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	33	33	33	28	27	27	29	29	28
N.S.	1	1.00	1.00	0.85	0.82	0.82	0.88	0.88	0.85
time (sec)	N/A	0.012	0.005	0.089	0.304	0.881	0.007	0.720	0.111


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	33	33	33	28	27	27	29	29	28
N.S.	1	1.00	1.00	0.85	0.82	0.82	0.88	0.88	0.85
time (sec)	N/A	0.022	0.007	0.051	0.300	0.876	0.006	0.959	0.021


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	28	28	28	25	24	24	26	26	25
N.S.	1	1.00	1.00	0.89	0.86	0.86	0.93	0.93	0.89
time (sec)	N/A	0.009	0.005	0.091	0.293	0.825	0.006	1.455	0.021


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	29	29	29	28	28	25	27	30	26
N.S.	1	1.00	1.00	0.97	0.97	0.86	0.93	1.03	0.90
time (sec)	N/A	0.015	0.007	0.035	0.292	0.724	0.031	1.234	0.035


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	26	26	26	24	24	28	20	23	24
N.S.	1	1.00	1.00	0.92	0.92	1.08	0.77	0.88	0.92
time (sec)	N/A	0.011	0.007	0.015	0.277	0.650	0.030	0.715	0.044


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	29	29	29	26	28	30	26	42	25
N.S.	1	1.00	1.00	0.90	0.97	1.03	0.90	1.45	0.86
time (sec)	N/A	0.015	0.009	0.020	0.289	0.792	0.073	0.839	0.034


Problem 7	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	27	25	26	29	27	28	26
N.S.	1	1.00	1.04	0.96	1.00	1.12	1.04	1.08	1.00
time (sec)	N/A	0.011	0.010	0.018	0.290	1.180	0.087	1.037	0.018


Problem 8	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	31	26	30	31	29	39	29
N.S.	1	1.00	1.07	0.90	1.03	1.07	1.00	1.34	1.00
time (sec)	N/A	0.016	0.013	0.020	0.314	1.182	0.172	0.804	0.040


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	31	31	33	28	29	29	32	31	29
N.S.	1	1.00	1.06	0.90	0.94	0.94	1.03	1.00	0.94
time (sec)	N/A	0.011	0.008	0.018	0.292	1.049	0.175	1.198	0.020


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	33	33	35	28	29	29	32	31	30
N.S.	1	1.00	1.06	0.85	0.88	0.88	0.97	0.94	0.91
time (sec)	N/A	0.015	0.008	0.020	0.289	1.355	0.246	1.091	0.020


Problem 11	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	0.093	0.357	0.952	0.010	1.053	0.042


Problem 12	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	0.047	0.009	0.075	0.394	1.497	0.011	0.822	0.024


Problem 13	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	0.015	0.007	0.103	0.400	3.140	0.010	0.834	0.023


Problem 14	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	0.060	0.291	1.287	0.045	0.955	0.021


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	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	0.012	0.060	0.279	0.834	0.042	1.321	0.026


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	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	0.032	0.020	0.089	0.294	1.043	0.097	1.182	0.024


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	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	0.065	0.283	0.745	0.106	1.028	0.037


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	51	51	50	46	54	55	51	72	51
N.S.	1	1.00	0.98	0.90	1.06	1.08	1.00	1.41	1.00
time (sec)	N/A	0.029	0.019	0.062	0.282	0.635	0.265	0.621	0.046


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	48	48	48	45	51	53	54	53	50
N.S.	1	1.00	1.00	0.94	1.06	1.10	1.12	1.10	1.04
time (sec)	N/A	0.019	0.015	0.063	0.283	0.626	0.305	0.857	0.025


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	51	51	54	46	55	55	56	66	51
N.S.	1	1.00	1.06	0.90	1.08	1.08	1.10	1.29	1.00
time (sec)	N/A	0.026	0.021	0.060	0.284	0.893	0.520	1.024	0.048


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	53	53	56	48	53	53	58	55	52
N.S.	1	1.00	1.06	0.91	1.00	1.00	1.09	1.04	0.98
time (sec)	N/A	0.019	0.013	0.058	0.280	0.725	0.565	1.210	0.019


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	48	48	55	48	53	53	58	55	53
N.S.	1	1.00	1.15	1.00	1.10	1.10	1.21	1.15	1.10
time (sec)	N/A	0.021	0.013	0.059	0.300	0.917	0.859	1.127	0.035


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	117	117	117	124	119	119	136	125	107
N.S.	1	1.00	1.00	1.06	1.02	1.02	1.16	1.07	0.91
time (sec)	N/A	0.114	0.014	0.099	0.285	0.882	0.017	0.658	0.087


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	117	117	117	124	119	119	138	125	107
N.S.	1	1.00	1.00	1.06	1.02	1.02	1.18	1.07	0.91
time (sec)	N/A	0.061	0.014	0.101	0.298	0.819	0.017	0.525	0.022


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	122	122	117	124	119	119	136	125	107
N.S.	1	1.00	0.96	1.02	0.98	0.98	1.11	1.02	0.88
time (sec)	N/A	0.194	0.012	0.100	0.297	0.760	0.019	0.473	0.022


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	117	117	117	124	119	119	136	125	107
N.S.	1	1.00	1.00	1.06	1.02	1.02	1.16	1.07	0.91
time (sec)	N/A	0.047	0.012	0.098	0.293	0.591	0.018	0.654	0.022


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	95	95	107	124	119	119	133	124	107
N.S.	1	1.00	1.13	1.31	1.25	1.25	1.40	1.31	1.13
time (sec)	N/A	0.149	0.018	0.096	0.281	0.669	0.019	0.643	0.024


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	117	117	117	124	119	119	136	125	107
N.S.	1	1.00	1.00	1.06	1.02	1.02	1.16	1.07	0.91
time (sec)	N/A	0.047	0.012	0.117	0.267	0.793	0.017	0.568	0.022


Problem 29	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	B	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	67	67	114	124	118	118	131	123	106
N.S.	1	1.00	1.70	1.85	1.76	1.76	1.96	1.84	1.58
time (sec)	N/A	0.100	0.012	0.079	0.281	0.723	0.019	0.647	0.023


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	117	117	117	124	119	119	134	124	106
N.S.	1	1.00	1.00	1.06	1.02	1.02	1.15	1.06	0.91
time (sec)	N/A	0.048	0.012	0.099	0.292	0.637	0.017	0.617	0.024


Problem 31	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	42	42	107	124	119	119	133	124	107
N.S.	1	1.00	2.55	2.95	2.83	2.83	3.17	2.95	2.55
time (sec)	N/A	0.046	0.017	0.081	0.285	0.804	0.019	0.603	0.022


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	109	109	109	121	115	115	129	121	103
N.S.	1	1.00	1.00	1.11	1.06	1.06	1.18	1.11	0.94
time (sec)	N/A	0.042	0.012	0.096	0.290	0.629	0.017	0.677	0.023


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	88	88	113	124	120	117	134	126	105
N.S.	1	1.00	1.28	1.41	1.36	1.33	1.52	1.43	1.19
time (sec)	N/A	0.044	0.022	0.063	0.284	0.717	0.087	0.634	0.025


Problem 34	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	108	108	108	121	116	121	126	120	104
N.S.	1	1.00	1.00	1.12	1.07	1.12	1.17	1.11	0.96
time (sec)	N/A	0.041	0.022	0.065	0.290	0.626	0.084	0.894	0.024


Problem 35	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	113	113	115	121	120	123	131	145	105
N.S.	1	1.00	1.02	1.07	1.06	1.09	1.16	1.28	0.93
time (sec)	N/A	0.075	0.033	0.065	0.298	0.702	0.142	0.720	0.045


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	108	108	110	118	118	121	128	122	106
N.S.	1	1.00	1.02	1.09	1.09	1.12	1.19	1.13	0.98
time (sec)	N/A	0.042	0.025	0.060	0.298	0.793	0.151	0.739	0.024


Problem 37	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	112	112	112	117	122	123	128	149	113
N.S.	1	1.00	1.00	1.04	1.09	1.10	1.14	1.33	1.01
time (sec)	N/A	0.074	0.028	0.070	0.295	0.705	0.333	0.701	0.027


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	111	111	111	113	120	121	129	123	111
N.S.	1	1.00	1.00	1.02	1.08	1.09	1.16	1.11	1.00
time (sec)	N/A	0.045	0.025	0.062	0.275	0.752	0.368	0.652	0.040


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	114	114	116	111	123	123	128	151	118
N.S.	1	1.00	1.02	0.97	1.08	1.08	1.12	1.32	1.04
time (sec)	N/A	0.072	0.029	0.066	0.298	0.957	0.720	0.647	0.044


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	111	111	111	108	120	121	131	124	116
N.S.	1	1.00	1.00	0.97	1.08	1.09	1.18	1.12	1.05
time (sec)	N/A	0.044	0.027	0.065	0.301	0.984	0.853	0.684	0.053


Problem 41	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	112	112	116	106	123	123	129	150	122
N.S.	1	1.00	1.04	0.95	1.10	1.10	1.15	1.34	1.09
time (sec)	N/A	0.068	0.038	0.086	0.292	0.799	1.545	0.639	0.033


Problem 42	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	108	108	115	102	119	121	129	123	119
N.S.	1	1.00	1.06	0.94	1.10	1.12	1.19	1.14	1.10
time (sec)	N/A	0.048	0.024	0.064	0.273	0.827	3.146	0.603	0.039


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	113	113	116	102	123	123	129	147	121
N.S.	1	1.00	1.03	0.90	1.09	1.09	1.14	1.30	1.07
time (sec)	N/A	0.060	0.041	0.067	0.297	0.887	5.033	0.640	0.059


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	108	108	122	101	119	121	131	125	119
N.S.	1	1.00	1.13	0.94	1.10	1.12	1.21	1.16	1.10
time (sec)	N/A	0.044	0.030	0.063	0.288	0.684	34.891	0.586	0.041


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	91	91	118	102	123	123	133	138	121
N.S.	1	1.00	1.30	1.12	1.35	1.35	1.46	1.52	1.33
time (sec)	N/A	0.038	0.045	0.068	0.291	0.750	26.604	0.626	0.068


Problem 46	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	113	113	119	104	121	121	0	127	120
N.S.	1	1.00	1.05	0.92	1.07	1.07	0.00	1.12	1.06
time (sec)	N/A	0.044	0.022	0.063	0.319	0.678	0.000	0.743	0.051


Problem 47	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	48	48	118	104	121	121	134	127	121
N.S.	1	1.00	2.46	2.17	2.52	2.52	2.79	2.65	2.52
time (sec)	N/A	0.021	0.023	0.069	0.322	0.772	134.476	1.100	0.035


Problem 48	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	117	117	121	104	121	121	0	127	121
N.S.	1	1.00	1.03	0.89	1.03	1.03	0.00	1.09	1.03
time (sec)	N/A	0.042	0.024	0.066	0.301	0.620	0.000	1.494	0.035


Problem 49	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	76	76	121	104	121	121	0	127	120
N.S.	1	1.00	1.59	1.37	1.59	1.59	0.00	1.67	1.58
time (sec)	N/A	0.036	0.022	0.067	0.294	0.953	0.000	1.646	0.052


Problem 50	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	117	117	117	104	121	121	0	127	122
N.S.	1	1.00	1.00	0.89	1.03	1.03	0.00	1.09	1.04
time (sec)	N/A	0.042	0.036	0.067	0.306	0.735	0.000	1.056	0.051


Problem 51	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	117	117	121	104	121	121	0	127	121
N.S.	1	1.00	1.03	0.89	1.03	1.03	0.00	1.09	1.03
time (sec)	N/A	0.060	0.023	0.071	0.297	0.661	0.000	1.570	0.034


Problem 52	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	117	117	117	104	121	121	0	127	122
N.S.	1	1.00	1.00	0.89	1.03	1.03	0.00	1.09	1.04
time (sec)	N/A	0.041	0.031	0.069	0.299	0.779	0.000	1.148	0.058


Problem 53	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	117	117	121	104	121	121	0	127	122
N.S.	1	1.00	1.03	0.89	1.03	1.03	0.00	1.09	1.04
time (sec)	N/A	0.056	0.024	0.069	0.288	0.786	0.000	0.860	0.052


Problem 54	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	117	117	117	104	121	121	0	127	122
N.S.	1	1.00	1.00	0.89	1.03	1.03	0.00	1.09	1.04
time (sec)	N/A	0.043	0.031	0.066	0.309	0.691	0.000	1.152	0.053


Problem 55	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	117	117	121	104	121	121	0	127	122
N.S.	1	1.00	1.03	0.89	1.03	1.03	0.00	1.09	1.04
time (sec)	N/A	0.055	0.023	0.068	0.303	1.021	0.000	1.672	0.035


Problem 56	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	98	98	98	99	100	228	180	108	118
N.S.	1	1.00	1.00	1.01	1.02	2.33	1.84	1.10	1.20
time (sec)	N/A	0.040	0.051	0.086	0.512	1.753	0.209	0.950	0.027


Problem 57	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	0.069	0.294	1.503	0.171	1.371	0.031


Problem 58	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	78	178	153	85	96
N.S.	1	1.00	1.00	0.97	1.01	2.31	1.99	1.10	1.25
time (sec)	N/A	0.033	0.037	0.082	0.588	1.167	0.236	0.833	0.054


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	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	0.038	0.016	0.084	0.295	0.976	0.220	0.793	0.054


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	58	58	57	51	53	129	90	57	70
N.S.	1	1.00	0.98	0.88	0.91	2.22	1.55	0.98	1.21
time (sec)	N/A	0.024	0.034	0.082	0.506	0.934	0.185	0.720	0.056


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	35	35	31	32	31	30	27	32	31
N.S.	1	1.00	0.89	0.91	0.89	0.86	0.77	0.91	0.89
time (sec)	N/A	0.023	0.009	0.066	0.308	1.111	0.133	1.396	0.029


Problem 62	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	40	34	34	99	82	34	31
N.S.	1	1.00	1.03	0.87	0.87	2.54	2.10	0.87	0.79
time (sec)	N/A	0.011	0.020	0.080	0.539	1.635	0.168	1.602	0.028


Problem 63	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	33	35	32	26	36	32
N.S.	1	1.00	1.00	0.97	1.03	0.94	0.76	1.06	0.94
time (sec)	N/A	0.023	0.010	0.070	0.299	1.005	0.502	1.072	0.064


Problem 64	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	43	43	42	37	36	105	82	36	35
N.S.	1	1.00	0.98	0.86	0.84	2.44	1.91	0.84	0.81
time (sec)	N/A	0.014	0.020	0.076	0.506	0.907	0.181	1.353	0.033


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	50	50	49	46	48	47	41	71	46
N.S.	1	1.00	0.98	0.92	0.96	0.94	0.82	1.42	0.92
time (sec)	N/A	0.034	0.017	0.074	0.280	0.774	0.402	1.526	0.073


Problem 66	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	59	59	60	54	56	135	129	57	53
N.S.	1	1.00	1.02	0.92	0.95	2.29	2.19	0.97	0.90
time (sec)	N/A	0.024	0.040	0.077	0.511	0.899	0.206	1.045	0.055


Problem 67	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	69	70	64	70	73	61	100	70
N.S.	1	1.00	1.01	0.93	1.01	1.06	0.88	1.45	1.01
time (sec)	N/A	0.043	0.022	0.075	0.286	0.610	0.593	1.214	0.070


Problem 68	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	80	80	78	74	79	184	163	81	70
N.S.	1	1.00	0.98	0.92	0.99	2.30	2.04	1.01	0.88
time (sec)	N/A	0.033	0.041	0.092	0.509	0.670	0.306	1.258	0.052


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	93	93	96	86	96	98	88	126	92
N.S.	1	1.00	1.03	0.92	1.03	1.05	0.95	1.35	0.99
time (sec)	N/A	0.057	0.028	0.077	0.311	0.579	0.583	0.924	0.086


Problem 70	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	99	99	101	91	103	234	187	106	89
N.S.	1	1.00	1.02	0.92	1.04	2.36	1.89	1.07	0.90
time (sec)	N/A	0.043	0.051	0.097	0.503	0.635	0.292	1.060	0.072


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	126	126	113	125	131	172	131	159	181
N.S.	1	1.00	0.90	0.99	1.04	1.37	1.04	1.26	1.44
time (sec)	N/A	0.120	0.056	0.066	0.329	0.630	0.422	1.231	0.056


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	131	131	134	123	136	350	238	139	203
N.S.	1	1.00	1.02	0.94	1.04	2.67	1.82	1.06	1.55
time (sec)	N/A	0.101	0.078	0.089	0.516	0.607	0.529	1.112	0.030


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	104	104	93	103	107	148	104	135	121
N.S.	1	1.00	0.89	0.99	1.03	1.42	1.00	1.30	1.16
time (sec)	N/A	0.087	0.047	0.066	0.294	0.703	0.409	1.055	0.051


Problem 74	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	110	110	111	100	112	298	211	115	141
N.S.	1	1.00	1.01	0.91	1.02	2.71	1.92	1.05	1.28
time (sec)	N/A	0.078	0.063	0.085	0.508	0.723	0.475	1.110	0.027


Problem 75	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	72	76	82	121	78	106	86
N.S.	1	1.00	0.88	0.93	1.00	1.48	0.95	1.29	1.05
time (sec)	N/A	0.062	0.048	0.083	0.294	0.665	0.487	0.974	0.038


Problem 76	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	89	75	85	240	129	88	104
N.S.	1	1.00	1.02	0.86	0.98	2.76	1.48	1.01	1.20
time (sec)	N/A	0.048	0.054	0.084	0.530	0.710	0.360	2.019	0.038


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	60	60	50	59	60	81	56	91	62
N.S.	1	1.00	0.83	0.98	1.00	1.35	0.93	1.52	1.03
time (sec)	N/A	0.041	0.026	0.069	0.292	0.645	0.309	1.625	0.041


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	67	67	68	57	61	208	114	59	59
N.S.	1	1.00	1.01	0.85	0.91	3.10	1.70	0.88	0.88
time (sec)	N/A	0.034	0.051	0.085	0.512	0.668	0.282	1.556	0.065


Problem 79	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	38	40	44	36	65	37
N.S.	1	1.00	1.00	0.93	0.98	1.07	0.88	1.59	0.90
time (sec)	N/A	0.027	0.010	0.064	0.280	0.718	0.226	1.291	0.046


Problem 80	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	63	57	57	182	112	57	51
N.S.	1	1.00	1.00	0.90	0.90	2.89	1.78	0.90	0.81
time (sec)	N/A	0.014	0.034	0.086	0.496	0.634	0.224	1.843	0.063


Problem 81	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	46	48	51	70	46	63	47
N.S.	1	1.00	0.90	0.94	1.00	1.37	0.90	1.24	0.92
time (sec)	N/A	0.031	0.022	0.068	0.326	0.829	0.332	0.919	0.086


Problem 82	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	70	62	63	210	114	62	63
N.S.	1	1.00	0.99	0.87	0.89	2.96	1.61	0.87	0.89
time (sec)	N/A	0.036	0.026	0.092	0.515	1.175	0.340	1.226	0.067


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	76	76	64	76	76	117	70	82	78
N.S.	1	1.00	0.84	1.00	1.00	1.54	0.92	1.08	1.03
time (sec)	N/A	0.053	0.036	0.073	0.299	1.281	0.562	1.399	0.075


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	90	90	90	78	93	250	184	85	83
N.S.	1	1.00	1.00	0.87	1.03	2.78	2.04	0.94	0.92
time (sec)	N/A	0.074	0.055	0.077	0.505	1.218	0.314	1.171	0.087


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	97	97	85	96	106	154	100	150	100
N.S.	1	1.00	0.88	0.99	1.09	1.59	1.03	1.55	1.03
time (sec)	N/A	0.070	0.076	0.076	0.328	1.004	0.687	2.623	0.074


Problem 86	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	113	113	112	99	119	308	218	112	104
N.S.	1	1.00	0.99	0.88	1.05	2.73	1.93	0.99	0.92
time (sec)	N/A	0.127	0.056	0.094	0.497	1.255	0.352	3.264	0.084


Problem 87	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	124	124	110	117	136	184	129	178	126
N.S.	1	1.00	0.89	0.94	1.10	1.48	1.04	1.44	1.02
time (sec)	N/A	0.091	0.072	0.082	0.275	1.339	0.705	1.263	0.093


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	150	150	136	151	165	231	170	183	225
N.S.	1	1.00	0.91	1.01	1.10	1.54	1.13	1.22	1.50
time (sec)	N/A	0.160	0.064	0.076	0.275	0.888	0.910	2.072	0.068


Problem 89	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	128	128	116	129	141	205	143	159	155
N.S.	1	1.00	0.91	1.01	1.10	1.60	1.12	1.24	1.21
time (sec)	N/A	0.114	0.055	0.068	0.293	0.700	0.978	1.205	0.040


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	109	109	94	102	116	179	119	132	118
N.S.	1	1.00	0.86	0.94	1.06	1.64	1.09	1.21	1.08
time (sec)	N/A	0.086	0.048	0.087	0.287	1.369	0.815	1.632	0.042


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	88	88	92	85	94	142	94	93	95
N.S.	1	1.00	1.05	0.97	1.07	1.61	1.07	1.06	1.08
time (sec)	N/A	0.064	0.029	0.070	0.286	0.884	1.038	1.187	0.069


Problem 92	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	64	61	72	89	70	61	70
N.S.	1	1.00	0.97	0.92	1.09	1.35	1.06	0.92	1.06
time (sec)	N/A	0.046	0.019	0.066	0.277	0.830	0.491	1.423	0.057


Problem 93	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	30	39	42	42	42	28	44
N.S.	1	1.00	0.94	1.22	1.31	1.31	1.31	0.88	1.38
time (sec)	N/A	0.014	0.010	0.072	0.280	0.926	0.276	1.439	0.039


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	68	68	59	63	77	119	75	76	71
N.S.	1	1.00	0.87	0.93	1.13	1.75	1.10	1.12	1.04
time (sec)	N/A	0.045	0.035	0.070	0.289	0.766	0.291	1.382	0.096


Problem 95	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	101	101	87	102	109	197	107	138	107
N.S.	1	1.00	0.86	1.01	1.08	1.95	1.06	1.37	1.06
time (sec)	N/A	0.072	0.044	0.076	0.308	0.638	0.605	1.486	0.060


Problem 96	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	124	124	108	123	137	229	136	133	131
N.S.	1	1.00	0.87	0.99	1.10	1.85	1.10	1.07	1.06
time (sec)	N/A	0.092	0.059	0.082	0.290	1.055	0.720	0.804	0.085


Problem 97	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	149	149	135	143	170	267	165	201	155
N.S.	1	1.00	0.91	0.96	1.14	1.79	1.11	1.35	1.04
time (sec)	N/A	0.115	0.090	0.080	0.281	0.712	0.707	1.387	0.100


Problem 98	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	158	158	158	144	171	468	280	162	246
N.S.	1	1.00	1.00	0.91	1.08	2.96	1.77	1.03	1.56
time (sec)	N/A	0.193	0.068	0.089	0.500	0.852	0.813	1.653	0.067


Problem 99	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	138	138	133	119	147	416	252	138	177
N.S.	1	1.00	0.96	0.86	1.07	3.01	1.83	1.00	1.28
time (sec)	N/A	0.146	0.077	0.101	0.495	0.709	0.810	1.714	0.038


Problem 100	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	A	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	116	116	113	95	120	358	214	111	138
N.S.	1	1.00	0.97	0.82	1.03	3.09	1.84	0.96	1.19
time (sec)	N/A	0.103	0.066	0.091	0.518	0.648	0.854	1.280	0.046

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