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Integrals 1 to 100

Detailed conclusion table per each integral is given by the 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 as F.

In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B A A A B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

33 0 40 39 105 41 39 56 113

N.S.

1 0.00 1.21 1.18 3.18 1.24 1.18 1.70 3.42

time (sec)

N/A 0.000 0.166 2.712 0.457 0.268 11.140 1.049 0.713

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 26 26 35 20 38 31 34 34

N.S.

1 0.96 0.96 1.30 0.74 1.41 1.15 1.26 1.26

time (sec)

N/A 1.286 0.179 0.300 0.213 0.282 0.153 0.289 7.463

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 28 26 26 37 78 32 91 36

N.S.

1 0.85 0.79 0.79 1.12 2.36 0.97 2.76 1.09

time (sec)

N/A 0.286 0.046 13.881 0.421 0.274 0.192 0.724 7.328

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 30 33 28 32 32 29 32 31

N.S.

1 1.11 1.22 1.04 1.19 1.19 1.07 1.19 1.15

time (sec)

N/A 0.009 0.004 0.019 0.203 0.270 0.022 0.291 7.097

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 42 18 26 0 27 20 27 23

N.S.

1 1.75 0.75 1.08 0.00 1.12 0.83 1.12 0.96

time (sec)

N/A 0.173 0.107 0.047 0.000 0.274 0.097 0.271 7.142

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 13 13 11 10 10 10 10 10

N.S.

1 0.50 0.50 0.42 0.38 0.38 0.38 0.38 0.38

time (sec)

N/A 0.008 0.006 0.011 0.169 0.263 0.044 0.290 0.048

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B A A F(-2) B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

24 0 24 23 125 25 26 0 29

N.S.

1 0.00 1.00 0.96 5.21 1.04 1.08 0.00 1.21

time (sec)

N/A 0.000 1.191 2.684 0.575 0.248 0.314 0.000 7.495

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F B A B B F(-2) B F(-1)

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

33 0 75 65 108 98 0 70 0

N.S.

1 0.00 2.27 1.97 3.27 2.97 0.00 2.12 0.00

time (sec)

N/A 0.000 55.714 1.895 0.254 0.269 0.000 0.529 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B B F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 23 23 82 0 45 41 0 0

N.S.

1 0.96 0.96 3.42 0.00 1.88 1.71 0.00 0.00

time (sec)

N/A 0.277 0.032 0.849 0.000 0.260 0.337 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

24 0 22 20 23 23 22 25 19

N.S.

1 0.00 0.92 0.83 0.96 0.96 0.92 1.04 0.79

time (sec)

N/A 0.000 0.052 0.138 0.212 0.260 0.074 0.280 7.432

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A B A B B B B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

29 0 28 87 53 58 155 86 743

N.S.

1 0.00 0.97 3.00 1.83 2.00 5.34 2.97 25.62

time (sec)

N/A 0.000 0.091 3.196 0.229 0.274 0.257 0.340 7.954

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 13 13 14 13 13 12 13 13

N.S.

1 0.57 0.57 0.61 0.57 0.57 0.52 0.57 0.57

time (sec)

N/A 0.329 0.032 0.056 0.260 0.282 0.075 0.249 7.271

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A F B B B B F(-1)

verified

N/A N/A Yes N/A TBD TBD TBD TBD TBD

size

25 0 42 0 131 217 148 1110 0

N.S.

1 0.00 1.68 0.00 5.24 8.68 5.92 44.40 0.00

time (sec)

N/A 0.000 0.148 0.000 0.842 0.285 0.502 78.983 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B B B B B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

36 0 40 45 68 94 54 118 62

N.S.

1 0.00 1.11 1.25 1.89 2.61 1.50 3.28 1.72

time (sec)

N/A 0.000 9.686 0.115 0.244 0.288 0.134 0.303 0.544

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B A B B B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

29 0 28 34 289 59 92 65 33

N.S.

1 0.00 0.97 1.17 9.97 2.03 3.17 2.24 1.14

time (sec)

N/A 0.000 4.650 0.278 0.320 0.268 0.107 0.270 0.405

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 19 18 17 17 17 17 17

N.S.

1 1.00 1.36 1.29 1.21 1.21 1.21 1.21 1.21

time (sec)

N/A 0.056 0.009 0.073 0.190 0.257 0.181 0.251 0.161

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 33 18 18 17 17 15 17 14

N.S.

1 2.20 1.20 1.20 1.13 1.13 1.00 1.13 0.93

time (sec)

N/A 0.024 0.053 0.023 0.181 0.269 0.054 0.286 7.357

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 90 12 70 456 69 78 69 69

N.S.

1 6.92 0.92 5.38 35.08 5.31 6.00 5.31 5.31

time (sec)

N/A 1.120 0.009 0.053 0.197 0.260 0.118 0.273 7.487

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F F B B B B B B

verified

N/A N/A N/A Yes TBD TBD TBD TBD TBD

size

28 0 0 62 135 137 199 185 33454

N.S.

1 0.00 0.00 2.21 4.82 4.89 7.11 6.61 1194.79

time (sec)

N/A 0.000 0.000 1.659 0.388 0.271 0.630 0.316 24.118

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A B B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

32 0 35 30 34 34 31 53 35

N.S.

1 0.00 1.09 0.94 1.06 1.06 0.97 1.66 1.09

time (sec)

N/A 0.000 5.033 0.147 0.231 0.262 0.114 0.261 7.408

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F F A B B F(-2) A F(-1)

verified

N/A N/A N/A Yes TBD TBD TBD TBD TBD

size

28 0 0 44 62 59 0 49 0

N.S.

1 0.00 0.00 1.57 2.21 2.11 0.00 1.75 0.00

time (sec)

N/A 0.000 0.000 0.718 0.225 0.256 0.000 0.362 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 17 17 17 16 16 14 16 16

N.S.

1 1.06 1.06 1.06 1.00 1.00 0.88 1.00 1.00

time (sec)

N/A 0.005 0.005 0.012 0.201 0.265 0.033 0.282 0.053

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A F(-2) B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 21 20 19 72 33 15 0 18

N.S.

1 0.91 0.87 0.83 3.13 1.43 0.65 0.00 0.78

time (sec)

N/A 60.183 0.891 51.653 0.368 0.273 0.194 0.000 7.510

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A F A A A B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

27 0 43 27 0 31 26 54 44

N.S.

1 0.00 1.59 1.00 0.00 1.15 0.96 2.00 1.63

time (sec)

N/A 0.000 0.066 5.544 0.000 0.273 0.241 0.270 7.324

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 21 19 19 29 17 17 17 19

N.S.

1 0.95 0.86 0.86 1.32 0.77 0.77 0.77 0.86

time (sec)

N/A 0.120 0.078 0.095 0.279 0.258 0.092 0.313 10.838

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 15 15 16 15 15 14 15 15

N.S.

1 0.75 0.75 0.80 0.75 0.75 0.70 0.75 0.75

time (sec)

N/A 0.004 0.000 0.019 0.205 0.253 0.018 0.303 0.035

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 67 50 49 47 47 46 51 63

N.S.

1 3.35 2.50 2.45 2.35 2.35 2.30 2.55 3.15

time (sec)

N/A 0.304 0.454 0.054 0.188 0.254 0.068 0.335 0.119

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 11 11 12 11 14 7 12 11

N.S.

1 0.92 0.92 1.00 0.92 1.17 0.58 1.00 0.92

time (sec)

N/A 0.005 0.002 0.012 0.190 0.258 0.028 0.262 0.027

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 14 15 15 25 21 17 15 15

N.S.

1 0.88 0.94 0.94 1.56 1.31 1.06 0.94 0.94

time (sec)

N/A 0.217 0.147 0.057 0.308 0.271 0.108 0.265 7.343

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

19 0 15 18 19 17 20 22 17

N.S.

1 0.00 0.79 0.95 1.00 0.89 1.05 1.16 0.89

time (sec)

N/A 0.000 0.088 0.147 0.284 0.254 0.088 0.273 7.975

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 19 19 27 23 17 23 18

N.S.

1 1.00 1.00 1.00 1.42 1.21 0.89 1.21 0.95

time (sec)

N/A 0.066 0.078 0.048 0.290 0.265 0.095 0.282 7.200

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 21 21 20 19 19 17 19 21

N.S.

1 1.11 1.11 1.05 1.00 1.00 0.89 1.00 1.11

time (sec)

N/A 0.177 0.814 0.065 0.324 0.277 0.089 0.254 7.277

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A B B B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

22 0 26 34 37 36 31 81 84

N.S.

1 0.00 1.18 1.55 1.68 1.64 1.41 3.68 3.82

time (sec)

N/A 0.000 1.275 0.272 0.430 0.262 0.098 0.267 7.360

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A B A F B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

20 0 17 17 18 48 15 0 16

N.S.

1 0.00 0.85 0.85 0.90 2.40 0.75 0.00 0.80

time (sec)

N/A 0.000 0.184 0.134 0.363 0.273 0.138 0.000 7.803

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 17 27 17 15 17 16

N.S.

1 1.00 1.00 0.94 1.50 0.94 0.83 0.94 0.89

time (sec)

N/A 0.046 0.060 0.018 0.180 0.261 0.042 0.244 0.048

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 79 30 28 30 33 31 33 33

N.S.

1 3.16 1.20 1.12 1.20 1.32 1.24 1.32 1.32

time (sec)

N/A 0.205 0.761 0.103 0.261 0.272 0.062 0.253 7.332

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A B B B B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 58 32 25 114 114 54 117 0

N.S.

1 2.76 1.52 1.19 5.43 5.43 2.57 5.57 0.00

time (sec)

N/A 1.392 0.046 0.207 0.220 0.260 0.104 0.309 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F F A A B A B F(-1)

verified

N/A N/A N/A Yes TBD TBD TBD TBD TBD

size

33 0 0 39 40 83 39 57 0

N.S.

1 0.00 0.00 1.18 1.21 2.52 1.18 1.73 0.00

time (sec)

N/A 0.000 0.000 0.085 0.542 0.267 1.110 0.846 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A B A B B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

29 0 26 25 54 76 31 108 24

N.S.

1 0.00 0.90 0.86 1.86 2.62 1.07 3.72 0.83

time (sec)

N/A 0.000 0.098 1.936 0.258 0.259 0.133 0.301 8.174

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

21 0 19 18 26 17 17 17 17

N.S.

1 0.00 0.90 0.86 1.24 0.81 0.81 0.81 0.81

time (sec)

N/A 0.000 0.101 0.223 0.226 0.264 0.073 0.279 8.462

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 25 25 23 0 41 19 0 0

N.S.

1 0.89 0.89 0.82 0.00 1.46 0.68 0.00 0.00

time (sec)

N/A 1.206 0.232 0.146 0.000 0.270 0.093 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A B A F B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

18 0 18 23 15 61 20 0 18

N.S.

1 0.00 1.00 1.28 0.83 3.39 1.11 0.00 1.00

time (sec)

N/A 0.000 0.680 0.056 0.492 0.255 0.116 0.000 8.827

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 9 8 7 7 7 7 7

N.S.

1 1.00 1.00 0.89 0.78 0.78 0.78 0.78 0.78

time (sec)

N/A 0.013 0.009 0.015 0.183 0.258 0.061 0.250 0.062

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 21 19 22 24 35 24 23 24

N.S.

1 0.81 0.73 0.85 0.92 1.35 0.92 0.88 0.92

time (sec)

N/A 0.185 0.042 0.070 0.204 0.254 0.085 0.257 8.153

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 25 21 26 25 27 22 29 25

N.S.

1 0.78 0.66 0.81 0.78 0.84 0.69 0.91 0.78

time (sec)

N/A 0.369 0.121 0.047 0.235 0.259 0.074 0.260 8.315

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 20 22 17 16 16 19 16 17

N.S.

1 1.05 1.16 0.89 0.84 0.84 1.00 0.84 0.89

time (sec)

N/A 0.008 0.003 0.035 0.175 0.242 0.034 0.248 7.840

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 20 18 28 23 31 17 18 18

N.S.

1 0.87 0.78 1.22 1.00 1.35 0.74 0.78 0.78

time (sec)

N/A 0.435 0.091 0.073 0.212 0.241 0.070 0.254 8.178

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 46 23 42 41 42 42 47 21

N.S.

1 1.84 0.92 1.68 1.64 1.68 1.68 1.88 0.84

time (sec)

N/A 0.105 0.108 0.034 0.169 0.245 0.077 0.267 8.006

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 38 34 34 39 31 26 2943 0

N.S.

1 1.12 1.00 1.00 1.15 0.91 0.76 86.56 0.00

time (sec)

N/A 1.800 0.090 1.676 0.460 0.250 0.647 0.820 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 42 34 36 39 39 32 39 33

N.S.

1 2.21 1.79 1.89 2.05 2.05 1.68 2.05 1.74

time (sec)

N/A 0.015 0.006 0.019 0.194 0.236 0.022 0.265 8.138

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

17 0 25 17 19 16 14 19 19

N.S.

1 0.00 1.47 1.00 1.12 0.94 0.82 1.12 1.12

time (sec)

N/A 0.000 0.137 0.099 0.218 0.245 0.114 0.275 8.975

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 28 28 29 36 36 37 37 28

N.S.

1 1.27 1.27 1.32 1.64 1.64 1.68 1.68 1.27

time (sec)

N/A 0.015 0.004 0.028 0.186 0.233 0.044 0.245 0.061

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 20 20 24 24 24 24 105 24

N.S.

1 0.83 0.83 1.00 1.00 1.00 1.00 4.38 1.00

time (sec)

N/A 0.367 0.139 0.451 0.329 0.260 0.121 0.323 10.300

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 34 22 28 63 26 29 30 33

N.S.

1 1.13 0.73 0.93 2.10 0.87 0.97 1.00 1.10

time (sec)

N/A 0.418 1.089 0.171 0.258 0.246 0.133 0.365 8.467

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 43 25 22 171 26 22 26 22

N.S.

1 1.59 0.93 0.81 6.33 0.96 0.81 0.96 0.81

time (sec)

N/A 0.256 0.154 0.051 0.291 0.253 0.042 0.254 8.458

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 21 21 37 36 36 39 42 42

N.S.

1 1.05 1.05 1.85 1.80 1.80 1.95 2.10 2.10

time (sec)

N/A 0.095 1.430 0.117 0.176 0.242 0.119 0.254 8.631

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B B F B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 267 70 57 0 80 48 96 67

N.S.

1 9.54 2.50 2.04 0.00 2.86 1.71 3.43 2.39

time (sec)

N/A 0.915 0.127 0.151 0.000 0.244 0.159 0.252 8.560

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B A A B B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

19 0 18 18 38 30 20 38 212

N.S.

1 0.00 0.95 0.95 2.00 1.58 1.05 2.00 11.16

time (sec)

N/A 0.000 0.269 0.066 0.223 0.259 0.057 0.264 8.321

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 29 29 30 29 29 29 30 29

N.S.

1 1.12 1.12 1.15 1.12 1.12 1.12 1.15 1.12

time (sec)

N/A 0.095 0.015 0.027 0.174 0.248 0.066 0.259 0.147

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 18 18 25 17 24 26 26 19

N.S.

1 0.75 0.75 1.04 0.71 1.00 1.08 1.08 0.79

time (sec)

N/A 0.499 0.119 0.245 0.210 0.246 0.103 0.291 8.222

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 47 58 42 49 49 49 49 42

N.S.

1 1.34 1.66 1.20 1.40 1.40 1.40 1.40 1.20

time (sec)

N/A 0.017 0.017 0.023 0.182 0.252 0.052 0.257 0.077

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 22 11 14 14 17 14 10

N.S.

1 1.00 1.22 0.61 0.78 0.78 0.94 0.78 0.56

time (sec)

N/A 0.003 0.002 0.008 0.196 0.244 0.018 0.265 0.045

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A B B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

21 0 19 21 25 25 22 52 37

N.S.

1 0.00 0.90 1.00 1.19 1.19 1.05 2.48 1.76

time (sec)

N/A 0.000 0.156 0.161 0.296 0.242 0.063 0.260 8.101

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

19 0 16 20 19 19 26 19 14

N.S.

1 0.00 0.84 1.05 1.00 1.00 1.37 1.00 0.74

time (sec)

N/A 0.000 0.037 0.487 0.223 0.255 0.144 0.261 8.805

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 26 21 25 24 24 0 24 24

N.S.

1 1.24 1.00 1.19 1.14 1.14 0.00 1.14 1.14

time (sec)

N/A 0.257 0.232 0.066 0.331 0.248 0.000 0.349 9.962

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 28 24 25 24 24 22 24 0

N.S.

1 1.08 0.92 0.96 0.92 0.92 0.85 0.92 0.00

time (sec)

N/A 0.273 0.137 0.148 0.232 0.239 0.075 0.250 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A B A A B B F(-1)

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

37 0 55 91 51 61 66 100 0

N.S.

1 0.00 1.49 2.46 1.38 1.65 1.78 2.70 0.00

time (sec)

N/A 0.000 0.083 0.259 0.227 0.250 0.236 0.339 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 73 32 34 100 39 37 43 38

N.S.

1 2.70 1.19 1.26 3.70 1.44 1.37 1.59 1.41

time (sec)

N/A 0.118 0.030 0.061 0.172 0.250 0.107 0.264 8.245

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 15 17 10 9 17 8 9 9

N.S.

1 0.58 0.65 0.38 0.35 0.65 0.31 0.35 0.35

time (sec)

N/A 0.011 0.007 0.069 0.168 0.239 0.032 0.260 8.093

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 18 15 20 0 22 15 17 14

N.S.

1 0.82 0.68 0.91 0.00 1.00 0.68 0.77 0.64

time (sec)

N/A 0.313 0.176 0.071 0.000 0.243 0.107 0.255 7.990

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 35 30 20 22 22 37 22 22

N.S.

1 1.17 1.00 0.67 0.73 0.73 1.23 0.73 0.73

time (sec)

N/A 0.122 0.034 0.060 0.183 0.241 0.871 0.260 0.119

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A F(-1)

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

30 0 33 32 33 33 29 33 0

N.S.

1 0.00 1.10 1.07 1.10 1.10 0.97 1.10 0.00

time (sec)

N/A 0.000 5.285 0.306 0.296 0.223 0.075 0.252 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 60 81 80 97 90 112 95 99

N.S.

1 2.31 3.12 3.08 3.73 3.46 4.31 3.65 3.81

time (sec)

N/A 0.108 0.047 0.097 0.202 0.231 0.326 0.246 0.335

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A F A A F(-2) B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

32 0 30 37 0 36 36 0 36

N.S.

1 0.00 0.94 1.16 0.00 1.12 1.12 0.00 1.12

time (sec)

N/A 0.000 0.130 34.749 0.000 0.240 2.583 0.000 9.484

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 7 7 8 7 9 3 7 7

N.S.

1 0.30 0.30 0.35 0.30 0.39 0.13 0.30 0.30

time (sec)

N/A 0.003 0.001 0.016 0.180 0.219 0.023 0.250 0.029

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 27 54 27 28 28 27 28 26

N.S.

1 1.08 2.16 1.08 1.12 1.12 1.08 1.12 1.04

time (sec)

N/A 0.085 0.019 0.189 0.238 0.233 0.776 0.259 8.740

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B A B A F(-1)

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

29 0 58 31 65 41 80 50 0

N.S.

1 0.00 2.00 1.07 2.24 1.41 2.76 1.72 0.00

time (sec)

N/A 0.000 5.058 0.706 0.315 0.240 9.372 0.259 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 14 14 11 10 10 12 10 10

N.S.

1 0.82 0.82 0.65 0.59 0.59 0.71 0.59 0.59

time (sec)

N/A 0.012 0.003 0.021 0.188 0.232 0.046 0.256 8.478

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 33 35 27 25 25 29 26 22

N.S.

1 1.18 1.25 0.96 0.89 0.89 1.04 0.93 0.79

time (sec)

N/A 0.020 0.006 0.028 0.172 0.231 0.054 0.259 8.311

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 249 50 50 53 63 51 57 72

N.S.

1 7.55 1.52 1.52 1.61 1.91 1.55 1.73 2.18

time (sec)

N/A 3.819 0.271 0.329 0.240 0.241 1.490 0.257 8.707

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

22 0 28 25 23 24 22 24 98

N.S.

1 0.00 1.27 1.14 1.05 1.09 1.00 1.09 4.45

time (sec)

N/A 0.000 3.412 0.304 0.265 0.232 0.107 0.276 8.429

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F(-1) F C F A A A B

verified

N/A N/A N/A No TBD TBD TBD TBD TBD

size

44 0 0 169 0 59 44 43 157

N.S.

1 0.00 0.00 3.84 0.00 1.34 1.00 0.98 3.57

time (sec)

N/A 0.000 0.000 0.295 0.000 0.254 8.118 4.083 9.112

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 21 27 19 18 25 17 20 18

N.S.

1 0.78 1.00 0.70 0.67 0.93 0.63 0.74 0.67

time (sec)

N/A 0.060 0.010 0.070 0.193 0.228 0.164 0.254 8.074

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 28 28 27 24 31 29 26 25

N.S.

1 0.82 0.82 0.79 0.71 0.91 0.85 0.76 0.74

time (sec)

N/A 0.273 0.238 0.237 0.316 0.240 0.114 0.329 8.204

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 22 21 18 21 17 24 21 0

N.S.

1 0.96 0.91 0.78 0.91 0.74 1.04 0.91 0.00

time (sec)

N/A 0.201 0.972 0.916 0.347 0.224 0.187 0.304 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A F(-2) A F(-2) A B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

27 0 15 15 0 19 0 19 14

N.S.

1 0.00 0.56 0.56 0.00 0.70 0.00 0.70 0.52

time (sec)

N/A 0.000 0.101 0.277 0.000 0.236 0.000 0.275 7.770

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 72 19 46 44 45 58 49 24

N.S.

1 3.79 1.00 2.42 2.32 2.37 3.05 2.58 1.26

time (sec)

N/A 0.146 0.018 0.033 0.200 0.232 0.087 0.279 7.893

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 23 23 18 18 18 19 18 18

N.S.

1 0.92 0.92 0.72 0.72 0.72 0.76 0.72 0.72

time (sec)

N/A 0.009 0.003 0.100 0.185 0.227 0.047 0.279 0.130

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A F(-2) A B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

23 0 23 31 20 20 0 22 20

N.S.

1 0.00 1.00 1.35 0.87 0.87 0.00 0.96 0.87

time (sec)

N/A 0.000 0.469 57.569 0.236 0.240 0.000 0.310 8.417

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 29 29 21 20 20 20 20 20

N.S.

1 1.12 1.12 0.81 0.77 0.77 0.77 0.77 0.77

time (sec)

N/A 0.011 0.018 0.020 0.177 0.227 0.040 0.271 7.632

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F F A B A A A B

verified

N/A N/A N/A Yes TBD TBD TBD TBD TBD

size

25 0 0 27 64 45 19 40 712

N.S.

1 0.00 0.00 1.08 2.56 1.80 0.76 1.60 28.48

time (sec)

N/A 0.000 0.000 0.331 0.316 0.231 0.079 0.330 9.623

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 21 21 21 20 20 17 20 20

N.S.

1 0.84 0.84 0.84 0.80 0.80 0.68 0.80 0.80

time (sec)

N/A 0.260 0.025 13.005 0.242 0.246 0.115 0.334 8.476

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 21 21 21 20 23 17 23 20

N.S.

1 0.75 0.75 0.75 0.71 0.82 0.61 0.82 0.71

time (sec)

N/A 0.021 0.021 0.036 0.186 0.231 0.069 0.270 7.372

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A C B F(-1) B B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

35 0 56 74 188 69 0 72 3724

N.S.

1 0.00 1.60 2.11 5.37 1.97 0.00 2.06 106.40

time (sec)

N/A 0.000 0.090 2.773 0.446 0.238 0.000 0.335 11.228

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 22 35 18 30 0 19 65

N.S.

1 1.00 1.00 1.59 0.82 1.36 0.00 0.86 2.95

time (sec)

N/A 1.460 0.492 2.301 0.292 0.225 0.000 0.378 7.628

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A F B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

24 0 24 26 37 24 24 0 38

N.S.

1 0.00 1.00 1.08 1.54 1.00 1.00 0.00 1.58

time (sec)

N/A 0.000 2.000 180.234 0.537 0.294 0.306 0.000 7.689

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 13 13 12 11 11 8 11 11

N.S.

1 0.59 0.59 0.55 0.50 0.50 0.36 0.50 0.50

time (sec)

N/A 0.140 0.053 0.042 0.220 0.236 0.049 0.303 7.555

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

24 0 21 24 17 28 27 27 17

N.S.

1 0.00 0.88 1.00 0.71 1.17 1.12 1.12 0.71

time (sec)

N/A 0.000 0.029 0.864 0.274 0.236 0.131 0.275 7.999

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F B B B B F(-2) B F(-1)

verified

N/A N/A Yes Yes TBD TBD TBD TBD TBD

size

30 0 70 52 64 65 0 53 0

N.S.

1 0.00 2.33 1.73 2.13 2.17 0.00 1.77 0.00

time (sec)

N/A 0.000 0.166 0.371 0.268 0.259 0.000 0.499 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 24 21 22 0 25 26 25 20

N.S.

1 1.09 0.95 1.00 0.00 1.14 1.18 1.14 0.91

time (sec)

N/A 0.324 1.139 0.060 0.000 0.249 0.082 0.260 8.679

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