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	A	A	B	C
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	16	16	11	10	13	15	22	20	18	22
N.S.	1	1.00	0.69	0.62	0.81	0.94	1.38	1.25	1.12	1.38
time (sec)	N/A	0.010	0.012	0.025	0.365	0.312	0.119	0.001	0.266	1.919


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

grade	A	A	B	A	F	B	F	A	B	F(-2)
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	19	38	46	13	0	48	0	21	12	0
N.S.	1	2.00	2.42	0.68	0.00	2.53	0.00	1.11	0.63	0.00
time (sec)	N/A	1.978	0.081	0.129	0.000	0.324	0.000	0.027	0.307	0.000


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

grade	A	B	A	A	B	B	A	A	B	F(-2)
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	19	42	19	35	53	43	32	49	32	0
N.S.	1	2.21	1.00	1.84	2.79	2.26	1.68	2.58	1.68	0.00
time (sec)	N/A	0.404	0.064	0.128	0.424	0.326	0.476	0.010	0.848	0.000


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

grade	A	A	A	A	B	B	F	A	B	F(-2)
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	19	31	19	26	39	41	0	36	23	0
N.S.	1	1.63	1.00	1.37	2.05	2.16	0.00	1.89	1.21	0.00
time (sec)	N/A	1.283	0.113	0.143	0.362	0.336	0.000	0.011	0.549	0.000


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

grade	A	F	A	A	A	A	F(-1)	A	B	F(-1)
veriﬁed	N/A	N/A	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	43	0	61	17	63	31	0	20	27	0
N.S.	1	0.00	1.42	0.40	1.47	0.72	0.00	0.47	0.63	0.00
time (sec)	N/A	0.524	0.082	0.092	1.761	0.330	0.000	0.007	0.304	0.000


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

grade	A	F	B	A	B	A	F(-1)	A	B	F(-1)
veriﬁed	N/A	N/A	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	25	0	63	19	63	37	0	20	25	0
N.S.	1	0.00	2.52	0.76	2.52	1.48	0.00	0.80	1.00	0.00
time (sec)	N/A	0.496	0.087	0.076	1.664	0.327	0.000	0.007	0.303	0.000


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

grade	A	A	B	A	A	A	B	A	B	C
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	14	14	79	12	15	13	27	32	20	24
N.S.	1	1.00	5.64	0.86	1.07	0.93	1.93	2.29	1.43	1.71
time (sec)	N/A	0.009	0.012	0.032	0.360	0.328	0.130	0.001	0.221	2.173


Problem 8	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	34	34	15	13	12	31	60	54	24	39
N.S.	1	1.00	0.44	0.38	0.35	0.91	1.76	1.59	0.71	1.15
time (sec)	N/A	0.011	0.015	0.038	0.354	0.314	0.264	0.001	0.209	2.815


Problem 9	Optimal	Rubi	MMA	Maple	Maxima	Fricas	Sympy	Giac	Mupad	Mathics

grade	A	A	A	A	F(-2)	A	A	A	B	F(-1)
veriﬁed	N/A	Yes	Yes	TBD	TBD	TBD	TBD	TBD	TBD	TBD
size	54	54	50	53	0	364	2453	82	68	0
N.S.	1	1.00	0.93	0.98	0.00	6.74	45.43	1.52	1.26	0.00
time (sec)	N/A	0.045	0.057	0.110	0.000	0.354	112.259	0.003	0.319	0.000

2.2 Detailed conclusion table per each integral for all CAS systems