Integrals 301 to 400

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2.2.4 Integrals 301 to 400

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 301	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	16	16	14	15	14	17	10	15	14
N.S.	1	1.00	0.88	0.94	0.88	1.06	0.62	0.94	0.88
time (sec)	N/A	0.017	0.007	0.015	0.282	0.375	0.024	5.416	0.043


Problem 302	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	21	21	14	16	17	17	14	12	12
N.S.	1	1.00	0.67	0.76	0.81	0.81	0.67	0.57	0.57
time (sec)	N/A	0.013	0.003	0.011	0.279	0.389	0.022	5.927	2.085


Problem 303	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	15	15	15	16	23	23	17	30	15
N.S.	1	1.00	1.00	1.07	1.53	1.53	1.13	2.00	1.00
time (sec)	N/A	0.019	0.009	0.229	0.268	0.372	0.032	4.348	2.089


Problem 304	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	31	31	31	29	28	28	3	29	57
N.S.	1	1.00	1.00	0.94	0.90	0.90	0.10	0.94	1.84
time (sec)	N/A	0.029	0.009	0.020	0.480	0.408	0.045	3.244	0.112


Problem 305	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	25	25	25	20	19	19	19	22	19
N.S.	1	1.00	1.00	0.80	0.76	0.76	0.76	0.88	0.76
time (sec)	N/A	0.029	0.005	0.017	0.275	0.397	0.049	2.668	0.060


Problem 306	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	30	30	29	25	24	36	20	26	22
N.S.	1	1.00	0.97	0.83	0.80	1.20	0.67	0.87	0.73
time (sec)	N/A	0.020	0.012	0.021	0.270	0.415	0.026	4.116	2.108


Problem 307	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	23	23	23	18	17	17	17	18	21
N.S.	1	1.00	1.00	0.78	0.74	0.74	0.74	0.78	0.91
time (sec)	N/A	0.026	0.004	0.186	0.482	0.404	0.047	2.852	2.121


Problem 308	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	103	103	93	73	77	136	88	74	96
N.S.	1	1.00	0.90	0.71	0.75	1.32	0.85	0.72	0.93
time (sec)	N/A	0.333	0.034	0.310	0.474	0.418	0.268	4.762	2.200


Problem 309	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	30	28	25	36	24	25	32
N.S.	1	1.00	0.91	0.85	0.76	1.09	0.73	0.76	0.97
time (sec)	N/A	0.012	0.009	0.181	0.502	0.381	0.041	5.790	0.035


Problem 310	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	28	29	44	27	30	33
N.S.	1	1.00	1.00	0.85	0.88	1.33	0.82	0.91	1.00
time (sec)	N/A	0.028	0.015	0.185	0.485	0.398	0.052	5.829	2.113


Problem 311	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	25	25	25	24	23	19	17	26	19
N.S.	1	1.00	1.00	0.96	0.92	0.76	0.68	1.04	0.76
time (sec)	N/A	0.028	0.005	0.207	0.268	0.393	0.025	4.654	0.043


Problem 312	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	36	36	36	32	31	31	36	31	56
N.S.	1	1.00	1.00	0.89	0.86	0.86	1.00	0.86	1.56
time (sec)	N/A	0.080	0.011	0.195	0.479	0.392	0.080	3.053	0.106


Problem 313	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	22	21	33	22	21	23
N.S.	1	1.00	1.00	0.76	0.72	1.14	0.76	0.72	0.79
time (sec)	N/A	0.072	0.013	0.194	0.503	0.376	0.064	3.988	0.042


Problem 314	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	46	46	46	36	35	39	46	36	49
N.S.	1	1.00	1.00	0.78	0.76	0.85	1.00	0.78	1.07
time (sec)	N/A	0.041	0.019	0.023	0.491	0.417	0.062	4.522	2.169


Problem 315	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	22	26	26	19	18	18	17	20	14
N.S.	1	1.18	1.18	0.86	0.82	0.82	0.77	0.91	0.64
time (sec)	N/A	0.011	0.004	0.246	0.267	0.393	0.026	4.654	0.039


Problem 316	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	15	15	15	18	15
N.S.	1	1.00	1.00	0.94	0.88	0.88	0.88	1.06	0.88
time (sec)	N/A	0.027	0.005	0.018	0.265	0.404	0.044	5.370	0.065


Problem 317	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	18	14	16	14
N.S.	1	1.00	1.00	1.07	1.00	1.29	1.00	1.14	1.00
time (sec)	N/A	0.016	0.003	0.190	0.290	0.389	0.034	3.623	2.120


Problem 318	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	25	18	17	17	17	20	17
N.S.	1	1.00	1.32	0.95	0.89	0.89	0.89	1.05	0.89
time (sec)	N/A	0.018	0.006	0.019	0.271	0.428	0.044	4.015	2.116


Problem 319	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	23	23	23	18	17	17	19	17	33
N.S.	1	1.00	1.00	0.78	0.74	0.74	0.83	0.74	1.43
time (sec)	N/A	0.021	0.008	0.020	0.523	0.380	0.070	2.877	0.054


Problem 320	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	63	63	57	51	50	50	68	53	58
N.S.	1	1.00	0.90	0.81	0.79	0.79	1.08	0.84	0.92
time (sec)	N/A	0.059	0.020	0.030	0.494	0.392	0.187	3.456	2.213


Problem 321	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	69	86	67	54	59	103	65	59	71
N.S.	1	1.25	0.97	0.78	0.86	1.49	0.94	0.86	1.03
time (sec)	N/A	0.066	0.035	0.030	0.487	0.407	0.089	4.906	2.177


Problem 322	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	14	13	19	12	13	13
N.S.	1	1.00	1.00	0.82	0.76	1.12	0.71	0.76	0.76
time (sec)	N/A	0.009	0.005	0.200	0.499	0.379	0.031	4.506	0.033


Problem 323	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	18	17	17	15	17	17
N.S.	1	1.00	1.00	0.95	0.89	0.89	0.79	0.89	0.89
time (sec)	N/A	0.018	0.004	0.201	0.484	0.364	0.029	4.575	2.098


Problem 324	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	9	9	9	8	7	7	7	28	19
N.S.	1	1.00	1.00	0.89	0.78	0.78	0.78	3.11	2.11
time (sec)	N/A	0.044	0.005	0.198	0.489	0.398	0.047	4.325	2.104


Problem 325	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	12	13	12	12	12	12	12
N.S.	1	1.00	1.00	1.08	1.00	1.00	1.00	1.00	1.00
time (sec)	N/A	0.010	0.004	0.268	0.276	0.381	0.019	3.680	0.028


Problem 326	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	65	65	58	41	51	66	99	55	48
N.S.	1	1.00	0.89	0.63	0.78	1.02	1.52	0.85	0.74
time (sec)	N/A	0.040	0.026	0.236	0.491	0.390	0.237	3.630	0.099


Problem 327	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	28	28	28	29	28	46	24	28	28
N.S.	1	1.00	1.00	1.04	1.00	1.64	0.86	1.00	1.00
time (sec)	N/A	0.016	0.009	0.276	0.483	0.370	0.040	3.682	0.038


Problem 328	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	32	32	32	27	26	26	29	26	26
N.S.	1	1.00	1.00	0.84	0.81	0.81	0.91	0.81	0.81
time (sec)	N/A	0.026	0.019	0.221	0.501	0.373	0.028	4.222	0.025


Problem 329	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	31	41	39	24	23	23	26	27	23
N.S.	1	1.32	1.26	0.77	0.74	0.74	0.84	0.87	0.74
time (sec)	N/A	0.032	0.006	0.021	0.290	0.400	0.077	4.796	0.050


Problem 330	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	22	26	19	23	30
N.S.	1	1.00	1.00	0.96	0.92	1.08	0.79	0.96	1.25
time (sec)	N/A	0.119	0.007	0.210	0.478	0.434	0.054	4.485	2.129


Problem 331	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	23	23	23	19	24	35	20	19	23
N.S.	1	1.00	1.00	0.83	1.04	1.52	0.87	0.83	1.00
time (sec)	N/A	0.017	0.009	0.195	0.930	0.374	0.041	4.889	0.033


Problem 332	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	23	23	23	19	24	35	20	19	23
N.S.	1	1.00	1.00	0.83	1.04	1.52	0.87	0.83	1.00
time (sec)	N/A	0.026	0.004	0.016	0.507	0.374	0.041	4.448	0.030


Problem 333	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	13	13	13	14	13	15	10	13	13
N.S.	1	1.00	1.00	1.08	1.00	1.15	0.77	1.00	1.00
time (sec)	N/A	0.031	0.005	0.018	0.537	0.368	0.027	3.882	2.144


Problem 334	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	C	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	206	206	193	227	199	4545	138	208	357
N.S.	1	1.00	0.94	1.10	0.97	22.06	0.67	1.01	1.73
time (sec)	N/A	0.193	0.079	0.227	0.502	1.153	0.703	6.014	0.231


Problem 335	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	F	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	45	45	45	41	0	47	44	38	42
N.S.	1	1.00	1.00	0.91	0.00	1.04	0.98	0.84	0.93
time (sec)	N/A	0.047	0.019	0.022	0.000	0.384	0.053	4.086	2.191


Problem 336	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	F	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	59	59	44	41	0	75	46	42	47
N.S.	1	1.00	0.75	0.69	0.00	1.27	0.78	0.71	0.80
time (sec)	N/A	0.044	0.018	0.024	0.000	0.386	0.067	5.753	0.049


Problem 337	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	F	C	F(-1)	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	209	209	234	240	0	578003	0	1589	2500
N.S.	1	1.00	1.12	1.15	0.00	2765.56	0.00	7.60	11.96
time (sec)	N/A	0.276	0.169	0.058	0.000	28.709	0.000	6.285	3.437


Problem 338	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	F	C	F(-1)	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	224	224	245	253	0	540080	0	1625	3046
N.S.	1	1.00	1.09	1.13	0.00	2411.07	0.00	7.25	13.60
time (sec)	N/A	0.202	0.163	0.187	0.000	113.356	0.000	6.128	3.220


Problem 339	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	56	56	56	57	60	65	190	62	61
N.S.	1	1.00	1.00	1.02	1.07	1.16	3.39	1.11	1.09
time (sec)	N/A	0.029	0.020	0.223	0.276	0.384	0.606	4.561	0.213


Problem 340	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	F(-1)	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	96	96	73	75	84	162	0	85	347
N.S.	1	1.00	0.76	0.78	0.88	1.69	0.00	0.89	3.61
time (sec)	N/A	0.070	0.026	0.219	0.497	0.455	0.000	4.496	1.131


Problem 341	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	C	F(-1)	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	264	264	228	245	279	5975	0	320	570
N.S.	1	1.00	0.86	0.93	1.06	22.63	0.00	1.21	2.16
time (sec)	N/A	0.339	0.067	0.227	0.486	1.284	0.000	3.474	2.496


Problem 342	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	C	F(-1)	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	417	417	370	281	349	259898	0	401	823
N.S.	1	1.00	0.89	0.67	0.84	623.26	0.00	0.96	1.97
time (sec)	N/A	0.379	0.170	0.233	0.511	27.979	0.000	3.794	2.449


Problem 343	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	16	16	24	21	20	26	19	21	12
N.S.	1	1.00	1.50	1.31	1.25	1.62	1.19	1.31	0.75
time (sec)	N/A	0.006	0.008	0.200	0.294	0.370	0.030	3.521	0.039


Problem 344	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	19	19	27	24	23	34	20	30	17
N.S.	1	1.00	1.42	1.26	1.21	1.79	1.05	1.58	0.89
time (sec)	N/A	0.009	0.009	0.200	0.262	0.396	0.038	4.079	2.138


Problem 345	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	97	97	85	90	75	106	92	77	103
N.S.	1	1.00	0.88	0.93	0.77	1.09	0.95	0.79	1.06
time (sec)	N/A	0.050	0.035	0.209	0.478	0.395	0.173	4.234	0.177


Problem 346	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	15	15	15	14	13	13	12	13	13
N.S.	1	1.00	1.00	0.93	0.87	0.87	0.80	0.87	0.87
time (sec)	N/A	0.073	0.006	0.197	0.481	0.372	0.037	4.006	2.120


Problem 347	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	13	13	13	12	11	11	10	11	11
N.S.	1	1.00	1.00	0.92	0.85	0.85	0.77	0.85	0.85
time (sec)	N/A	0.063	0.006	0.197	0.476	0.377	0.036	3.727	0.035


Problem 348	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	25	24	24	29	24	51
N.S.	1	1.00	1.00	0.86	0.83	0.83	1.00	0.83	1.76
time (sec)	N/A	0.081	0.012	0.200	0.479	0.394	0.074	3.929	2.153


Problem 349	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	17	10	14	14
N.S.	1	1.00	1.00	1.07	1.00	1.21	0.71	1.00	1.00
time (sec)	N/A	0.008	0.007	0.290	0.499	0.380	0.042	3.780	0.042


Problem 350	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	12	11	10	12	7	11	10
N.S.	1	1.00	1.00	0.92	0.83	1.00	0.58	0.92	0.83
time (sec)	N/A	0.007	0.003	0.209	0.264	0.369	0.023	4.423	0.037


Problem 351	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	11	10	9	9	8	10	17
N.S.	1	1.00	1.00	0.91	0.82	0.82	0.73	0.91	1.55
time (sec)	N/A	0.024	0.004	0.196	0.489	0.389	0.044	4.407	2.166


Problem 352	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	12	11	10	13	8	11	10
N.S.	1	1.00	1.00	0.92	0.83	1.08	0.67	0.92	0.83
time (sec)	N/A	0.015	0.003	0.208	0.278	0.391	0.022	4.867	0.039


Problem 353	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	12	13	12	12	12	14	12
N.S.	1	1.00	1.00	1.08	1.00	1.00	1.00	1.17	1.00
time (sec)	N/A	0.012	0.003	0.184	0.272	0.381	0.030	4.743	0.047


Problem 354	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	15	15	15	16	23
N.S.	1	1.00	1.00	0.94	0.88	0.88	0.88	0.94	1.35
time (sec)	N/A	0.025	0.004	0.199	0.484	0.389	0.046	4.168	2.284


Problem 355	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	13	13	13	14	13	13	10	14	19
N.S.	1	1.00	1.00	1.08	1.00	1.00	0.77	1.08	1.46
time (sec)	N/A	0.022	0.007	0.200	0.491	0.380	0.044	3.639	0.060


Problem 356	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	28	28	22	21	20	26	20	22	20
N.S.	1	1.00	0.79	0.75	0.71	0.93	0.71	0.79	0.71
time (sec)	N/A	0.007	0.013	0.225	0.266	0.392	0.034	3.852	0.069


Problem 357	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	32	32	32	27	26	37	26	43	22
N.S.	1	1.00	1.00	0.84	0.81	1.16	0.81	1.34	0.69
time (sec)	N/A	0.016	0.013	0.206	0.272	0.382	0.047	3.429	2.226


Problem 358	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	23	23	28	20	19	19	19	20	25
N.S.	1	1.00	1.22	0.87	0.83	0.83	0.83	0.87	1.09
time (sec)	N/A	0.023	0.007	0.207	0.479	0.388	0.047	3.911	0.049


Problem 359	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	24	24	22	21	20	36	20	47	28
N.S.	1	1.00	0.92	0.88	0.83	1.50	0.83	1.96	1.17
time (sec)	N/A	0.023	0.012	0.215	0.501	0.399	0.048	3.178	2.111


Problem 360	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	49	49	49	40	39	39	44	39	41
N.S.	1	1.00	1.00	0.82	0.80	0.80	0.90	0.80	0.84
time (sec)	N/A	0.099	0.011	0.351	0.489	0.390	0.088	3.700	2.156


Problem 361	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	25	25	19	20	19	19	19	22	19
N.S.	1	1.00	0.76	0.80	0.76	0.76	0.76	0.88	0.76
time (sec)	N/A	0.036	0.007	0.220	0.269	0.396	0.048	3.382	2.135


Problem 362	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	54	48	47	60	63	60	61
N.S.	1	1.00	0.90	0.80	0.78	1.00	1.05	1.00	1.02
time (sec)	N/A	0.173	0.040	0.329	0.489	0.393	0.106	4.410	0.130


Problem 363	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	11	10	9	9	5	9	6
N.S.	1	1.00	1.00	0.91	0.82	0.82	0.45	0.82	0.55
time (sec)	N/A	0.005	0.001	0.316	0.262	0.375	0.007	5.099	0.016


Problem 364	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	22	21	21	22	23	21
N.S.	1	1.00	1.00	0.76	0.72	0.72	0.76	0.79	0.72
time (sec)	N/A	0.011	0.004	0.228	0.283	0.400	0.035	5.623	2.124


Problem 365	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	45	45	45	37	37	52	37	37	49
N.S.	1	1.00	1.00	0.82	0.82	1.16	0.82	0.82	1.09
time (sec)	N/A	0.017	0.010	0.310	0.493	0.382	0.046	7.238	0.041


Problem 366	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	32	32	32	29	28	52	29	29	44
N.S.	1	1.00	1.00	0.91	0.88	1.62	0.91	0.91	1.38
time (sec)	N/A	0.176	0.014	0.207	0.496	0.379	0.109	6.752	0.069


Problem 367	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	148	148	159	99	132	179	146	122	124
N.S.	1	1.00	1.07	0.67	0.89	1.21	0.99	0.82	0.84
time (sec)	N/A	0.095	0.046	0.033	0.495	0.406	0.197	7.938	2.189


Problem 368	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	C	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	112	112	101	74	99	515	61	92	170
N.S.	1	1.00	0.90	0.66	0.88	4.60	0.54	0.82	1.52
time (sec)	N/A	0.078	0.035	0.201	0.490	1.156	0.524	8.670	2.228


Problem 369	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	13	12	12	10	14	12
N.S.	1	1.00	1.00	0.93	0.86	0.86	0.71	1.00	0.86
time (sec)	N/A	0.011	0.003	0.201	0.261	0.401	0.030	9.070	0.044


Problem 370	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	12	11	10	10	8	12	10
N.S.	1	1.00	1.00	0.92	0.83	0.83	0.67	1.00	0.83
time (sec)	N/A	0.018	0.004	0.199	0.277	0.397	0.027	8.831	2.138


Problem 371	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	15	21	14	17	15
N.S.	1	1.00	1.00	0.94	0.88	1.24	0.82	1.00	0.88
time (sec)	N/A	0.020	0.003	0.201	0.283	0.399	0.034	7.407	0.027


Problem 372	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	15	15	14	17	15
N.S.	1	1.00	1.00	0.94	0.88	0.88	0.82	1.00	0.88
time (sec)	N/A	0.020	0.004	0.200	0.287	0.409	0.027	5.462	0.033


Problem 373	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	18	18	18	17	16	25	15	23	16
N.S.	1	1.00	1.00	0.94	0.89	1.39	0.83	1.28	0.89
time (sec)	N/A	0.021	0.004	0.215	0.496	0.401	0.030	5.484	0.050


Problem 374	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	10	10	10	11	10	14	7	11	10
N.S.	1	1.00	1.00	1.10	1.00	1.40	0.70	1.10	1.00
time (sec)	N/A	0.013	0.004	0.016	0.281	0.397	0.021	5.466	0.034


Problem 375	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	42	31	30	30	36	33	30
N.S.	1	1.00	1.00	0.74	0.71	0.71	0.86	0.79	0.71
time (sec)	N/A	0.027	0.006	0.023	0.270	0.414	0.055	5.423	0.053


Problem 376	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	46	46	46	41	38	38	51	38	88
N.S.	1	1.00	1.00	0.89	0.83	0.83	1.11	0.83	1.91
time (sec)	N/A	0.090	0.014	0.312	0.481	0.424	0.083	5.090	0.002


Problem 377	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	15	14	17	8
N.S.	1	1.00	1.00	0.84	0.79	0.79	0.74	0.89	0.42
time (sec)	N/A	0.042	0.003	0.185	0.277	0.438	0.033	5.704	0.084


Problem 378	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	40	40	40	31	30	30	34	32	26
N.S.	1	1.00	1.00	0.78	0.75	0.75	0.85	0.80	0.65
time (sec)	N/A	0.015	0.004	0.020	0.269	0.416	0.039	3.804	2.093


Problem 379	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	26	25	25	27	27	21
N.S.	1	1.00	1.00	0.79	0.76	0.76	0.82	0.82	0.64
time (sec)	N/A	0.014	0.004	0.017	0.280	0.412	0.038	4.817	0.033


Problem 380	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	26	26	26	21	20	20	20	22	16
N.S.	1	1.00	1.00	0.81	0.77	0.77	0.77	0.85	0.62
time (sec)	N/A	0.010	0.004	0.017	0.273	0.404	0.038	3.598	2.117


Problem 381	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	21	21	21	18	17	17	17	19	13
N.S.	1	1.00	1.00	0.86	0.81	0.81	0.81	0.90	0.62
time (sec)	N/A	0.005	0.003	0.014	0.282	0.386	0.033	3.302	2.110


Problem 382	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	21	21	21	18	17	17	15	19	8
N.S.	1	1.00	1.00	0.86	0.81	0.81	0.71	0.90	0.38
time (sec)	N/A	0.007	0.003	0.014	0.266	0.389	0.032	3.382	0.078


Problem 383	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	27	27	27	22	21	21	24	24	17
N.S.	1	1.00	1.00	0.81	0.78	0.78	0.89	0.89	0.63
time (sec)	N/A	0.011	0.004	0.016	0.270	0.374	0.050	4.668	0.095


Problem 384	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	34	34	34	27	26	30	31	29	22
N.S.	1	1.00	1.00	0.79	0.76	0.88	0.91	0.85	0.65
time (sec)	N/A	0.020	0.004	0.020	0.284	0.415	0.059	3.920	0.035


Problem 385	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	41	32	31	39	36	34	26
N.S.	1	1.00	1.00	0.78	0.76	0.95	0.88	0.83	0.63
time (sec)	N/A	0.022	0.004	0.019	0.274	0.374	0.063	4.919	0.036


Problem 386	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	37	36	44	41	39	32
N.S.	1	1.00	1.00	0.77	0.75	0.92	0.85	0.81	0.67
time (sec)	N/A	0.028	0.004	0.020	0.277	0.388	0.069	4.689	0.037


Problem 387	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	C	C	F	B	A	F	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	157	157	61	54	0	1506	41	0	144
N.S.	1	1.00	0.39	0.34	0.00	9.59	0.26	0.00	0.92
time (sec)	N/A	0.117	0.012	0.030	0.000	1.148	0.098	0.000	2.745


Problem 388	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	C	C	F	B	A	F	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	157	157	61	56	0	1546	41	0	142
N.S.	1	1.00	0.39	0.36	0.00	9.85	0.26	0.00	0.90
time (sec)	N/A	0.082	0.012	0.027	0.000	1.204	0.100	0.000	2.805


Problem 389	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	C	C	F	B	A	F	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	188	188	61	54	0	2271	39	0	142
N.S.	1	1.00	0.32	0.29	0.00	12.08	0.21	0.00	0.76
time (sec)	N/A	0.198	0.010	0.023	0.000	1.208	0.083	0.000	2.780


Problem 390	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	C	C	F	B	A	F	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	188	188	61	56	0	2259	39	0	142
N.S.	1	1.00	0.32	0.30	0.00	12.02	0.21	0.00	0.76
time (sec)	N/A	0.124	0.010	0.021	0.000	1.247	0.084	0.000	2.740


Problem 391	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	C	C	F	C	A	F	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	663	663	63	69	0	322185	133	0	328
N.S.	1	1.00	0.10	0.10	0.00	485.95	0.20	0.00	0.49
time (sec)	N/A	0.934	0.027	0.101	0.000	1.898	2.158	0.000	2.699


Problem 392	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	C	C	F	C	A	F	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	663	663	63	69	0	322185	133	0	328
N.S.	1	1.00	0.10	0.10	0.00	485.95	0.20	0.00	0.49
time (sec)	N/A	0.707	0.023	0.029	0.000	1.914	2.151	0.000	0.002


Problem 393	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	F	C	C	F	C	A	F	B
veriﬁed	N/A	N/A	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	168	0	95	67	0	5653	42	0	504
N.S.	1	0.00	0.57	0.40	0.00	33.65	0.25	0.00	3.00
time (sec)	N/A	0.278	0.044	0.300	0.000	1.118	1.081	0.000	3.082


Problem 394	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	C	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	320	320	322	250	306	141845	384	311	894
N.S.	1	1.00	1.01	0.78	0.96	443.27	1.20	0.97	2.79
time (sec)	N/A	0.174	0.178	0.207	0.499	20.594	27.765	3.100	2.843


Problem 395	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	C	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	291	291	243	230	273	86139	277	285	556
N.S.	1	1.00	0.84	0.79	0.94	296.01	0.95	0.98	1.91
time (sec)	N/A	0.145	0.070	0.203	0.506	3.035	1.705	3.574	2.657


Problem 396	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	C	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	219	219	184	124	209	41851	124	215	160
N.S.	1	1.00	0.84	0.57	0.95	191.10	0.57	0.98	0.73
time (sec)	N/A	0.120	0.040	0.192	0.515	1.397	0.435	3.689	2.323


Problem 397	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	185	185	134	102	169	121	20	179	33
N.S.	1	1.00	0.72	0.55	0.91	0.65	0.11	0.97	0.18
time (sec)	N/A	0.071	0.013	0.184	0.522	0.383	0.059	3.634	0.083


Problem 398	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	C	F(-1)	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	416	416	404	289	341	352864	0	371	874
N.S.	1	1.00	0.97	0.69	0.82	848.23	0.00	0.89	2.10
time (sec)	N/A	0.309	0.107	0.231	0.505	138.075	0.000	3.908	0.418


Problem 399	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	F(-1)	F(-1)	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	552	552	524	354	540	0	0	646	2436
N.S.	1	1.00	0.95	0.64	0.98	0.00	0.00	1.17	4.41
time (sec)	N/A	0.572	0.453	0.242	0.492	0.000	0.000	5.097	2.779


Problem 400	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	F(-1)	F(-1)	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	680	680	738	446	779	0	0	901	1955
N.S.	1	1.00	1.09	0.66	1.15	0.00	0.00	1.32	2.88
time (sec)	N/A	0.675	0.638	0.272	0.504	0.000	0.000	4.030	3.674

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