Integrals 401 to 500

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2.2.5 Integrals 401 to 500

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 401	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	C	A	F	C	F	F	F
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	173	173	60	141	0	87	0	0	-1
N.S.	1	1.00	0.35	0.82	0.00	0.50	0.00	0.00	-0.01
time (sec)	N/A	0.150	10.023	0.129	0.000	0.088	0.000	0.000	0.000


Problem 402	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	C	A	F	C	F	F	F
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	350	350	60	237	0	108	0	0	-1
N.S.	1	1.00	0.17	0.68	0.00	0.31	0.00	0.00	-0.00
time (sec)	N/A	0.277	10.031	0.132	0.000	0.088	0.000	0.000	0.000


Problem 403	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	B	A	B	B	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	73	73	59	181	76	161	731	264	171
N.S.	1	1.00	0.81	2.48	1.04	2.21	10.01	3.62	2.34
time (sec)	N/A	0.035	0.058	0.105	0.284	0.354	0.737	5.690	4.290


Problem 404	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	52	52	43	96	55	89	337	141	97
N.S.	1	1.00	0.83	1.85	1.06	1.71	6.48	2.71	1.87
time (sec)	N/A	0.026	0.050	0.103	0.290	0.370	0.427	5.015	4.195


Problem 405	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	34	34	27	36	34	39	112	56	38
N.S.	1	1.00	0.79	1.06	1.00	1.15	3.29	1.65	1.12
time (sec)	N/A	0.010	0.026	0.013	0.280	0.363	0.192	7.171	4.148


Problem 406	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	F	F	F	F	F	F
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	45	45	42	0	0	0	0	0	-1
N.S.	1	1.00	0.93	0.00	0.00	0.00	0.00	0.00	-0.02
time (sec)	N/A	0.023	0.027	0.023	0.000	0.000	0.000	0.000	0.000


Problem 407	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	F	F	F	F	F	F
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	45	45	44	0	0	0	0	0	-1
N.S.	1	1.00	0.98	0.00	0.00	0.00	0.00	0.00	-0.02
time (sec)	N/A	0.022	0.030	0.015	0.000	0.000	0.000	0.000	0.000


Problem 408	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	F	F	F	F	F	F
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	45	45	44	0	0	0	0	0	-1
N.S.	1	1.00	0.98	0.00	0.00	0.00	0.00	0.00	-0.02
time (sec)	N/A	0.022	0.032	0.015	0.000	0.000	0.000	0.000	0.000


Problem 409	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	30	25	24	24	24	24	24
N.S.	1	1.00	1.00	0.83	0.80	0.80	0.80	0.80	0.80
time (sec)	N/A	0.007	0.001	0.063	0.288	0.306	0.007	5.224	0.038


Problem 410	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	30	25	24	24	26	24	24
N.S.	1	1.00	1.00	0.83	0.80	0.80	0.87	0.80	0.80
time (sec)	N/A	0.006	0.001	0.011	0.305	0.338	0.006	3.585	0.033


Problem 411	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	16	25	24	24	24	24	24
N.S.	1	1.00	0.53	0.83	0.80	0.80	0.80	0.80	0.80
time (sec)	N/A	0.007	0.002	0.008	0.281	0.336	0.007	4.905	0.031


Problem 412	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	22	21	21	22	21	21
N.S.	1	1.00	1.00	0.88	0.84	0.84	0.88	0.84	0.84
time (sec)	N/A	0.003	0.000	0.010	0.276	0.313	0.006	15.230	0.028


Problem 413	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	22	24	21	20	24	21
N.S.	1	1.00	1.00	0.96	1.04	0.91	0.87	1.04	0.91
time (sec)	N/A	0.005	0.001	0.025	0.284	0.368	0.023	12.316	4.097


Problem 414	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	25	19	22	22
N.S.	1	1.00	1.00	0.96	0.92	1.04	0.79	0.92	0.92
time (sec)	N/A	0.006	0.001	0.011	0.299	0.329	0.022	14.257	0.034


Problem 415	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	24	24	27	24	32	23
N.S.	1	1.00	1.00	0.89	0.89	1.00	0.89	1.19	0.85
time (sec)	N/A	0.007	0.001	0.014	0.289	0.333	0.039	7.866	0.032


Problem 416	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	22	22	26	22	22	24
N.S.	1	1.00	1.00	0.96	0.96	1.13	0.96	0.96	1.04
time (sec)	N/A	0.006	0.001	0.013	0.287	0.340	0.045	4.971	4.106


Problem 417	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	26	28	24	34	24
N.S.	1	1.00	1.00	0.96	1.08	1.17	1.00	1.42	1.00
time (sec)	N/A	0.006	0.001	0.013	0.282	0.338	0.063	3.490	0.044


Problem 418	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	25	26	26	27	26	25
N.S.	1	1.00	1.00	0.89	0.93	0.93	0.96	0.93	0.89
time (sec)	N/A	0.006	0.001	0.011	0.286	0.333	0.064	4.300	0.036


Problem 419	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	30	25	24	24	26	24	26
N.S.	1	1.00	1.00	0.83	0.80	0.80	0.87	0.80	0.87
time (sec)	N/A	0.007	0.001	0.013	0.302	0.345	0.067	3.655	0.035


Problem 420	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	30	25	26	26	27	26	26
N.S.	1	1.00	1.00	0.83	0.87	0.87	0.90	0.87	0.87
time (sec)	N/A	0.006	0.001	0.015	0.306	0.326	0.075	3.947	0.034


Problem 421	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	56	56	56	47	46	46	53	46	46
N.S.	1	1.00	1.00	0.84	0.82	0.82	0.95	0.82	0.82
time (sec)	N/A	0.020	0.002	0.053	0.296	0.320	0.010	2.978	0.025


Problem 422	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	56	47	46	46	49	46	46
N.S.	1	1.00	1.06	0.89	0.87	0.87	0.92	0.87	0.87
time (sec)	N/A	0.044	0.002	0.052	0.280	0.324	0.013	3.638	0.022


Problem 423	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	56	56	56	47	46	46	53	46	46
N.S.	1	1.00	1.00	0.84	0.82	0.82	0.95	0.82	0.82
time (sec)	N/A	0.017	0.002	0.048	0.301	0.341	0.010	3.392	0.023


Problem 424	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	56	47	46	46	53	46	46
N.S.	1	1.00	1.65	1.38	1.35	1.35	1.56	1.35	1.35
time (sec)	N/A	0.027	0.002	0.049	0.289	0.352	0.012	4.201	0.022


Problem 425	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	56	56	56	47	46	46	53	46	46
N.S.	1	1.00	1.00	0.84	0.82	0.82	0.95	0.82	0.82
time (sec)	N/A	0.017	0.002	0.046	0.281	0.337	0.010	4.282	0.022


Problem 426	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	B	B	B	B	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	16	16	16	45	44	44	44	44	44
N.S.	1	1.00	1.00	2.81	2.75	2.75	2.75	2.75	2.75
time (sec)	N/A	0.003	0.002	0.045	0.281	0.335	0.012	4.203	0.022


Problem 427	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	51	44	55	43	49	43	43
N.S.	1	1.00	1.00	0.86	1.08	0.84	0.96	0.84	0.84
time (sec)	N/A	0.015	0.001	0.010	0.276	0.331	0.010	5.405	0.021


Problem 428	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	45	47	44	49	47	44
N.S.	1	1.00	1.00	0.90	0.94	0.88	0.98	0.94	0.88
time (sec)	N/A	0.024	0.003	0.045	0.285	0.372	0.034	6.359	0.027


Problem 429	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	45	44	48	44	44	44
N.S.	1	1.00	1.00	0.94	0.92	1.00	0.92	0.92	0.92
time (sec)	N/A	0.017	0.006	0.039	0.292	0.352	0.031	7.395	0.025


Problem 430	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	45	46	49	46	56	44
N.S.	1	1.00	1.00	0.94	0.96	1.02	0.96	1.17	0.92
time (sec)	N/A	0.026	0.004	0.020	0.304	0.349	0.050	3.819	0.027


Problem 431	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	45	45	48	49	45	47
N.S.	1	1.00	1.00	0.90	0.90	0.96	0.98	0.90	0.94
time (sec)	N/A	0.017	0.005	0.017	0.287	0.369	0.055	5.958	0.045


Problem 432	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	46	48	49	49	59	48
N.S.	1	1.00	1.00	0.94	0.98	1.00	1.00	1.20	0.98
time (sec)	N/A	0.024	0.004	0.031	0.300	0.392	0.078	3.190	0.038


Problem 433	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	45	47	48	49	47	47
N.S.	1	1.00	1.00	0.90	0.94	0.96	0.98	0.94	0.94
time (sec)	N/A	0.017	0.008	0.018	0.310	0.336	0.082	3.333	0.045


Problem 434	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	46	48	50	49	57	47
N.S.	1	1.00	1.00	0.94	0.98	1.02	1.00	1.16	0.96
time (sec)	N/A	0.023	0.004	0.017	0.296	0.334	0.107	3.444	0.038


Problem 435	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	47	47	47	44	46	48	48	46	46
N.S.	1	1.00	1.00	0.94	0.98	1.02	1.02	0.98	0.98
time (sec)	N/A	0.017	0.005	0.015	0.321	0.324	0.116	3.739	4.190


Problem 436	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	45	50	50	49	58	47
N.S.	1	1.00	1.00	0.90	1.00	1.00	0.98	1.16	0.94
time (sec)	N/A	0.022	0.004	0.017	0.322	0.367	0.146	3.890	0.051


Problem 437	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	54	47	48	48	51	48	47
N.S.	1	1.00	1.00	0.87	0.89	0.89	0.94	0.89	0.87
time (sec)	N/A	0.018	0.006	0.014	0.280	0.333	0.143	3.385	0.034


Problem 438	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	19	19	52	47	46	46	49	46	46
N.S.	1	1.00	2.74	2.47	2.42	2.42	2.58	2.42	2.42
time (sec)	N/A	0.004	0.003	0.014	0.381	0.367	0.157	3.622	0.034


Problem 439	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	56	56	56	47	48	48	51	48	48
N.S.	1	1.00	1.00	0.84	0.86	0.86	0.91	0.86	0.86
time (sec)	N/A	0.017	0.005	0.015	0.306	0.343	0.161	4.028	4.840


Problem 440	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	56	47	48	48	51	48	48
N.S.	1	1.00	1.40	1.18	1.20	1.20	1.28	1.20	1.20
time (sec)	N/A	0.017	0.003	0.016	0.337	0.311	0.173	4.025	4.218


Problem 441	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	56	56	56	47	48	48	51	48	48
N.S.	1	1.00	1.00	0.84	0.86	0.86	0.91	0.86	0.86
time (sec)	N/A	0.017	0.006	0.017	0.300	0.319	0.173	4.022	0.037


Problem 442	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	56	56	56	47	48	48	51	48	48
N.S.	1	1.00	1.00	0.84	0.86	0.86	0.91	0.86	0.86
time (sec)	N/A	0.023	0.003	0.017	0.300	0.320	0.189	4.183	4.329


Problem 443	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	56	56	56	47	48	48	51	48	48
N.S.	1	1.00	1.00	0.84	0.86	0.86	0.91	0.86	0.86
time (sec)	N/A	0.017	0.005	0.018	0.426	0.326	0.190	3.902	4.351


Problem 444	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	69	68	68	80	68	68
N.S.	1	1.00	1.00	0.84	0.83	0.83	0.98	0.83	0.83
time (sec)	N/A	0.030	0.003	0.053	0.541	0.358	0.013	3.319	0.033


Problem 445	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	72	72	82	69	68	68	78	68	68
N.S.	1	1.00	1.14	0.96	0.94	0.94	1.08	0.94	0.94
time (sec)	N/A	0.078	0.002	0.053	0.313	0.323	0.016	3.353	0.031


Problem 446	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	79	68	67	67	76	67	67
N.S.	1	1.00	1.00	0.86	0.85	0.85	0.96	0.85	0.85
time (sec)	N/A	0.025	0.002	0.053	0.348	0.341	0.013	4.275	0.031


Problem 447	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	82	69	68	68	80	68	68
N.S.	1	1.00	1.55	1.30	1.28	1.28	1.51	1.28	1.28
time (sec)	N/A	0.052	0.002	0.052	0.314	0.346	0.016	4.581	0.033


Problem 448	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	69	68	68	80	68	68
N.S.	1	1.00	1.00	0.84	0.83	0.83	0.98	0.83	0.83
time (sec)	N/A	0.025	0.002	0.052	0.298	0.333	0.012	4.126	0.033


Problem 449	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	34	34	77	68	67	67	75	67	67
N.S.	1	1.00	2.26	2.00	1.97	1.97	2.21	1.97	1.97
time (sec)	N/A	0.029	0.002	0.054	0.289	0.338	0.016	3.952	0.032


Problem 450	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	69	68	68	80	68	68
N.S.	1	1.00	1.00	0.84	0.83	0.83	0.98	0.83	0.83
time (sec)	N/A	0.026	0.002	0.053	0.292	0.359	0.012	5.430	0.032


Problem 451	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	B	B	B	B	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	16	16	16	69	68	68	78	68	68
N.S.	1	1.00	1.00	4.31	4.25	4.25	4.88	4.25	4.25
time (sec)	N/A	0.003	0.002	0.050	0.299	0.331	0.016	4.928	0.031


Problem 452	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	73	73	73	66	100	65	73	65	65
N.S.	1	1.00	1.00	0.90	1.37	0.89	1.00	0.89	0.89
time (sec)	N/A	0.023	0.001	0.010	0.353	0.358	0.012	6.163	0.030


Problem 453	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	76	76	76	67	69	66	76	69	66
N.S.	1	1.00	1.00	0.88	0.91	0.87	1.00	0.91	0.87
time (sec)	N/A	0.034	0.004	0.060	0.356	0.333	0.042	4.006	0.036


Problem 454	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	72	72	72	67	66	70	70	66	66
N.S.	1	1.00	1.00	0.93	0.92	0.97	0.97	0.92	0.92
time (sec)	N/A	0.027	0.006	0.093	0.292	0.314	0.040	7.552	0.034


Problem 455	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	77	77	77	68	69	72	76	79	67
N.S.	1	1.00	1.00	0.88	0.90	0.94	0.99	1.03	0.87
time (sec)	N/A	0.038	0.006	0.022	0.303	0.342	0.058	11.147	0.039


Problem 456	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	74	74	74	67	67	70	75	67	69
N.S.	1	1.00	1.00	0.91	0.91	0.95	1.01	0.91	0.93
time (sec)	N/A	0.025	0.009	0.020	0.357	0.326	0.064	4.087	0.032


Problem 457	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	72	72	72	67	69	71	73	80	69
N.S.	1	1.00	1.00	0.93	0.96	0.99	1.01	1.11	0.96
time (sec)	N/A	0.036	0.004	0.039	0.290	0.346	0.087	3.289	0.036


Problem 458	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	72	72	72	67	67	70	73	67	69
N.S.	1	1.00	1.00	0.93	0.93	0.97	1.01	0.93	0.96
time (sec)	N/A	0.026	0.005	0.027	0.295	0.331	0.090	3.566	0.033


Problem 459	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	79	68	70	71	76	81	70
N.S.	1	1.00	1.00	0.86	0.89	0.90	0.96	1.03	0.89
time (sec)	N/A	0.036	0.004	0.023	0.326	0.331	0.122	4.319	4.344


Problem 460	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	72	72	72	67	69	70	73	69	69
N.S.	1	1.00	1.00	0.93	0.96	0.97	1.01	0.96	0.96
time (sec)	N/A	0.025	0.007	0.018	0.291	0.362	0.128	3.460	0.055


Problem 461	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	73	73	73	68	70	72	73	81	69
N.S.	1	1.00	1.00	0.93	0.96	0.99	1.00	1.11	0.95
time (sec)	N/A	0.035	0.006	0.031	0.301	0.406	0.163	3.563	0.047


Problem 462	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	74	74	74	67	69	70	73	69	70
N.S.	1	1.00	1.00	0.91	0.93	0.95	0.99	0.93	0.95
time (sec)	N/A	0.026	0.007	0.019	0.301	0.336	0.164	4.199	0.053


Problem 463	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	77	77	77	68	72	72	75	81	70
N.S.	1	1.00	1.00	0.88	0.94	0.94	0.97	1.05	0.91
time (sec)	N/A	0.033	0.004	0.025	0.298	0.333	0.208	3.896	4.403


Problem 464	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	71	66	68	70	71	68	68
N.S.	1	1.00	1.00	0.93	0.96	0.99	1.00	0.96	0.96
time (sec)	N/A	0.025	0.004	0.016	0.280	0.347	0.206	4.035	4.300


Problem 465	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	76	76	76	67	72	72	73	80	69
N.S.	1	1.00	1.00	0.88	0.95	0.95	0.96	1.05	0.91
time (sec)	N/A	0.032	0.004	0.018	0.325	0.346	0.256	5.019	0.065


Problem 466	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	76	76	76	69	70	70	75	70	69
N.S.	1	1.00	1.00	0.91	0.92	0.92	0.99	0.92	0.91
time (sec)	N/A	0.026	0.007	0.020	0.376	0.320	0.241	4.093	0.053


Problem 467	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	19	19	82	69	68	68	73	68	70
N.S.	1	1.00	4.32	3.63	3.58	3.58	3.84	3.58	3.68
time (sec)	N/A	0.004	0.006	0.019	0.367	0.361	0.268	4.037	4.357


Problem 468	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	69	70	70	75	70	70
N.S.	1	1.00	1.00	0.84	0.85	0.85	0.91	0.85	0.85
time (sec)	N/A	0.026	0.007	0.039	0.277	0.351	0.258	3.733	0.051


Problem 469	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	40	40	78	69	70	70	75	70	69
N.S.	1	1.00	1.95	1.72	1.75	1.75	1.88	1.75	1.72
time (sec)	N/A	0.017	0.004	0.019	0.294	0.344	0.297	4.023	4.366


Problem 470	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	69	70	70	75	70	70
N.S.	1	1.00	1.00	0.84	0.85	0.85	0.91	0.85	0.85
time (sec)	N/A	0.026	0.005	0.021	0.294	0.348	0.284	4.494	0.047


Problem 471	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	82	69	70	70	75	70	70
N.S.	1	1.00	1.32	1.11	1.13	1.13	1.21	1.13	1.13
time (sec)	N/A	0.027	0.004	0.021	0.295	0.318	0.309	4.671	4.313


Problem 472	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	69	70	70	75	70	69
N.S.	1	1.00	1.00	0.86	0.88	0.88	0.94	0.88	0.86
time (sec)	N/A	0.026	0.007	0.020	0.281	0.317	0.300	4.250	0.053


Problem 473	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	82	69	70	70	75	70	70
N.S.	1	1.00	0.98	0.82	0.83	0.83	0.89	0.83	0.83
time (sec)	N/A	0.037	0.006	0.030	0.294	0.346	0.327	3.870	0.053


Problem 474	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	69	70	70	75	70	70
N.S.	1	1.00	1.00	0.84	0.85	0.85	0.91	0.85	0.85
time (sec)	N/A	0.025	0.007	0.022	0.276	0.342	0.314	3.876	0.053


Problem 475	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	83	83	72	75	77	93	80	92	79
N.S.	1	1.00	0.87	0.90	0.93	1.12	0.96	1.11	0.95
time (sec)	N/A	0.054	0.016	0.027	0.282	0.336	0.126	5.359	4.361


Problem 476	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	70	70	60	64	65	81	66	80	68
N.S.	1	1.00	0.86	0.91	0.93	1.16	0.94	1.14	0.97
time (sec)	N/A	0.044	0.016	0.025	0.271	0.344	0.116	4.423	0.044


Problem 477	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	57	57	49	53	54	70	53	67	57
N.S.	1	1.00	0.86	0.93	0.95	1.23	0.93	1.18	1.00
time (sec)	N/A	0.035	0.012	0.033	0.277	0.357	0.108	5.229	0.055


Problem 478	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	44	44	38	41	43	56	39	49	45
N.S.	1	1.00	0.86	0.93	0.98	1.27	0.89	1.11	1.02
time (sec)	N/A	0.027	0.013	0.020	0.283	0.348	0.094	6.365	0.052


Problem 479	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	27	30	32	35	29	30	29
N.S.	1	1.00	0.82	0.91	0.97	1.06	0.88	0.91	0.88
time (sec)	N/A	0.020	0.007	0.037	0.290	0.335	0.073	2.601	0.051


Problem 480	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	16	15	15	15	15	14	14
N.S.	1	1.00	1.00	0.94	0.94	0.94	0.94	0.88	0.88
time (sec)	N/A	0.004	0.002	0.013	0.275	0.340	0.055	2.987	4.325


Problem 481	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	33	42	37	47	34	47	34
N.S.	1	1.00	0.87	1.11	0.97	1.24	0.89	1.24	0.89
time (sec)	N/A	0.027	0.011	0.027	0.274	0.352	0.130	3.558	4.388


Problem 482	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	41	55	52	73	51	51	51
N.S.	1	1.00	0.84	1.12	1.06	1.49	1.04	1.04	1.04
time (sec)	N/A	0.031	0.027	0.030	0.285	0.325	0.165	3.391	0.077


Problem 483	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	66	66	57	65	70	90	68	86	67
N.S.	1	1.00	0.86	0.98	1.06	1.36	1.03	1.30	1.02
time (sec)	N/A	0.036	0.039	0.031	0.291	0.331	0.199	4.051	0.072


Problem 484	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	82	76	82	212	134	84	77
N.S.	1	1.00	0.89	0.83	0.89	2.30	1.46	0.91	0.84
time (sec)	N/A	0.035	0.038	0.036	0.493	0.367	0.144	4.678	0.044


Problem 485	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	71	65	71	190	124	73	66
N.S.	1	1.00	0.90	0.82	0.90	2.41	1.57	0.92	0.84
time (sec)	N/A	0.030	0.033	0.055	0.491	0.332	0.133	4.652	4.274


Problem 486	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	66	66	60	54	59	164	107	61	56
N.S.	1	1.00	0.91	0.82	0.89	2.48	1.62	0.92	0.85
time (sec)	N/A	0.025	0.031	0.030	0.502	0.365	0.124	4.475	0.064


Problem 487	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	51	42	45	136	83	42	43
N.S.	1	1.00	0.93	0.76	0.82	2.47	1.51	0.76	0.78
time (sec)	N/A	0.016	0.023	0.027	0.521	0.367	0.110	4.457	4.286


Problem 488	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	45	45	45	36	36	120	78	35	33
N.S.	1	1.00	1.00	0.80	0.80	2.67	1.73	0.78	0.73
time (sec)	N/A	0.011	0.015	0.029	0.512	0.342	0.084	7.087	0.046


Problem 489	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	45	45	45	36	35	120	78	35	33
N.S.	1	1.00	1.00	0.80	0.78	2.67	1.73	0.78	0.73
time (sec)	N/A	0.012	0.017	0.024	0.505	0.355	0.088	4.115	0.043


Problem 490	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	57	57	54	45	49	136	92	47	44
N.S.	1	1.00	0.95	0.79	0.86	2.39	1.61	0.82	0.77
time (sec)	N/A	0.018	0.027	0.033	0.542	0.350	0.128	3.950	4.489


Problem 491	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	68	68	67	55	64	172	114	59	58
N.S.	1	1.00	0.99	0.81	0.94	2.53	1.68	0.87	0.85
time (sec)	N/A	0.024	0.026	0.037	0.518	0.377	0.158	3.972	4.431


Problem 492	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	80	67	75	198	126	70	70
N.S.	1	1.00	0.99	0.83	0.93	2.44	1.56	0.86	0.86
time (sec)	N/A	0.031	0.033	0.040	0.508	0.361	0.183	3.422	4.713


Problem 493	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	91	91	78	90	99	137	100	91	98
N.S.	1	1.00	0.86	0.99	1.09	1.51	1.10	1.00	1.08
time (sec)	N/A	0.063	0.022	0.056	0.285	0.321	0.275	4.543	4.483


Problem 494	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	77	77	59	79	88	124	90	73	88
N.S.	1	1.00	0.77	1.03	1.14	1.61	1.17	0.95	1.14
time (sec)	N/A	0.050	0.035	0.034	0.286	0.328	0.253	3.589	4.506


Problem 495	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	50	64	77	102	76	53	75
N.S.	1	1.00	0.70	0.90	1.08	1.44	1.07	0.75	1.06
time (sec)	N/A	0.043	0.014	0.049	0.286	0.357	0.208	3.935	4.327


Problem 496	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	B	B	B	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	19	19	35	48	58	58	60	33	60
N.S.	1	1.00	1.84	2.53	3.05	3.05	3.16	1.74	3.16
time (sec)	N/A	0.005	0.010	0.027	0.331	0.338	0.175	4.019	4.287


Problem 497	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	24	31	47	47	48	22	48
N.S.	1	1.00	0.71	0.91	1.38	1.38	1.41	0.65	1.41
time (sec)	N/A	0.021	0.006	0.027	0.298	0.348	0.156	3.751	4.229


Problem 498	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	B	B	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	16	16	16	15	37	37	39	14	39
N.S.	1	1.00	1.00	0.94	2.31	2.31	2.44	0.88	2.44
time (sec)	N/A	0.004	0.002	0.023	0.324	0.316	0.142	2.815	4.284


Problem 499	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	70	70	54	76	82	134	80	70	78
N.S.	1	1.00	0.77	1.09	1.17	1.91	1.14	1.00	1.11
time (sec)	N/A	0.047	0.029	0.039	0.297	0.352	0.246	2.789	4.467


Problem 500	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	84	84	70	89	99	163	102	93	97
N.S.	1	1.00	0.83	1.06	1.18	1.94	1.21	1.11	1.15
time (sec)	N/A	0.058	0.047	0.043	0.295	0.346	0.295	3.945	0.152

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