Chapter 1
Introduction

This report gives the result of running the computer algebra independent integration problems.

The listing of the problems used by this report are

1. MIT_bee_integration_problems.zip
2. handbook_integration_problems.zip
3. CAS_integration_tests_2023_Mathematica_format.m
4. CAS_integration_tests_2023_Maple_and_Mupad_format.zip
5. CAS_integration_tests_2023_SAGE_format.zip
6. CAS_integration_tests_2023_Sympy_format.zip

The Mathematica/Rubi format file above can be read into Mathematica using the following commands

SetDirectory[NotebookDirectory[]] (*where the above .m file was save*) 
lst=First@ReadList["CAS_integration_tests_2023_Mathematica_format.m",Expression]; 
Length[lst]
 

lst[[1]] will be the first integrand,var and lst[[2]] will be the second one and so on.

The Rubi test suite files were downloaded from rulebasedintegration.org.

The current number of problems in this test suite is [106812].

1.1 Listing of CAS systems tested

The following are the CAS systems tested:

1. Mathematica 14 (January 9, 2024) on windows 10 pro.
2. Rubi 4.17.3 (Sept 25, 2023) on Mathematica 14 on windows 10m pro.
3. Maple 2024 (March 1, 2024) on windows 10 pro.
4. Maxima 5.47 (June 1, 2023) using Lisp SBCL 2.4.0 on Linux Manjaro 23.1.2 KDE via sagemath 10.3.
5. FriCAS 1.3.10 built with sbcl 2.3.11 (January 10, 2024) on Linux Manjaro 23.1.2 KDE via sagemath 10.3.
6. Giac/Xcas 1.9.0-99 on Linux via sagemath 10.3.
7. Sympy 1.12 using Python 3.11.6 (Nov 14 2023, 09:36:21) [GCC 13.2.1 20230801] on Linux Manjaro 23.1.2 KDE.
8. Mupad using Matlab 2021a with Symbolic Math Toolbox Version 8.7 on windows 10.
9. Reduce CSL rev 6687 (January 9, 2024) on Linux Manjaro 23.1.2 KDE.

Maxima and Fricas and Giac are called using Sagemath. This was done using Sagemath integrate command by changing the name of the algorithm to use the different CAS systems.

Sympy was run directly in Python not via sagemath.

Reduce was called directly.

1.2 Results

Important note: A number of problems in this test suite have no antiderivative in closed form. This means the antiderivative of these integrals can not be expressed in terms of elementary, special functions or Hypergeometric2F1 functions.

If a CAS returns the above integral unevaluated within the time limit, then the result is counted as passed and assigned an A grade.

However, if CAS times out, then it is assigned an F grade even if the integral is not integrable, as this implies CAS could not determine that the integral is not integrable in the time limit.

If a CAS returns an antiderivative to such an integral, it is assigned an A grade automatically and this special result is listed in the introduction section of each individual test report to make it easy to identify as this can be important result to investigate.

The results given in in the table below reflects the above.

Table 1.1: Percentage solved for each CAS

System	solved	Failed
Mathematica	% 97.367 ( 104000 )	% 2.633 ( 2812 )
Rubi	% 93.136 ( 99480 )	% 6.864 ( 7332 )
Maple	% 83.761 ( 89467 )	% 16.239 ( 17345 )
Fricas	% 77.213 ( 82473 )	% 22.787 ( 24339 )
Giac	% 57.511 ( 61429 )	% 42.489 ( 45383 )
Reduce	% 54.34 ( 58042 )	% 45.66 ( 48770 )
Mupad	% 52.841 ( 56440 )	% 47.159 ( 50372 )
Maxima	% 52.537 ( 56116 )	% 47.463 ( 50696 )
Sympy	% 42.166 ( 45038 )	% 57.834 ( 61774 )

The table below gives additional break down of the grading of quality of the antiderivatives generated by each CAS. The grading is given using the letters A,B,C and F with A being the best quality. The grading is accomplished by comparing the antiderivative generated with the optimal antiderivatives included in the test suite. The following table describes the meaning of these grades.

Table 1.2: Description of grading applied to integration result

grade	description
A	Integral was solved and antiderivative is optimal in quality and leaf size.
B	Integral was solved and antiderivative is optimal in quality but leaf size is larger than twice the optimal antiderivatives leaf size.
C	Integral was solved and antiderivative is non-optimal in quality. This can be due to one or more of the following reasons antiderivative contains a hypergeometric function and the optimal antiderivative does not. antiderivative contains a special function and the optimal antiderivative does not. antiderivative contains the imaginary unit and the optimal antiderivative does not.
F	Integral was not solved. Either the integral was returned unevaluated within the time limit, or it timed out, or CAS hanged or crashed or an exception was raised.

Grading is implemented for all CAS systems in this version except for CAS Mupad where a grade of B is automatically assigned as a place holder for all integrals it completes on time.

The following table summarizes the grading results.

Table 1.3: Antiderivative Grade distribution for each CAS

System	% A grade	% B grade	% C grade	% F grade
Rubi	84.74	2.5	2.12	6.86
Mathematica	73.46	5.21	15.02	2.63
Maple	58.11	14.06	7.21	16.24
Fricas	50.54	18.94	4.54	22.79
Giac	37.65	14.92	1.14	42.49
Maxima	36.59	10.61	1.54	47.46
Sympy	24.09	9.76	4.8	57.83
Reduce	N/A	49.91	N/A	45.66
Mupad	N/A	48.44	N/A	47.16

The following Bar chart is an illustration of the data in the above table.

The figure below compares the CAS systems for each grade level.

1.3 Time and leaf size Performance

The table below summarizes the performance of each CAS system in terms of time used and leaf size of results.

Mean size is the average leaf size produced by the CAS (before any normalization). The Normalized mean is relative to the mean size of the optimal anti-derivative given in the input files.

For example, if CAS has Normalized mean of \(3\), then the mean size of its leaf size is 3 times as large as the mean size of the optimal leaf size.

Median size is value of leaf size where half the values are larger than this and half are smaller (before any normalization). i.e. The Middle value.

Similarly the Normalized median is relative to the median leaf size of the optimal.

For example, if a CAS has Normalized median of \(1.2\), then its median is \(1.2\) as large as the median leaf size of the optimal.

Table 1.4: Time and leaf size performance for each CAS

System	Mean time (sec)	Mean size	Normalized mean	Median size	Normalized median
Maxima	0.25	774.72	238.38	69.	1.1
Rubi	0.67	165.33	1.4	106.	1.
Giac	0.9	594.73	43.61	78.	1.15
Fricas	0.94	1115.97	7.02	108.	1.37
Reduce	1.51	457.15	9.73	76.	1.31
Mathematica	2.5	369.49	2.4	85.	0.98
Maple	5.16	30161.5	336.1	89.	1.
Sympy	5.74	405.38	21.33	51.	1.12
Mupad	7.51	1442.7	10.3	66.	1.05

1.4 Performance based on number of rules Rubi used

This section shows how each CAS performed based on the number of rules Rubi needed to solve the same integral. One diagram is given for each CAS.

On the \(y\) axis is the percentage solved which Rubi itself needed the number of rules given the \(x\) axis. These plots show that as more rules are needed then most CAS system percentage of solving decreases which indicates the integral is becoming more complicated to solve.

Figure 1.1: Solving statistics per number of Rubi rules used

1.5 Performance based on number of steps Rubi used

This section shows how each CAS performed based on the number of steps Rubi needed to solve the same integral. Note that the number of steps Rubi needed can be much higher than the number of rules, as the same rule could be used more than once.

Figure 1.2: Solving statistics per number of Rubi steps used

The above diagram show that the precentage of solved intergals decreases for most CAS systems as the number of steps increases. As expected, for integrals that required less steps by Rubi, CAS systems had more success which indicates the integral was not as hard to solve. As Rubi needed more steps to solve the integral, the solved percentage decreased for most CAS systems which indicates the integral is becoming harder to solve.

1.6 Solved integrals histogram based on leaf size of result

The following shows the distribution of solved integrals for each CAS system based on leaf size of the antiderivatives produced by each CAS. It shows that most integrals solved produced leaf size less than about 100 to 150. The bin size used is \(40\).

Figure 1.3: Solved integrals based on leaf size distribution

1.7 Solved integrals histogram based on CPU time used

The following shows the distribution of solved integrals for each CAS system based on CPU time used in seconds. The bin size used is \(0.1\) second.

Figure 1.4: Solved integrals histogram based on CPU time used

1.8 Leaf size vs. CPU time used

The following shows the relation between the CPU time used to solve an integral and the leaf size of the antiderivative.

The result for Fricas, Maxima and Giac is shifted more to the right than the other CAS system due to the use of sagemath to call them, which causes an initial slight delay in the timing to start the integration due to overhead of starting a new process each time. This should also be taken into account when looking at the timing of these three CAS systems. Direct calls not using sagemath would result in faster timings, but current implementation uses sagemath as this makes testing much easier to do.

Figure 1.5: Leaf size vs. CPU time. Full range

1.9 Performance per integrand type

The following are the different integrand types the test suite contains.

1. Independent tests.
2. Algebraic Binomial problems (products involving powers of binomials and monomials).
3. Algebraic Trinomial problems (products involving powers of trinomials, binomials and monomials).
4. Miscellaneous Algebraic functions.
5. Exponentials.
6. Logarithms.
7. Trigonometric.
8. Inverse Trigonometric.
9. Hyperbolic functions.
10. Inverse Hyperbolic functions.
11. Special functions.
12. Sam Blake input files.
13. Waldek Hebisch input file.
14. MIT Bee integration.
15. Few problems from Ryzhik and Gradshteyn table of integrals handbook.

The following table gives percentage solved of each CAS per integrand type.

Table 1.5: Percentage solved per integrand type

Integrand type	#	Rubi	MMa	Maple	Maxima	Fricas	Sympy	Giac	Reduce	Mupad
Independent tests	1968	98.88	99.24	94.51	82.83	95.68	76.73	87.6	77.29	82.72
Algebraic Binomial	25785	97.84	97.91	77.25	48.43	73.73	53.96	57.9	58.89	49.76
Algebraic Trinomial	13812	94.98	95.71	86.61	41.33	78.63	36.45	62.83	61.96	47.39
Algebraic Miscellaneous	2432	95.11	96.63	84.46	47.62	80.43	51.23	52.59	62.13	57.44
Exponentials	5375	98.83	97.51	77.67	49.66	82.9	33.04	52.91	67.83	53.95
Logarithms	3237	96.2	97.25	65.31	53.72	58.02	35.06	46.74	47.76	41.74
Trigonometric	23422	98.39	97.84	85.27	49.	79.55	17.16	50.54	35.58	49.76
Inverse Trigonometric	5082	99.35	98.58	89.81	35.58	46.03	37.01	48.15	39.14	35.36
Hyperbolic	5513	97.08	98.4	82.42	62.6	90.15	24.42	64.28	53.22	54.58
Inverse Hyperbolic	4349	99.63	98.92	82.69	45.5	49.9	24.88	30.35	29.8	30.83
Special functions	1738	95.51	93.1	71.17	35.5	62.6	40.85	25.2	28.19	35.67
Sam Blake files	3265	63.37	94.09	83.92	40.18	74.06	36.81	42.51	36.45	49.25
Waldek Hebisch file	10335	62.56	96.81	99.17	93.19	99.92	94.57	87.35	91.16	90.15
MIT Bee integration	321	94.7	99.38	95.95	92.52	95.95	81.93	92.21	81.93	90.03
Table of integrals	163	100.	100.	97.55	92.64	100.	88.34	100.	96.32	92.64

In addition to the above table, for each type of integrand listed above, 3D chart is made which shows how each CAS performed on that specific integrand type.

These charts and the table above can be used to show where each CAS relative strength or weakness in the area of integration.

1.10 Maximum leaf size ratio for each CAS against the optimal result

The following table gives the largest ratio found in each test file, between each CAS antiderivative and the optimal antiderivative.

For each test input file, the problem with the largest ratio \(\frac {\text {CAS leaf size}}{\text {Optimal leaf size}}\) is recorded with the corresponding problem number.

In each column in the table below, the first number is the maximum leaf size ratio, and the number that follows inside the parentheses is the problem number in that specific file where this maximum ratio was found. This ratio is determined only when CAS solved the the problem and also when an optimal antiderivative is known.

If it happens that a CAS was not able to solve all the integrals in the input test file, or if it was not possible to obtain leaf size for the CAS result for all the problems in the file, then a zero is used for the ratio and -1 is used for the problem number.

This makes it easier to locate the problem. In the future, a direct link will be added as well.

#	Rubi	Mathematica	Maple	Maxima	FriCAS	Sympy	Giac	Mupad	Reduce
1	1.8 (133)	3.9 (50)	4.5 (170)	3.8 (169)	4. (45)	4789.3 (145)	4.2 (164)	0. (-1)	5.7 (61)
2	1.9 (26)	5. (26)	3.6 (17)	113.1 (21)	14.3 (13)	16.8 (5)	4.6 (2)	0. (-1)	1.8 (2)
3	1.1 (4)	1.1 (14)	2. (6)	11.1 (7)	2. (8)	1.9 (5)	1.9 (5)	0. (-1)	2.4 (1)
4	1.5 (72)	2. (11)	1.8 (11)	1.7 (11)	2.2 (20)	1.5 (69)	3.1 (67)	0. (-1)	3.9 (20)
5	6.8 (5)	14.3 (13)	11.7 (8)	29.7 (8)	5.5 (43)	4.8 (40)	5.3 (1)	0. (-1)	3.4 (30)
6	2. (225)	54.7 (278)	11.9 (280)	8.1 (280)	7.7 (280)	39.8 (123)	19.5 (141)	0. (-1)	8.4 (278)
7	1. (1)	1.4 (3)	2.2 (4)	1.9 (1)	1.4 (7)	0.8 (4)	2.3 (5)	0. (-1)	1.5 (7)
8	2.2 (3)	5.6 (7)	1.8 (3)	2.8 (3)	6.7 (9)	45.4 (9)	1.9 (3)	0. (-1)	1.8 (3)
9	2.9 (70)	5.3 (31)	4.6 (70)	6.5 (11)	5. (42)	26.4 (71)	5.8 (40)	0. (-1)	7.2 (31)
10	2.2 (112)	6.8 (316)	3.5 (323)	12.1 (328)	4.2 (341)	4789.3 (251)	15. (328)	0. (-1)	5.7 (14)
11	4. (604)	5.9 (446)	142.8 (417)	36.9 (399)	93.4 (137)	124.9 (217)	27.9 (625)	0. (-1)	9.9 (197)
12	7.7 (82)	5.4 (54)	16.4 (55)	2.7 (2)	13.4 (59)	43. (17)	6.6 (50)	0. (-1)	19.9 (49)
13	1.8 (6)	2.3 (4)	1.2 (8)	1.5 (2)	3.3 (3)	3.4 (3)	1.5 (2)	0. (-1)	1.8 (8)
14	1. (3)	1.3 (38)	2. (1)	1.7 (37)	4.5 (97)	11.7 (97)	19.3 (97)	0. (-1)	4.6 (97)
15	7.1 (798)	527.7 (115)	438.1 (115)	438.1 (115)	10.9 (185)	522.8 (115)	438.1 (115)	0. (-1)	438. (115)
16	1.7 (135)	10. (114)	13.5 (114)	8.6 (102)	11. (114)	36.1 (78)	6.5 (114)	0. (-1)	7. (114)
17	5.1 (641)	23.8 (117)	27.7 (117)	32.9 (117)	429.1 (673)	36.9 (754)	34. (117)	0. (-1)	34.6 (117)
18	1.5 (196)	9. (141)	9.7 (141)	10.1 (141)	10.1 (141)	53.8 (351)	10.1 (141)	0. (-1)	10.1 (141)
19	4.1 (141)	10. (269)	15.5 (281)	7. (223)	11. (269)	84.5 (306)	12.6 (97)	0. (-1)	8.5 (281)
20	2.2 (436)	15.3 (254)	10. (411)	6.3 (3)	13.8 (142)	63. (549)	46.7 (434)	0. (-1)	16.6 (362)
21	1.5 (264)	16.5 (91)	22. (91)	21.8 (91)	21.8 (91)	76.7 (230)	25.9 (91)	0. (-1)	13.5 (91)
22	2.3 (1492)	4.9 (1487)	19.7 (1188)	22.2 (480)	19.8 (1249)	76.7 (714)	28.1 (991)	0. (-1)	85.2 (480)
23	1.8 (177)	17.5 (104)	11.4 (195)	2. (159)	40.4 (102)	9.5 (237)	17.3 (205)	0. (-1)	44.7 (149)
24	6. (102)	10.4 (104)	32.1 (16)	2.8 (130)	12.7 (14)	49.2 (130)	15.8 (27)	0. (-1)	14.5 (25)
25	1. (1)	1.6 (1)	2.5 (30)	1.9 (29)	3.2 (30)	30.6 (30)	5.9 (30)	0. (-1)	3.1 (30)
26	1.5 (181)	1.9 (126)	13.1 (126)	4. (174)	9.7 (100)	143.6 (174)	19.9 (174)	0. (-1)	8.1 (174)
27	1.6 (12)	9.3 (88)	24.4 (82)	1.5 (22)	10.1 (81)	5.1 (4)	37. (75)	0. (-1)	53.4 (51)
28	1.6 (37)	36.4 (38)	5. (9)	1.7 (16)	2.4 (3)	0. (-1)	1.9 (16)	0. (-1)	7.1 (16)
29	1.3 (106)	3.8 (27)	1.5 (30)	4.8 (30)	4.1 (29)	30.6 (29)	2.9 (53)	0. (-1)	3.1 (17)
30	8.2 (713)	6.9 (712)	5.3 (196)	10. (196)	10. (196)	55.3 (538)	8. (444)	0. (-1)	13.7 (712)
31	1547. (517)	655. (517)	18. (357)	6.5 (302)	16.1 (42)	10.2 (24)	7.5 (302)	0. (-1)	16.8 (117)
32	15.5 (1368)	17.9 (996)	8.3 (1408)	8. (491)	16.3 (823)	46.9 (879)	13.9 (1260)	0. (-1)	39.2 (1037)
33	5.1 (307)	8.3 (569)	22.5 (50)	2.2 (364)	19.1 (373)	4.5 (234)	19.9 (336)	0. (-1)	43. (353)
34	3.1 (236)	3.2 (260)	10.4 (15)	2. (15)	7. (15)	53. (15)	13.8 (15)	0. (-1)	6.3 (15)
35	3.8 (97)	3.8 (97)	2.3 (73)	3.8 (97)	3.8 (97)	43.7 (107)	3.9 (73)	0. (-1)	5.2 (106)
36	1.6 (4)	1.1 (104)	6.5 (252)	3.4 (240)	11.7 (126)	48.7 (11)	9.3 (252)	0. (-1)	5.9 (136)
37	3.2 (45)	3.7 (24)	2.2 (52)	1.9 (57)	10.8 (8)	1.7 (4)	4.8 (8)	0. (-1)	8.2 (7)
38	2.3 (25)	6.3 (8)	12.2 (13)	0. (-1)	0. (-1)	0. (-1)	7.2 (4)	0. (-1)	25.8 (7)
39	1.7 (8)	2. (7)	1.5 (14)	0. (-1)	0. (-1)	0. (-1)	0. (-1)	0. (-1)	0. (-1)
40	1.2 (30)	284.1 (30)	1.4 (35)	1.6 (24)	4.7 (26)	20.1 (30)	1.1 (9)	0. (-1)	1.8 (8)
41	1.5 (5)	1.9 (8)	3. (22)	3.8 (8)	2.5 (32)	20.1 (37)	3.2 (8)	0. (-1)	2.8 (7)
42	2. (35)	4.6 (36)	4.1 (151)	2.9 (95)	3754.9 (4)	35.5 (163)	3.1 (163)	0. (-1)	3.6 (139)
43	1.2 (447)	6.8 (86)	6.8 (437)	4.7 (96)	5.6 (86)	40.5 (444)	8.4 (437)	0. (-1)	6.8 (437)
44	2.4 (307)	2.7 (34)	3. (258)	4.1 (402)	3.5 (103)	23. (687)	5.3 (193)	0. (-1)	12.6 (333)
45	15.7 (204)	4.1 (245)	2.1 (233)	4.1 (426)	3.5 (69)	12.2 (499)	3.4 (496)	0. (-1)	12.6 (284)
46	1.5 (520)	6. (55)	7.5 (511)	6.1 (45)	60.2 (569)	84.8 (163)	11.5 (169)	0. (-1)	8.9 (540)
47	8.4 (604)	10. (448)	13.7 (447)	13.2 (176)	11.3 (447)	146.8 (156)	11.3 (447)	0. (-1)	11.2 (447)
48	1.3 (110)	13.4 (112)	15.7 (129)	5.9 (42)	38.1 (122)	41.4 (30)	28.5 (12)	0. (-1)	26.4 (84)
49	1.7 (20)	1.7 (5)	1.2 (14)	2.2 (13)	2.7 (13)	2.2 (26)	9.6 (66)	0. (-1)	2.6 (42)
50	1.9 (182)	13.7 (5)	14.2 (51)	4.1 (80)	5.3 (83)	12.9 (71)	1.7 (35)	0. (-1)	4.3 (28)
51	1.5 (51)	6.2 (78)	2.2 (106)	2.3 (91)	11.5 (27)	7.8 (83)	2.4 (21)	0. (-1)	6.4 (21)
52	1.4 (58)	48.5 (142)	6.7 (127)	2.1 (27)	15. (45)	38. (73)	6.1 (75)	0. (-1)	17.4 (45)
53	1.1 (6)	3.4 (5)	0. (-1)	0. (-1)	1.9 (1)	0. (-1)	0. (-1)	0. (-1)	0. (-1)
54	2.1 (890)	7.7 (672)	15.7 (671)	2.8 (25)	41.3 (630)	36.6 (377)	9. (377)	0. (-1)	4.1 (377)
55	3.6 (274)	4.8 (193)	1.6 (112)	2.1 (75)	8.5 (216)	12. (204)	3.1 (228)	0. (-1)	82.7 (257)
56	8.8 (531)	13.6 (239)	11. (467)	29.1 (476)	11. (464)	112.6 (403)	53. (403)	0. (-1)	10.9 (464)
57	1.2 (6)	4.6 (43)	2.9 (37)	1.6 (16)	2.1 (36)	35.2 (43)	4.9 (3)	0. (-1)	3.4 (39)
58	1.4 (5)	29.7 (2)	6.2 (3)	0. (-1)	4.4 (6)	0. (-1)	2.1 (6)	0. (-1)	2.5 (6)
59	1.6 (83)	2. (9)	48.5 (33)	2.4 (33)	27. (33)	847.2 (33)	332.3 (33)	0. (-1)	29.8 (33)
60	1.2 (6)	4.6 (43)	2.9 (37)	1.6 (16)	2.1 (36)	35.2 (43)	4.9 (3)	0. (-1)	3.4 (39)
61	1.4 (100)	3.2 (22)	5. (21)	10. (37)	73.5 (25)	5.9 (39)	2.4 (33)	0. (-1)	3.2 (8)
62	5.9 (16)	1.9 (62)	2.3 (14)	3.1 (83)	4003.6 (100)	13. (45)	2.6 (37)	0. (-1)	6.1 (110)
63	5.8 (50)	2.1 (32)	1.4 (54)	1.7 (32)	153.2 (5)	29.7 (60)	4.7 (54)	0. (-1)	5.8 (29)
64	1.2 (271)	2. (166)	1.5 (256)	1.2 (205)	60.2 (205)	3.1 (203)	2. (32)	0. (-1)	4.5 (61)
65	1.5 (108)	1.6 (9)	1.3 (36)	1.3 (9)	1826.9 (9)	2. (13)	2.1 (9)	0. (-1)	5.1 (17)
66	1.2 (1)	1.3 (22)	3.1 (36)	2.1 (4)	5. (22)	5.6 (13)	8.1 (35)	0. (-1)	3.2 (8)
67	12.2 (5)	2.2 (4)	2.7 (1)	2.1 (5)	2. (5)	0. (-1)	4.2 (5)	0. (-1)	1.8 (5)
68	1.2 (2)	1. (1)	1.5 (3)	0.9 (1)	1.6 (1)	0.9 (1)	0.9 (1)	0. (-1)	2.3 (1)
69	0. (-1)	1. (1)	2.6 (1)	2.5 (1)	2.4 (1)	0. (-1)	8.2 (1)	0. (-1)	2.6 (1)
70	1.6 (381)	3.2 (341)	8.8 (149)	16.3 (71)	5. (150)	23.4 (336)	6.6 (336)	0. (-1)	7.6 (71)
71	1.7 (178)	4.7 (250)	96.2 (265)	28.7 (265)	64.3 (222)	71.7 (392)	9.9 (264)	0. (-1)	24.5 (290)
72	1053. (573)	92. (573)	13.2 (311)	2.5 (7)	6.2 (913)	141. (1230)	8. (1107)	0. (-1)	3.9 (1082)
73	7.2 (1618)	3.7 (1251)	170. (1152)	30.6 (1152)	54.5 (684)	260.1 (418)	11.5 (1772)	0. (-1)	26.5 (739)
74	1.7 (175)	2.4 (114)	4.9 (162)	20.5 (166)	3.9 (113)	10.5 (188)	6.5 (36)	0. (-1)	5.7 (36)
75	3.8 (354)	2.7 (204)	6.5 (203)	2.3 (203)	6.3 (203)	104.9 (203)	10.8 (203)	0. (-1)	7.5 (203)
76	1.6 (16)	5.7 (13)	7.5 (20)	3.1 (25)	8.6 (20)	12.8 (25)	4. (25)	0. (-1)	5.9 (9)
77	4.4 (159)	59.2 (275)	33.5 (49)	2.5 (207)	783. (158)	27.1 (7)	23.1 (284)	0. (-1)	39.1 (91)
78	1.8 (32)	3.2 (29)	5.4 (9)	3.4 (34)	238.5 (12)	3.3 (34)	41.7 (103)	0. (-1)	2.2 (61)
79	20.7 (56)	4.8 (36)	2.4 (126)	1.8 (36)	2.5 (103)	10.2 (126)	5.8 (28)	0. (-1)	2.4 (126)
80	3.8 (205)	2.9 (71)	4.4 (435)	4.9 (31)	4.2 (435)	44.7 (435)	10.8 (435)	0. (-1)	4.7 (435)
81	2.9 (234)	6.4 (231)	5.6 (231)	7.1 (11)	13.8 (120)	78.7 (238)	9.5 (238)	0. (-1)	12. (163)
82	1.5 (260)	1.8 (26)	10. (364)	4.5 (137)	8. (364)	128. (364)	23.1 (364)	0. (-1)	10.3 (364)
83	6.4 (121)	17. (49)	3.1 (211)	3.4 (89)	9.7 (47)	3.2 (70)	8.3 (106)	0. (-1)	12.3 (47)
84	1.4 (8)	1. (1)	1.6 (10)	1.5 (1)	2.2 (1)	0. (-1)	1.7 (9)	0. (-1)	1. (8)
85	2.8 (11)	3.5 (5)	1.7 (21)	0. (-1)	7.7 (9)	0. (-1)	6.8 (12)	0. (-1)	5.1 (12)
86	1.4 (342)	10. (306)	12.5 (309)	11.2 (327)	16.3 (176)	166.2 (416)	2304.6 (313)	0. (-1)	11.7 (416)
87	1.4 (121)	6.4 (283)	4.9 (273)	3.2 (179)	4.1 (123)	21.6 (273)	6.3 (273)	0. (-1)	4.9 (273)
88	17.5 (140)	6.2 (135)	3.1 (1)	6.3 (22)	7.9 (22)	9.7 (107)	3.1 (135)	0. (-1)	12. (22)
89	2. (163)	6.4 (51)	4.6 (18)	6.9 (18)	12.6 (264)	19.6 (77)	12.1 (281)	0. (-1)	18.6 (281)
90	1.3 (199)	9.7 (100)	11.2 (100)	34.4 (399)	14.3 (200)	137.9 (411)	37.7 (5)	0. (-1)	13.7 (100)
91	22.1 (331)	3.3 (36)	26.6 (265)	14. (382)	8.9 (382)	55.8 (235)	30.1 (273)	0. (-1)	10.8 (69)
92	12.9 (698)	13.8 (216)	25.5 (602)	17.5 (371)	67.3 (544)	239.3 (761)	35.4 (592)	0. (-1)	76.1 (371)
93	3.3 (116)	5.8 (78)	21.4 (45)	6.4 (56)	13.5 (54)	2.3 (18)	3.5 (56)	0. (-1)	23.4 (54)
94	12.5 (16)	6.9 (16)	7.9 (16)	11.9 (16)	46.2 (128)	123.8 (295)	134.1 (140)	0. (-1)	39.6 (183)
95	4.2 (140)	9. (7)	73.7 (109)	2.9 (156)	34.7 (108)	104.4 (156)	58.2 (12)	0. (-1)	10.2 (156)
96	1.7 (131)	6.1 (77)	115.8 (60)	0.8 (87)	7.1 (76)	5.8 (28)	21.7 (127)	0. (-1)	16.5 (136)
97	1.5 (51)	2.9 (249)	40.4 (274)	6.1 (163)	16. (294)	58.7 (159)	79. (193)	0. (-1)	92.7 (281)
98	1.3 (243)	2.8 (228)	4.4 (162)	2.5 (172)	27.6 (91)	1537.6 (88)	16.5 (99)	0. (-1)	41.2 (167)
99	3. (27)	10.7 (87)	43.1 (85)	5.8 (326)	33.1 (51)	133.2 (312)	41. (85)	0. (-1)	47.5 (34)
100	1.3 (74)	4.5 (108)	4.6 (167)	3.2 (167)	18.2 (85)	122.2 (167)	13.8 (167)	0. (-1)	19.5 (125)
101	3.9 (1104)	26.2 (898)	322.2 (913)	50.9 (2)	78.6 (590)	973.9 (147)	83.4 (1001)	0. (-1)	60.2 (977)
102	18.2 (731)	66.5 (648)	116.2 (666)	14.7 (731)	62. (661)	308. (771)	197.8 (739)	0. (-1)	31.2 (388)
103	18.2 (814)	68.4 (556)	454.7 (372)	14.7 (814)	68.7 (359)	308. (854)	197.8 (822)	0. (-1)	92.7 (772)
104	1.2 (5)	1.1 (10)	3.3 (5)	1. (4)	6.3 (5)	3.9 (8)	2. (6)	0. (-1)	2.5 (2)
105	5.5 (26)	10.3 (37)	24.4 (144)	6.4 (26)	30.2 (150)	11. (23)	92.3 (39)	0. (-1)	84.8 (39)
106	1.4 (55)	9.5 (111)	14650.2 (88)	89. (201)	89. (201)	135.3 (194)	123.4 (201)	0. (-1)	147.9 (85)
107	5.5 (37)	4.9 (36)	8.8 (36)	3. (21)	10.2 (10)	10.1 (26)	8.5 (36)	0. (-1)	14.6 (34)
108	1.8 (57)	9.1 (141)	226.5 (100)	79.6 (100)	7.4 (114)	12.4 (117)	23. (98)	0. (-1)	25.9 (112)
109	228. (1)	259. (1)	669. (1)	89. (111)	6132. (1)	232.5 (203)	123.4 (111)	0. (-1)	6499. (1)
110	3.7 (259)	12.2 (230)	5.9 (1)	5.4 (160)	21.6 (1)	8.7 (74)	6.2 (73)	0. (-1)	25.5 (118)
111	2.5 (41)	3.9 (50)	7.7 (29)	2.2 (32)	15.9 (29)	10.1 (33)	1.8 (29)	0. (-1)	9.6 (29)
112	3.5 (25)	7130. (1)	1903. (1)	2.3 (34)	8.5 (18)	1.4 (41)	31.2 (33)	0. (-1)	93.5 (41)
113	1.2 (8)	2.8 (7)	1.3 (23)	4.7 (23)	1.9 (23)	1.1 (1)	1.8 (7)	0. (-1)	12.4 (25)
114	2.9 (128)	8.8 (82)	7. (82)	1.5 (331)	32.8 (335)	6.6 (334)	10.7 (326)	0. (-1)	19.1 (327)
115	3.7 (719)	6.1 (491)	5. (1083)	5.4 (399)	36.3 (946)	27.8 (1083)	15.9 (898)	0. (-1)	34.1 (964)
116	5. (77)	21. (174)	17.5 (2)	7. (212)	40.5 (174)	23.7 (372)	2.7 (203)	0. (-1)	7.9 (323)
117	1.4 (4)	4.7 (14)	22.4 (22)	0. (-1)	7.4 (30)	0. (-1)	0.7 (15)	0. (-1)	11.4 (14)
118	14. (1071)	33.1 (819)	8.5 (583)	5.6 (557)	69.1 (689)	80.3 (583)	60.3 (713)	0. (-1)	58.1 (962)
119	18.4 (22)	3.6 (100)	3.1 (17)	2.2 (24)	3428.4 (33)	48.5 (28)	26.2 (53)	0. (-1)	28.5 (54)
120	1.5 (177)	5.3 (140)	13.8 (38)	1.7 (189)	4782.7 (22)	119.4 (38)	20.4 (61)	0. (-1)	20. (128)
121	3.4 (35)	51.4 (154)	21.6 (152)	0. (-1)	10.2 (150)	2.3 (1)	6.8 (153)	0. (-1)	12.7 (152)
122	1.7 (1)	2.2 (6)	2.7 (101)	0. (-1)	6.7 (26)	0. (-1)	2.2 (27)	0. (-1)	3.5 (90)
123	1.5 (60)	11.1 (99)	3. (69)	3.5 (69)	12.7 (55)	25.3 (94)	11.8 (21)	0. (-1)	8. (64)
124	2.5 (139)	7. (92)	3. (233)	5.1 (47)	5.4 (176)	14.5 (233)	4.5 (233)	0. (-1)	4.2 (139)
125	1.9 (93)	6.1 (40)	1.3 (83)	1.2 (5)	28.9 (62)	3.9 (45)	11.2 (52)	0. (-1)	8.8 (86)
126	1.6 (162)	10.7 (244)	18.8 (240)	5.8 (266)	44.4 (289)	342.5 (240)	128.3 (240)	0. (-1)	19.4 (240)
127	4.7 (18)	41. (6)	6.4 (6)	1. (2)	10.4 (14)	7.4 (34)	2.4 (14)	0. (-1)	1.8 (15)
128	2.5 (20)	68.3 (18)	5.7 (20)	1.8 (62)	29.9 (59)	42.2 (62)	15.3 (55)	0. (-1)	8.8 (62)
129	1.4 (31)	2.8 (4)	1.5 (34)	1.2 (5)	18.7 (41)	4.7 (36)	2.2 (53)	0. (-1)	4.7 (3)
130	2.1 (65)	1.7 (65)	1.7 (108)	0.9 (66)	74.9 (84)	4.5 (48)	49.1 (113)	0. (-1)	30.5 (91)
131	2.8 (9)	25.1 (173)	88.8 (83)	88.7 (83)	77.1 (80)	82.9 (80)	73.6 (83)	0. (-1)	90.5 (80)
132	1.4 (13)	51. (23)	1.7 (16)	1.8 (16)	1.8 (16)	3.2 (16)	3.3 (16)	0. (-1)	1.6 (16)
133	1. (5)	2.2 (4)	3.1 (5)	2.1 (5)	2.2 (5)	1.9 (2)	3.3 (5)	0. (-1)	1.4 (3)
134	103. (1)	4.4 (7)	0. (-1)	0. (-1)	0. (-1)	4.8 (3)	0. (-1)	0. (-1)	0.1 (8)
135	3.6 (38)	6.2 (39)	5053. (40)	1.3 (37)	18. (39)	4.5 (7)	6.1 (11)	0. (-1)	19.3 (12)
136	1.8 (43)	3.4 (58)	55.5 (42)	0. (-1)	1.5 (38)	0. (-1)	2.4 (54)	0. (-1)	3.7 (45)
137	1.2 (3)	2.9 (5)	58.8 (7)	1.7 (2)	4.3 (13)	141.7 (17)	2.6 (5)	0. (-1)	4. (7)
138	1.7 (68)	1.6 (82)	17.7 (82)	1.6 (82)	12.7 (82)	22.9 (84)	40.8 (82)	0. (-1)	23.9 (77)
139	2.2 (7)	1.5 (7)	1.1 (1)	0.9 (1)	0.9 (1)	1. (2)	1. (2)	0. (-1)	1. (1)
140	237. (1)	202. (1)	150273. (1)	321. (1)	55772. (1)	771647. (2)	33969. (2)	0. (-1)	124219. (1)
141	1.1 (4)	1. (1)	0.8 (7)	0.8 (4)	1. (8)	0.9 (7)	0.9 (4)	0. (-1)	1. (8)
142	7.9 (131)	13. (142)	22.5 (30)	22.2 (125)	16. (141)	16.3 (19)	14.4 (125)	0. (-1)	85.2 (125)
143	6.7 (96)	916.2 (159)	6.7 (149)	13.7 (114)	70.3 (164)	1277.6 (139)	14.4 (114)	0. (-1)	161.1 (144)
144	2.1 (19)	19.3 (64)	13.8 (51)	1.5 (31)	9346.9 (24)	18.6 (7)	61.6 (49)	0. (-1)	24. (49)
145	1.8 (64)	15.6 (38)	7.8 (41)	1.6 (17)	14716.2 (31)	113.9 (62)	2.7 (6)	0. (-1)	24.4 (26)
146	3.3 (35)	4.4 (21)	11.7 (19)	42.3 (19)	11.6 (19)	13.2 (19)	11.6 (19)	0. (-1)	11.7 (19)
147	4.7 (70)	11.3 (258)	20.8 (141)	16.8 (80)	2411.1 (236)	20.2 (80)	129.9 (245)	0. (-1)	20.1 (80)
148	4.3 (16)	11.6 (4)	146.6 (224)	29.1 (13)	780.5 (84)	163.8 (35)	12.5 (36)	0. (-1)	10.2 (2)
149	2.4 (513)	3.5 (535)	2.3 (536)	3.2 (370)	5.5 (197)	6.9 (416)	2.6 (432)	0. (-1)	1.6 (528)
150	3.3 (73)	3.1 (132)	49.7 (189)	11.5 (30)	5.6 (194)	4.4 (176)	4.1 (184)	0. (-1)	4.7 (194)
151	4.3 (60)	3.3 (69)	1.4 (21)	0. (-1)	2.1 (53)	21.8 (15)	0.8 (76)	0. (-1)	4.7 (37)
152	1.2 (19)	9. (16)	0. (-1)	0. (-1)	2.6 (20)	0. (-1)	4.1 (7)	0. (-1)	7. (20)
153	2.5 (51)	15.5 (38)	3.1 (22)	1.6 (25)	4.1 (15)	6.8 (52)	16.9 (14)	0. (-1)	7.4 (30)
154	4.1 (377)	1113.9 (276)	70.8 (50)	5.1 (95)	40.5 (214)	9.8 (187)	12.5 (213)	0. (-1)	8.1 (22)
155	8.8 (1)	6. (571)	39. (201)	125.2 (201)	28.5 (226)	11.9 (485)	53.7 (485)	0. (-1)	37.2 (201)
156	4.3 (3)	1.5 (37)	8. (122)	7.4 (2)	2.1 (26)	3. (14)	62.4 (38)	0. (-1)	1.8 (38)
157	1.4 (83)	1.7 (96)	16. (33)	3.8 (95)	3.9 (17)	9.7 (69)	37.4 (19)	0. (-1)	4.3 (95)
158	1.6 (18)	1.6 (4)	16. (46)	2.5 (46)	4.6 (58)	3.2 (25)	37.7 (39)	0. (-1)	2.6 (25)
159	1.9 (358)	2.7 (262)	13.5 (71)	8.6 (194)	10. (389)	11.6 (389)	7.9 (389)	0. (-1)	10. (199)
160	1.1 (7)	82. (17)	1. (2)	100. (13)	125. (17)	37. (13)	77. (13)	0. (-1)	1.1 (5)
161	1.2 (5)	1.5 (4)	5.1 (9)	4.6 (4)	2.4 (4)	4. (4)	6. (9)	0. (-1)	3.2 (9)
162	1.1 (4)	2.2 (4)	4.7 (4)	4.6 (4)	3.1 (6)	2.8 (4)	4.9 (4)	0. (-1)	3.5 (9)
163	2.3 (913)	3.7 (913)	14.5 (228)	18.3 (1189)	12.2 (1406)	31. (1034)	9.7 (1406)	0. (-1)	15.6 (904)
164	2.5 (297)	78. (5)	168. (5)	57. (1)	119. (8)	15.5 (461)	53. (1)	0. (-1)	2.9 (63)
165	91. (42)	145. (42)	40.3 (32)	1.1 (51)	2.9 (80)	1.5 (50)	4.2 (46)	0. (-1)	5.9 (34)
166	64. (24)	57. (24)	5.2 (44)	2.7 (5)	3.6 (5)	65. (36)	2.8 (5)	0. (-1)	6.7 (32)
167	2.3 (898)	3.7 (898)	14.5 (213)	18.3 (1174)	12.2 (1391)	31. (1019)	9.7 (1391)	0. (-1)	15.6 (889)
168	1.6 (202)	13.1 (44)	39.2 (172)	10.6 (23)	11.2 (91)	15.9 (189)	15.3 (28)	0. (-1)	15. (91)
169	1.2 (15)	1.3 (133)	10.6 (99)	4.9 (149)	5. (150)	11. (150)	10.2 (81)	0. (-1)	3.4 (150)
170	2.1 (71)	3.9 (361)	33.8 (438)	5.1 (346)	20.3 (438)	29.5 (318)	11. (390)	0. (-1)	25.6 (438)
171	1.6 (221)	12.4 (70)	94.2 (93)	2.9 (172)	10.1 (243)	2.4 (252)	45.6 (193)	0. (-1)	3.9 (243)
172	1.7 (249)	39.2 (308)	20.1 (156)	7.4 (10)	7.3 (171)	7. (6)	56. (66)	0. (-1)	27. (270)
173	1.4 (256)	16.3 (81)	12.5 (213)	79.5 (81)	9.2 (212)	8. (71)	17.7 (108)	0. (-1)	9.7 (81)
174	1.9 (39)	51.5 (68)	11.2 (75)	14.2 (44)	4.5 (15)	4.3 (27)	12.4 (34)	0. (-1)	48.7 (34)
175	2.6 (133)	12.4 (497)	31.3 (88)	9. (341)	8.8 (423)	38.1 (446)	35. (475)	0. (-1)	7.1 (446)
176	1.8 (503)	38.5 (131)	13.2 (148)	7.4 (390)	33.9 (197)	34.4 (183)	13.8 (45)	0. (-1)	41.4 (197)
177	0.9 (7)	5.4 (27)	21. (27)	4.8 (27)	5.2 (27)	0. (-1)	0. (-1)	0. (-1)	0. (-1)
178	1.5 (289)	5. (360)	10.3 (231)	2.6 (126)	4.6 (414)	32.3 (355)	3.4 (340)	0. (-1)	5.5 (130)
179	1.1 (47)	3.3 (34)	4.3 (77)	2.5 (6)	5.7 (79)	17.1 (75)	2.8 (33)	0. (-1)	2. (63)
180	2.2 (612)	47.7 (614)	9. (603)	9. (151)	24.4 (506)	68.3 (341)	248.2 (364)	0. (-1)	51.5 (88)
181	2. (114)	35. (118)	3.1 (17)	4. (53)	7. (201)	2.6 (40)	86.2 (156)	0. (-1)	12.7 (192)
182	1.9 (628)	357.8 (774)	1249.3 (802)	30.7 (264)	15.9 (718)	79.3 (478)	19.3 (640)	0. (-1)	25.2 (719)
183	2.1 (466)	24.7 (1558)	56.7 (174)	8.6 (46)	15.7 (934)	223.9 (697)	424.5 (175)	0. (-1)	21.1 (1355)
184	1.5 (12)	49.4 (31)	641. (48)	7.2 (16)	28.8 (35)	3.4 (1)	2.4 (6)	0. (-1)	8.2 (39)
185	1.3 (335)	9.3 (100)	1296.8 (353)	35.1 (48)	16.5 (327)	66.6 (265)	256.7 (14)	0. (-1)	23.6 (285)
186	1. (13)	10.5 (13)	2.7 (2)	12.4 (1)	2.3 (2)	13.1 (3)	24.8 (1)	0. (-1)	1.8 (9)
187	1.5 (30)	2.4 (17)	5.2 (15)	3.3 (19)	2.2 (17)	2.3 (30)	0.9 (30)	0. (-1)	1.3 (30)
188	6.2 (79)	2.5 (38)	7.4 (127)	15.3 (100)	3554.2 (74)	542.9 (50)	15.4 (32)	0. (-1)	42.1 (139)
189	1.9 (178)	11.6 (505)	2431.2 (524)	17.6 (418)	198.5 (324)	9937.7 (40)	544.2 (299)	0. (-1)	33.7 (257)
190	1.1 (9)	2.2 (2)	1.3 (6)	1.3 (2)	4.6 (1)	11.7 (4)	2.3 (2)	0. (-1)	3.6 (2)
191	1.2 (18)	1.5 (8)	1.3 (13)	1. (19)	51.7 (13)	2.8 (11)	1.9 (14)	0. (-1)	1.3 (11)
192	1.5 (58)	12.7 (250)	10.5 (343)	21.4 (209)	13.1 (209)	30. (193)	633.3 (22)	0. (-1)	3.9 (322)
193	2.1 (109)	1.8 (113)	3.5 (27)	21.3 (45)	1.7 (38)	2.2 (12)	69.6 (38)	0. (-1)	1.7 (12)
194	1.2 (110)	3.3 (203)	7.8 (201)	168.3 (37)	4.7 (44)	23.3 (45)	13.9 (217)	0. (-1)	2.1 (45)
195	1.1 (11)	1.1 (10)	1.4 (29)	8.1 (33)	1.1 (10)	3.9 (12)	1.6 (13)	0. (-1)	0. (-1)
196	39. (7)	87. (19)	361. (21)	502. (30)	186. (18)	381. (17)	324. (26)	0. (-1)	282. (18)
197	1.2 (60)	3.7 (284)	8.3 (12)	16.5 (170)	4.1 (42)	2.5 (64)	12.5 (64)	0. (-1)	1.7 (44)
198	1.1 (21)	2.6 (61)	3.4 (50)	788.2 (7)	6.2 (52)	6. (41)	1.5 (6)	0. (-1)	1.9 (41)
199	4.3 (11)	4.3 (89)	5.5 (80)	3.2 (3)	4.2 (32)	35.5 (25)	3.7 (11)	0. (-1)	3.9 (22)
200	1.5 (16)	3.2 (1)	4.3 (20)	4.1 (3)	4.1 (20)	0. (-1)	3. (3)	0. (-1)	4.7 (11)
201	1.5 (28)	4.4 (139)	8.3 (76)	12.1 (133)	6.9 (33)	4.1 (9)	627.4 (22)	0. (-1)	3.4 (35)
202	1.5 (45)	1.3 (94)	4.2 (26)	4.2 (86)	1.4 (87)	6. (61)	4.3 (35)	0. (-1)	1.2 (37)
203	1.1 (11)	1. (10)	1.4 (29)	8.1 (32)	1.1 (10)	3.8 (12)	1.6 (13)	0. (-1)	0. (-1)
204	1.4 (370)	34.4 (773)	7.5 (598)	6489.4 (123)	7.2 (484)	208.2 (474)	28.4 (782)	0. (-1)	11.8 (485)
205	1.1 (1)	2.8 (2)	2.4 (2)	0. (-1)	0. (-1)	0. (-1)	0. (-1)	0. (-1)	0. (-1)
206	1. (1)	3. (1)	1.3 (1)	3.5 (1)	1.7 (1)	0. (-1)	1.5 (1)	0. (-1)	2.3 (1)
207	1.3 (496)	36.7 (454)	8.3 (79)	7944.2 (100)	8.1 (279)	77.7 (251)	7.2 (259)	0. (-1)	5.6 (280)
208	1.2 (268)	53.1 (393)	5.2 (59)	20.3 (115)	3.4 (319)	9. (35)	39.9 (35)	0. (-1)	4.5 (7)
209	1.5 (940)	41.8 (1158)	11.2 (398)	7808.5 (402)	7.5 (1007)	29.3 (565)	7.5 (994)	0. (-1)	17.4 (592)
210	1.6 (23)	1.8 (7)	4.6 (49)	18.9 (40)	3020.2 (18)	364.1 (22)	5.5 (7)	0. (-1)	12.8 (66)
211	1.3 (32)	2.6 (30)	5.9 (41)	5.5 (46)	6.9 (23)	1914.1 (28)	3.7 (47)	0. (-1)	7.6 (31)
212	1.2 (14)	2.1 (9)	2. (17)	1. (2)	15.2 (14)	13.9 (4)	7. (4)	0. (-1)	10.7 (15)
213	1.2 (11)	1.9 (5)	1.4 (20)	0.8 (11)	51.4 (8)	3.2 (12)	66.7 (8)	0. (-1)	15.2 (1)
214	1.5 (92)	19.4 (184)	186.8 (52)	1.3 (7)	5. (317)	3. (376)	2.3 (351)	0. (-1)	1.3 (1)
215	1.7 (555)	30.1 (617)	60.4 (628)	19. (393)	8.6 (80)	40. (172)	772.4 (550)	0. (-1)	73.6 (574)
216	1.6 (57)	7. (46)	1.8 (42)	2.9 (67)	7.5 (75)	1.3 (2)	324.8 (32)	0. (-1)	8.7 (74)
217	1.5 (507)	242.3 (678)	11965. (516)	141. (1121)	226.8 (1313)	68.3 (1213)	11.9 (657)	0. (-1)	31.4 (1222)
218	1.5 (365)	145.1 (338)	15275. (454)	144. (373)	197.8 (463)	42.4 (280)	5.4 (477)	0. (-1)	4.3 (295)
219	1.2 (152)	3777.8 (109)	123.6 (126)	3. (83)	406.4 (150)	145.8 (74)	5.4 (83)	0. (-1)	33. (83)
220	2.1 (386)	44. (159)	612.9 (479)	18.1 (272)	20.7 (379)	62.9 (245)	776.9 (30)	0. (-1)	61.3 (82)
221	1.1 (20)	3.4 (19)	30046.9 (4)	0. (-1)	104.6 (22)	0. (-1)	0. (-1)	0. (-1)	0. (-1)
222	1.3 (1)	4.5 (44)	9.4 (61)	11.2 (49)	4.9 (54)	2.5 (24)	6. (22)	0. (-1)	1.3 (16)
223	1.1 (21)	2.5 (44)	1.1 (21)	7.9 (52)	4.5 (39)	16.9 (21)	1.7 (21)	0. (-1)	2.6 (21)
224	1.3 (13)	9.4 (48)	1.6 (1)	1.3 (4)	4.9 (20)	2.6 (1)	2.3 (2)	0. (-1)	2.8 (1)
225	1.9 (15)	2.5 (11)	2.1 (9)	3.3 (11)	4. (7)	1.3 (2)	2.5 (7)	0. (-1)	3.1 (13)
226	145. (15)	400. (15)	311. (15)	396. (15)	236. (15)	1.2 (2)	329. (15)	0. (-1)	784. (20)
227	1.5 (44)	3.8 (22)	26.7 (102)	1.9 (94)	40.1 (103)	35.7 (93)	2.4 (94)	0. (-1)	1.7 (94)
228	1.4 (57)	13.4 (37)	7.1 (30)	22.4 (42)	13.3 (57)	59.8 (7)	17.1 (37)	0. (-1)	3.9 (7)
229	1.1 (13)	3.8 (21)	31763.8 (3)	0. (-1)	98.2 (11)	0. (-1)	0. (-1)	0. (-1)	0. (-1)
230	1.5 (1)	5.6 (42)	9.4 (59)	18.7 (47)	4.9 (59)	2.4 (22)	33.1 (8)	0. (-1)	2.5 (8)
231	1.4 (54)	4.7 (42)	7.4 (269)	25.9 (47)	5.7 (42)	3.3 (1)	11.7 (42)	0. (-1)	5.7 (42)
232	2.1 (819)	251.5 (874)	8.1 (839)	1460.2 (263)	7. (515)	2.6 (5)	5.8 (513)	0. (-1)	11.5 (514)
233	1.6 (140)	40.2 (153)	4.2 (290)	2.9 (65)	5.2 (110)	0. (-1)	4.5 (230)	0. (-1)	12.8 (224)
234	1.8 (319)	19.3 (232)	19. (335)	3.7 (67)	37.3 (336)	13.1 (90)	6.1 (295)	0. (-1)	20.6 (296)
235	1.4 (83)	84.4 (211)	74.6 (153)	37.5 (109)	8.8 (159)	0. (-1)	5.1 (159)	0. (-1)	12.8 (197)
236	2.5 (212)	227.9 (265)	13.3 (243)	43.2 (130)	15.3 (263)	3. (170)	4.3 (256)	0. (-1)	23.9 (258)
237	1.4 (346)	374.7 (634)	8.5 (171)	1629.1 (267)	8.2 (336)	2.2 (47)	6.9 (335)	0. (-1)	5. (336)
238	1.1 (48)	5.1 (25)	4.9 (19)	13.5 (25)	2.6 (58)	2.9 (33)	2.7 (41)	0. (-1)	4.5 (4)
239	1.4 (930)	471.8 (1351)	9. (1067)	2062.5 (624)	7.8 (923)	3. (930)	7.6 (489)	0. (-1)	14.7 (923)
240	1.5 (19)	65.3 (138)	67. (431)	58. (256)	27.3 (461)	6. (459)	15. (389)	0. (-1)	15.5 (367)
241	1. (1)	13.2 (39)	4.1 (29)	14.9 (16)	5.1 (6)	0. (-1)	5.7 (18)	0. (-1)	1. (13)
242	1.2 (68)	3.2 (18)	5.7 (73)	120.4 (20)	4.5 (68)	2.2 (53)	4.2 (20)	0. (-1)	3.2 (68)
243	1.4 (54)	3. (42)	5.7 (21)	33.4 (39)	3.8 (42)	3.1 (1)	3.1 (41)	0. (-1)	1.7 (2)
244	1.3 (50)	5.3 (36)	6.6 (15)	6.4 (13)	7.8 (20)	0. (-1)	13.6 (15)	0. (-1)	7.5 (51)
245	1.5 (15)	2.5 (8)	2. (9)	4.9 (8)	3.7 (14)	0. (-1)	2.2 (8)	0. (-1)	3.8 (15)
246	1.3 (20)	3.3 (10)	1.9 (5)	3.5 (1)	5. (22)	0. (-1)	2.2 (10)	0. (-1)	6.5 (12)
247	1.3 (6)	2.2 (3)	2.1 (8)	2.5 (8)	2.3 (9)	3.2 (8)	3.3 (12)	0. (-1)	2. (8)
248	1. (1)	1.2 (1)	1.8 (1)	0. (-1)	1.4 (1)	0. (-1)	0. (-1)	0. (-1)	0. (-1)
249	1.2 (7)	3.1 (18)	7.3 (15)	39.7 (11)	16.6 (11)	0. (-1)	5.3 (16)	0. (-1)	38.3 (8)
250	1.3 (27)	4.2 (25)	5.2 (74)	39.4 (15)	4.6 (69)	2.3 (53)	2.9 (61)	0. (-1)	3.1 (27)
251	2. (50)	4.5 (102)	3.1 (3)	48.6 (89)	2.6 (88)	13.6 (15)	238.6 (66)	0. (-1)	2.6 (77)
252	8.8 (128)	4.5 (73)	5.5 (8)	13. (82)	2. (102)	17. (87)	2104.7 (129)	0. (-1)	7.1 (44)
253	4. (22)	2.7 (29)	2.5 (12)	16.4 (22)	7.2 (20)	35.2 (22)	47.7 (20)	0. (-1)	14.3 (7)
254	10.8 (702)	718.9 (361)	170.3 (378)	5742.6 (430)	264.3 (437)	4789.3 (407)	808.7 (345)	0. (-1)	73.7 (490)
255	3.3 (23)	24.3 (272)	4.6 (211)	9.5 (209)	8.5 (143)	18.8 (124)	406.5 (236)	0. (-1)	34. (142)
256	7.7 (600)	1972. (326)	4100740.7 (487)	2494919. (184)	1339. (108)	6948.3 (449)	1957357. (237)	0. (-1)	106.1 (75)
257	1.8 (299)	9.8 (164)	9.4 (331)	58.8 (171)	13.9 (273)	10.3 (396)	5930.5 (96)	0. (-1)	6. (80)
258	1. (1)	2.7 (1)	6.9 (9)	0.4 (5)	12. (4)	1.1 (5)	0.7 (5)	0. (-1)	0.4 (5)
259	4.3 (259)	7.9 (276)	8.4 (1)	90.9 (225)	4.2 (235)	5.6 (18)	2097.9 (70)	0. (-1)	7.2 (259)
260	19.2 (46)	9.1 (145)	1.8 (82)	81.3 (46)	4.2 (75)	16.2 (57)	264.4 (43)	0. (-1)	6. (75)
261	6697. (6)	547. (6)	374. (6)	158. (33)	640. (6)	3.6 (19)	311. (6)	0. (-1)	0. (-1)
262	1.7 (26)	11.3 (344)	7.7 (276)	12.1 (56)	3.6 (6)	8.1 (85)	16.6 (134)	0. (-1)	4.5 (87)
263	1.1 (14)	2. (8)	2.9 (14)	2.4 (1)	1.7 (1)	2.7 (1)	8.5 (8)	0. (-1)	2.4 (1)
264	1.7 (30)	2.5 (28)	4.3 (25)	1.8 (24)	1.7 (7)	2.2 (11)	11.5 (53)	0. (-1)	1.8 (24)
265	1.5 (12)	2.6 (6)	10.1 (57)	3.1 (12)	5.9 (169)	3.8 (46)	7.3 (87)	0. (-1)	1.6 (153)
266	2.4 (172)	3.9 (475)	19.9 (90)	3.3 (192)	6. (468)	2.9 (377)	56.7 (447)	0. (-1)	16.3 (460)
267	1.3 (101)	5962. (103)	15.5 (127)	1.8 (170)	8.6 (167)	2.9 (177)	3.5 (22)	0. (-1)	2.1 (170)
268	1.1 (4)	1.7 (5)	1. (28)	0.9 (28)	0.9 (28)	1.5 (15)	1.3 (3)	0. (-1)	1. (28)
269	1.2 (40)	11. (91)	7.7 (50)	2.2 (1)	5.7 (6)	2. (35)	4.6 (57)	0. (-1)	2.1 (8)
270	1.1 (3)	2.1 (1)	2.9 (14)	2.4 (1)	1.7 (1)	2.7 (1)	8.5 (8)	0. (-1)	2.4 (1)
271	1.8 (32)	4.9 (41)	2.7 (157)	1.8 (155)	3. (7)	2.3 (11)	26.4 (147)	0. (-1)	1.8 (155)
272	1.5 (12)	1.8 (16)	10.1 (57)	4.2 (46)	5.9 (105)	4. (46)	7. (32)	0. (-1)	1.6 (46)
273	2.4 (177)	3.9 (1)	19.9 (92)	3.3 (197)	8.3 (645)	3.1 (415)	67.5 (622)	0. (-1)	16.3 (636)
274	1.3 (15)	2. (5)	2.8 (5)	2.4 (11)	2.4 (21)	2. (23)	36.3 (23)	0. (-1)	1.3 (19)
275	1.1 (21)	4.7 (20)	3. (12)	0.9 (16)	0. (-1)	0. (-1)	0. (-1)	0. (-1)	0.6 (16)
276	1.4 (50)	11.4 (54)	27.1 (147)	5.4 (67)	5.6 (50)	13.1 (131)	10.3 (121)	0. (-1)	5.3 (1)
277	2.1 (24)	4. (83)	114.6 (118)	1.5 (165)	2.3 (105)	7.5 (105)	1.9 (134)	0. (-1)	2.4 (101)
278	1.3 (22)	3.7 (25)	42.8 (20)	1.8 (8)	9212.2 (24)	44.7 (8)	11.8 (6)	0. (-1)	3.9 (8)
279	6.7 (315)	6.4 (428)	183.8 (1264)	4.8 (218)	12.6 (1222)	4.3 (197)	5.9 (1165)	0. (-1)	3.1 (1165)
280	1.9 (67)	3.3 (44)	24.6 (45)	26.7 (53)	3. (38)	9.5 (20)	26.3 (37)	0. (-1)	4.9 (38)
281	2. (78)	11.4 (16)	27.3 (81)	5.4 (16)	5.6 (12)	3. (9)	3. (1)	0. (-1)	5.1 (1)
282	2.3 (23)	1.3 (54)	28.2 (31)	1.8 (40)	1.3 (61)	6.3 (45)	1.9 (6)	0. (-1)	1.8 (41)
283	1. (1)	0. (-1)	5.8 (1)	0. (-1)	0. (-1)	0. (-1)	0. (-1)	0. (-1)	0. (-1)
284	1.7 (33)	3.2 (33)	2.7 (6)	1.3 (20)	6.8 (18)	2. (37)	1.7 (4)	0. (-1)	2. (10)
285	2.6 (36)	4.1 (28)	11.1 (28)	26.7 (37)	3.2 (22)	5.9 (8)	27.1 (22)	0. (-1)	7.1 (22)
286	1.3 (23)	12.7 (22)	2.9 (26)	1.7 (14)	4. (24)	2.7 (8)	2.6 (2)	0. (-1)	1. (11)
287	1.4 (8)	2.7 (107)	6. (105)	3.4 (31)	8.7 (151)	2.5 (12)	84.8 (69)	0. (-1)	0. (-1)
288	1.3 (26)	13. (21)	3.3 (26)	1.6 (13)	4. (23)	2.7 (8)	3.5 (26)	0. (-1)	1. (10)
289	1.4 (71)	3. (114)	6. (112)	1.9 (22)	8.7 (156)	2.6 (12)	27.3 (91)	0. (-1)	0. (-1)
290	2.7 (319)	515.8 (537)	140.9 (527)	18.8 (590)	105. (505)	138.5 (570)	7. (689)	0. (-1)	180.6 (554)
291	1.7 (53)	2.5 (120)	38.5 (68)	26. (79)	36.5 (102)	43.6 (33)	12.2 (33)	0. (-1)	10.1 (100)
292	2.9 (87)	4.5 (153)	7.6 (62)	7.7 (104)	147.8 (155)	18.4 (25)	3.6 (83)	0. (-1)	8.1 (155)
293	1.5 (178)	10.9 (193)	7.5 (379)	3.7 (327)	24.5 (496)	5.3 (96)	8.7 (6)	0. (-1)	8.2 (474)
294	1.4 (36)	2.1 (3)	3.4 (98)	12.9 (90)	6.6 (20)	1.9 (10)	6.9 (29)	0. (-1)	2.2 (52)
295	1.8 (11)	1.5 (24)	1.8 (28)	6. (7)	5.4 (21)	0. (-1)	1.1 (7)	0. (-1)	1.4 (11)
296	1.7 (312)	8.7 (365)	7.3 (126)	21.3 (134)	32.5 (87)	26.4 (102)	25.9 (273)	0. (-1)	13.2 (87)
297	1.9 (22)	1.9 (7)	4.6 (28)	5.8 (23)	2699.3 (18)	464.2 (15)	21.2 (7)	0. (-1)	8. (8)
298	1.9 (233)	9.9 (358)	3.9 (35)	21.9 (279)	100.7 (58)	396.8 (35)	23.5 (75)	0. (-1)	222.4 (304)
299	1.5 (16)	13.6 (173)	3.4 (15)	3.6 (1)	16.2 (36)	4.1 (8)	8.7 (6)	0. (-1)	4.8 (16)
300	2.1 (109)	1.8 (38)	8. (107)	3.5 (5)	4.3 (108)	2.3 (12)	18. (32)	0. (-1)	2.1 (84)
301	1.3 (29)	2.1 (3)	3.4 (64)	12.9 (56)	6.6 (20)	1.9 (10)	5.2 (25)	0. (-1)	1.9 (17)
302	1.8 (11)	1.5 (12)	1.8 (28)	6. (7)	5.4 (21)	0. (-1)	1.1 (7)	0. (-1)	1.4 (11)
303	1.6 (262)	8.7 (329)	6.8 (10)	11.4 (196)	40.1 (177)	27.1 (68)	25.9 (246)	0. (-1)	10.6 (219)
304	1.9 (29)	2.2 (14)	5.5 (8)	5.8 (30)	2966.3 (25)	376.7 (15)	16.8 (23)	0. (-1)	32.2 (46)
305	1.4 (21)	2.5 (11)	3.3 (13)	7.4 (13)	56.7 (12)	376.7 (16)	2.9 (37)	0. (-1)	31.5 (32)
306	1.3 (2)	3.6 (63)	5.5 (68)	3. (8)	23.5 (11)	1.5 (8)	3. (8)	0. (-1)	3.3 (8)
307	2. (73)	4.1 (73)	4.1 (145)	12.6 (198)	65.9 (210)	98.5 (64)	4.2 (103)	0. (-1)	45.7 (144)
308	1.6 (23)	10.7 (101)	7.5 (221)	23.3 (190)	177.3 (253)	7.3 (171)	13. (219)	0. (-1)	146.8 (44)
309	1.7 (2)	3.7 (47)	5.8 (37)	3.7 (8)	20. (47)	11.7 (27)	3.2 (8)	0. (-1)	4.1 (8)
310	2.4 (114)	6.4 (118)	6.2 (35)	13. (198)	66.3 (210)	11.6 (153)	5.8 (118)	0. (-1)	15.8 (104)
311	1.3 (46)	10.3 (47)	7.5 (24)	6.3 (10)	177.8 (46)	5.5 (5)	13. (45)	0. (-1)	5.3 (8)
312	1.3 (6)	1.9 (1)	2.9 (5)	2.5 (7)	16.2 (9)	0. (-1)	2.7 (7)	0. (-1)	3.1 (7)
313	1.2 (76)	2.8 (87)	3.6 (86)	2. (19)	22.6 (89)	1.5 (3)	2. (38)	0. (-1)	4.7 (76)
314	3.5 (186)	2.7 (27)	11.8 (27)	8.6 (59)	247.8 (146)	2.3 (191)	5.4 (186)	0. (-1)	11.2 (113)
315	1.7 (19)	14.4 (168)	8.7 (48)	21.9 (158)	169.2 (218)	5. (142)	6.4 (219)	0. (-1)	64.3 (95)
316	1.4 (6)	4.6 (26)	4.6 (5)	3.1 (7)	15.7 (9)	0. (-1)	2.8 (7)	0. (-1)	4.1 (7)
317	1.3 (19)	4.7 (89)	3.9 (85)	2.3 (19)	28.8 (19)	1.4 (3)	1.9 (3)	0. (-1)	5.7 (19)
318	3.3 (160)	5.7 (24)	22.3 (24)	6.3 (24)	33.8 (124)	2.1 (165)	9. (24)	0. (-1)	14.1 (124)
319	1.2 (7)	3.4 (24)	5.6 (18)	6.2 (1)	96.8 (15)	0. (-1)	8.8 (22)	0. (-1)	29.6 (8)
320	2.5 (4)	3. (4)	1.2 (2)	1.2 (8)	12.4 (7)	12.6 (1)	11.8 (8)	0. (-1)	1.2 (8)
321	1.9 (115)	4.1 (103)	2.2 (42)	3.2 (78)	44. (111)	14.9 (16)	9.6 (14)	0. (-1)	2.9 (20)
322	8.3 (136)	4.4 (94)	3.8 (102)	3.5 (68)	38.8 (102)	14.2 (103)	9.6 (103)	0. (-1)	3.4 (90)
323	5. (22)	2. (31)	8.2 (22)	12. (7)	46. (21)	40.3 (22)	10.1 (34)	0. (-1)	9.1 (34)
324	1.5 (137)	7.3 (287)	7.5 (256)	12.3 (57)	4.9 (287)	8.2 (86)	8.5 (57)	0. (-1)	4.7 (88)
325	1.2 (14)	2.1 (1)	2.1 (1)	2.5 (1)	2.5 (1)	2.7 (1)	3.8 (1)	0. (-1)	2.4 (1)
326	1.7 (36)	1724. (3)	2.7 (41)	1.4 (20)	324. (1)	1. (36)	2.3 (24)	0. (-1)	1.9 (13)
327	1.5 (12)	3.4 (254)	10.2 (56)	3.1 (12)	6. (170)	3.6 (46)	2.4 (154)	0. (-1)	2. (46)
328	2.4 (229)	3.5 (242)	23. (87)	3.4 (231)	4.9 (480)	3.5 (95)	2.6 (127)	0. (-1)	1.5 (95)
329	1.2 (14)	4.8 (46)	4. (52)	1.6 (12)	5.3 (11)	2. (12)	2.9 (9)	0. (-1)	1.7 (14)
330	1.4 (144)	5.5 (143)	7.2 (149)	9.2 (11)	5.9 (188)	1.2 (159)	6.3 (11)	0. (-1)	3.2 (11)
331	1.1 (13)	2.8 (8)	2.1 (1)	2.2 (1)	2.3 (1)	0. (-1)	3.4 (1)	0. (-1)	0.9 (4)
332	1.8 (32)	3.2 (39)	2.3 (18)	1.2 (135)	2. (7)	0. (-1)	2. (19)	0. (-1)	1.1 (135)
333	1.5 (13)	5.5 (145)	9.9 (44)	2.7 (13)	5.2 (147)	0. (-1)	2.2 (131)	0. (-1)	1.4 (121)
334	1.8 (307)	11.8 (165)	17.2 (90)	2.6 (22)	7.4 (406)	0. (-1)	1.7 (135)	0. (-1)	1.4 (378)
335	1.4 (60)	3.7 (53)	3.8 (58)	1.2 (14)	9.7 (20)	0. (-1)	2.8 (18)	0. (-1)	1.3 (14)
336	2.1 (81)	8.2 (323)	22.1 (318)	4.3 (72)	6.3 (315)	5.1 (98)	7.6 (133)	0. (-1)	8.6 (28)
337	2.5 (201)	3. (219)	43.8 (156)	5.3 (201)	13.7 (215)	30.9 (63)	7.5 (1)	0. (-1)	2. (104)
338	1.6 (21)	7.9 (18)	53. (20)	2.3 (41)	31.4 (36)	62.9 (8)	10.6 (1)	0. (-1)	9. (8)
339	3.3 (439)	5.6 (156)	71.1 (235)	16.1 (244)	7.1 (512)	4.5 (307)	6.7 (15)	0. (-1)	2.7 (126)
340	1.9 (78)	17.8 (42)	32. (46)	5.2 (15)	5. (37)	118.9 (37)	15.4 (37)	0. (-1)	12.9 (37)
341	2.1 (170)	8.2 (121)	1614.5 (38)	3.3 (68)	6.3 (113)	4.3 (75)	5.1 (172)	0. (-1)	8.8 (172)
342	2.3 (23)	1.8 (43)	36.8 (31)	3.9 (49)	3.4 (49)	5.3 (48)	6.1 (6)	0. (-1)	1.4 (48)
343	1. (1)	5.3 (1)	5.3 (1)	0. (-1)	0. (-1)	0. (-1)	0. (-1)	0. (-1)	0. (-1)
344	1.6 (5)	2.4 (7)	5.8 (7)	2.8 (20)	7.1 (18)	1.8 (26)	6. (1)	0. (-1)	1.7 (26)
345	2.8 (41)	10.8 (36)	23.5 (34)	3.8 (20)	5. (27)	118.9 (27)	15.3 (27)	0. (-1)	12.9 (27)
346	1.4 (5)	3.6 (29)	5.2 (5)	0.8 (4)	9.3 (6)	0. (-1)	0. (-1)	0. (-1)	0. (-1)
347	1.4 (7)	18.4 (85)	7.9 (123)	1.4 (47)	8.9 (167)	1.5 (35)	0. (-1)	0. (-1)	0. (-1)
348	1.4 (4)	8.2 (13)	2.8 (6)	1.3 (28)	7.3 (28)	0.9 (22)	0. (-1)	0. (-1)	0.8 (22)
349	2.4 (72)	3.2 (115)	5.8 (113)	2.1 (10)	9.7 (157)	1.2 (9)	0. (-1)	0. (-1)	0. (-1)
350	1.8 (283)	1.6 (138)	2.1 (190)	1.1 (31)	2. (140)	2.7 (221)	2. (150)	0. (-1)	3. (121)
351	2. (181)	2.5 (57)	1.5 (92)	3.3 (136)	2.5 (60)	2. (179)	0. (-1)	0. (-1)	0. (-1)
352	1.7 (54)	1.1 (5)	2.2 (55)	2.2 (65)	1.5 (69)	114.2 (16)	2.7 (55)	0. (-1)	1.2 (44)
353	1.8 (52)	1.8 (35)	3.3 (134)	5. (88)	5.7 (117)	7.8 (69)	557.1 (66)	0. (-1)	1.2 (103)
354	1.7 (45)	1.8 (35)	1.2 (7)	0. (-1)	0. (-1)	9.1 (69)	0. (-1)	0. (-1)	1.2 (35)
355	4.2 (130)	4.3 (159)	92.4 (68)	26. (60)	1534.9 (86)	160. (81)	92.9 (68)	0. (-1)	43.7 (60)
356	1.1 (1)	1. (2)	1.2 (14)	0. (-1)	0. (-1)	0. (-1)	0. (-1)	0. (-1)	0. (-1)
357	1.4 (161)	1.3 (153)	2.4 (41)	4.1 (155)	2.7 (28)	4.9 (30)	0. (-1)	0. (-1)	2.3 (155)
358	1.3 (105)	1.1 (366)	2.2 (291)	1.4 (4)	2.1 (364)	1.9 (358)	0. (-1)	0. (-1)	1.3 (4)
359	66.8 (46)	527.7 (105)	439.4 (227)	439.4 (227)	21.8 (64)	522.8 (105)	573.4 (258)	0. (-1)	439.4 (227)
360	3.2 (77)	10. (17)	1.5 (2)	6.5 (16)	10. (23)	23.3 (162)	12.5 (18)	0. (-1)	8. (23)
361	224.7 (703)	5605.6 (2439)	6816.7 (2524)	152.4 (703)	145.9 (2571)	164.5 (2571)	4761.5 (2727)	0. (-1)	392.3 (1086)
362	265. (1928)	5645.2 (2956)	1580.6 (1154)	430.8 (948)	78.3 (2418)	52.7 (2449)	39084.8 (2246)	0. (-1)	153.5 (2418)
363	130.3 (400)	21182. (1738)	767.1 (1263)	1205. (99)	126.2 (731)	363.2 (2409)	2340.2 (284)	0. (-1)	242. (731)
364	430.4 (1124)	365.7 (72)	892063.8 (1190)	205.3 (735)	25.6 (735)	37. (735)	395.1 (755)	0. (-1)	60.7 (735)
365	2.9 (6)	1. (1)	7.5 (9)	1.4 (1)	1.2 (8)	0.7 (2)	0. (-1)	0. (-1)	0. (-1)
366	88.4 (910)	650.2 (1384)	182975.9 (2420)	6.9 (1028)	14782.7 (2646)	20.4 (315)	31. (1760)	0. (-1)	44.9 (2310)
367	10.1 (38)	14.4 (41)	1.6 (50)	7.3 (7)	4953.2 (18)	11.2 (93)	16.1 (3)	0. (-1)	16. (80)

1.11 Pass/Fail per test file for each CAS system

The following table gives the number of passed integrals and number of failed integrals per test number. There are 210 tests. Each tests corresponds to one input file.

#	Rubi		MMA		Maple		Maxima		FriCAS		Sympy		Giac		Mupad		Reduce
	Pass	Fail	Pass	Fail	Pass	Fail	Pass	Fail	Pass	Fail	Pass	Fail	Pass	Fail	Pass	Fail	Pass	Fail
1	175	0	175	0	173	2	166	9	174	1	165	10	171	4	169	6	160	15
2	33	2	34	1	28	7	16	19	25	10	9	26	17	18	9	26	11	24
3	13	1	14	0	12	2	8	6	13	1	9	5	10	4	11	3	8	6
4	76	0	76	0	76	0	76	0	76	0	76	0	76	0	76	0	76	0
5	48	2	50	0	33	17	26	24	50	0	19	31	41	9	12	38	23	27
6	279	5	284	0	283	1	251	33	281	3	255	29	270	14	270	14	267	17
7	3	4	7	0	5	2	3	4	7	0	5	2	5	2	7	0	4	3
8	7	2	9	0	9	0	7	2	9	0	5	4	9	0	9	0	6	3
9	113	0	113	0	113	0	111	2	112	1	107	6	111	2	106	7	109	4
10	376	0	376	0	376	0	374	2	376	0	363	13	376	0	372	4	357	19
11	705	0	705	0	656	49	565	140	662	43	460	245	594	111	542	163	465	240
12	110	6	102	14	88	28	20	96	90	26	29	87	36	80	37	79	27	89
13	8	0	8	0	8	0	7	1	8	0	8	0	8	0	8	0	8	0
14	111	0	111	0	111	0	111	0	111	0	111	0	111	0	111	0	111	0
15	832	0	832	0	691	141	687	145	691	141	811	21	632	200	596	236	664	168
16	299	0	299	0	207	92	141	158	218	81	134	165	141	158	123	176	158	141
17	802	0	802	0	507	295	347	455	559	243	306	496	444	358	465	337	488	314
18	352	0	352	0	347	5	347	5	347	5	338	14	339	13	319	33	348	4
19	354	0	354	0	294	60	193	161	294	60	173	181	215	139	172	182	220	134
20	626	0	626	0	471	155	146	480	500	126	156	470	410	216	214	412	405	221
21	264	0	264	0	243	21	155	109	242	22	130	134	239	25	213	51	238	26
22	1836	1	1835	2	1616	221	1174	663	1654	183	847	990	1237	600	937	900	1244	593
23	233	6	236	3	224	15	40	199	177	62	74	165	216	23	192	47	205	34
24	157	1	153	5	121	37	15	143	44	114	8	150	32	126	18	140	26	132
25	30	0	30	0	30	0	30	0	30	0	30	0	30	0	23	7	30	0
26	192	0	192	0	177	15	94	98	166	26	86	106	177	15	26	166	140	52
27	100	0	100	0	100	0	49	51	84	16	11	89	71	29	64	36	68	32
28	43	0	43	0	43	0	1	42	9	34	0	43	1	42	1	42	1	42
29	136	0	134	2	68	68	60	76	65	71	136	0	61	75	136	0	65	71
30	1304	0	1304	0	805	499	633	671	749	555	1264	40	612	692	734	570	655	649
31	564	0	564	0	339	225	105	459	347	217	173	391	124	440	86	478	139	425
32	1662	1	1661	2	1301	362	830	833	1227	436	882	781	971	692	889	774	956	707
33	378	193	424	147	381	190	44	527	229	342	53	518	168	403	60	511	138	433
34	186	210	304	92	264	132	14	382	115	281	29	367	14	382	14	382	17	379
35	151	0	151	0	107	44	107	44	107	44	151	0	107	44	91	60	107	44
36	270	0	270	0	251	19	244	26	251	19	242	28	247	23	123	147	250	20
37	57	0	57	0	52	5	7	50	52	5	5	52	8	49	5	52	9	48
38	30	18	31	17	31	17	0	48	0	48	0	48	6	42	0	48	7	41
39	15	3	15	3	15	3	0	18	0	18	0	18	0	18	0	18	0	18
40	41	0	41	0	32	9	19	22	32	9	41	0	12	29	41	0	12	29
41	52	0	52	0	42	10	20	32	42	10	52	0	8	44	52	0	8	44
42	197	0	197	0	140	57	121	76	119	78	190	7	122	75	197	0	122	75
43	456	0	456	0	418	38	290	166	401	55	442	14	275	181	340	116	267	189
44	727	0	727	0	592	135	432	295	571	156	709	18	388	339	441	286	352	375
45	658	0	658	0	368	290	321	337	437	221	650	8	338	320	321	337	324	334
46	573	0	573	0	565	8	504	69	544	29	567	6	485	88	483	90	504	69
47	701	0	701	0	552	149	543	158	589	112	690	11	441	260	499	202	546	155
48	132	0	132	0	129	3	79	53	123	9	111	21	114	18	117	15	123	9
49	69	0	69	0	47	22	43	26	48	21	11	58	52	17	20	49	52	17
50	189	1	190	0	111	79	70	120	88	102	72	118	32	158	52	138	32	158
51	134	0	134	0	87	47	40	94	54	80	54	80	28	106	34	100	28	106
52	147	0	146	1	74	73	42	105	73	74	68	79	39	108	66	81	63	84
53	6	0	5	1	0	6	0	6	3	3	0	6	0	6	0	6	0	6
54	894	2	894	2	760	136	333	563	666	230	419	477	439	457	447	449	243	653
55	299	0	299	0	215	84	114	185	189	110	187	112	103	196	116	183	82	217
56	608	2	607	3	262	348	195	415	299	311	309	301	190	420	196	414	225	385
57	43	0	43	0	43	0	43	0	43	0	18	25	42	1	37	6	43	0
58	16	1	16	1	12	5	6	11	7	10	0	17	5	12	6	11	7	10
59	86	5	87	4	32	59	32	59	28	63	24	67	32	59	32	59	35	56
60	43	0	43	0	43	0	43	0	43	0	18	25	42	1	37	6	43	0
61	115	0	115	0	98	17	44	71	98	17	111	4	51	64	67	48	51	64
62	122	0	122	0	116	6	104	18	116	6	107	15	104	18	104	18	104	18
63	70	0	70	0	57	13	54	16	56	14	56	14	56	14	60	10	54	16
64	273	0	273	0	270	3	226	47	270	3	199	74	226	47	228	45	226	47
65	113	0	113	0	92	21	18	95	69	44	104	9	18	95	21	92	18	95
66	38	0	38	0	31	7	31	7	33	5	31	7	25	13	26	12	31	7
67	4	1	5	0	4	1	2	3	2	3	0	5	2	3	2	3	2	3
68	6	0	6	0	5	1	1	5	5	1	1	5	1	5	1	5	1	5
69	0	1	1	0	1	0	1	0	1	0	0	1	1	0	1	0	1	0
70	391	0	391	0	282	109	222	169	299	92	123	268	252	139	212	179	248	143
71	477	0	472	5	368	109	231	246	352	125	210	267	264	213	271	206	268	209
72	1299	0	1299	0	1104	195	487	812	1097	202	406	893	928	371	359	940	993	306
73	1904	44	1856	92	1635	313	766	1182	1460	488	812	1136	1181	767	933	1015	1206	742
74	252	0	252	0	219	33	162	90	219	33	54	198	206	46	57	195	211	41
75	371	0	283	88	54	317	54	317	54	317	177	194	53	318	55	316	54	317
76	28	1	27	2	22	7	18	11	19	10	18	11	18	11	20	9	19	10
77	325	61	322	64	230	156	113	273	245	141	79	307	180	206	107	279	209	177
78	104	0	103	1	102	2	31	73	100	4	12	92	61	43	35	69	69	35
79	144	0	144	0	95	49	68	76	79	65	51	93	79	65	143	1	75	69
80	462	0	462	0	300	162	136	326	288	174	40	422	250	212	178	284	270	192
81	261	0	261	0	238	23	135	126	238	23	116	145	177	84	146	115	172	89
82	376	0	376	0	357	19	229	147	357	19	126	250	347	29	202	174	357	19
83	272	3	275	0	243	32	111	164	257	18	28	247	159	116	60	215	222	53
84	9	1	10	0	10	0	4	6	10	0	0	10	10	0	0	10	10	0
85	22	0	22	0	22	0	0	22	22	0	0	22	4	18	0	22	13	9
86	438	0	438	0	368	70	164	274	320	118	129	309	250	188	199	239	274	164
87	298	0	296	2	275	23	212	86	277	21	141	157	227	71	197	101	228	70
88	170	0	170	0	131	39	119	51	131	39	122	48	129	41	128	42	131	39
89	343	1	344	0	329	15	252	92	329	15	211	133	295	49	258	86	297	47
90	454	0	454	0	438	16	312	142	438	16	248	206	394	60	327	127	434	20
91	404	0	404	0	338	66	204	200	338	66	204	200	296	108	275	129	332	72
92	797	1	793	5	654	144	272	526	646	152	308	490	508	290	442	356	504	294
93	143	0	121	22	107	36	54	89	107	36	31	112	79	64	66	77	89	54
94	309	1	301	9	286	24	227	83	276	34	142	168	239	71	214	96	236	74
95	176	6	170	12	156	26	58	124	128	54	50	132	95	87	85	97	87	95
96	151	0	151	0	145	6	1	150	145	6	12	139	73	78	29	122	126	25
97	316	0	316	0	287	29	72	244	273	43	22	294	246	70	130	186	274	42
98	240	6	246	0	230	16	70	176	230	16	102	144	171	75	125	121	155	91
99	505	2	503	4	489	18	355	152	456	51	239	268	397	110	283	224	389	118
100	167	5	172	0	169	3	87	85	167	5	78	94	131	41	101	71	127	45
101	1130	2	1126	6	1087	45	613	519	1048	84	496	636	938	194	653	479	921	211
102	754	40	787	7	749	45	534	260	681	113	382	412	634	160	462	332	618	176
103	844	33	869	8	812	65	232	645	613	264	195	682	634	243	428	449	580	297
104	11	2	11	2	7	6	1	12	6	7	5	8	5	8	4	9	5	8
105	169	11	173	7	163	17	106	74	154	26	102	78	135	45	92	88	121	59
106	205	7	212	0	205	7	33	179	136	76	37	175	102	110	39	173	95	117
107	37	0	37	0	37	0	19	18	37	0	28	9	37	0	32	5	32	5
108	168	0	165	3	165	3	135	33	126	42	71	97	122	46	53	115	96	72
109	206	1	204	3	181	26	128	79	181	26	82	125	175	32	75	132	177	30
110	237	23	260	0	259	1	128	132	167	93	86	174	98	162	3	257	124	136
111	33	17	50	0	50	0	5	45	21	29	2	48	8	42	0	50	20	30
112	51	24	75	0	75	0	8	67	20	55	8	67	19	56	11	64	28	47
113	29	3	29	3	25	7	17	15	25	7	10	22	23	9	4	28	19	13
114	344	0	344	0	343	1	7	337	344	0	29	315	14	330	35	309	14	330
115	1104	5	1107	2	1041	68	736	373	1037	72	511	598	900	209	759	350	881	228
116	401	92	445	48	436	57	42	451	402	91	232	261	110	383	80	413	127	366
117	30	0	30	0	30	0	0	30	30	0	0	30	6	24	6	24	25	5
118	881	200	868	213	810	271	178	903	610	471	230	851	417	664	317	764	364	717
119	108	0	108	0	104	4	63	45	92	16	41	67	81	27	82	26	81	27
120	190	0	190	0	187	3	60	130	158	32	76	114	131	59	131	59	113	77
121	183	79	189	73	180	82	0	262	94	168	31	231	15	247	0	262	30	232
122	46	88	47	87	47	87	0	134	16	118	0	134	10	124	1	133	2	132
123	117	0	117	0	99	18	64	53	75	42	50	67	86	31	61	56	87	30
124	255	0	255	0	160	95	135	120	201	54	49	206	156	99	99	156	132	123
125	143	0	143	0	135	8	73	70	135	8	127	16	126	17	135	8	81	62
126	294	0	292	2	182	112	83	211	181	113	76	218	135	159	101	193	151	143
127	56	0	38	18	13	43	5	51	8	48	16	40	7	49	7	49	7	49
128	92	1	87	6	63	30	18	75	59	34	48	45	39	54	51	42	39	54
129	109	4	110	3	89	24	52	61	79	34	51	62	73	40	77	36	49	64
130	108	11	100	19	73	46	2	117	42	77	25	94	52	67	52	67	13	106
131	219	5	199	25	95	129	70	154	87	137	51	173	82	142	89	135	87	137
132	24	12	36	0	3	33	2	34	3	33	2	34	2	34	2	34	3	33
133	5	0	5	0	1	4	1	4	5	0	1	4	3	2	3	2	3	2
134	10	3	12	1	0	13	0	13	0	13	3	10	0	13	0	13	3	10
135	45	5	50	0	43	7	12	38	43	7	19	31	32	18	16	34	34	16
136	62	0	62	0	59	3	0	62	62	0	0	62	58	4	0	62	22	40
137	53	0	53	0	11	42	3	50	39	14	7	46	9	44	6	47	33	20
138	90	0	90	0	88	2	24	66	88	2	33	57	71	19	48	42	83	7
139	7	1	8	0	8	0	3	5	6	2	3	5	3	5	8	0	3	5
140	84	3	83	4	79	8	24	63	77	10	42	45	68	19	52	35	65	22
141	9	0	9	0	9	0	9	0	9	0	9	0	9	0	9	0	9	0
142	161	12	171	2	147	26	81	92	148	25	84	89	99	74	121	52	99	74
143	168	10	160	18	149	29	85	93	155	23	85	93	97	81	123	55	105	73
144	93	1	94	0	94	0	39	55	69	25	56	38	54	40	62	32	42	52
145	67	0	67	0	67	0	33	34	52	15	48	19	33	34	52	15	38	29
146	54	0	54	0	54	0	50	4	54	0	54	0	50	4	54	0	50	4
147	298	22	298	22	259	61	125	195	190	130	186	134	153	167	192	128	145	175
148	238	2	237	3	173	67	53	187	178	62	45	195	62	178	116	124	60	180
149	536	0	536	0	499	37	412	124	466	70	366	170	289	247	313	223	477	59
150	195	0	176	19	141	54	56	139	127	68	44	151	72	123	43	152	113	82
151	48	50	90	8	41	57	0	98	89	9	82	16	2	96	2	96	20	78
152	19	8	17	10	0	27	0	27	1	26	0	27	12	15	0	27	2	25
153	52	0	52	0	52	0	15	37	52	0	11	41	52	0	52	0	52	0
154	384	14	398	0	378	20	209	189	375	23	185	213	304	94	267	131	308	90
155	701	9	692	18	586	124	469	241	629	81	338	372	344	366	551	159	368	342
156	137	0	137	0	115	22	86	51	132	5	60	77	72	65	79	58	75	62
157	120	4	112	12	95	29	90	34	113	11	62	62	80	44	67	57	65	59
158	93	0	85	8	81	12	78	15	93	0	50	43	54	39	53	40	54	39
159	385	14	383	16	204	195	146	253	299	100	98	301	147	252	148	251	112	287
160	12	8	20	0	6	14	9	11	14	6	7	13	5	15	6	14	6	14
161	15	0	15	0	11	4	11	4	11	4	6	9	11	4	4	11	10	5
162	15	0	15	0	11	4	6	9	11	4	3	12	11	4	11	4	10	5
163	1402	14	1387	29	1110	306	631	785	1127	289	460	956	780	636	706	710	1067	349
164	909	10	897	22	756	163	473	446	812	107	194	725	529	390	482	437	721	198
165	76	4	80	0	64	16	14	66	63	17	3	77	6	74	58	22	58	22
166	46	0	46	0	39	7	32	14	38	8	36	10	32	14	36	10	34	12
167	1401	0	1372	29	1097	304	624	777	1114	287	459	942	773	628	699	702	1066	335
168	314	0	314	0	267	47	220	94	279	35	133	181	190	124	183	131	186	128
169	193	0	193	0	121	72	106	87	123	70	79	114	102	91	60	133	79	114
170	454	0	445	9	331	123	224	230	280	174	272	182	191	263	146	308	259	195
171	255	0	249	6	143	112	70	185	93	162	49	206	61	194	49	206	51	204
172	314	0	301	13	225	89	238	76	210	104	125	189	191	123	200	114	197	117
173	261	0	247	14	159	102	178	83	154	107	54	207	118	143	125	136	131	130
174	106	2	107	1	42	66	68	40	41	67	20	88	36	72	35	73	43	65
175	553	13	562	4	360	206	226	340	221	345	170	396	217	349	209	357	195	371
176	640	88	686	42	426	302	373	355	441	287	217	511	391	337	328	400	389	339
177	24	20	44	0	40	4	36	8	36	8	16	28	16	28	16	28	16	28
178	537	1	538	0	446	92	243	295	439	99	99	439	213	325	248	290	162	376
179	98	0	98	0	73	25	44	54	73	25	44	54	65	33	50	48	44	54
180	645	1	633	13	569	77	288	358	533	113	106	540	314	332	258	388	215	431
181	206	2	201	7	178	30	142	66	178	30	5	203	164	44	154	54	154	54
182	835	3	796	42	633	205	219	619	581	257	166	672	433	405	345	493	267	571
183	1545	14	1508	51	1343	216	979	580	1291	268	243	1316	1189	370	1126	433	1033	526
184	51	0	45	6	50	1	16	35	31	20	4	47	20	31	13	38	12	39
185	356	2	334	24	296	62	133	225	275	83	102	256	201	157	178	180	129	229
186	19	0	15	4	13	6	13	6	13	6	8	11	13	6	13	6	12	7
187	32	0	18	14	5	27	7	25	9	23	1	31	1	31	9	23	2	30
188	145	0	145	0	134	11	77	68	121	24	71	74	94	51	94	51	77	68
189	523	2	516	9	467	58	300	225	428	97	62	463	293	232	298	227	188	337
190	9	0	9	0	9	0	2	7	9	0	5	4	9	0	9	0	9	0
191	19	0	19	0	19	0	5	14	17	2	6	13	9	10	19	0	6	13
192	331	17	346	2	264	84	203	145	322	26	117	231	181	167	143	205	138	210
193	113	0	113	0	113	0	53	60	113	0	26	87	71	42	20	93	20	93
194	357	0	349	8	245	112	270	87	305	52	115	242	183	174	129	228	138	219
195	36	0	36	0	34	2	34	2	36	0	20	16	34	2	16	20	10	26
196	12	24	36	0	33	3	31	5	36	0	22	14	31	5	35	1	25	11
197	294	0	294	0	197	97	92	202	197	97	18	276	66	228	80	214	83	211
198	62	0	62	0	45	17	39	23	45	17	32	30	39	23	35	27	32	30
199	89	0	89	0	88	1	27	62	57	32	23	66	32	57	34	55	32	57
200	22	0	22	0	22	0	17	5	21	1	1	21	21	1	18	4	18	4
201	189	0	189	0	135	54	140	49	137	52	55	134	112	77	74	115	51	138
202	99	0	99	0	87	12	69	30	91	8	34	65	52	47	30	69	29	70
203	34	0	34	0	32	2	32	2	34	0	18	16	32	2	15	19	10	24
204	932	0	929	3	853	79	325	607	675	257	105	827	296	636	310	622	238	694
205	4	0	4	0	4	0	0	4	0	4	0	4	0	4	0	4	0	4
206	1	0	1	0	1	0	1	0	1	0	0	1	1	0	1	0	1	0
207	644	0	635	9	628	16	209	435	470	174	68	576	190	454	231	413	164	480
208	392	1	389	4	238	155	119	274	238	155	15	378	71	322	75	318	117	276
209	1541	0	1535	6	1495	46	496	1045	1160	381	123	1418	497	1044	629	912	438	1103
210	72	0	72	0	72	0	33	39	61	11	23	49	45	27	45	27	26	46
211	54	0	54	0	52	2	53	1	53	1	11	43	53	1	40	14	39	15
212	21	0	21	0	21	0	2	19	18	3	6	15	19	2	19	2	19	2
213	20	0	20	0	20	0	4	16	18	2	5	15	20	0	20	0	10	10
214	387	0	387	0	267	120	137	250	241	146	18	369	92	295	122	265	29	358
215	709	0	709	0	590	119	412	297	581	128	127	582	265	444	377	332	191	518
216	91	0	90	1	83	8	79	12	83	8	8	83	82	9	83	8	73	18
217	1332	12	1271	73	1124	220	589	755	1177	167	295	1049	506	838	853	491	226	1118
218	855	0	819	36	777	78	428	427	783	72	209	646	311	544	529	326	149	706
219	167	4	169	2	122	49	84	87	105	66	63	108	84	87	104	67	77	94
220	500	1	499	2	412	89	269	232	416	85	96	405	301	200	283	218	233	268
221	45	4	49	0	30	19	0	49	40	9	0	49	0	49	0	49	0	49
222	62	1	63	0	58	5	49	14	63	0	28	35	35	28	32	31	21	42
223	66	0	66	0	36	30	61	5	48	18	36	30	36	30	38	28	36	30
224	52	0	52	0	37	15	37	15	37	15	8	44	17	35	26	26	16	36
225	24	0	23	1	23	1	19	5	23	1	6	18	23	1	23	1	11	13
226	21	0	21	0	21	0	17	4	21	0	4	17	21	0	21	0	11	10
227	106	0	104	2	103	3	3	103	103	3	2	104	3	103	103	3	3	103
228	64	0	64	0	63	1	23	41	64	0	11	53	61	3	39	25	7	57
229	28	3	31	0	19	12	0	31	31	0	0	31	0	31	0	31	0	31
230	61	0	61	0	58	3	49	12	61	0	28	33	35	26	28	33	19	42
231	299	0	299	0	227	72	93	206	218	81	29	270	88	211	78	221	83	216
232	878	1	871	8	733	146	323	556	609	270	47	832	342	537	323	556	251	628
233	301	5	306	0	267	39	175	131	243	63	7	299	191	115	193	113	191	115
234	356	6	342	20	328	34	186	176	257	105	38	324	251	111	178	184	169	193
235	240	2	235	7	219	23	98	144	146	96	5	237	122	120	56	186	60	182
236	286	0	282	4	264	22	166	120	238	48	1	285	225	61	191	95	140	146
237	628	6	633	1	578	56	214	420	458	176	8	626	295	339	195	439	151	483
238	70	0	70	0	70	0	48	22	70	0	3	67	46	24	49	21	45	25
239	1361	12	1341	32	1251	122	511	862	1036	337	11	1362	717	656	552	821	397	976
240	468	2	438	32	430	40	290	180	416	54	22	448	287	183	243	227	219	251
241	46	0	46	0	42	4	36	10	46	0	20	26	24	22	24	22	24	22
242	83	0	79	4	51	32	48	35	63	20	37	46	43	40	47	36	46	37
243	70	0	70	0	53	17	28	42	53	17	9	61	28	42	16	54	31	39
244	59	0	53	6	41	18	25	34	41	18	3	56	40	19	33	26	33	26
245	16	0	16	0	16	0	12	4	16	0	0	16	16	0	16	0	16	0
246	23	0	23	0	23	0	18	5	23	0	0	23	23	0	23	0	23	0
247	24	0	24	0	24	0	24	0	24	0	4	20	24	0	24	0	24	0
248	1	0	1	0	1	0	0	1	1	0	0	1	0	1	0	1	0	1
249	27	0	27	0	27	0	18	9	27	0	0	27	19	8	8	19	8	19
250	84	0	80	4	52	32	51	33	64	20	37	47	44	40	47	37	48	36
251	114	4	114	4	68	50	84	34	92	26	54	64	88	30	56	62	29	89
252	138	32	150	20	91	79	99	71	103	67	59	111	100	70	73	97	22	148
253	17	20	33	4	23	14	20	17	28	9	23	14	28	9	17	20	18	19
254	877	16	886	7	852	41	617	276	854	39	391	502	676	217	643	250	519	374
255	291	3	294	0	290	4	271	23	290	4	66	228	287	7	290	4	255	39
256	456	163	611	8	528	91	429	190	528	91	212	407	451	168	397	222	189	430
257	395	2	397	0	359	38	341	56	365	32	123	274	244	153	155	242	141	256
258	9	0	9	0	9	0	1	8	9	0	1	8	1	8	1	8	1	8
259	330	0	305	25	150	180	141	189	183	147	67	263	90	240	149	181	109	221
260	144	2	146	0	114	32	114	32	115	31	43	103	63	83	50	96	42	104
261	44	10	54	0	54	0	22	32	53	1	1	53	48	6	54	0	0	54
262	346	3	345	4	276	73	90	259	164	185	130	219	213	136	73	276	85	264
263	15	0	15	0	14	1	4	11	4	11	4	11	11	4	4	11	4	11
264	187	4	191	0	182	9	57	134	68	123	83	108	131	60	64	127	75	116
265	199	0	199	0	177	22	70	129	59	140	81	118	131	68	65	134	87	112
266	498	3	500	1	470	31	191	310	207	294	147	354	161	340	90	411	140	361
267	180	3	181	2	163	20	35	148	44	139	31	152	40	143	15	168	29	154
268	30	0	30	0	7	23	7	23	18	12	18	12	15	15	7	23	11	19
269	95	0	91	4	64	31	28	67	49	46	33	62	55	40	20	75	24	71
270	15	0	15	0	14	1	4	11	4	11	4	11	11	4	4	11	4	11
271	227	0	224	3	216	11	75	152	85	142	100	127	161	66	73	154	89	138
272	117	0	116	1	113	4	55	62	55	62	55	62	71	46	33	84	47	70
273	703	2	689	16	650	55	247	458	264	441	207	498	256	449	146	559	206	499
274	23	0	23	0	23	0	7	16	7	16	6	17	7	16	1	22	6	17
275	23	0	23	0	20	3	3	20	2	21	1	22	2	21	2	21	3	20
276	153	0	151	2	134	19	86	67	143	10	51	102	62	91	55	98	72	81
277	166	0	163	3	151	15	93	73	92	74	93	73	98	68	108	58	103	63
278	31	0	27	4	30	1	14	17	12	19	11	20	13	18	14	17	14	17
279	1283	16	1278	21	1198	101	406	893	564	735	563	736	626	673	753	546	757	542
280	70	1	68	3	70	1	36	35	28	43	24	47	28	43	30	41	29	42
281	86	0	84	2	86	0	46	40	83	3	10	76	29	57	29	57	29	57
282	61	0	61	0	60	1	42	19	39	22	38	23	38	23	38	23	38	23
283	1	0	0	1	1	0	0	1	0	1	0	1	0	1	0	1	0	1
284	37	0	37	0	33	4	24	13	24	13	15	22	20	17	17	20	20	17
285	52	1	49	4	52	1	30	23	22	31	19	34	26	27	24	29	23	30
286	50	0	49	1	37	13	18	32	28	22	13	37	27	23	10	40	2	48
287	174	0	174	0	140	34	62	112	124	50	67	107	96	78	53	121	44	130
288	49	0	49	0	36	13	15	34	27	22	12	37	25	24	12	37	2	47
289	178	0	178	0	147	31	63	115	123	55	65	113	94	84	57	121	46	132
290	711	10	717	4	651	70	534	187	683	38	254	467	525	196	459	262	454	267
291	123	0	123	0	102	21	104	19	123	0	26	97	97	26	104	19	93	30
292	123	48	171	0	165	6	120	51	165	6	41	130	165	6	129	42	154	17
293	448	54	496	6	341	161	289	213	465	37	118	384	205	297	209	293	183	319
294	102	0	102	0	80	22	84	18	78	24	32	70	54	48	29	73	44	58
295	33	0	33	0	31	2	31	2	33	0	9	24	31	2	9	24	10	23
296	369	0	369	0	334	35	266	103	353	16	121	248	280	89	221	148	147	222
297	43	0	43	0	43	0	16	27	35	8	13	30	27	16	22	21	11	32
298	489	0	466	23	451	38	183	306	418	71	67	422	224	265	231	258	213	276
299	183	0	182	1	111	72	143	40	150	33	61	122	103	80	70	113	61	122
300	111	0	111	0	111	0	64	47	111	0	26	85	71	40	20	91	41	70
301	68	0	68	0	58	10	62	6	60	8	24	44	43	25	21	47	36	32
302	33	0	33	0	31	2	31	2	33	0	9	24	31	2	9	24	11	22
303	337	0	337	0	307	30	208	129	326	11	104	233	254	83	190	147	202	135
304	50	0	50	0	50	0	18	32	41	9	16	34	32	18	27	23	15	35
305	42	0	42	0	40	2	19	23	41	1	7	35	21	21	34	8	33	9
306	77	0	72	5	69	8	63	14	64	13	30	47	44	33	39	38	39	38
307	258	0	257	1	215	43	161	97	219	39	71	187	189	69	185	73	167	91
308	263	0	263	0	249	14	177	86	263	0	39	224	227	36	185	78	193	70
309	61	0	61	0	58	3	55	6	61	0	28	33	35	26	28	33	28	33
310	229	0	228	1	169	60	108	121	183	46	35	194	129	100	135	94	117	112
311	53	0	53	0	43	10	16	37	53	0	7	46	36	17	32	21	10	43
312	16	0	16	0	8	8	5	11	12	4	3	13	4	12	4	12	4	12
313	91	0	87	4	57	34	46	45	71	20	43	48	51	40	54	37	54	37
314	200	1	192	9	140	61	90	111	183	18	14	187	111	90	94	107	107	94
315	220	0	220	0	180	40	147	73	220	0	10	210	144	76	121	99	169	51
316	27	2	29	0	19	10	13	16	25	4	4	25	8	21	8	21	8	21
317	90	0	85	5	56	34	62	28	70	20	43	47	50	40	54	36	53	37
318	174	1	175	0	136	39	109	66	169	6	3	172	107	68	91	84	78	97
319	27	0	27	0	14	13	10	17	27	0	0	27	20	7	5	22	8	19
320	12	0	12	0	4	8	4	8	4	8	4	8	4	8	4	8	2	10
321	117	2	117	2	84	35	84	35	92	27	32	87	88	31	70	49	66	53
322	146	32	156	22	111	67	109	69	111	67	35	143	106	72	95	83	98	80
323	26	11	32	5	26	11	20	17	28	9	17	20	28	9	21	16	25	12
324	288	2	290	0	185	105	69	221	118	172	72	218	65	225	54	236	70	220
325	15	0	15	0	7	8	4	11	4	11	4	11	4	11	1	14	4	11
326	187	4	191	0	141	50	78	113	67	124	74	117	59	132	59	132	73	118
327	271	1	272	0	221	51	95	177	64	208	78	194	65	207	64	208	86	186
328	481	3	481	3	431	53	206	278	205	279	151	333	58	426	96	388	127	357
329	57	0	56	1	50	7	21	36	20	37	16	41	13	44	11	46	17	40
330	190	0	186	4	116	74	42	148	74	116	22	168	43	147	33	157	41	149
331	15	0	15	0	7	8	4	11	4	11	0	15	4	11	1	14	1	14
332	166	0	160	6	120	46	57	109	52	114	25	141	39	127	32	134	46	120
333	177	0	176	1	148	29	69	108	56	121	37	140	59	118	56	121	62	115
334	414	3	415	2	352	65	170	247	177	240	51	366	51	366	79	338	120	297
335	69	1	68	2	61	9	16	54	28	42	9	61	16	54	12	58	16	54
336	361	0	359	2	342	19	268	93	350	11	98	263	261	100	239	122	74	287
337	242	0	231	11	205	37	154	88	147	95	82	160	127	115	128	114	145	97
338	50	0	49	1	49	1	30	20	17	33	10	40	17	33	17	33	16	34
339	537	0	534	3	508	29	269	268	261	276	144	393	177	360	177	360	177	360
340	78	1	76	3	78	1	35	44	17	62	15	64	17	62	17	62	17	62
341	179	0	175	4	157	22	149	30	159	20	60	119	90	89	98	81	54	125
342	49	0	49	0	48	1	41	8	28	21	23	26	27	22	26	23	27	22
343	1	0	1	0	1	0	0	1	0	1	0	1	0	1	0	1	0	1
344	27	0	27	0	23	4	25	2	21	6	11	16	20	7	14	13	14	13
345	49	1	49	1	49	1	33	17	17	33	15	35	17	33	17	33	17	33
346	34	0	32	2	26	8	11	23	17	17	0	34	0	34	5	29	0	34
347	189	0	189	0	153	36	62	127	129	60	49	140	45	144	51	138	45	144
348	28	0	27	1	14	14	10	18	15	13	1	27	0	28	5	23	1	27
349	179	0	179	0	104	75	61	118	123	56	35	144	46	133	49	130	46	133
350	311	0	300	11	188	123	140	171	258	53	196	115	136	175	203	108	149	162
351	206	12	190	28	154	64	120	98	190	28	118	100	60	158	60	158	60	158
352	74	0	72	2	64	10	42	32	73	1	33	41	54	20	47	27	38	36
353	136	0	134	2	118	18	57	79	126	10	51	85	72	64	34	102	56	80
354	135	1	136	0	104	32	34	102	34	102	51	85	34	102	34	102	56	80
355	233	0	226	7	199	34	74	159	185	48	128	105	51	182	153	80	75	158
356	14	0	12	2	14	0	6	8	6	8	6	8	3	11	6	8	6	8
357	196	0	193	3	152	44	127	69	104	92	45	151	16	180	71	125	19	177
358	355	65	355	65	244	176	17	403	112	308	82	338	12	408	12	408	31	389
359	304	17	319	2	308	13	297	24	308	13	263	58	296	25	289	32	263	58
360	163	0	163	0	159	4	151	12	163	0	144	19	163	0	151	12	157	6
361	1891	1109	2904	96	2974	26	2800	200	2997	3	2835	165	2628	372	2719	281	2728	272
362	1867	1133	2910	90	2970	30	2805	195	2996	4	2835	165	2639	361	2689	311	2722	278
363	1866	1134	2893	107	2974	26	2793	207	2999	1	2832	168	2604	396	2699	301	2738	262
364	842	493	1298	37	1331	4	1233	102	1335	0	1272	63	1157	178	1210	125	1233	102
365	8	7	11	4	15	0	2	13	14	1	2	13	0	15	1	14	0	15
366	1996	1158	2962	192	2630	524	1270	1884	2321	833	1124	2030	1315	1839	1501	1653	1142	2012
367	73	38	110	1	110	1	42	69	97	14	78	33	73	38	107	4	48	63

1.12 Timing

The command AbsoluteTiming[] was used in Mathematica to obtain the elapsed time for each integrate call. In Maple, the command Usage was used as in the following example

cpu_time := Usage(assign ('result_of_int',int(expr,x)),output='realtime'

For all other CAS systems, the elapsed time to complete each integral was found by taking the difference between the time after the call completed from the time before the call was made. This was done using Python’s time.time() call.

All elapsed times shown are in seconds. A time limit of 3 CPU minutes was used for each integral. If the integrate command did not complete within this time limit, the integral was aborted and considered to have failed and assigned an F grade. The time used by failed integrals due to time out was not counted in the final statistics.

1.13 Verification

A verification phase was applied on the result of integration for Rubi and Mathematica.

Future version of this report will implement verification for the other CAS systems. For the integrals whose result was not run through a verification phase, it is assumed that the antiderivative was correct.

Verification phase also had 3 minutes time out. An integral whose result was not verified could still be correct, but further investigation is needed on those integrals. These integrals were marked in the summary table below and also in each integral separate section so they are easy to identify and locate.

1.14 Important notes about some of the results

Important note about Maxima results

Since tests were run in a batch mode, and using an automated script, then any integral where Maxima needed an interactive response from the user to answer a question during the evaluation of the integral will fail.

The exception raised is ValueError. Therefore Maxima results is lower than what would result if Maxima was run directly and each question was answered correctly.

The percentage of such failures were not counted for each test file, but for an example, for the Timofeev test file, there were about 14 such integrals out of total 705, or about 2 percent. This percentage can be higher or lower depending on the specific input test file.

Such integrals can be identified by looking at the output of the integration in each section for Maxima. The exception message will indicate the cause of error.

Maxima integrate was run using SageMath with the following settings set by default

'besselexpand : true' 
'display2d : false' 
'domain : complex' 
'keepfloat : true' 
'load(to_poly_solve)' 
'load(simplify_sum)' 
'load(abs_integrate)' 'load(diag)'
 

SageMath automatic loading of Maxima abs_integrate was found to cause some problems. So the following code was added to disable this effect.

 from sage.interfaces.maxima_lib import maxima_lib 
 maxima_lib.set('extra_definite_integration_methods', '[]') 
 maxima_lib.set('extra_integration_methods', '[]')
 

See https://ask.sagemath.org/question/43088/integrate-results-that-are-different-from-using-maxima/ for reference.

Important note about FriCAS result

There were few integrals which failed due to SageMath interface and not because FriCAS system could not do the integration.

These will fail With error Exception raised: NotImplementedError.

The number of such cases seems to be very small. About 1 or 2 percent of all integrals. These can be identified by looking at the exception message given in the result.

Important note about finding leaf size of antiderivative

For Mathematica, Rubi, and Maple, the builtin system function LeafSize was used to find the leaf size of each antiderivative.

The other CAS systems (SageMath and Sympy) do not have special builtin function for this purpose at this time. Therefore the leaf size for Fricas and Sympy antiderivative was determined using the following function, thanks to user slelievre at https://ask.sagemath.org/question/57123/could-we-have-a-leaf_count-function-in-base-sagemath/

def tree_size(expr): 
    r""" 
    Return the tree size of this expression. 
    """ 
    if expr not in SR: 
        # deal with lists, tuples, vectors 
        return 1 + sum(tree_size(a) for a in expr) 
    expr = SR(expr) 
    x, aa = expr.operator(), expr.operands() 
    if x is None: 
        return 1 
    else: 
        return 1 + sum(tree_size(a) for a in aa)
 

For Sympy, which was called directly from Python, the following code was used to obtain the leafsize of its result

try: 
  # 1.7 is a fudge factor since it is low side from actual leaf count 
  leafCount = round(1.7*count_ops(anti)) 
 
  except Exception as ee: 
         leafCount =1
 

Important note about Mupad results

Matlab’s symbolic toolbox does not have a leaf count function to measure the size of the antiderivative. Maple was used to determine the leaf size of Mupad output by post processing Mupad result.

Currently no grading of the antiderivative for Mupad is implemented. If it can integrate the problem, it was assigned a B grade automatically as a placeholder. In the future, when grading function is implemented for Mupad, the tests will be rerun again.

The following is an example of using Matlab’s symbolic toolbox (Mupad) to solve an integral

integrand = evalin(symengine,'cos(x)*sin(x)') 
the_variable = evalin(symengine,'x') 
anti = int(integrand,the_variable)
 

Which gives sin(x)^2/2

1.15 Current tree layout of integration tests

1.16 Design of the test system

The following diagram gives a high level view of the current test build system.