Integrals 1 to 100

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2.2.1 Integrals 1 to 100

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 1	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	12	11	10	12	11	20
N.S.	1	1.00	1.00	1.09	1.00	0.91	1.09	1.00	1.82
time (sec)	N/A	0.002	0.001	0.006	0.284	0.967	0.006	0.660	0.321


Problem 2	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	3	2	2	2	2	2
N.S.	1	1.00	1.00	1.00	0.67	0.67	0.67	0.67	0.67
time (sec)	N/A	0.001	0.000	0.000	1.126	0.485	0.017	0.650	0.006


Problem 3	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	2	2	2	3	2	2	2	3	2
N.S.	1	1.00	1.00	1.50	1.00	1.00	1.00	1.50	1.00
time (sec)	N/A	0.000	0.000	0.002	1.608	0.455	0.022	0.515	0.002


Problem 4	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	9	8	8	8	8	8
N.S.	1	1.00	1.00	1.12	1.00	1.00	1.00	1.00	1.00
time (sec)	N/A	0.002	0.001	0.008	2.869	0.458	0.024	0.558	0.185


Problem 5	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	4	4	3	4	4
N.S.	1	1.00	1.00	1.25	1.00	1.00	0.75	1.00	1.00
time (sec)	N/A	0.002	0.002	0.000	1.197	0.623	0.025	0.777	0.020


Problem 6	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	2	2	2	3	2	2	2	2	2
N.S.	1	1.00	1.00	1.50	1.00	1.00	1.00	1.00	1.00
time (sec)	N/A	0.002	0.002	0.000	1.646	0.726	0.024	0.671	0.003


Problem 7	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	2	2	2	3	2	7	5	2	2
N.S.	1	1.00	1.00	1.50	1.00	3.50	2.50	1.00	1.00
time (sec)	N/A	0.004	0.002	0.014	2.064	0.832	0.028	1.199	0.023


Problem 8	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	4	4	4	5	6	8	7	6	4
N.S.	1	1.00	1.00	1.25	1.50	2.00	1.75	1.50	1.00
time (sec)	N/A	0.003	0.002	0.016	2.942	0.948	0.028	1.240	0.009


Problem 9	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	2	2	2	3	4	4	3	4	12
N.S.	1	1.00	1.00	1.50	2.00	2.00	1.50	2.00	6.00
time (sec)	N/A	0.004	0.002	0.017	0.971	1.049	0.011	1.240	0.265


Problem 10	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	6	6	5	6	6
N.S.	1	1.00	1.00	1.25	1.50	1.50	1.25	1.50	1.50
time (sec)	N/A	0.005	0.002	0.013	1.331	0.900	0.029	0.865	0.261


Problem 11	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	2	2	2	3	2	2	2	11	2
N.S.	1	1.00	1.00	1.50	1.00	1.00	1.00	5.50	1.00
time (sec)	N/A	0.002	0.002	0.011	1.331	0.637	0.056	0.596	0.019


Problem 12	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	2	2	2	3	2	2	2	11	2
N.S.	1	1.00	1.00	1.50	1.00	1.00	1.00	5.50	1.00
time (sec)	N/A	0.002	0.002	0.010	2.660	0.634	0.056	0.532	0.016


Problem 13	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	5	5	5	6	3	11	5	6	5
N.S.	1	1.00	1.00	1.20	0.60	2.20	1.00	1.20	1.00
time (sec)	N/A	0.002	0.002	0.003	0.990	0.927	0.027	0.574	0.027


Problem 14	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	3	3	3	4	3	11	3	4	3
N.S.	1	1.00	1.00	1.33	1.00	3.67	1.00	1.33	1.00
time (sec)	N/A	0.002	0.002	0.003	1.119	0.957	0.027	0.572	0.002


Problem 15	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	9	8	8	7	8	8
N.S.	1	1.00	1.00	1.12	1.00	1.00	0.88	1.00	1.00
time (sec)	N/A	0.006	0.003	0.015	1.244	0.820	0.053	0.681	0.021


Problem 16	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	9	8	8	5	8	6
N.S.	1	1.00	1.00	1.12	1.00	1.00	0.62	1.00	0.75
time (sec)	N/A	0.001	0.001	0.000	2.261	0.593	0.021	0.757	0.018


Problem 17	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	12	17	11	11	10	11	11
N.S.	1	1.00	0.63	0.89	0.58	0.58	0.53	0.58	0.58
time (sec)	N/A	0.010	0.005	0.000	1.689	0.588	0.022	0.767	0.023


Problem 18	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	14	14	11	13	15	11	11
N.S.	1	1.00	0.74	0.74	0.58	0.68	0.79	0.58	0.58
time (sec)	N/A	0.005	0.005	0.013	1.460	0.771	0.083	0.861	0.002


Problem 19	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	0.003	0.002	0.031	1.597	0.619	0.059	0.739	0.157


Problem 20	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	20	20	15	15	11	11	10	11	11
N.S.	1	1.00	0.75	0.75	0.55	0.55	0.50	0.55	0.55
time (sec)	N/A	0.005	0.009	0.012	4.203	0.719	0.021	0.786	0.019


Problem 21	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	7	7	7	8	7	7	7	7	7
N.S.	1	1.00	1.00	1.14	1.00	1.00	1.00	1.00	1.00
time (sec)	N/A	0.006	0.002	0.000	2.160	0.930	0.052	0.602	0.002


Problem 22	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	15	14	14	14	14	14
N.S.	1	1.00	1.00	0.83	0.78	0.78	0.78	0.78	0.78
time (sec)	N/A	0.007	0.011	0.023	1.558	0.726	0.056	0.596	0.028


Problem 23	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	13	12	13	9
N.S.	1	1.00	1.00	0.82	0.76	0.76	0.71	0.76	0.53
time (sec)	N/A	0.003	0.001	0.000	2.237	0.797	0.024	0.597	0.002


Problem 24	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	25	24	21	21	27	21	23
N.S.	1	1.00	0.86	0.83	0.72	0.72	0.93	0.72	0.79
time (sec)	N/A	0.018	0.020	0.030	2.541	0.727	0.083	0.642	0.065


Problem 25	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	25	24	21	21	24	21	24
N.S.	1	1.00	0.86	0.83	0.72	0.72	0.83	0.72	0.83
time (sec)	N/A	0.016	0.020	0.023	2.442	0.754	0.083	0.566	0.030


Problem 26	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	12	15	15	15	12
N.S.	1	1.00	1.00	1.07	0.80	1.00	1.00	1.00	0.80
time (sec)	N/A	0.003	0.002	0.000	2.332	0.554	0.029	0.637	0.032


Problem 27	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	14	14	12	14	14
N.S.	1	1.00	1.00	0.94	0.88	0.88	0.75	0.88	0.88
time (sec)	N/A	0.003	0.002	0.002	3.102	1.114	0.042	0.589	0.002


Problem 28	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	18	18	14	17	24	14	18
N.S.	1	1.00	0.78	0.78	0.61	0.74	1.04	0.61	0.78
time (sec)	N/A	0.009	0.003	0.017	1.308	0.763	0.085	0.762	0.046


Problem 29	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	B	B	F	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	8	8	8	9	74	18	0	103	8
N.S.	1	1.00	1.00	1.12	9.25	2.25	0.00	12.88	1.00
time (sec)	N/A	0.013	0.005	0.023	2.249	0.795	0.000	1.026	0.022


Problem 30	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	13	12	13	9
N.S.	1	1.00	1.00	0.82	0.76	0.76	0.71	0.76	0.53
time (sec)	N/A	0.006	0.002	0.006	1.008	0.759	0.024	1.219	0.028


Problem 31	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	17	24	16	16	15	16	16
N.S.	1	1.00	0.63	0.89	0.59	0.59	0.56	0.59	0.59
time (sec)	N/A	0.020	0.012	0.011	3.052	0.651	0.023	0.951	0.018


Problem 32	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	22	22	19	21	26	19	19
N.S.	1	1.00	0.81	0.81	0.70	0.78	0.96	0.70	0.70
time (sec)	N/A	0.007	0.031	0.024	1.505	0.777	0.089	0.852	0.027


Problem 33	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	20	22	17	21	20	17	17
N.S.	1	1.00	0.74	0.81	0.63	0.78	0.74	0.63	0.63
time (sec)	N/A	0.007	0.027	0.026	1.563	0.872	0.165	0.838	0.026


Problem 34	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	B	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	9	9	9	10	34	9	7	17	9
N.S.	1	1.00	1.00	1.11	3.78	1.00	0.78	1.89	1.00
time (sec)	N/A	0.008	0.004	0.015	1.563	0.713	0.058	0.891	0.019


Problem 35	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	B	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	19	19	19	19	57	18	20	30	18
N.S.	1	1.00	1.00	1.00	3.00	0.95	1.05	1.58	0.95
time (sec)	N/A	0.011	0.012	0.026	0.781	0.664	0.068	0.870	0.060


Problem 36	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	11	15	9	9	7	9	9
N.S.	1	1.00	0.69	0.94	0.56	0.56	0.44	0.56	0.56
time (sec)	N/A	0.006	0.005	0.000	2.211	0.947	0.021	1.029	0.021


Problem 37	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	21	21	15	14	13	14	105	13	9
N.S.	1	1.00	0.71	0.67	0.62	0.67	5.00	0.62	0.43
time (sec)	N/A	0.005	0.003	0.042	2.067	0.928	0.888	0.908	0.031


Problem 38	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	15	14	14	14	14	14
N.S.	1	1.00	1.00	0.83	0.78	0.78	0.78	0.78	0.78
time (sec)	N/A	0.007	0.011	0.034	1.780	0.749	0.056	0.991	0.020


Problem 39	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	16	24	14	14	12	14	14
N.S.	1	1.00	0.62	0.92	0.54	0.54	0.46	0.54	0.54
time (sec)	N/A	0.012	0.013	0.008	1.634	0.890	0.022	0.996	0.029


Problem 40	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	16	12	16	16
N.S.	1	1.00	1.00	0.94	0.89	0.89	0.67	0.89	0.89
time (sec)	N/A	0.003	0.002	0.003	1.429	1.103	0.043	1.305	0.169


Problem 41	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	B	B	F	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	9	9	9	10	104	20	0	52	9
N.S.	1	1.00	1.00	1.11	11.56	2.22	0.00	5.78	1.00
time (sec)	N/A	0.010	0.013	0.020	1.894	0.618	0.000	0.823	0.147


Problem 42	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	17	17	17	14	13	25	26	13	13
N.S.	1	1.00	1.00	0.82	0.76	1.47	1.53	0.76	0.76
time (sec)	N/A	0.006	0.008	0.094	2.036	0.957	0.123	0.824	0.040


Problem 43	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	9	13	14	22	8	13
N.S.	1	1.00	1.00	0.53	0.76	0.82	1.29	0.47	0.76
time (sec)	N/A	0.006	0.009	0.032	1.072	0.652	0.125	0.709	0.173


Problem 44	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	12	11	11	10	11	8
N.S.	1	1.00	1.00	1.09	1.00	1.00	0.91	1.00	0.73
time (sec)	N/A	0.007	0.003	0.126	1.445	0.856	0.195	0.730	0.201


Problem 45	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	22	14	17	11	11	10	11	11
N.S.	1	1.00	0.64	0.77	0.50	0.50	0.45	0.50	0.50
time (sec)	N/A	0.012	0.015	0.010	1.441	0.678	0.022	0.940	0.029


Problem 46	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	9	9	12	8	7	8	8
N.S.	1	1.00	0.60	0.60	0.80	0.53	0.47	0.53	0.53
time (sec)	N/A	0.005	0.014	0.010	1.390	0.559	0.023	0.972	0.033


Problem 47	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	14	15	14	14	14	14	14
N.S.	1	1.00	0.74	0.79	0.74	0.74	0.74	0.74	0.74
time (sec)	N/A	0.006	0.008	0.016	4.529	0.849	0.030	0.974	0.023


Problem 48	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	10	13	15	13	13
N.S.	1	1.00	1.00	0.82	0.59	0.76	0.88	0.76	0.76
time (sec)	N/A	0.002	0.004	0.015	3.234	0.717	0.106	0.741	0.167


Problem 49	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	16	17	11	11	20	11	11
N.S.	1	1.00	0.67	0.71	0.46	0.46	0.83	0.46	0.46
time (sec)	N/A	0.006	0.007	0.000	2.346	0.750	0.060	0.651	0.021


Problem 50	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	12	10	9	9	8	9	7
N.S.	1	1.00	0.86	0.71	0.64	0.64	0.57	0.64	0.50
time (sec)	N/A	0.001	0.002	0.004	2.924	0.481	0.022	0.481	0.024


Problem 51	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	12	13	15	13	13
N.S.	1	1.00	1.00	0.82	0.71	0.76	0.88	0.76	0.76
time (sec)	N/A	0.002	0.003	0.007	4.460	0.876	0.106	0.474	0.022


Problem 52	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	22	22	17	16	16	20	16	16
N.S.	1	1.00	1.00	0.77	0.73	0.73	0.91	0.73	0.73
time (sec)	N/A	0.008	0.011	0.010	1.476	0.657	0.086	0.481	0.244


Problem 53	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	20	20	20	17	16	16	15	16	16
N.S.	1	1.00	1.00	0.85	0.80	0.80	0.75	0.80	0.80
time (sec)	N/A	0.011	0.009	0.036	3.371	0.775	0.300	0.514	0.194


Problem 54	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	19	24	16	16	15	16	16
N.S.	1	1.00	0.68	0.86	0.57	0.57	0.54	0.57	0.57
time (sec)	N/A	0.021	0.016	0.012	1.404	0.662	0.024	0.480	0.028


Problem 55	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	16	15	13	15	15	14
N.S.	1	1.00	1.00	0.76	0.71	0.62	0.71	0.71	0.67
time (sec)	N/A	0.005	0.003	0.000	2.023	0.809	0.072	0.678	0.019


Problem 56	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	16	15	18	16
N.S.	1	1.00	1.00	0.94	0.89	0.89	0.83	1.00	0.89
time (sec)	N/A	0.009	0.012	0.036	1.151	0.636	0.057	0.672	0.023


Problem 57	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	21	21	15	14	13	14	105	13	9
N.S.	1	1.00	0.71	0.67	0.62	0.67	5.00	0.62	0.43
time (sec)	N/A	0.004	0.003	0.038	2.148	0.731	0.883	0.756	0.017


Problem 58	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	14	15	10	14	14	10	10
N.S.	1	1.00	0.78	0.83	0.56	0.78	0.78	0.56	0.56
time (sec)	N/A	0.004	0.008	0.023	1.909	0.645	0.011	0.738	0.050


Problem 59	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	11	10	10	10	10	10
N.S.	1	1.00	1.00	0.79	0.71	0.71	0.71	0.71	0.71
time (sec)	N/A	0.004	0.002	0.015	3.347	0.647	0.008	0.662	0.002


Problem 60	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	22	18	16	19	24	16	16
N.S.	1	1.00	0.92	0.75	0.67	0.79	1.00	0.67	0.67
time (sec)	N/A	0.009	0.002	0.000	1.474	0.886	0.008	0.778	0.031


Problem 61	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	15	11	11	11	8	11	10
N.S.	1	1.00	1.15	0.85	0.85	0.85	0.62	0.85	0.77
time (sec)	N/A	0.004	0.002	0.000	2.581	0.877	0.011	0.766	0.034


Problem 62	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	31	18	13	13	12	13	14
N.S.	1	1.00	1.82	1.06	0.76	0.76	0.71	0.76	0.82
time (sec)	N/A	0.015	0.016	0.032	2.135	0.706	0.010	0.899	0.039


Problem 63	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	17	17	31	30	13	22	12	13	14
N.S.	1	1.00	1.82	1.76	0.76	1.29	0.71	0.76	0.82
time (sec)	N/A	0.016	0.015	0.029	1.754	0.501	0.010	1.056	0.151


Problem 64	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	30	29	18	25	31	22	24
N.S.	1	1.00	0.83	0.81	0.50	0.69	0.86	0.61	0.67
time (sec)	N/A	0.032	0.013	0.027	1.117	0.656	0.008	0.975	0.044


Problem 65	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	14	19	10	19	14	10	18
N.S.	1	1.00	0.58	0.79	0.42	0.79	0.58	0.42	0.75
time (sec)	N/A	0.017	0.005	0.016	1.145	0.836	0.012	1.047	0.041


Problem 66	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	22	18	19	14	18	37	14	14
N.S.	1	1.00	0.82	0.86	0.64	0.82	1.68	0.64	0.64
time (sec)	N/A	0.007	0.011	0.042	3.028	0.813	0.060	0.902	0.261


Problem 67	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	20	20	20	15	14	31	37	14	18
N.S.	1	1.00	1.00	0.75	0.70	1.55	1.85	0.70	0.90
time (sec)	N/A	0.012	0.011	0.067	1.497	0.661	0.126	0.635	0.146


Problem 68	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	28	19	19	19	19	19
N.S.	1	1.00	1.00	1.12	0.76	0.76	0.76	0.76	0.76
time (sec)	N/A	0.028	0.015	0.021	0.932	0.792	0.012	0.546	0.050


Problem 69	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	30	24	24	25	36	22	22
N.S.	1	1.00	0.88	0.71	0.71	0.74	1.06	0.65	0.65
time (sec)	N/A	0.011	0.002	0.000	2.989	0.824	0.010	0.733	0.036


Problem 70	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	30	24	24	25	36	22	22
N.S.	1	1.00	0.88	0.71	0.71	0.74	1.06	0.65	0.65
time (sec)	N/A	0.013	0.003	0.066	1.526	0.689	0.008	0.494	0.035


Problem 71	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	30	36	18	33	41	22	37
N.S.	1	1.00	0.65	0.78	0.39	0.72	0.89	0.48	0.80
time (sec)	N/A	0.026	0.017	0.034	1.016	1.104	0.010	0.644	0.071


Problem 72	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	23	17	17	17	17	17	17
N.S.	1	1.00	1.10	0.81	0.81	0.81	0.81	0.81	0.81
time (sec)	N/A	0.005	0.002	0.020	1.581	0.709	0.013	0.701	0.038


Problem 73	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	22	36	16	31	31	16	32
N.S.	1	1.00	0.48	0.78	0.35	0.67	0.67	0.35	0.70
time (sec)	N/A	0.036	0.009	0.031	1.576	0.583	0.014	0.806	0.042


Problem 74	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	B	A	A	F(-1)	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	21	21	34	39	13	17	0	13	13
N.S.	1	1.00	1.62	1.86	0.62	0.81	0.00	0.62	0.62
time (sec)	N/A	0.016	0.058	0.060	2.396	0.598	0.000	0.775	0.086


Problem 75	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	21	21	18	14	13	14	170	13	25
N.S.	1	1.00	0.86	0.67	0.62	0.67	8.10	0.62	1.19
time (sec)	N/A	0.016	0.010	0.046	1.669	0.621	4.675	0.881	0.207


Problem 76	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	19	19	18	14	12	13	39	12	12
N.S.	1	1.00	0.95	0.74	0.63	0.68	2.05	0.63	0.63
time (sec)	N/A	0.014	0.021	0.031	1.166	0.873	0.096	1.145	0.273


Problem 77	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	15	15	15	22	15	14
N.S.	1	1.00	1.00	0.79	0.79	0.79	1.16	0.79	0.74
time (sec)	N/A	0.009	0.014	0.029	3.402	0.700	0.132	1.131	0.177


Problem 78	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	16	14	10	13	16
N.S.	1	1.00	1.00	0.93	1.14	1.00	0.71	0.93	1.14
time (sec)	N/A	0.010	0.005	0.024	2.953	0.701	0.023	1.145	0.199


Problem 79	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	22	22	20	29	20	37	20	28	32
N.S.	1	1.00	0.91	1.32	0.91	1.68	0.91	1.27	1.45
time (sec)	N/A	0.020	0.018	0.033	2.564	0.664	0.031	1.214	0.226


Problem 80	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	B	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	5	5	36	6	5	5	19	5	5
N.S.	1	1.00	7.20	1.20	1.00	1.00	3.80	1.00	1.00
time (sec)	N/A	0.010	0.008	0.036	3.090	0.965	0.119	1.127	0.166


Problem 81	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	B	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	11	11	25	11	15	17	8	10	10
N.S.	1	1.00	2.27	1.00	1.36	1.55	0.73	0.91	0.91
time (sec)	N/A	0.007	0.012	0.024	1.085	0.698	0.174	0.824	0.029


Problem 82	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	6	6	6	9	6	6	7	6	6
N.S.	1	1.00	1.00	1.50	1.00	1.00	1.17	1.00	1.00
time (sec)	N/A	0.003	0.003	0.006	1.422	0.657	0.011	0.913	0.026


Problem 83	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	18	15	12	12	19	12	12
N.S.	1	1.00	1.29	1.07	0.86	0.86	1.36	0.86	0.86
time (sec)	N/A	0.006	0.003	0.001	2.281	0.833	0.015	0.768	0.025


Problem 84	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	11	11	17	13	9	16	19	9	17
N.S.	1	1.00	1.55	1.18	0.82	1.45	1.73	0.82	1.55
time (sec)	N/A	0.006	0.003	0.061	2.631	0.677	0.012	0.817	0.029


Problem 85	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	27	19	15	22	31	15	27
N.S.	1	1.00	1.42	1.00	0.79	1.16	1.63	0.79	1.42
time (sec)	N/A	0.007	0.003	0.066	1.623	0.835	0.013	0.777	0.038


Problem 86	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	8	8	8	11	6	20	29	6	6
N.S.	1	1.00	1.00	1.38	0.75	2.50	3.62	0.75	0.75
time (sec)	N/A	0.015	0.001	0.029	1.825	0.725	0.012	0.970	0.029


Problem 87	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	17	17	27	22	13	20	29	13	13
N.S.	1	1.00	1.59	1.29	0.76	1.18	1.71	0.76	0.76
time (sec)	N/A	0.016	0.017	0.029	1.518	0.653	0.012	0.757	0.172


Problem 88	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	0.009	0.005	0.030	2.237	0.605	0.011	0.933	0.290


Problem 89	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	17	17	17	42	14	14	14	14	13
N.S.	1	1.00	1.00	2.47	0.82	0.82	0.82	0.82	0.76
time (sec)	N/A	0.016	0.020	0.035	1.613	0.676	0.030	0.944	0.379


Problem 90	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	22	20	23	34	24	20	22	18
N.S.	1	1.00	0.91	1.05	1.55	1.09	0.91	1.00	0.82
time (sec)	N/A	0.007	0.004	0.019	1.966	0.607	0.037	0.787	0.033


Problem 91	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	22	30	21	18	18	31	18	18
N.S.	1	1.00	1.36	0.95	0.82	0.82	1.41	0.82	0.82
time (sec)	N/A	0.009	0.005	0.017	1.606	0.643	0.017	0.819	0.034


Problem 92	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	19	19	19	48	20	20	22	20	17
N.S.	1	1.00	1.00	2.53	1.05	1.05	1.16	1.05	0.89
time (sec)	N/A	0.011	0.011	0.040	1.772	0.721	0.037	0.762	0.269


Problem 93	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	25	25	25	58	20	20	22	20	19
N.S.	1	1.00	1.00	2.32	0.80	0.80	0.88	0.80	0.76
time (sec)	N/A	0.021	0.011	0.036	2.082	0.605	0.041	0.760	0.529


Problem 94	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	10	6	7	6	18
N.S.	1	1.00	1.00	0.88	1.25	0.75	0.88	0.75	2.25
time (sec)	N/A	0.009	0.006	0.025	1.210	0.471	0.011	0.931	0.173


Problem 95	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	B	B	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	17	17	17	32	36	14	14	14	20
N.S.	1	1.00	1.00	1.88	2.12	0.82	0.82	0.82	1.18
time (sec)	N/A	0.018	0.013	0.036	1.716	0.786	0.037	1.158	0.167


Problem 96	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	10	6	7	6	6
N.S.	1	1.00	1.00	0.88	1.25	0.75	0.88	0.75	0.75
time (sec)	N/A	0.009	0.004	0.026	1.232	0.596	0.015	1.089	0.032


Problem 97	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	B	B	A	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	16	16	16	24	27	34	27	29	30
N.S.	1	1.00	1.00	1.50	1.69	2.12	1.69	1.81	1.88
time (sec)	N/A	0.010	0.006	0.029	1.959	0.682	0.041	0.782	0.258


Problem 98	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	B	A	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	8	8	8	14	10	20	8	18	8
N.S.	1	1.00	1.00	1.75	1.25	2.50	1.00	2.25	1.00
time (sec)	N/A	0.004	0.003	0.005	1.949	0.757	0.013	0.695	0.018


Problem 99	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	14	14	14	17	14	28	14	22	18
N.S.	1	1.00	1.00	1.21	1.00	2.00	1.00	1.57	1.29
time (sec)	N/A	0.006	0.003	0.017	1.773	0.679	0.029	0.876	0.026


Problem 100	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	B	A	A	B	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	17	17	37	22	14	39	41	14	14
N.S.	1	1.00	2.18	1.29	0.82	2.29	2.41	0.82	0.82
time (sec)	N/A	0.020	0.021	0.035	1.157	0.583	0.015	0.860	0.185

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