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2.2.2 Integrals 101 to 200

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 101

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

18 55 64 57 86 86 49 86 53

N.S.

1 3.06 3.56 3.17 4.78 4.78 2.72 4.78 2.94

time (sec)

N/A 0.196 0.008 0.027 0.185 0.241 0.029 0.276 0.159

Problem 102

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

17 24 20 23 78 19 17 22 19

N.S.

1 1.41 1.18 1.35 4.59 1.12 1.00 1.29 1.12

time (sec)

N/A 0.259 0.217 0.033 0.185 0.225 0.051 0.245 0.070

Problem 103

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 29 29 25 24 24 22 24 27

N.S.

1 1.16 1.16 1.00 0.96 0.96 0.88 0.96 1.08

time (sec)

N/A 0.750 0.064 1.060 0.212 0.241 0.071 0.277 7.809

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 167 25 29 0 44 29 47 27

N.S.

1 6.68 1.00 1.16 0.00 1.76 1.16 1.88 1.08

time (sec)

N/A 1.490 5.097 0.093 0.000 0.234 0.102 0.264 7.778

Problem 105

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 44 28 30 35 25 29 24 24

N.S.

1 1.76 1.12 1.20 1.40 1.00 1.16 0.96 0.96

time (sec)

N/A 0.182 0.183 0.031 0.208 0.249 0.069 0.250 0.093

Problem 106

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

33 34 23 21 88 22 22 25 20

N.S.

1 1.03 0.70 0.64 2.67 0.67 0.67 0.76 0.61

time (sec)

N/A 0.302 0.159 0.043 0.187 0.238 0.048 0.253 0.066

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F B B B B B B B

verified

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

size

31 0 85 93 196 157 134 229 231

N.S.

1 0.00 2.74 3.00 6.32 5.06 4.32 7.39 7.45

time (sec)

N/A 0.000 0.130 0.175 0.321 0.253 0.104 0.283 8.681

Problem 108

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 34 32 32 45 31 34 51 31

N.S.

1 1.13 1.07 1.07 1.50 1.03 1.13 1.70 1.03

time (sec)

N/A 0.973 0.084 0.429 0.303 0.233 0.149 0.404 9.343

Problem 109

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 23 24 23 23 23 19 23 22

N.S.

1 1.35 1.41 1.35 1.35 1.35 1.12 1.35 1.29

time (sec)

N/A 0.158 0.000 0.011 0.173 0.229 0.020 0.245 0.042

Problem 110

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

24 82 33 37 150 47 31 51 35

N.S.

1 3.42 1.38 1.54 6.25 1.96 1.29 2.12 1.46

time (sec)

N/A 1.019 0.359 0.145 0.213 0.244 0.116 0.251 8.742

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A F A A B B

verified

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

size

26 0 24 36 0 33 29 49 54

N.S.

1 0.00 0.92 1.38 0.00 1.27 1.12 1.88 2.08

time (sec)

N/A 0.000 0.791 0.134 0.000 0.241 0.106 0.319 8.412

Problem 112

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 10 10 10 10 10 10 15 9

N.S.

1 0.59 0.59 0.59 0.59 0.59 0.59 0.88 0.53

time (sec)

N/A 0.142 0.008 0.036 0.170 0.235 0.059 0.245 0.103

Problem 113

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

23 0 28 25 24 26 32 26 24

N.S.

1 0.00 1.22 1.09 1.04 1.13 1.39 1.13 1.04

time (sec)

N/A 0.000 0.339 0.268 0.198 0.243 0.091 0.254 8.355

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 38 34 46 120 120 117 135 0

N.S.

1 1.27 1.13 1.53 4.00 4.00 3.90 4.50 0.00

time (sec)

N/A 1.462 0.220 0.977 0.612 0.261 0.303 0.665 0.000

Problem 115

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 26 30 26 59 32 24 25 25

N.S.

1 0.96 1.11 0.96 2.19 1.19 0.89 0.93 0.93

time (sec)

N/A 0.343 0.077 0.028 0.201 0.266 0.046 0.250 0.097

Problem 116

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

13 15 15 16 15 15 17 15 15

N.S.

1 1.15 1.15 1.23 1.15 1.15 1.31 1.15 1.15

time (sec)

N/A 0.312 0.251 3.127 0.243 0.246 0.843 0.298 8.047

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F F A B A B B B

verified

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

size

30 0 0 57 197 61 63 213 272

N.S.

1 0.00 0.00 1.90 6.57 2.03 2.10 7.10 9.07

time (sec)

N/A 0.000 0.000 11.050 0.851 0.238 0.964 1.801 9.081

Problem 118

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

29 32 23 19 47 17 20 22 23

N.S.

1 1.10 0.79 0.66 1.62 0.59 0.69 0.76 0.79

time (sec)

N/A 0.463 1.515 0.083 0.315 0.234 0.250 0.246 0.139

Problem 119

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 20 22 17 27 16 19 16 16

N.S.

1 0.91 1.00 0.77 1.23 0.73 0.86 0.73 0.73

time (sec)

N/A 0.294 0.029 0.016 0.200 0.234 0.054 0.259 7.675

Problem 120

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 22 19 18 17 17 15 17 33

N.S.

1 0.81 0.70 0.67 0.63 0.63 0.56 0.63 1.22

time (sec)

N/A 0.365 0.048 0.093 0.208 0.235 0.064 0.250 0.351

Problem 121

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

24 54 25 36 35 38 36 31 18

N.S.

1 2.25 1.04 1.50 1.46 1.58 1.50 1.29 0.75

time (sec)

N/A 0.212 0.183 0.036 0.192 0.237 0.069 0.247 7.707

Problem 122

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 21 23 20 25 19 20 22

N.S.

1 1.00 0.91 1.00 0.87 1.09 0.83 0.87 0.96

time (sec)

N/A 0.350 0.070 0.092 0.248 0.226 0.069 0.249 7.965

Problem 123

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 18 18 14 46 15 0 15

N.S.

1 0.00 0.90 0.90 0.70 2.30 0.75 0.00 0.75

time (sec)

N/A 0.000 0.159 0.690 0.315 0.230 0.127 0.000 8.229

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 22 20 75 34 72 70 84 38

N.S.

1 0.73 0.67 2.50 1.13 2.40 2.33 2.80 1.27

time (sec)

N/A 0.733 0.052 7.515 1.245 0.236 0.565 1.520 0.408

Problem 125

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 26 26 21 20 20 20 20 21

N.S.

1 1.18 1.18 0.95 0.91 0.91 0.91 0.91 0.95

time (sec)

N/A 0.167 0.005 0.029 0.205 0.224 0.144 0.244 8.581

Problem 126

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 26 21 20 19 26 19 19 19

N.S.

1 1.00 0.81 0.77 0.73 1.00 0.73 0.73 0.73

time (sec)

N/A 0.201 0.012 0.024 0.185 0.259 0.039 0.246 8.111

Problem 127

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

28 36 28 30 35 31 27 735 27

N.S.

1 1.29 1.00 1.07 1.25 1.11 0.96 26.25 0.96

time (sec)

N/A 0.621 0.225 2.798 0.318 0.241 0.155 1.094 9.808

Problem 128

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 28 18 20 19 28 15 29 19

N.S.

1 1.08 0.69 0.77 0.73 1.08 0.58 1.12 0.73

time (sec)

N/A 0.337 0.869 0.068 0.284 0.226 0.081 0.260 8.021

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 33 50 30 60 30 26 30 30

N.S.

1 1.18 1.79 1.07 2.14 1.07 0.93 1.07 1.07

time (sec)

N/A 0.724 0.199 0.425 0.233 0.234 0.143 0.247 8.190

Problem 130

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

17 16 15 17 0 16 26 16 14

N.S.

1 0.94 0.88 1.00 0.00 0.94 1.53 0.94 0.82

time (sec)

N/A 0.500 0.034 0.079 0.000 0.233 0.191 0.247 8.198

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 41 41 27 58 41 36 73 23

N.S.

1 1.41 1.41 0.93 2.00 1.41 1.24 2.52 0.79

time (sec)

N/A 0.434 1.369 0.057 0.271 0.230 0.952 0.255 0.180

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

22 0 0 26 25 34 19 71 0

N.S.

1 0.00 0.00 1.18 1.14 1.55 0.86 3.23 0.00

time (sec)

N/A 0.000 0.000 0.060 0.246 0.244 0.164 0.257 0.000

Problem 133

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

30 0 27 26 22 27 24 27 22

N.S.

1 0.00 0.90 0.87 0.73 0.90 0.80 0.90 0.73

time (sec)

N/A 0.000 0.267 0.158 0.260 0.242 0.121 0.263 8.486

Problem 134

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

25 0 23 25 90 29 24 33 63

N.S.

1 0.00 0.92 1.00 3.60 1.16 0.96 1.32 2.52

time (sec)

N/A 0.000 1.088 0.150 0.284 0.229 0.075 0.291 8.638

Problem 135

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

30 31 26 26 40 23 29 25 22

N.S.

1 1.03 0.87 0.87 1.33 0.77 0.97 0.83 0.73

time (sec)

N/A 0.277 0.078 0.046 0.224 0.247 0.081 0.261 8.437

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A C B B A B B

verified

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

size

39 0 35 337 92 80 41 88 42

N.S.

1 0.00 0.90 8.64 2.36 2.05 1.05 2.26 1.08

time (sec)

N/A 0.000 0.167 0.050 0.522 0.250 57.620 2.256 8.753

Problem 137

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

29 28 28 32 51 35 36 31 29

N.S.

1 0.97 0.97 1.10 1.76 1.21 1.24 1.07 1.00

time (sec)

N/A 0.661 0.074 0.337 0.317 0.235 0.100 0.269 8.390

Problem 138

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

18 0 17 17 24 24 17 17 23

N.S.

1 0.00 0.94 0.94 1.33 1.33 0.94 0.94 1.28

time (sec)

N/A 0.000 0.087 0.061 0.280 0.227 0.087 0.261 8.184

Problem 139

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 35 35 33 38 32 29 34 32

N.S.

1 1.25 1.25 1.18 1.36 1.14 1.04 1.21 1.14

time (sec)

N/A 0.421 0.124 0.066 0.303 0.230 0.104 0.248 8.378

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F B B B B B B B

verified

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

size

25 0 55 50 142 58 66 92 780

N.S.

1 0.00 2.20 2.00 5.68 2.32 2.64 3.68 31.20

time (sec)

N/A 0.000 0.252 0.246 0.474 0.237 0.503 1.664 8.689

Problem 141

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

23 27 21 17 174 31 20 22 22

N.S.

1 1.17 0.91 0.74 7.57 1.35 0.87 0.96 0.96

time (sec)

N/A 0.215 0.057 0.032 0.309 0.243 0.061 0.261 8.324

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 0 45 0 78 60 97 103 0

N.S.

1 0.00 1.55 0.00 2.69 2.07 3.34 3.55 0.00

time (sec)

N/A 0.000 0.382 0.000 0.317 0.263 2.679 0.441 0.000

Problem 143

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 19 20 19 19 15 19 19

N.S.

1 0.00 1.00 1.05 1.00 1.00 0.79 1.00 1.00

time (sec)

N/A 0.000 0.355 8.880 0.255 0.268 1.627 0.414 9.351

Problem 144

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 11 9 9 8 8 7 8 8

N.S.

1 0.65 0.53 0.53 0.47 0.47 0.41 0.47 0.47

time (sec)

N/A 0.216 0.008 0.223 0.194 0.236 0.051 0.248 0.089

Problem 145

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 21 15 21 19 19 26 19 19

N.S.

1 1.05 0.75 1.05 0.95 0.95 1.30 0.95 0.95

time (sec)

N/A 0.277 0.140 0.143 0.316 0.239 0.107 0.249 0.273

Problem 146

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

16 18 16 18 26 17 15 46 17

N.S.

1 1.12 1.00 1.12 1.62 1.06 0.94 2.88 1.06

time (sec)

N/A 0.147 0.003 0.095 0.172 0.243 0.054 0.255 8.548

Problem 147

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 25 25 24 40 25 19 27 23

N.S.

1 1.04 1.04 1.00 1.67 1.04 0.79 1.12 0.96

time (sec)

N/A 1.032 0.115 0.248 0.326 0.262 0.133 0.268 8.871

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A C B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 377 38 68 138 62 68 70 60

N.S.

1 12.57 1.27 2.27 4.60 2.07 2.27 2.33 2.00

time (sec)

N/A 1.574 0.057 0.602 0.297 0.252 0.099 0.259 8.487

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 20 17 17 19 0 17

N.S.

1 1.00 1.00 1.00 0.85 0.85 0.95 0.00 0.85

time (sec)

N/A 0.328 0.084 0.866 0.208 0.261 0.117 0.000 8.898

Problem 150

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

20 0 20 35 100 28 32 30 34

N.S.

1 0.00 1.00 1.75 5.00 1.40 1.60 1.50 1.70

time (sec)

N/A 0.000 4.779 0.479 0.321 0.251 0.409 0.478 9.744

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 35 32 33 317 35 32 64 69

N.S.

1 1.06 0.97 1.00 9.61 1.06 0.97 1.94 2.09

time (sec)

N/A 0.192 0.028 0.090 0.309 0.251 0.177 0.266 8.769

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 26 28 27 0 26 0 26 26

N.S.

1 0.79 0.85 0.82 0.00 0.79 0.00 0.79 0.79

time (sec)

N/A 1.261 0.675 7.166 0.000 0.253 0.000 0.256 9.095

Problem 153

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

22 24 24 37 52 39 32 39 36

N.S.

1 1.09 1.09 1.68 2.36 1.77 1.45 1.77 1.64

time (sec)

N/A 0.481 0.032 0.346 0.344 0.254 0.107 0.312 9.008

Problem 154

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

25 109 24 26 32 29 27 41 40

N.S.

1 4.36 0.96 1.04 1.28 1.16 1.08 1.64 1.60

time (sec)

N/A 2.112 5.071 0.447 0.342 0.261 0.129 0.262 0.393

Problem 155

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

25 0 29 20 26 25 24 35 23

N.S.

1 0.00 1.16 0.80 1.04 1.00 0.96 1.40 0.92

time (sec)

N/A 0.000 0.367 0.211 0.257 0.249 0.072 0.251 8.676

Problem 156

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 53 28 32 32 28 37 31 33

N.S.

1 2.12 1.12 1.28 1.28 1.12 1.48 1.24 1.32

time (sec)

N/A 0.341 0.024 0.093 0.199 0.243 0.414 0.254 0.206

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 0 0 666 81 72 76 0 0

N.S.

1 0.00 0.00 22.20 2.70 2.40 2.53 0.00 0.00

time (sec)

N/A 0.000 0.000 0.063 0.379 0.260 38.939 0.000 0.000

Problem 158

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

20 27 27 22 39 24 22 27 24

N.S.

1 1.35 1.35 1.10 1.95 1.20 1.10 1.35 1.20

time (sec)

N/A 0.240 0.799 0.053 0.264 0.259 0.074 0.256 8.403

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 130 48 28 42 53 68 45 60

N.S.

1 4.33 1.60 0.93 1.40 1.77 2.27 1.50 2.00

time (sec)

N/A 0.490 0.040 0.155 0.216 0.240 0.681 0.270 0.270

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F F A B A A B B

verified

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

size

28 0 0 37 591 43 44 94 76

N.S.

1 0.00 0.00 1.32 21.11 1.54 1.57 3.36 2.71

time (sec)

N/A 0.000 0.000 18.152 10.115 0.249 0.336 0.480 8.805

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 0 20 29 18 26 0 0 26

N.S.

1 0.00 1.00 1.45 0.90 1.30 0.00 0.00 1.30

time (sec)

N/A 0.000 4.513 26.937 0.246 0.250 0.000 0.000 8.627

Problem 162

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 24 24 23 22 22 27 22 23

N.S.

1 1.26 1.26 1.21 1.16 1.16 1.42 1.16 1.21

time (sec)

N/A 0.198 0.029 0.037 0.183 0.256 0.050 0.249 8.629

Problem 163

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

15 23 16 15 15 15 12 15 14

N.S.

1 1.53 1.07 1.00 1.00 1.00 0.80 1.00 0.93

time (sec)

N/A 0.473 0.185 0.089 0.217 0.250 0.050 0.251 8.432

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A B C B B B B

verified

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

size

32 0 36 127 201 120 129 137 33

N.S.

1 0.00 1.12 3.97 6.28 3.75 4.03 4.28 1.03

time (sec)

N/A 0.000 0.077 0.143 0.283 0.252 0.087 0.256 8.672

Problem 165

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

26 32 21 24 0 19 29 24 19

N.S.

1 1.23 0.81 0.92 0.00 0.73 1.12 0.92 0.73

time (sec)

N/A 0.228 0.062 0.073 0.000 0.243 0.109 0.252 8.459

Problem 166

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

32 28 30 24 0 34 22 36 23

N.S.

1 0.88 0.94 0.75 0.00 1.06 0.69 1.12 0.72

time (sec)

N/A 0.393 0.181 0.106 0.000 0.254 0.080 0.250 0.110

Problem 167

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

30 0 28 27 26 50 22 0 26

N.S.

1 0.00 0.93 0.90 0.87 1.67 0.73 0.00 0.87

time (sec)

N/A 0.000 2.099 6.192 0.192 0.268 0.192 0.000 0.302

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

27 0 25 0 71 24 0 0 24

N.S.

1 0.00 0.93 0.00 2.63 0.89 0.00 0.00 0.89

time (sec)

N/A 0.000 0.063 0.000 0.368 0.255 0.000 0.000 10.311

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 80 46 44 61 58 76 236 541

N.S.

1 2.76 1.59 1.52 2.10 2.00 2.62 8.14 18.66

time (sec)

N/A 0.326 0.020 0.072 0.181 0.250 0.412 0.255 8.437

Problem 170

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

19 146 19 109 108 108 126 108 108

N.S.

1 7.68 1.00 5.74 5.68 5.68 6.63 5.68 5.68

time (sec)

N/A 0.574 0.101 0.110 0.193 0.254 0.177 0.264 8.890

Problem 171

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 18 18 16 17 17 17 18 17

N.S.

1 0.72 0.72 0.64 0.68 0.68 0.68 0.72 0.68

time (sec)

N/A 0.188 0.015 0.127 0.172 0.241 0.101 0.245 0.090

Problem 172

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 9 9 12 8 11 10 8 9

N.S.

1 0.75 0.75 1.00 0.67 0.92 0.83 0.67 0.75

time (sec)

N/A 0.180 0.008 0.059 0.177 0.222 0.049 0.260 8.500

Problem 173

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

24 0 20 21 85 25 24 44 46

N.S.

1 0.00 0.83 0.88 3.54 1.04 1.00 1.83 1.92

time (sec)

N/A 0.000 1.978 0.100 0.269 0.241 0.134 0.285 0.198

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 30 29 26 25 28 26 0 27

N.S.

1 1.03 1.00 0.90 0.86 0.97 0.90 0.00 0.93

time (sec)

N/A 1.819 5.152 7.537 0.446 0.249 4.825 0.000 8.876

Problem 175

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 24 24 22 21 43 24 25 23

N.S.

1 0.92 0.92 0.85 0.81 1.65 0.92 0.96 0.88

time (sec)

N/A 0.403 0.033 0.087 0.173 0.254 0.086 0.251 0.269

Problem 176

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 0 26 24 23 111 27 0 26

N.S.

1 0.00 1.08 1.00 0.96 4.62 1.12 0.00 1.08

time (sec)

N/A 0.000 4.609 6.943 0.420 0.259 13.503 0.000 8.593

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 54 47 115 104 104 109 0 0

N.S.

1 2.00 1.74 4.26 3.85 3.85 4.04 0.00 0.00

time (sec)

N/A 5.418 0.492 2.927 0.414 0.270 0.376 0.000 0.000

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A F B A F B

verified

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

size

28 0 33 23 0 46 34 0 33

N.S.

1 0.00 1.18 0.82 0.00 1.64 1.21 0.00 1.18

time (sec)

N/A 0.000 0.313 3.221 0.000 0.289 5.500 0.000 8.367

Problem 179

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

23 21 20 40 69 45 53 75 24

N.S.

1 0.91 0.87 1.74 3.00 1.96 2.30 3.26 1.04

time (sec)

N/A 0.577 0.041 1.959 0.281 0.265 0.141 0.268 8.755

Problem 180

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 5 5 6 5 5 3 5 5

N.S.

1 0.50 0.50 0.60 0.50 0.50 0.30 0.50 0.50

time (sec)

N/A 0.116 0.000 0.007 0.176 0.265 0.015 0.253 0.023

Problem 181

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 8 7 7 7 7 7

N.S.

1 1.00 1.00 1.00 0.88 0.88 0.88 0.88 0.88

time (sec)

N/A 0.156 0.004 0.075 0.180 0.248 0.033 0.260 8.600

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F B A B B B B B

verified

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

size

26 0 89 48 98 92 105 103 108

N.S.

1 0.00 3.42 1.85 3.77 3.54 4.04 3.96 4.15

time (sec)

N/A 0.000 0.064 0.193 0.183 0.257 1.307 0.263 0.231

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B A B A B

verified

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

size

28 0 43 43 95 41 44 42 106

N.S.

1 0.00 1.54 1.54 3.39 1.46 1.57 1.50 3.79

time (sec)

N/A 0.000 0.142 0.187 0.479 0.249 0.228 0.513 8.789

Problem 184

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B B A B B

verified

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

size

29 0 31 30 57 55 26 61 56

N.S.

1 0.00 1.07 1.03 1.97 1.90 0.90 2.10 1.93

time (sec)

N/A 0.000 0.106 0.907 0.222 0.249 0.123 0.272 8.516

Problem 185

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

29 54 33 30 99 29 39 29 35

N.S.

1 1.86 1.14 1.03 3.41 1.00 1.34 1.00 1.21

time (sec)

N/A 0.962 0.529 0.093 0.317 0.250 0.245 0.253 8.336

Problem 186

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

17 0 44 217 1150 307 350 478 0

N.S.

1 0.00 2.59 12.76 67.65 18.06 20.59 28.12 0.00

time (sec)

N/A 0.000 0.113 2.127 0.732 0.269 1.576 3.325 0.000

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

22 0 0 22 21 22 19 0 29

N.S.

1 0.00 0.00 1.00 0.95 1.00 0.86 0.00 1.32

time (sec)

N/A 0.000 0.000 5.639 0.269 0.252 3.723 0.000 0.292

Problem 188

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

20 57 21 17 24 17 17 24 13

N.S.

1 2.85 1.05 0.85 1.20 0.85 0.85 1.20 0.65

time (sec)

N/A 0.526 0.073 0.073 0.186 0.262 36.031 0.256 8.257

Problem 189

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 37 20 25 26 25 27 28 29

N.S.

1 1.42 0.77 0.96 1.00 0.96 1.04 1.08 1.12

time (sec)

N/A 0.280 0.023 0.067 0.174 0.234 0.288 0.246 0.130

Problem 190

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 44 25 40 34 37 37 38 38

N.S.

1 1.52 0.86 1.38 1.17 1.28 1.28 1.31 1.31

time (sec)

N/A 0.685 0.302 0.317 0.310 0.234 0.154 0.295 8.542

Problem 191

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 9 9 6 5 5 5 5 5

N.S.

1 0.82 0.82 0.55 0.45 0.45 0.45 0.45 0.45

time (sec)

N/A 0.154 0.008 0.033 0.166 0.235 0.049 0.253 7.555

Problem 192

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 20 20 16 15 15 19 15 17

N.S.

1 1.00 1.00 0.80 0.75 0.75 0.95 0.75 0.85

time (sec)

N/A 0.188 0.070 0.108 0.191 0.267 0.159 0.255 8.854

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 15 15 13 12 39 12 0 12

N.S.

1 0.62 0.62 0.54 0.50 1.62 0.50 0.00 0.50

time (sec)

N/A 0.163 0.029 0.058 0.190 0.248 0.108 0.000 0.103

Problem 194

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

18 29 15 15 24 14 12 35 14

N.S.

1 1.61 0.83 0.83 1.33 0.78 0.67 1.94 0.78

time (sec)

N/A 0.187 0.032 0.052 0.187 0.242 0.053 0.249 0.112

Problem 195

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A F A A A A A B

verified

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

size

20 21 0 20 23 23 24 28 23

N.S.

1 1.05 0.00 1.00 1.15 1.15 1.20 1.40 1.15

time (sec)

N/A 0.472 0.000 0.957 0.303 0.249 0.237 0.369 11.368

Problem 196

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F F C A A A F B

verified

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

size

41 0 0 164 41 33 27 0 27

N.S.

1 0.00 0.00 4.00 1.00 0.80 0.66 0.00 0.66

time (sec)

N/A 0.000 0.000 0.907 0.454 0.263 22.186 0.000 8.453

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 87 30 48 41 26 44 42 59

N.S.

1 3.22 1.11 1.78 1.52 0.96 1.63 1.56 2.19

time (sec)

N/A 1.042 1.002 0.681 0.229 0.243 0.257 0.257 8.061

Problem 198

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

21 26 17 17 0 16 14 22 16

N.S.

1 1.24 0.81 0.81 0.00 0.76 0.67 1.05 0.76

time (sec)

N/A 0.262 0.153 0.423 0.000 0.248 0.056 0.256 0.089

Problem 199

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 25 18 18 23 22 24 23 25

N.S.

1 1.14 0.82 0.82 1.05 1.00 1.09 1.05 1.14

time (sec)

N/A 0.292 0.448 0.183 0.260 0.245 0.110 0.271 7.677

Problem 200

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 16 16 15 15 22 15 29

N.S.

1 1.00 1.00 1.00 0.94 0.94 1.38 0.94 1.81

time (sec)

N/A 0.995 0.133 0.247 0.315 0.243 0.102 0.247 8.291

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