Detailed conclusion table per each integral for all CAS systems

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	Mathics

grade	A	A	A	A	A	A	B	A	B	A
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	40	40	23	29	23	36	116	40	23	31
N.S.	1	1.00	0.58	0.72	0.58	0.90	2.90	1.00	0.58	0.78
time (sec)	N/A	0.005	0.020	0.117	0.242	0.313	0.340	0.004	0.348	2.907


Problem 2	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad	Mathics

grade	A	A	A	A	A	B	A	B	B	B
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	24	24	24	19	35	40	20	51	18	29
N.S.	1	1.00	1.00	0.79	1.46	1.67	0.83	2.12	0.75	1.21
time (sec)	N/A	0.014	0.040	0.026	0.352	0.317	0.077	0.001	0.461	1.951


Problem 3	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad	Mathics

grade	A	A	A	A	F(-2)	A	A	A	B	C
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	42	42	41	36	0	137	144	72	38	228
N.S.	1	1.00	0.98	0.86	0.00	3.26	3.43	1.71	0.90	5.43
time (sec)	N/A	0.029	0.023	0.044	0.000	0.333	1.824	0.001	0.588	3.771


Problem 4	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad	Mathics

grade	A	A	B	A	A	B	A	A	B	A
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	15	15	34	12	15	23	10	15	11	11
N.S.	1	1.00	2.27	0.80	1.00	1.53	0.67	1.00	0.73	0.73
time (sec)	N/A	0.009	0.014	0.083	0.245	0.331	0.126	0.003	0.081	1.751


Problem 5	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad	Mathics

grade	A	A	A	A	A	A	A	A	B	A
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	21	21	39	20	29	21	19	28	11	19
N.S.	1	1.00	1.86	0.95	1.38	1.00	0.90	1.33	0.52	0.90
time (sec)	N/A	0.008	0.012	0.076	0.242	0.325	0.128	0.003	0.409	1.881


Problem 6	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad	Mathics

grade	A	A	B	A	A	A	A	A	B	A
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	12	21	26	11	15	20	8	13	10	10
N.S.	1	1.75	2.17	0.92	1.25	1.67	0.67	1.08	0.83	0.83
time (sec)	N/A	0.008	0.022	0.075	0.248	0.326	0.217	0.002	0.359	1.740


Problem 7	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad	Mathics

grade	A	A	A	A	A	A	A	A	B	C
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	43	43	24	20	23	39	42	62	21	31
N.S.	1	1.00	0.56	0.47	0.53	0.91	0.98	1.44	0.49	0.72
time (sec)	N/A	0.026	0.019	0.084	0.335	0.322	0.213	0.001	0.048	2.214


Problem 8	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad	Mathics

grade	A	A	A	A	A	A	A	A	B	A
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	30	30	31	35	34	38	32	42	28	35
N.S.	1	1.00	1.03	1.17	1.13	1.27	1.07	1.40	0.93	1.17
time (sec)	N/A	0.008	0.004	0.023	0.249	0.304	0.090	0.003	0.398	1.949

2.2 Detailed conclusion table per each integral for all CAS systems