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2.2.1 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 A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 26 31 25 20 33 14

N.S.

1 1.00 1.00 1.86 2.21 1.79 1.43 2.36 1.00

time (sec)

N/A 0.120 0.005 0.189 0.199 0.254 0.058 0.280 0.055

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 14 15 14 14 26 14 14

N.S.

1 1.00 1.00 1.07 1.00 1.00 1.86 1.00 1.00

time (sec)

N/A 0.116 0.004 0.220 0.283 0.243 0.054 0.276 0.041

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 13 18 17 26 27 40 11

N.S.

1 1.00 1.00 1.38 1.31 2.00 2.08 3.08 0.85

time (sec)

N/A 0.142 0.003 0.125 0.182 0.297 0.067 0.279 0.252

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 23 8 19 23 22 21 7

N.S.

1 1.00 2.09 0.73 1.73 2.09 2.00 1.91 0.64

time (sec)

N/A 0.137 0.033 0.135 0.192 0.259 0.059 0.271 0.079

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 21 27 29 22 29 24

N.S.

1 1.00 1.00 1.40 1.80 1.93 1.47 1.93 1.60

time (sec)

N/A 0.147 0.009 0.293 0.214 0.255 0.092 0.280 0.243

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

2 2 2 3 4 4 3 4 12

N.S.

1 1.00 1.00 1.50 2.00 2.00 1.50 2.00 6.00

time (sec)

N/A 0.141 0.002 0.069 0.194 0.254 0.020 0.313 0.331

Problem 7

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

4 4 4 5 6 6 5 6 6

N.S.

1 1.00 1.00 1.25 1.50 1.50 1.25 1.50 1.50

time (sec)

N/A 0.145 0.002 0.052 0.196 0.261 0.037 0.284 0.253

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

6 6 6 5 27 4 7 4 4

N.S.

1 1.00 1.00 0.83 4.50 0.67 1.17 0.67 0.67

time (sec)

N/A 0.168 0.026 0.102 0.231 0.248 0.319 0.293 0.205

Problem 9

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

9 9 6 5 9 9 3 30 4

N.S.

1 1.00 0.67 0.56 1.00 1.00 0.33 3.33 0.44

time (sec)

N/A 0.152 0.003 0.059 0.192 0.247 0.086 0.287 0.211

Problem 10

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 12 8 9 10 10 7 8 6

N.S.

1 1.00 0.67 0.75 0.83 0.83 0.58 0.67 0.50

time (sec)

N/A 0.157 0.002 0.069 0.204 0.240 0.163 0.285 0.002

Problem 11

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 12 12 13 13 12 15 14 13

N.S.

1 1.00 1.00 1.08 1.08 1.00 1.25 1.17 1.08

time (sec)

N/A 0.172 0.048 0.237 0.226 0.252 0.092 0.306 0.220

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 16 15 15 31 15 15

N.S.

1 1.00 1.00 1.07 1.00 1.00 2.07 1.00 1.00

time (sec)

N/A 0.183 0.013 0.692 0.288 0.282 0.222 0.288 0.049

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 33 33 26 44 35 15

N.S.

1 1.00 1.00 2.20 2.20 1.73 2.93 2.33 1.00

time (sec)

N/A 0.183 0.013 0.500 0.212 0.252 0.252 0.275 0.204

Problem 14

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 17 17 18 17 21 32 17 48

N.S.

1 1.00 1.00 1.06 1.00 1.24 1.88 1.00 2.82

time (sec)

N/A 0.207 0.012 6.745 0.224 0.265 0.872 0.298 0.597

Problem 15

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 20 20 23 34 21 48

N.S.

1 1.00 1.00 1.05 1.05 1.21 1.79 1.11 2.53

time (sec)

N/A 0.203 0.013 6.177 0.226 0.275 0.914 0.280 0.592

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

18 22 22 19 18 18 34 18 58

N.S.

1 1.22 1.22 1.06 1.00 1.00 1.89 1.00 3.22

time (sec)

N/A 0.204 0.018 10.257 0.214 0.265 0.872 0.279 0.462

Problem 17

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 22 22 19 19 19 32 20 58

N.S.

1 1.22 1.22 1.06 1.06 1.06 1.78 1.11 3.22

time (sec)

N/A 0.204 0.016 9.131 0.207 0.270 0.937 0.287 0.470

Problem 18

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

41 21 19 14 13 31 61 46 26

N.S.

1 0.51 0.46 0.34 0.32 0.76 1.49 1.12 0.63

time (sec)

N/A 0.171 0.109 0.151 0.306 0.271 0.223 0.299 0.257

Problem 19

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

6 6 6 6 15 15 15 16 15

N.S.

1 1.00 1.00 1.00 2.50 2.50 2.50 2.67 2.50

time (sec)

N/A 0.150 0.001 0.033 0.221 0.251 0.048 0.284 0.002

Problem 20

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

3 3 3 4 3 3 3 4 3

N.S.

1 1.00 1.00 1.33 1.00 1.00 1.00 1.33 1.00

time (sec)

N/A 0.138 0.001 0.025 0.197 0.243 0.035 0.271 0.206

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

3 3 3 4 3 3 15 3 3

N.S.

1 1.00 1.00 1.33 1.00 1.00 5.00 1.00 1.00

time (sec)

N/A 0.150 0.005 0.103 0.285 0.268 0.068 0.293 0.411

Problem 22

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

9 9 7 8 7 7 7 22 7

N.S.

1 1.00 0.78 0.89 0.78 0.78 0.78 2.44 0.78

time (sec)

N/A 0.148 0.034 0.040 0.210 0.235 0.039 0.325 0.261

Problem 23

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 10 9 9 7 9 9

N.S.

1 1.00 1.00 1.11 1.00 1.00 0.78 1.00 1.00

time (sec)

N/A 0.146 0.035 0.033 0.201 0.241 0.041 0.285 0.278

Problem 24

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 37 25 22 22 24 22 23 24

N.S.

1 1.48 1.00 0.88 0.88 0.96 0.88 0.92 0.96

time (sec)

N/A 0.169 0.026 0.066 0.209 0.248 0.151 0.294 0.047

Problem 25

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 38 30 21 20 22 31 21 22

N.S.

1 1.27 1.00 0.70 0.67 0.73 1.03 0.70 0.73

time (sec)

N/A 0.280 0.034 0.027 0.196 0.237 0.933 0.274 0.036

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

10 10 10 9 10 10 8 11 8

N.S.

1 1.00 1.00 0.90 1.00 1.00 0.80 1.10 0.80

time (sec)

N/A 0.137 0.003 0.155 0.200 0.244 0.024 0.287 0.086

Problem 27

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

47 30 47 24 36 40 42 37 47

N.S.

1 0.64 1.00 0.51 0.77 0.85 0.89 0.79 1.00

time (sec)

N/A 0.142 0.034 0.194 0.284 0.248 0.045 0.274 0.138

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

30 30 30 24 23 23 27 21 21

N.S.

1 1.00 1.00 0.80 0.77 0.77 0.90 0.70 0.70

time (sec)

N/A 0.137 0.016 0.190 0.289 0.255 0.044 0.278 0.042

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

21 21 21 14 13 24 22 17 13

N.S.

1 1.00 1.00 0.67 0.62 1.14 1.05 0.81 0.62

time (sec)

N/A 0.162 0.052 0.249 0.199 0.246 0.128 0.301 0.190

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 12 11 24 26 11 11

N.S.

1 1.00 1.00 0.80 0.73 1.60 1.73 0.73 0.73

time (sec)

N/A 0.164 0.002 0.237 0.210 0.254 0.127 0.282 0.059

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 25 21 20 186 89 138 18 118

N.S.

1 1.19 1.00 0.95 8.86 4.24 6.57 0.86 5.62

time (sec)

N/A 0.255 0.088 0.240 0.299 0.273 0.560 0.286 1.426

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

14 14 14 11 10 10 10 10 10

N.S.

1 1.00 1.00 0.79 0.71 0.71 0.71 0.71 0.71

time (sec)

N/A 0.150 0.002 0.059 0.197 0.245 0.022 0.269 0.029

Problem 33

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 14 11 10 10 10 10 10

N.S.

1 1.00 1.00 0.79 0.71 0.71 0.71 0.71 0.71

time (sec)

N/A 0.152 0.002 0.063 0.198 0.241 0.016 0.271 0.027

Problem 34

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

8 8 8 7 6 6 7 6 12

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.88 0.75 1.50

time (sec)

N/A 0.157 0.002 0.125 0.203 0.249 0.017 0.303 0.030

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

11 11 11 15 14 22 15 14 11

N.S.

1 1.00 1.00 1.36 1.27 2.00 1.36 1.27 1.00

time (sec)

N/A 0.178 0.010 0.308 0.216 0.238 0.033 0.290 0.099

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

7 7 6 11 9 18 12 9 6

N.S.

1 1.00 0.86 1.57 1.29 2.57 1.71 1.29 0.86

time (sec)

N/A 0.176 0.003 0.287 0.201 0.247 0.024 0.293 0.254

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 28 17 12 23 19 18 10

N.S.

1 1.00 2.00 1.21 0.86 1.64 1.36 1.29 0.71

time (sec)

N/A 0.162 0.017 0.052 0.273 0.240 0.025 0.435 0.232

Problem 38

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 16 26 19 12 20 17 22 18

N.S.

1 1.00 1.62 1.19 0.75 1.25 1.06 1.38 1.12

time (sec)

N/A 0.201 0.017 0.059 0.287 0.247 0.058 0.304 0.331

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 12 29 11 12 19 10 12 12

N.S.

1 1.20 2.90 1.10 1.20 1.90 1.00 1.20 1.20

time (sec)

N/A 0.195 0.014 0.183 0.274 0.240 0.143 0.291 0.285

Problem 40

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 14 15 14 25 10 14 14

N.S.

1 1.00 1.00 1.07 1.00 1.79 0.71 1.00 1.00

time (sec)

N/A 0.275 0.009 0.438 0.279 0.248 0.325 0.296 0.297

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 25 15 28 24 29 12 12

N.S.

1 1.00 2.27 1.36 2.55 2.18 2.64 1.09 1.09

time (sec)

N/A 0.198 0.046 0.101 0.290 0.251 0.230 0.292 0.243

Problem 42

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 16 31 17 23 14 8 12 10

N.S.

1 1.00 1.94 1.06 1.44 0.88 0.50 0.75 0.62

time (sec)

N/A 0.215 0.094 0.093 0.272 0.268 0.211 0.292 0.180

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

25 36 33 19 18 22 19 18 18

N.S.

1 1.44 1.32 0.76 0.72 0.88 0.76 0.72 0.72

time (sec)

N/A 0.175 0.033 0.052 0.197 0.242 0.046 0.286 0.238

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

21 21 21 14 13 13 12 15 8

N.S.

1 1.00 1.00 0.67 0.62 0.62 0.57 0.71 0.38

time (sec)

N/A 0.152 0.004 0.224 0.208 0.249 0.042 0.292 0.242

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

14 16 14 11 10 10 10 10 10

N.S.

1 1.14 1.00 0.79 0.71 0.71 0.71 0.71 0.71

time (sec)

N/A 0.153 0.008 0.078 0.271 0.228 0.043 0.277 0.068

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

51 51 47 29 35 45 42 44 34

N.S.

1 1.00 0.92 0.57 0.69 0.88 0.82 0.86 0.67

time (sec)

N/A 0.208 0.027 0.283 0.271 0.260 0.050 0.277 0.129

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 No Yes Yes TBD TBD TBD TBD TBD

size

33 22 33 26 25 25 29 25 25

N.S.

1 0.67 1.00 0.79 0.76 0.76 0.88 0.76 0.76

time (sec)

N/A 0.155 0.022 0.136 0.200 0.232 0.056 0.290 0.246

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 29 19 18 68 73 18 19

N.S.

1 1.00 1.00 0.66 0.62 2.34 2.52 0.62 0.66

time (sec)

N/A 0.143 0.025 0.181 0.289 0.244 0.377 0.284 0.217

Problem 49

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 31 20 17 22 19 37 19 20

N.S.

1 1.15 0.74 0.63 0.81 0.70 1.37 0.70 0.74

time (sec)

N/A 0.150 0.019 0.178 0.284 0.236 0.135 0.300 0.035

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 28 19 18 25 29 10 18

N.S.

1 1.00 1.27 0.86 0.82 1.14 1.32 0.45 0.82

time (sec)

N/A 0.140 0.127 0.256 0.281 0.243 0.498 0.309 0.069

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 22 21 12 26 22 20 24

N.S.

1 1.00 1.00 0.95 0.55 1.18 1.00 0.91 1.09

time (sec)

N/A 0.143 0.026 0.438 0.286 0.261 0.498 0.287 0.311

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 53 37 34 25 22 43 21

N.S.

1 1.00 2.30 1.61 1.48 1.09 0.96 1.87 0.91

time (sec)

N/A 0.143 0.051 0.208 0.210 0.243 0.522 0.305 0.554

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 21 49 35 12 40 7 37 26

N.S.

1 1.00 2.33 1.67 0.57 1.90 0.33 1.76 1.24

time (sec)

N/A 0.158 0.041 0.221 0.201 0.245 0.508 0.310 0.107

Problem 54

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

12 12 21 7 8 30 8 26 6

N.S.

1 1.00 1.75 0.58 0.67 2.50 0.67 2.17 0.50

time (sec)

N/A 0.129 0.082 0.250 0.275 0.246 0.229 0.292 0.243

Problem 55

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

19 21 33 15 16 38 20 53 26

N.S.

1 1.11 1.74 0.79 0.84 2.00 1.05 2.79 1.37

time (sec)

N/A 0.137 0.086 0.796 0.286 0.264 0.260 0.298 0.382

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

8 8 40 7 6 16 5 25 6

N.S.

1 1.00 5.00 0.88 0.75 2.00 0.62 3.12 0.75

time (sec)

N/A 0.124 0.044 0.424 0.308 0.244 0.192 0.286 0.219

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 36 22 21 43 22 21 40

N.S.

1 1.00 1.33 0.81 0.78 1.59 0.81 0.78 1.48

time (sec)

N/A 0.146 0.128 0.254 0.323 0.278 0.358 0.289 0.419

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 30 25 33 39 0 71 28

N.S.

1 1.00 0.94 0.78 1.03 1.22 0.00 2.22 0.88

time (sec)

N/A 0.144 0.108 0.250 0.300 0.258 0.000 0.305 0.427

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 23 21 16 17 17 0 28 19

N.S.

1 1.10 1.00 0.76 0.81 0.81 0.00 1.33 0.90

time (sec)

N/A 0.136 0.139 0.276 0.298 0.245 0.000 0.318 0.301

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

28 28 54 21 33 39 22 31 22

N.S.

1 1.00 1.93 0.75 1.18 1.39 0.79 1.11 0.79

time (sec)

N/A 0.296 0.160 0.216 0.221 0.271 0.299 0.292 0.361

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 18 17 14 13 31 0 46 26

N.S.

1 0.49 0.46 0.38 0.35 0.84 0.00 1.24 0.70

time (sec)

N/A 0.173 0.541 0.155 0.313 0.258 0.000 0.285 0.294

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 12 21 11 47 32 27 11 10

N.S.

1 0.86 1.50 0.79 3.36 2.29 1.93 0.79 0.71

time (sec)

N/A 0.199 0.064 0.200 0.221 0.255 0.499 0.273 0.281

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 3 9 4 15 45 15 17 3

N.S.

1 0.27 0.82 0.36 1.36 4.09 1.36 1.55 0.27

time (sec)

N/A 0.187 0.007 0.063 0.218 0.252 0.061 0.280 0.392

Problem 64

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

18 19 19 15 14 14 0 14 14

N.S.

1 1.06 1.06 0.83 0.78 0.78 0.00 0.78 0.78

time (sec)

N/A 0.213 0.021 0.184 0.213 0.267 0.000 0.269 0.424

Problem 65

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 15 14 15 17 14 14

N.S.

1 1.00 1.00 0.83 0.78 0.83 0.94 0.78 0.78

time (sec)

N/A 0.206 0.024 0.257 0.216 0.269 0.795 0.259 0.376

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 17 16 15 15 0 15 37

N.S.

1 1.00 1.00 0.94 0.88 0.88 0.00 0.88 2.18

time (sec)

N/A 0.152 0.036 0.132 0.296 0.251 0.000 0.279 0.355

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F A A A A B

verified

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

size

20 20 22 0 18 16 19 16 16

N.S.

1 1.00 1.10 0.00 0.90 0.80 0.95 0.80 0.80

time (sec)

N/A 0.162 0.039 0.000 0.215 0.256 0.281 0.273 0.411

Problem 68

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 12 12 13 12 12 15 12 12

N.S.

1 1.00 1.00 1.08 1.00 1.00 1.25 1.00 1.00

time (sec)

N/A 0.167 0.008 0.546 0.221 0.256 0.833 0.268 0.296

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 42 38 0 38 0 15 0

N.S.

1 1.00 1.00 0.90 0.00 0.90 0.00 0.36 0.00

time (sec)

N/A 0.190 0.049 0.247 0.000 0.256 0.000 0.285 0.000

Problem 70

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

8 8 8 7 6 6 7 6 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.88 0.75 0.75

time (sec)

N/A 0.160 0.009 0.168 0.305 0.254 0.411 0.260 0.394

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

28 28 28 23 17 22 22 22 17

N.S.

1 1.00 1.00 0.82 0.61 0.79 0.79 0.79 0.61

time (sec)

N/A 0.160 0.000 0.021 0.211 0.239 0.040 0.287 0.034

Problem 72

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 17 17 11 13 11 15 13 9

N.S.

1 1.00 1.00 0.65 0.76 0.65 0.88 0.76 0.53

time (sec)

N/A 0.138 0.003 0.034 0.210 0.252 0.040 0.269 0.229

Problem 73

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

36 39 38 29 28 28 26 70 40

N.S.

1 1.08 1.06 0.81 0.78 0.78 0.72 1.94 1.11

time (sec)

N/A 0.201 0.009 0.108 0.212 0.257 0.048 0.285 0.413

Problem 74

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 17 15 18 17 15 21

N.S.

1 1.00 1.00 0.89 0.79 0.95 0.89 0.79 1.11

time (sec)

N/A 0.173 0.001 0.302 0.204 0.262 0.022 0.276 0.002

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

34 44 30 23 18 25 31 22 26

N.S.

1 1.29 0.88 0.68 0.53 0.74 0.91 0.65 0.76

time (sec)

N/A 0.260 0.001 0.318 0.207 0.255 0.017 0.270 0.024

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 31 71 26 42 69 46 38 33

N.S.

1 1.19 2.73 1.00 1.62 2.65 1.77 1.46 1.27

time (sec)

N/A 0.238 0.014 0.329 0.210 0.250 0.069 0.269 0.261

Problem 77

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 23 14 12 11 17 17 11 11

N.S.

1 1.00 0.61 0.52 0.48 0.74 0.74 0.48 0.48

time (sec)

N/A 0.151 0.015 0.125 0.207 0.248 0.163 0.277 0.022

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

27 27 22 20 19 21 26 19 19

N.S.

1 1.00 0.81 0.74 0.70 0.78 0.96 0.70 0.70

time (sec)

N/A 0.156 0.053 0.132 0.206 0.257 0.093 0.270 0.030

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 20 21 24 20 107 329 20

N.S.

1 1.00 0.65 0.68 0.77 0.65 3.45 10.61 0.65

time (sec)

N/A 0.162 0.022 0.161 0.215 0.243 0.269 0.304 0.030

Problem 80

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 17 17 11 10 13 15 13 13

N.S.

1 1.00 1.00 0.65 0.59 0.76 0.88 0.76 0.76

time (sec)

N/A 0.146 0.003 0.073 0.207 0.259 0.127 0.271 0.240

Problem 81

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

12 12 12 13 94 22 15 12 35

N.S.

1 1.00 1.00 1.08 7.83 1.83 1.25 1.00 2.92

time (sec)

N/A 0.190 0.019 0.565 0.286 0.246 17.259 0.282 0.506

Problem 82

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

15 15 15 20 107 21 19 23 13

N.S.

1 1.00 1.00 1.33 7.13 1.40 1.27 1.53 0.87

time (sec)

N/A 0.205 0.006 0.031 0.296 0.248 0.073 0.270 0.026

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

22 22 22 21 33 39 22 38 20

N.S.

1 1.00 1.00 0.95 1.50 1.77 1.00 1.73 0.91

time (sec)

N/A 0.168 0.001 0.013 0.290 0.268 0.980 0.267 0.023

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

25 26 25 24 23 23 22 23 22

N.S.

1 1.04 1.00 0.96 0.92 0.92 0.88 0.92 0.88

time (sec)

N/A 0.204 0.003 0.040 0.284 0.246 0.074 0.284 0.041

Problem 85

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 23 23 20 24 19 19 19 19

N.S.

1 1.00 1.00 0.87 1.04 0.83 0.83 0.83 0.83

time (sec)

N/A 0.262 0.019 0.234 0.292 0.249 0.108 0.282 0.294

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 54 49 45 78 30 58 0 0

N.S.

1 1.42 1.29 1.18 2.05 0.79 1.53 0.00 0.00

time (sec)

N/A 0.232 0.056 0.053 0.300 0.257 4.078 0.000 0.000

Problem 87

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 25 25 21 21 21 22 21 21

N.S.

1 1.00 1.00 0.84 0.84 0.84 0.88 0.84 0.84

time (sec)

N/A 0.154 0.003 0.161 0.209 0.235 0.018 0.286 0.046

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

39 39 39 29 29 29 34 29 29

N.S.

1 1.00 1.00 0.74 0.74 0.74 0.87 0.74 0.74

time (sec)

N/A 0.168 0.001 0.238 0.201 0.232 0.021 0.274 0.036

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 23 29 23 27 78 23 23

N.S.

1 1.00 1.00 1.26 1.00 1.17 3.39 1.00 1.00

time (sec)

N/A 0.158 0.037 0.865 0.212 0.248 12.029 0.279 0.817

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

30 30 27 21 22 22 20 23 20

N.S.

1 1.00 0.90 0.70 0.73 0.73 0.67 0.77 0.67

time (sec)

N/A 0.149 0.010 0.168 0.214 0.258 0.026 0.282 0.037

Problem 91

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

41 41 35 27 26 32 34 26 32

N.S.

1 1.00 0.85 0.66 0.63 0.78 0.83 0.63 0.78

time (sec)

N/A 0.152 0.013 0.182 0.298 0.238 0.036 0.278 0.044

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

21 23 21 14 15 15 14 17 8

N.S.

1 1.10 1.00 0.67 0.71 0.71 0.67 0.81 0.38

time (sec)

N/A 0.152 0.004 0.226 0.220 0.244 0.042 0.268 0.095

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

33 32 32 29 28 28 36 28 30

N.S.

1 0.97 0.97 0.88 0.85 0.85 1.09 0.85 0.91

time (sec)

N/A 0.168 0.008 0.710 0.291 0.255 0.047 0.273 0.046

Problem 94

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 25 25 22 21 21 22 21 21

N.S.

1 1.00 1.00 0.88 0.84 0.84 0.88 0.84 0.84

time (sec)

N/A 0.157 0.005 0.301 0.284 0.239 0.045 0.283 0.048

Problem 95

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

47 47 47 39 38 38 46 38 40

N.S.

1 1.00 1.00 0.83 0.81 0.81 0.98 0.81 0.85

time (sec)

N/A 0.232 0.019 0.411 0.293 0.263 0.046 0.275 0.284

Problem 96

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 25 25 18 17 17 17 20 17

N.S.

1 1.00 1.00 0.72 0.68 0.68 0.68 0.80 0.68

time (sec)

N/A 0.200 0.007 0.039 0.202 0.239 0.054 0.279 0.261

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

33 33 29 26 25 25 26 28 25

N.S.

1 1.00 0.88 0.79 0.76 0.76 0.79 0.85 0.76

time (sec)

N/A 0.211 0.019 0.053 0.213 0.242 0.117 0.276 0.109

Problem 98

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

37 64 37 26 25 25 29 29 29

N.S.

1 1.73 1.00 0.70 0.68 0.68 0.78 0.78 0.78

time (sec)

N/A 0.258 0.008 0.047 0.203 0.256 0.077 0.290 0.064

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 69 26 43 51 60 59 25

N.S.

1 1.00 2.23 0.84 1.39 1.65 1.94 1.90 0.81

time (sec)

N/A 0.154 0.020 0.060 0.287 0.251 0.289 0.291 0.098

Problem 100

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

41 41 41 26 25 25 26 29 15

N.S.

1 1.00 1.00 0.63 0.61 0.61 0.63 0.71 0.37

time (sec)

N/A 0.168 0.008 0.259 0.206 0.242 0.075 0.273 0.272

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