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	0.018	0.005	0.163	0.285	2.913	0.007	1.457	0.179


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	0.028	0.006	0.206	0.286	3.156	0.007	1.656	0.059


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	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	0.016	0.004	0.134	0.299	2.928	0.006	1.149	0.040


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	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	0.025	0.005	0.117	0.645	2.434	0.006	0.695	0.059


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	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	0.013	0.004	0.168	0.309	1.431	0.006	0.773	0.060


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	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	0.019	0.007	0.088	0.273	1.595	0.032	0.655	0.061


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	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	0.016	0.007	0.026	0.278	1.140	0.030	0.743	0.073


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	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	0.019	0.008	0.034	0.270	1.334	0.075	0.629	0.042


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	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	0.016	0.009	0.030	0.295	1.549	0.087	0.620	0.057


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	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	0.019	0.013	0.031	0.272	2.139	0.178	0.685	0.074


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	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	0.015	0.008	0.023	0.276	3.694	0.179	0.594	0.038


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	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	0.034	0.007	0.430	0.283	2.604	0.011	0.620	0.085


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	55	55	55	52	51	51	53	53	51
N.S.	1	1.00	1.00	0.95	0.93	0.93	0.96	0.96	0.93
time (sec)	N/A	0.051	0.006	0.400	0.282	1.806	0.011	0.650	0.047


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	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	0.026	0.007	0.425	0.268	1.246	0.011	1.137	0.049


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	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	0.049	0.009	0.524	0.288	1.907	0.012	1.838	0.045


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	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	0.022	0.007	0.501	0.282	2.498	0.011	0.883	0.047


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	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	0.027	0.012	0.361	0.275	2.061	0.047	0.926	0.042


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	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	0.025	0.013	0.351	0.282	2.100	0.044	0.804	0.051


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	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	0.036	0.020	0.403	0.289	1.042	0.099	0.717	0.047


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	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	0.025	0.014	0.359	0.280	1.706	0.109	0.602	0.049


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	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	0.031	0.025	0.364	0.278	1.566	0.267	0.613	0.081


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	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	0.028	0.015	0.358	0.281	1.316	0.311	1.120	0.068


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	51	51	53	46	55	55	56	66	51
N.S.	1	1.00	1.04	0.90	1.08	1.08	1.10	1.29	1.00
time (sec)	N/A	0.032	0.019	0.360	0.284	1.639	0.533	1.786	0.091


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	53	53	59	48	53	53	58	55	52
N.S.	1	1.00	1.11	0.91	1.00	1.00	1.09	1.04	0.98
time (sec)	N/A	0.025	0.013	0.363	0.281	1.687	0.573	1.603	0.038


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	75	75	75	76	73	73	80	77	69
N.S.	1	1.00	1.00	1.01	0.97	0.97	1.07	1.03	0.92
time (sec)	N/A	0.044	0.010	0.568	0.274	1.540	0.014	0.937	0.060


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	68	68	69	76	73	73	82	77	69
N.S.	1	1.00	1.01	1.12	1.07	1.07	1.21	1.13	1.01
time (sec)	N/A	0.095	0.013	0.401	0.273	1.838	0.016	0.927	0.030


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	75	75	75	76	73	73	82	77	69
N.S.	1	1.00	1.00	1.01	0.97	0.97	1.09	1.03	0.92
time (sec)	N/A	0.036	0.008	0.413	0.287	1.431	0.014	1.442	0.030


Problem 28	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	42	42	69	76	73	73	80	77	69
N.S.	1	1.00	1.64	1.81	1.74	1.74	1.90	1.83	1.64
time (sec)	N/A	0.047	0.013	0.391	0.289	1.397	0.015	1.380	0.031


Problem 29	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	70	73	70	70	76	73	65
N.S.	1	1.00	1.00	1.04	1.00	1.00	1.09	1.04	0.93
time (sec)	N/A	0.031	0.008	0.492	0.279	1.386	0.014	1.084	0.031


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	60	60	71	76	74	71	80	78	67
N.S.	1	1.00	1.18	1.27	1.23	1.18	1.33	1.30	1.12
time (sec)	N/A	0.034	0.014	0.418	0.282	1.574	0.063	0.707	0.035


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	65	65	65	71	69	75	68	70	65
N.S.	1	1.00	1.00	1.09	1.06	1.15	1.05	1.08	1.00
time (sec)	N/A	0.030	0.015	0.369	0.280	1.476	0.059	0.771	0.033


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	71	71	73	73	74	77	78	97	67
N.S.	1	1.00	1.03	1.03	1.04	1.08	1.10	1.37	0.94
time (sec)	N/A	0.052	0.020	0.368	0.290	1.704	0.117	0.683	0.039


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	69	69	71	70	73	75	75	74	68
N.S.	1	1.00	1.03	1.01	1.06	1.09	1.09	1.07	0.99
time (sec)	N/A	0.033	0.017	0.375	0.273	1.678	0.126	0.706	0.057


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	72	72	73	68	76	76	75	98	76
N.S.	1	1.00	1.01	0.94	1.06	1.06	1.04	1.36	1.06
time (sec)	N/A	0.049	0.021	0.460	0.276	1.550	0.301	0.822	0.074


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	68	68	68	64	73	75	78	75	73
N.S.	1	1.00	1.00	0.94	1.07	1.10	1.15	1.10	1.07
time (sec)	N/A	0.033	0.017	0.377	0.278	1.419	0.336	0.754	0.057


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	71	71	71	64	77	77	78	99	75
N.S.	1	1.00	1.00	0.90	1.08	1.08	1.10	1.39	1.06
time (sec)	N/A	0.042	0.026	0.379	0.281	1.703	0.679	0.693	0.087


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	66	66	66	63	73	75	80	77	71
N.S.	1	1.00	1.00	0.95	1.11	1.14	1.21	1.17	1.08
time (sec)	N/A	0.033	0.020	0.361	0.273	1.375	0.796	0.615	0.080


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	63	63	77	64	77	77	82	90	75
N.S.	1	1.00	1.22	1.02	1.22	1.22	1.30	1.43	1.19
time (sec)	N/A	0.031	0.025	0.369	0.304	1.772	1.328	0.571	0.103


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	73	73	73	66	75	75	83	79	74
N.S.	1	1.00	1.00	0.90	1.03	1.03	1.14	1.08	1.01
time (sec)	N/A	0.035	0.021	0.463	0.279	1.438	2.457	0.671	0.070


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	49	49	78	66	75	75	83	79	76
N.S.	1	1.00	1.59	1.35	1.53	1.53	1.69	1.61	1.55
time (sec)	N/A	0.026	0.013	0.409	0.280	1.465	3.546	0.636	0.071


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	119	119	119	123	124	274	204	133	144
N.S.	1	1.00	1.00	1.03	1.04	2.30	1.71	1.12	1.21
time (sec)	N/A	0.060	0.053	0.461	0.487	1.451	0.223	0.609	0.171


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	96	96	92	98	97	98	94	101	100
N.S.	1	1.00	0.96	1.02	1.01	1.02	0.98	1.05	1.04
time (sec)	N/A	0.087	0.025	0.376	0.277	1.505	0.176	0.633	0.058


Problem 43	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	0.047	0.043	0.411	0.493	1.318	0.204	0.601	0.043


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	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	0.064	0.020	0.378	0.295	1.613	0.163	0.639	0.087


Problem 45	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	0.042	0.035	0.398	0.492	1.482	0.185	0.621	0.066


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	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	0.046	0.015	0.434	0.274	1.538	0.144	0.663	0.074


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	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	0.031	0.027	0.391	0.501	1.547	0.167	0.660	0.107


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	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	0.027	0.008	0.373	0.277	1.594	0.121	0.890	0.056


Problem 49	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	40	34	34	99	82	34	31
N.S.	1	1.00	1.00	0.85	0.85	2.48	2.05	0.85	0.78
time (sec)	N/A	0.018	0.016	0.422	0.493	1.843	0.136	0.683	0.054


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	34	34	34	33	35	32	26	34	32
N.S.	1	1.00	1.00	0.97	1.03	0.94	0.76	1.00	0.94
time (sec)	N/A	0.029	0.009	0.379	0.289	2.194	0.380	0.638	0.085


Problem 51	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	42	42	42	37	36	105	82	36	35
N.S.	1	1.00	1.00	0.88	0.86	2.50	1.95	0.86	0.83
time (sec)	N/A	0.021	0.018	0.413	0.490	2.029	0.162	0.641	0.092


Problem 52	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	41	41	41	39	51	103	75	38	33
N.S.	1	1.00	1.00	0.95	1.24	2.51	1.83	0.93	0.80
time (sec)	N/A	0.022	0.018	0.500	0.510	1.621	0.170	0.848	0.145


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	49	49	49	46	48	47	41	71	46
N.S.	1	1.00	1.00	0.94	0.98	0.96	0.84	1.45	0.94
time (sec)	N/A	0.038	0.016	0.438	0.296	0.808	0.387	0.852	0.137


Problem 54	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	61	61	60	54	56	135	129	57	53
N.S.	1	1.00	0.98	0.89	0.92	2.21	2.11	0.93	0.87
time (sec)	N/A	0.032	0.037	0.412	0.495	1.774	0.205	0.686	0.106


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	70	70	70	64	70	73	61	100	70
N.S.	1	1.00	1.00	0.91	1.00	1.04	0.87	1.43	1.00
time (sec)	N/A	0.050	0.021	0.385	0.276	0.924	0.444	0.781	0.137


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	78	78	78	74	79	184	163	81	70
N.S.	1	1.00	1.00	0.95	1.01	2.36	2.09	1.04	0.90
time (sec)	N/A	0.042	0.038	0.421	0.503	1.710	0.246	0.845	0.106


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	92	92	96	86	96	98	88	126	92
N.S.	1	1.00	1.04	0.93	1.04	1.07	0.96	1.37	1.00
time (sec)	N/A	0.063	0.027	0.382	0.275	0.955	0.482	0.682	0.153


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	133	133	134	123	136	350	238	139	203
N.S.	1	1.00	1.01	0.92	1.02	2.63	1.79	1.05	1.53
time (sec)	N/A	0.110	0.070	0.415	0.496	2.080	0.412	0.634	0.104


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	105	105	93	103	107	148	104	135	121
N.S.	1	1.00	0.89	0.98	1.02	1.41	0.99	1.29	1.15
time (sec)	N/A	0.095	0.047	0.383	0.267	1.088	0.393	0.736	0.097


Problem 60	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	0.084	0.057	0.394	0.509	1.840	0.384	0.885	0.085


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	83	83	72	76	82	121	78	106	86
N.S.	1	1.00	0.87	0.92	0.99	1.46	0.94	1.28	1.04
time (sec)	N/A	0.071	0.037	0.410	0.277	1.307	0.359	0.816	0.072


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	89	89	89	75	85	240	129	88	104
N.S.	1	1.00	1.00	0.84	0.96	2.70	1.45	0.99	1.17
time (sec)	N/A	0.061	0.049	0.398	0.498	1.631	0.347	0.699	0.110


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	61	61	50	59	60	81	56	70	62
N.S.	1	1.00	0.82	0.97	0.98	1.33	0.92	1.15	1.02
time (sec)	N/A	0.048	0.025	0.376	0.275	1.405	0.312	1.375	0.116


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	68	68	68	57	61	208	114	59	59
N.S.	1	1.00	1.00	0.84	0.90	3.06	1.68	0.87	0.87
time (sec)	N/A	0.040	0.036	0.390	0.496	1.726	0.279	1.474	0.126


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	41	41	41	38	40	44	36	37	37
N.S.	1	1.00	1.00	0.93	0.98	1.07	0.88	0.90	0.90
time (sec)	N/A	0.033	0.009	0.375	0.270	1.514	0.181	1.325	0.086


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	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	0.023	0.032	0.419	0.488	1.889	0.206	0.957	0.120


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	51	51	46	48	51	70	46	52	47
N.S.	1	1.00	0.90	0.94	1.00	1.37	0.90	1.02	0.92
time (sec)	N/A	0.040	0.021	0.371	0.274	1.483	0.208	1.201	0.159


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	70	70	70	62	63	210	114	62	63
N.S.	1	1.00	1.00	0.89	0.90	3.00	1.63	0.89	0.90
time (sec)	N/A	0.048	0.023	0.405	0.487	1.866	0.252	1.625	0.129


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	73	73	64	76	76	117	70	80	78
N.S.	1	1.00	0.88	1.04	1.04	1.60	0.96	1.10	1.07
time (sec)	N/A	0.057	0.036	0.383	0.277	2.019	0.493	1.410	0.147


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	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	0.084	0.049	0.474	0.498	2.164	0.302	1.681	0.137


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	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	0.074	0.066	0.447	0.276	2.102	0.558	0.849	0.138


Problem 72	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	111	111	112	99	119	308	218	112	104
N.S.	1	1.00	1.01	0.89	1.07	2.77	1.96	1.01	0.94
time (sec)	N/A	0.135	0.061	0.424	0.501	1.371	0.339	0.775	0.158


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	140	140	133	119	147	416	252	138	177
N.S.	1	1.00	0.95	0.85	1.05	2.97	1.80	0.99	1.26
time (sec)	N/A	0.155	0.070	0.424	0.499	2.234	0.765	0.829	0.120


Problem 74	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	94	102	116	179	119	132	118
N.S.	1	1.00	0.85	0.92	1.05	1.61	1.07	1.19	1.06
time (sec)	N/A	0.098	0.043	0.429	0.280	1.457	0.802	0.833	0.118


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	118	118	113	95	120	358	214	111	138
N.S.	1	1.00	0.96	0.81	1.02	3.03	1.81	0.94	1.17
time (sec)	N/A	0.109	0.058	0.417	0.485	2.379	0.705	0.700	0.078


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	89	89	92	85	94	142	94	93	95
N.S.	1	1.00	1.03	0.96	1.06	1.60	1.06	1.04	1.07
time (sec)	N/A	0.071	0.026	0.395	0.286	1.195	0.707	0.823	0.091


Problem 77	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	95	95	92	77	94	328	194	80	92
N.S.	1	1.00	0.97	0.81	0.99	3.45	2.04	0.84	0.97
time (sec)	N/A	0.072	0.049	0.409	0.503	2.070	0.589	0.989	0.152


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	64	61	72	89	70	55	70
N.S.	1	1.00	0.96	0.91	1.07	1.33	1.04	0.82	1.04
time (sec)	N/A	0.054	0.017	0.393	0.267	1.629	0.489	1.394	0.108


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	90	90	83	76	92	301	155	78	82
N.S.	1	1.00	0.92	0.84	1.02	3.34	1.72	0.87	0.91
time (sec)	N/A	0.048	0.057	0.436	0.501	2.268	0.385	1.343	0.146


Problem 80	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	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	0.020	0.010	0.366	0.274	1.261	0.265	1.122	0.076


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	92	92	84	77	92	300	150	78	82
N.S.	1	1.00	0.91	0.84	1.00	3.26	1.63	0.85	0.89
time (sec)	N/A	0.031	0.041	0.481	0.500	2.115	0.294	2.368	0.140


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	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	0.049	0.033	0.380	0.278	1.684	0.291	1.713	0.178


Problem 83	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	96	96	96	82	96	324	194	82	113
N.S.	1	1.00	1.00	0.85	1.00	3.38	2.02	0.85	1.18
time (sec)	N/A	0.076	0.042	0.405	0.503	1.653	0.350	1.053	0.176


Problem 84	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	97	97	86	102	109	197	107	105	107
N.S.	1	1.00	0.89	1.05	1.12	2.03	1.10	1.08	1.10
time (sec)	N/A	0.086	0.043	0.385	0.270	1.795	0.586	1.356	0.152


Problem 85	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	B	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	117	117	119	98	128	368	226	108	114
N.S.	1	1.00	1.02	0.84	1.09	3.15	1.93	0.92	0.97
time (sec)	N/A	0.123	0.049	0.428	0.486	1.276	0.399	1.016	0.179


Problem 86	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	121	121	108	123	137	229	136	132	131
N.S.	1	1.00	0.89	1.02	1.13	1.89	1.12	1.09	1.08
time (sec)	N/A	0.094	0.055	0.391	0.291	1.594	0.650	1.081	0.174


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	140	140	140	119	154	426	260	135	135
N.S.	1	1.00	1.00	0.85	1.10	3.04	1.86	0.96	0.96
time (sec)	N/A	0.224	0.051	0.408	0.502	1.492	0.440	0.939	0.195


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	148	148	135	143	170	267	165	201	155
N.S.	1	1.00	0.91	0.97	1.15	1.80	1.11	1.36	1.05
time (sec)	N/A	0.125	0.085	0.388	0.289	1.380	0.698	0.839	0.185


Problem 89	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	F	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	218	218	187	290	321	368	0	245	289
N.S.	1	1.00	0.86	1.33	1.47	1.69	0.00	1.12	1.33
time (sec)	N/A	0.246	0.289	0.410	0.298	1.922	0.000	1.044	1.470


Problem 90	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	F	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	181	181	168	248	273	321	0	211	233
N.S.	1	1.00	0.93	1.37	1.51	1.77	0.00	1.17	1.29
time (sec)	N/A	0.217	0.253	0.382	0.285	2.723	0.000	0.770	0.886


Problem 91	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	B	A	F	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	125	125	145	206	225	272	0	177	177
N.S.	1	1.00	1.16	1.65	1.80	2.18	0.00	1.42	1.42
time (sec)	N/A	0.133	0.204	0.384	0.293	1.823	0.000	1.181	0.736


Problem 92	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	F	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	107	107	123	164	177	223	0	140	140
N.S.	1	1.00	1.15	1.53	1.65	2.08	0.00	1.31	1.31
time (sec)	N/A	0.102	0.150	0.393	0.287	1.858	0.000	0.899	0.752


Problem 93	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	F	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	100	100	97	124	128	172	0	103	117
N.S.	1	1.00	0.97	1.24	1.28	1.72	0.00	1.03	1.17
time (sec)	N/A	0.130	0.111	0.432	0.288	2.039	0.000	1.129	0.609


Problem 94	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	F	A	F
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	97	97	90	132	105	161	0	92	-1
N.S.	1	1.00	0.93	1.36	1.08	1.66	0.00	0.95	-0.01
time (sec)	N/A	0.135	0.119	0.379	0.278	1.801	0.000	1.695	0.000


Problem 95	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	F	B	F
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	80	80	99	109	96	160	0	163	-1
N.S.	1	1.00	1.24	1.36	1.20	2.00	0.00	2.04	-0.01
time (sec)	N/A	0.125	0.105	0.390	0.281	1.212	0.000	1.291	0.000


Problem 96	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	B	A	F	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	61	61	44	48	111	59	0	250	113
N.S.	1	1.00	0.72	0.79	1.82	0.97	0.00	4.10	1.85
time (sec)	N/A	0.102	0.097	0.388	0.298	2.784	0.000	1.080	0.469


Problem 97	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	F	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	96	96	66	70	161	85	0	310	160
N.S.	1	1.00	0.69	0.73	1.68	0.89	0.00	3.23	1.67
time (sec)	N/A	0.138	0.117	0.383	0.278	1.820	0.000	1.411	0.676


Problem 98	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	F	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	133	133	88	94	209	109	0	370	210
N.S.	1	1.00	0.66	0.71	1.57	0.82	0.00	2.78	1.58
time (sec)	N/A	0.160	0.147	0.380	0.288	1.289	0.000	1.742	1.039


Problem 99	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	F	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	170	170	110	118	257	133	0	430	260
N.S.	1	1.00	0.65	0.69	1.51	0.78	0.00	2.53	1.53
time (sec)	N/A	0.198	0.164	0.396	0.304	1.743	0.000	2.196	1.406


Problem 100	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad

grade	A	A	A	A	A	A	F	A	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD
size	131	131	82	91	106	106	0	140	103
N.S.	1	1.00	0.63	0.69	0.81	0.81	0.00	1.07	0.79
time (sec)	N/A	0.145	0.055	0.406	0.289	1.335	0.000	0.627	0.252

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