055	0.113	1.570	0.026


Problem 150	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	87	87	87	90	85	85	100	94	78
N.S.	1	1.00	1.00	1.03	0.98	0.98	1.15	1.08	0.90
time (sec)	N/A	0.043	0.013	0.104	0.278	0.675	0.014	1.018	0.028


Problem 151	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	87	87	81	90	85	85	92	94	78
N.S.	1	1.00	0.93	1.03	0.98	0.98	1.06	1.08	0.90
time (sec)	N/A	0.075	0.019	0.088	0.295	1.053	0.021	0.869	0.016


Problem 152	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	87	87	87	90	85	85	100	94	78
N.S.	1	1.00	1.00	1.03	0.98	0.98	1.15	1.08	0.90
time (sec)	N/A	0.036	0.014	0.107	0.268	1.030	0.014	0.859	0.016


Problem 153	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	71	71	81	90	85	85	94	94	78
N.S.	1	1.00	1.14	1.27	1.20	1.20	1.32	1.32	1.10
time (sec)	N/A	0.073	0.017	0.086	0.272	0.965	0.018	1.470	0.016


Problem 154	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	82	82	82	87	82	82	97	91	75
N.S.	1	1.00	1.00	1.06	1.00	1.00	1.18	1.11	0.91
time (sec)	N/A	0.027	0.012	0.066	0.274	0.649	0.020	1.077	0.016


Problem 155	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	80	80	80	90	85	82	85	92	74
N.S.	1	1.00	1.00	1.12	1.06	1.02	1.06	1.15	0.92
time (sec)	N/A	0.052	0.018	0.126	0.283	0.854	0.071	1.277	0.018


Problem 156	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	81	81	81	91	83	87	92	90	76
N.S.	1	1.00	1.00	1.12	1.02	1.07	1.14	1.11	0.94
time (sec)	N/A	0.030	0.029	0.093	0.300	0.923	0.064	0.994	0.017


Problem 157	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	84	84	83	88	85	88	87	114	82
N.S.	1	1.00	0.99	1.05	1.01	1.05	1.04	1.36	0.98
time (sec)	N/A	0.054	0.031	0.072	0.347	0.749	0.155	1.399	0.020


Problem 158	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	80	80	80	81	84	87	92	88	82
N.S.	1	1.00	1.00	1.01	1.05	1.09	1.15	1.10	1.02
time (sec)	N/A	0.035	0.031	0.074	0.301	0.761	0.152	1.172	0.028


Problem 159	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	127	127	127	128	127	127	143	135	119
N.S.	1	1.00	1.00	1.01	1.00	1.00	1.13	1.06	0.94
time (sec)	N/A	0.062	0.020	0.102	0.325	0.775	0.018	1.013	0.053


Problem 160	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	106	106	119	128	127	127	138	135	119
N.S.	1	1.00	1.12	1.21	1.20	1.20	1.30	1.27	1.12
time (sec)	N/A	0.164	0.024	0.086	0.344	0.781	0.019	1.091	0.022


Problem 161	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	127	127	127	128	127	127	143	135	119
N.S.	1	1.00	1.00	1.01	1.00	1.00	1.13	1.06	0.94
time (sec)	N/A	0.049	0.015	0.120	0.329	0.648	0.028	0.749	0.021


Problem 162	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	71	71	119	128	127	127	136	134	118
N.S.	1	1.00	1.68	1.80	1.79	1.79	1.92	1.89	1.66
time (sec)	N/A	0.088	0.021	0.093	0.404	0.875	0.018	1.322	0.021


Problem 163	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	122	122	122	125	124	124	136	131	116
N.S.	1	1.00	1.00	1.02	1.02	1.02	1.11	1.07	0.95
time (sec)	N/A	0.038	0.016	0.066	0.328	0.724	0.017	0.896	0.023


Problem 164	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	123	123	123	132	128	125	133	134	116
N.S.	1	1.00	1.00	1.07	1.04	1.02	1.08	1.09	0.94
time (sec)	N/A	0.072	0.023	0.081	0.268	0.769	0.128	3.874	0.024


Problem 165	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	120	120	120	131	124	129	131	130	115
N.S.	1	1.00	1.00	1.09	1.03	1.08	1.09	1.08	0.96
time (sec)	N/A	0.040	0.029	0.070	0.297	0.750	0.105	1.734	0.047


Problem 166	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	123	123	120	130	128	131	133	160	121
N.S.	1	1.00	0.98	1.06	1.04	1.07	1.08	1.30	0.98
time (sec)	N/A	0.069	0.038	0.075	0.281	0.904	0.213	0.885	0.049


Problem 167	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	120	120	120	124	126	129	131	129	121
N.S.	1	1.00	1.00	1.03	1.05	1.08	1.09	1.08	1.01
time (sec)	N/A	0.040	0.032	0.076	0.292	0.975	0.209	0.651	0.022


Problem 168	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	104	104	104	143	139	302	246	153	169
N.S.	1	1.00	1.00	1.38	1.34	2.90	2.37	1.47	1.62
time (sec)	N/A	0.048	0.071	0.130	0.506	1.018	0.416	0.677	0.032


Problem 169	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	79	79	82	102	100	101	83	107	106
N.S.	1	1.00	1.04	1.29	1.27	1.28	1.05	1.35	1.34
time (sec)	N/A	0.060	0.031	0.082	0.282	1.406	0.313	0.724	0.035


Problem 170	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	83	83	83	102	104	228	194	113	128
N.S.	1	1.00	1.00	1.23	1.25	2.75	2.34	1.36	1.54
time (sec)	N/A	0.044	0.052	0.104	0.486	1.152	0.323	0.891	0.035


Problem 171	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	61	61	49	64	65	66	49	67	68
N.S.	1	1.00	0.80	1.05	1.07	1.08	0.80	1.10	1.11
time (sec)	N/A	0.033	0.018	0.097	0.281	1.288	0.186	0.690	0.064


Problem 172	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	63	63	59	64	68	179	172	72	90
N.S.	1	1.00	0.94	1.02	1.08	2.84	2.73	1.14	1.43
time (sec)	N/A	0.027	0.037	0.072	0.514	1.463	0.331	0.797	0.041


Problem 173	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	51	51	50	59	61	59	41	62	58
N.S.	1	1.00	0.98	1.16	1.20	1.16	0.80	1.22	1.14
time (sec)	N/A	0.033	0.017	0.082	0.284	1.080	0.771	0.695	0.089


Problem 174	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	55	55	55	65	63	164	165	63	80
N.S.	1	1.00	1.00	1.18	1.15	2.98	3.00	1.15	1.45
time (sec)	N/A	0.033	0.035	0.102	0.523	1.418	0.396	0.579	0.067


Problem 175	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	58	58	60	66	70	74	49	91	67
N.S.	1	1.00	1.03	1.14	1.21	1.28	0.84	1.57	1.16
time (sec)	N/A	0.041	0.022	0.089	0.308	1.051	0.840	0.626	0.097


Problem 176	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	66	66	64	68	71	192	172	71	90
N.S.	1	1.00	0.97	1.03	1.08	2.91	2.61	1.08	1.36
time (sec)	N/A	0.038	0.040	0.086	0.683	1.062	0.393	0.672	0.085


Problem 177	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	75	75	72	91	96	98	66	139	93
N.S.	1	1.00	0.96	1.21	1.28	1.31	0.88	1.85	1.24
time (sec)	N/A	0.047	0.033	0.085	0.311	1.200	0.831	0.613	0.087


Problem 178	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	87	87	86	100	107	236	207	112	129
N.S.	1	1.00	0.99	1.15	1.23	2.71	2.38	1.29	1.48
time (sec)	N/A	0.046	0.053	0.092	0.518	1.332	0.486	0.548	0.050


Problem 179	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	98	98	108	123	134	136	105	184	129
N.S.	1	1.00	1.10	1.26	1.37	1.39	1.07	1.88	1.32
time (sec)	N/A	0.056	0.048	0.086	0.290	1.061	0.988	0.513	0.078


Problem 180	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	145	145	138	141	149	400	286	156	200
N.S.	1	1.00	0.95	0.97	1.03	2.76	1.97	1.08	1.38
time (sec)	N/A	0.090	0.069	0.114	0.506	1.490	0.573	0.552	0.075


Problem 181	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	90	90	87	80	107	161	99	163	112
N.S.	1	1.00	0.97	0.89	1.19	1.79	1.10	1.81	1.24
time (sec)	N/A	0.072	0.047	0.091	0.281	1.408	0.515	0.507	0.067


Problem 182	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	118	118	105	101	109	342	246	114	146
N.S.	1	1.00	0.89	0.86	0.92	2.90	2.08	0.97	1.24
time (sec)	N/A	0.074	0.053	0.112	0.510	1.039	0.593	0.510	0.044


Problem 183	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	62	62	56	63	74	101	68	110	77
N.S.	1	1.00	0.90	1.02	1.19	1.63	1.10	1.77	1.24
time (sec)	N/A	0.042	0.035	0.076	0.284	1.154	0.531	0.529	0.046


Problem 184	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	B	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	82	82	89	92	96	302	236	95	124
N.S.	1	1.00	1.09	1.12	1.17	3.68	2.88	1.16	1.51
time (sec)	N/A	0.070	0.046	0.066	0.491	1.116	0.378	1.065	0.088


Problem 185	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	67	67	70	67	86	116	80	99	80
N.S.	1	1.00	1.04	1.00	1.28	1.73	1.19	1.48	1.19
time (sec)	N/A	0.044	0.032	0.079	0.299	1.045	0.823	1.208	0.068


Problem 186	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	106	104	91	97	100	305	238	102	128
N.S.	1	0.98	0.86	0.92	0.94	2.88	2.25	0.96	1.21
time (sec)	N/A	0.052	0.045	0.110	0.541	0.964	0.524	1.011	0.116


Problem 187	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	B	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	81	81	72	77	100	159	92	109	100
N.S.	1	1.00	0.89	0.95	1.23	1.96	1.14	1.35	1.23
time (sec)	N/A	0.059	0.066	0.090	0.274	1.245	0.822	1.654	0.052


Problem 188	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	126	126	107	107	118	356	248	111	147
N.S.	1	1.00	0.85	0.85	0.94	2.83	1.97	0.88	1.17
time (sec)	N/A	0.092	0.047	0.091	0.508	1.315	0.541	1.771	0.108


Problem 189	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	163	163	148	137	159	522	240	154	159
N.S.	1	1.00	0.91	0.84	0.98	3.20	1.47	0.94	0.98
time (sec)	N/A	0.110	0.067	0.114	0.531	0.961	1.203	1.435	0.086


Problem 190	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	99	99	114	113	120	178	122	107	123
N.S.	1	1.00	1.15	1.14	1.21	1.80	1.23	1.08	1.24
time (sec)	N/A	0.071	0.038	0.080	0.279	1.389	3.635	1.060	0.083


Problem 191	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	B	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	127	127	130	123	143	475	223	133	135
N.S.	1	1.00	1.02	0.97	1.13	3.74	1.76	1.05	1.06
time (sec)	N/A	0.083	0.075	0.102	0.547	1.176	1.225	1.183	0.098


Problem 192	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	67	67	75	76	87	108	87	76	83
N.S.	1	1.00	1.12	1.13	1.30	1.61	1.30	1.13	1.24
time (sec)	N/A	0.046	0.019	0.086	0.292	0.909	0.887	0.692	0.042


Problem 193	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	B	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	116	116	121	124	138	449	223	126	130
N.S.	1	1.00	1.04	1.07	1.19	3.87	1.92	1.09	1.12
time (sec)	N/A	0.051	0.072	0.065	0.533	0.966	0.547	1.270	0.110


Problem 194	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	B	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	86	86	103	98	109	163	107	110	106
N.S.	1	1.00	1.20	1.14	1.27	1.90	1.24	1.28	1.23
time (sec)	N/A	0.058	0.035	0.086	0.369	1.032	0.695	1.727	0.069


Problem 195	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	152	149	133	128	146	475	224	135	135
N.S.	1	0.98	0.88	0.84	0.96	3.12	1.47	0.89	0.89
time (sec)	N/A	0.073	0.064	0.111	0.553	1.467	0.733	1.451	0.117


Problem 196	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	B	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	106	106	99	114	142	256	139	177	132
N.S.	1	1.00	0.93	1.08	1.34	2.42	1.31	1.67	1.25
time (sec)	N/A	0.082	0.066	0.088	0.279	0.842	1.247	1.033	0.065


Problem 197	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	161	161	148	142	167	536	240	151	156
N.S.	1	1.00	0.92	0.88	1.04	3.33	1.49	0.94	0.97
time (sec)	N/A	0.133	0.053	0.117	0.506	1.088	0.869	1.390	0.111


Problem 198	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	75	75	71	74	74	75	70	77	76
N.S.	1	1.00	0.95	0.99	0.99	1.00	0.93	1.03	1.01
time (sec)	N/A	0.061	0.023	0.073	0.291	1.345	0.161	1.144	0.063


Problem 199	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	77	77	77	75	77	178	153	84	96
N.S.	1	1.00	1.00	0.97	1.00	2.31	1.99	1.09	1.25
time (sec)	N/A	0.033	0.039	0.089	0.533	1.079	0.258	1.038	0.064


Problem 200	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	54	54	47	50	50	51	46	52	52
N.S.	1	1.00	0.87	0.93	0.93	0.94	0.85	0.96	0.96
time (sec)	N/A	0.040	0.015	0.093	0.307	0.950	0.148	1.224	0.035

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