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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 123 121 95 159 0 0 235

N.S.

1 1.00 1.07 1.05 0.83 1.38 0.00 0.00 2.04

time (sec)

N/A 0.053 0.315 0.202 0.275 0.372 0.000 0.000 6.628

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 77 81 51 87 0 26228 154

N.S.

1 1.00 1.08 1.14 0.72 1.23 0.00 369.41 2.17

time (sec)

N/A 0.035 0.083 0.141 0.276 0.367 0.000 171.227 6.469

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 38 23 25 27 0 1456 43

N.S.

1 1.00 1.27 0.77 0.83 0.90 0.00 48.53 1.43

time (sec)

N/A 0.015 0.018 0.132 0.280 0.353 0.000 7.546 6.623

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

24 24 26 20 22 24 0 23 38

N.S.

1 1.00 1.08 0.83 0.92 1.00 0.00 0.96 1.58

time (sec)

N/A 0.014 0.026 0.092 0.275 0.363 0.000 6.036 6.578

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 60 67 45 69 0 60 146

N.S.

1 1.00 1.11 1.24 0.83 1.28 0.00 1.11 2.70

time (sec)

N/A 0.027 0.086 0.176 0.267 0.361 0.000 4.887 6.540

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

81 81 87 101 69 110 0 82 207

N.S.

1 1.00 1.07 1.25 0.85 1.36 0.00 1.01 2.56

time (sec)

N/A 0.032 0.141 0.214 0.280 0.358 0.000 4.607 6.697

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 111 143 91 158 0 104 267

N.S.

1 1.00 0.97 1.24 0.79 1.37 0.00 0.90 2.32

time (sec)

N/A 0.041 0.267 0.238 0.273 0.379 0.000 3.460 7.368

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 110 135 87 116 0 0 351

N.S.

1 1.00 1.09 1.34 0.86 1.15 0.00 0.00 3.48

time (sec)

N/A 0.065 0.045 0.189 0.498 0.349 0.000 0.000 11.223

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 81 98 65 88 0 0 231

N.S.

1 1.00 1.12 1.36 0.90 1.22 0.00 0.00 3.21

time (sec)

N/A 0.055 0.038 0.185 0.493 0.350 0.000 0.000 9.418

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 47 59 39 80 0 1008 111

N.S.

1 1.00 1.21 1.51 1.00 2.05 0.00 25.85 2.85

time (sec)

N/A 0.078 0.033 0.132 0.514 0.336 0.000 7.403 6.768

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 75 49 54 84 0 108 108

N.S.

1 1.00 1.83 1.20 1.32 2.05 0.00 2.63 2.63

time (sec)

N/A 0.039 0.034 0.116 0.509 0.369 0.000 4.234 6.906

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 125 86 92 160 0 141 228

N.S.

1 1.00 1.52 1.05 1.12 1.95 0.00 1.72 2.78

time (sec)

N/A 0.059 0.043 0.124 0.497 0.395 0.000 3.722 6.602

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 164 129 125 222 0 199 291

N.S.

1 1.00 1.34 1.06 1.02 1.82 0.00 1.63 2.39

time (sec)

N/A 0.074 0.047 0.164 0.487 0.362 0.000 4.800 6.673

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 75 206 96 168 0 0 283

N.S.

1 1.00 0.63 1.73 0.81 1.41 0.00 0.00 2.38

time (sec)

N/A 0.059 0.164 0.184 0.279 0.369 0.000 0.000 6.567

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 54 136 58 90 0 0 204

N.S.

1 1.00 0.75 1.89 0.81 1.25 0.00 0.00 2.83

time (sec)

N/A 0.044 0.072 0.168 0.292 0.348 0.000 0.000 7.111

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

52 52 40 70 43 45 0 6695 178

N.S.

1 1.00 0.77 1.35 0.83 0.87 0.00 128.75 3.42

time (sec)

N/A 0.028 0.026 0.116 0.272 0.360 0.000 5.259 6.669

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 28 94 53 76 0 47 56

N.S.

1 1.00 0.93 3.13 1.77 2.53 0.00 1.57 1.87

time (sec)

N/A 0.028 0.029 0.208 0.274 0.347 0.000 3.622 6.669

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 86 228 107 206 0 121 392

N.S.

1 1.00 0.65 1.73 0.81 1.56 0.00 0.92 2.97

time (sec)

N/A 0.053 0.150 0.232 0.281 0.397 0.000 4.022 11.182

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

149 149 174 251 152 152 0 0 392

N.S.

1 1.00 1.17 1.68 1.02 1.02 0.00 0.00 2.63

time (sec)

N/A 0.124 0.574 0.237 0.512 0.366 0.000 0.000 10.917

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 159 186 120 196 0 0 287

N.S.

1 1.00 1.32 1.55 1.00 1.63 0.00 0.00 2.39

time (sec)

N/A 0.141 0.851 0.243 0.506 0.369 0.000 0.000 10.072

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 145 117 84 125 0 5370 213

N.S.

1 1.00 2.04 1.65 1.18 1.76 0.00 75.63 3.00

time (sec)

N/A 0.068 0.291 0.204 0.494 0.358 0.000 12.030 8.693

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 34 52 47 41 78 38 123

N.S.

1 1.00 0.76 1.16 1.04 0.91 1.73 0.84 2.73

time (sec)

N/A 0.010 0.130 0.085 0.287 0.357 0.079 5.655 6.583

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 94 80 79 105 0 143 201

N.S.

1 1.00 1.27 1.08 1.07 1.42 0.00 1.93 2.72

time (sec)

N/A 0.077 0.396 0.129 0.497 0.357 0.000 7.514 6.520

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 191 146 139 192 0 209 293

N.S.

1 1.00 1.95 1.49 1.42 1.96 0.00 2.13 2.99

time (sec)

N/A 0.119 4.014 0.203 0.512 0.387 0.000 6.022 6.517

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

160 160 99 392 133 240 0 0 398

N.S.

1 1.00 0.62 2.45 0.83 1.50 0.00 0.00 2.49

time (sec)

N/A 0.077 0.362 0.230 0.278 0.396 0.000 0.000 6.469

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 66 204 72 104 0 0 262

N.S.

1 1.00 0.73 2.24 0.79 1.14 0.00 0.00 2.88

time (sec)

N/A 0.051 0.110 0.167 0.280 0.366 0.000 0.000 7.460

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 52 108 57 61 0 28789 281

N.S.

1 1.00 0.74 1.54 0.81 0.87 0.00 411.27 4.01

time (sec)

N/A 0.032 0.032 0.157 0.292 0.359 0.000 32.144 7.265

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 67 116 80 118 0 94 253

N.S.

1 1.00 0.68 1.18 0.82 1.20 0.00 0.96 2.58

time (sec)

N/A 0.046 0.139 0.204 0.292 0.384 0.000 8.263 6.760

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

180 180 243 359 209 289 0 0 438

N.S.

1 1.00 1.35 1.99 1.16 1.61 0.00 0.00 2.43

time (sec)

N/A 0.250 3.240 0.273 0.499 0.364 0.000 0.000 11.047

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 177 266 165 220 0 0 371

N.S.

1 1.00 1.49 2.24 1.39 1.85 0.00 0.00 3.12

time (sec)

N/A 0.140 1.358 0.278 0.507 0.371 0.000 0.000 10.500

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 115 167 117 154 0 0 288

N.S.

1 1.00 1.29 1.88 1.31 1.73 0.00 0.00 3.24

time (sec)

N/A 0.092 0.324 0.227 0.537 0.365 0.000 0.000 10.331

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 44 74 72 54 121 55 156

N.S.

1 1.00 0.70 1.17 1.14 0.86 1.92 0.87 2.48

time (sec)

N/A 0.039 0.214 0.146 0.289 0.358 0.125 6.705 8.919

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

92 92 106 94 93 121 0 162 264

N.S.

1 1.00 1.15 1.02 1.01 1.32 0.00 1.76 2.87

time (sec)

N/A 0.099 0.741 0.125 0.500 0.403 0.000 6.295 6.774

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

129 129 83 393 109 154 0 0 379

N.S.

1 1.00 0.64 3.05 0.84 1.19 0.00 0.00 2.94

time (sec)

N/A 0.067 0.301 0.210 0.285 0.373 0.000 0.000 7.880

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

107 107 76 267 85 116 0 0 320

N.S.

1 1.00 0.71 2.50 0.79 1.08 0.00 0.00 2.99

time (sec)

N/A 0.056 0.105 0.174 0.277 0.354 0.000 0.000 7.564

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 62 143 70 74 0 67058 131

N.S.

1 1.00 0.70 1.62 0.80 0.84 0.00 762.02 1.49

time (sec)

N/A 0.037 0.047 0.178 0.276 0.351 0.000 19.831 6.633

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 78 129 82 131 0 96 298

N.S.

1 1.00 0.76 1.26 0.80 1.28 0.00 0.94 2.92

time (sec)

N/A 0.045 0.093 0.210 0.280 0.376 0.000 15.679 6.398

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

143 143 252 360 238 247 0 0 437

N.S.

1 1.00 1.76 2.52 1.66 1.73 0.00 0.00 3.06

time (sec)

N/A 0.147 1.082 0.313 0.510 0.350 0.000 0.000 11.050

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F(-1) B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 113 125 231 181 179 0 0 363

N.S.

1 1.00 1.11 2.04 1.60 1.58 0.00 0.00 3.21

time (sec)

N/A 0.117 0.710 0.267 0.528 0.344 0.000 0.000 10.255

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 57 111 108 70 224 72 237

N.S.

1 1.00 0.66 1.28 1.24 0.80 2.57 0.83 2.72

time (sec)

N/A 0.058 0.269 0.208 0.283 0.354 0.233 3.678 8.591

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 136 136 117 135 0 194 295

N.S.

1 1.00 1.17 1.17 1.01 1.16 0.00 1.67 2.54

time (sec)

N/A 0.116 1.019 0.128 0.514 0.367 0.000 8.123 6.779

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 685 222 218 219 0 274 384

N.S.

1 1.00 4.89 1.59 1.56 1.56 0.00 1.96 2.74

time (sec)

N/A 0.161 6.232 0.226 0.498 0.393 0.000 12.879 6.709

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

198 198 283 353 313 291 0 339 454

N.S.

1 1.00 1.43 1.78 1.58 1.47 0.00 1.71 2.29

time (sec)

N/A 0.288 1.074 0.263 0.526 0.394 0.000 14.062 6.853

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

130 130 101 115 175 167 0 136 388

N.S.

1 1.00 0.78 0.88 1.35 1.28 0.00 1.05 2.98

time (sec)

N/A 0.117 0.645 0.239 0.279 0.369 0.000 16.364 10.740

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 84 91 130 147 0 116 281

N.S.

1 1.00 0.79 0.86 1.23 1.39 0.00 1.09 2.65

time (sec)

N/A 0.098 0.216 0.214 0.297 0.376 0.000 12.551 10.425

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 54 67 89 125 0 96 172

N.S.

1 1.00 0.66 0.82 1.09 1.52 0.00 1.17 2.10

time (sec)

N/A 0.080 0.116 0.211 0.290 0.356 0.000 5.718 9.111

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 58 28 43 47 58 0 58 61

N.S.

1 1.57 0.76 1.16 1.27 1.57 0.00 1.57 1.65

time (sec)

N/A 0.047 0.026 0.155 0.313 0.368 0.000 9.666 6.658

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

32 32 32 27 31 28 0 33 32

N.S.

1 1.00 1.00 0.84 0.97 0.88 0.00 1.03 1.00

time (sec)

N/A 0.027 0.013 0.113 0.275 0.348 0.000 9.183 6.531

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

32 32 24 30 26 30 0 26 23

N.S.

1 1.00 0.75 0.94 0.81 0.94 0.00 0.81 0.72

time (sec)

N/A 0.049 0.023 0.115 0.279 0.353 0.000 6.348 6.576

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 30 49 46 63 0 46 45

N.S.

1 1.00 0.59 0.96 0.90 1.24 0.00 0.90 0.88

time (sec)

N/A 0.065 0.037 0.243 0.286 0.349 0.000 5.302 6.560

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 61 67 66 96 0 66 63

N.S.

1 1.00 0.90 0.99 0.97 1.41 0.00 0.97 0.93

time (sec)

N/A 0.067 0.094 0.244 0.297 0.368 0.000 4.263 6.795

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 84 77 87 86 127 0 86 83

N.S.

1 1.00 0.92 1.04 1.02 1.51 0.00 1.02 0.99

time (sec)

N/A 0.071 0.134 0.324 0.301 0.353 0.000 4.224 6.767

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 84 146 175 338 95 0 172 99

N.S.

1 1.00 1.74 2.08 4.02 1.13 0.00 2.05 1.18

time (sec)

N/A 0.070 0.213 0.198 0.306 0.345 0.000 8.844 8.486

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 106 130 214 75 0 120 73

N.S.

1 1.00 1.54 1.88 3.10 1.09 0.00 1.74 1.06

time (sec)

N/A 0.067 0.222 0.217 0.298 0.351 0.000 17.136 6.732

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 106 70 90 47 0 68 47

N.S.

1 1.00 2.12 1.40 1.80 0.94 0.00 1.36 0.94

time (sec)

N/A 0.063 0.109 0.187 0.307 0.341 0.000 5.991 6.402

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

23 23 48 22 27 42 27 21 21

N.S.

1 1.00 2.09 0.96 1.17 1.83 1.17 0.91 0.91

time (sec)

N/A 0.009 0.032 0.088 0.303 0.344 0.371 8.194 6.428

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

29 29 69 44 70 62 0 65 25

N.S.

1 1.00 2.38 1.52 2.41 2.14 0.00 2.24 0.86

time (sec)

N/A 0.038 0.176 0.180 0.283 0.353 0.000 10.356 6.636

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 124 94 155 111 0 127 115

N.S.

1 1.00 2.14 1.62 2.67 1.91 0.00 2.19 1.98

time (sec)

N/A 0.065 0.358 0.213 0.287 0.357 0.000 8.765 6.635

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 189 148 234 155 0 187 183

N.S.

1 1.00 2.30 1.80 2.85 1.89 0.00 2.28 2.23

time (sec)

N/A 0.082 0.518 0.233 0.295 0.355 0.000 8.235 6.662

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 284 200 315 198 0 244 387

N.S.

1 1.00 2.68 1.89 2.97 1.87 0.00 2.30 3.65

time (sec)

N/A 0.100 0.627 0.253 0.308 0.371 0.000 12.649 8.221

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

189 189 112 127 202 218 0 146 444

N.S.

1 1.00 0.59 0.67 1.07 1.15 0.00 0.77 2.35

time (sec)

N/A 0.107 1.061 0.269 0.284 0.402 0.000 14.212 10.464

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

146 146 91 103 167 198 0 126 361

N.S.

1 1.00 0.62 0.71 1.14 1.36 0.00 0.86 2.47

time (sec)

N/A 0.080 0.299 0.267 0.285 0.365 0.000 8.192 10.504

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 70 79 110 178 0 102 240

N.S.

1 1.00 0.67 0.76 1.06 1.71 0.00 0.98 2.31

time (sec)

N/A 0.062 0.222 0.243 0.273 0.358 0.000 6.293 10.052

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 36 55 70 104 0 90 116

N.S.

1 1.00 0.60 0.92 1.17 1.73 0.00 1.50 1.93

time (sec)

N/A 0.035 0.057 0.218 0.283 0.355 0.000 4.267 7.640

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

52 52 36 37 46 59 0 45 87

N.S.

1 1.00 0.69 0.71 0.88 1.13 0.00 0.87 1.67

time (sec)

N/A 0.035 0.040 0.170 0.285 0.368 0.000 3.604 6.590

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 49 49 55 76 0 115 103

N.S.

1 1.00 0.75 0.75 0.85 1.17 0.00 1.77 1.58

time (sec)

N/A 0.041 0.048 0.246 0.279 0.373 0.000 4.132 6.528

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 38 39 36 57 0 36 36

N.S.

1 1.00 0.69 0.71 0.65 1.04 0.00 0.65 0.65

time (sec)

N/A 0.035 0.050 0.248 0.279 0.349 0.000 5.704 6.335

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 73 49 46 94 0 46 46

N.S.

1 1.00 1.00 0.67 0.63 1.29 0.00 0.63 0.63

time (sec)

N/A 0.040 0.048 0.322 0.276 0.364 0.000 26.116 6.375

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 78 79 76 127 0 76 76

N.S.

1 1.00 0.61 0.62 0.60 1.00 0.00 0.60 0.60

time (sec)

N/A 0.051 0.098 0.336 0.287 0.348 0.000 11.055 6.542

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 88 89 86 162 0 86 85

N.S.

1 1.00 0.61 0.61 0.59 1.12 0.00 0.59 0.59

time (sec)

N/A 0.058 0.143 0.457 0.280 0.360 0.000 14.518 6.633

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

199 199 118 119 116 195 0 116 116

N.S.

1 1.00 0.59 0.60 0.58 0.98 0.00 0.58 0.58

time (sec)

N/A 0.070 0.224 0.582 0.278 0.381 0.000 10.218 6.849

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 102 115 188 248 0 136 418

N.S.

1 1.00 0.60 0.67 1.10 1.45 0.00 0.80 2.44

time (sec)

N/A 0.090 0.450 0.315 0.291 0.371 0.000 12.502 10.051

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 82 91 146 226 0 114 302

N.S.

1 1.00 0.65 0.72 1.16 1.79 0.00 0.90 2.40

time (sec)

N/A 0.065 0.245 0.276 0.278 0.377 0.000 9.470 9.925

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 52 67 98 154 0 81 186

N.S.

1 1.00 0.63 0.82 1.20 1.88 0.00 0.99 2.27

time (sec)

N/A 0.041 0.103 0.264 0.302 0.360 0.000 13.213 8.819

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 52 49 72 104 0 59 148

N.S.

1 1.00 0.70 0.66 0.97 1.41 0.00 0.80 2.00

time (sec)

N/A 0.040 0.126 0.197 0.277 0.354 0.000 9.824 6.648

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 61 61 80 147 0 154 169

N.S.

1 1.00 0.71 0.71 0.93 1.71 0.00 1.79 1.97

time (sec)

N/A 0.050 0.134 0.312 0.282 0.370 0.000 7.562 6.701

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

96 96 69 67 75 131 0 174 171

N.S.

1 1.00 0.72 0.70 0.78 1.36 0.00 1.81 1.78

time (sec)

N/A 0.050 0.212 0.302 0.289 0.389 0.000 8.397 6.717

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 48 49 46 84 0 46 46

N.S.

1 1.00 0.66 0.67 0.63 1.15 0.00 0.63 0.63

time (sec)

N/A 0.039 0.069 0.298 0.295 0.342 0.000 7.554 6.693

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

109 109 68 69 66 117 0 66 66

N.S.

1 1.00 0.62 0.63 0.61 1.07 0.00 0.61 0.61

time (sec)

N/A 0.046 0.055 0.371 0.280 0.354 0.000 6.477 6.629

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-1) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 88 89 86 152 0 86 86

N.S.

1 1.00 0.61 0.61 0.59 1.05 0.00 0.59 0.59

time (sec)

N/A 0.067 0.078 0.453 0.278 0.406 0.000 6.054 6.811

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-2) A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 88 89 86 185 0 86 85

N.S.

1 1.00 0.61 0.61 0.59 1.28 0.00 0.59 0.59

time (sec)

N/A 0.057 0.086 0.567 0.281 0.382 0.000 6.735 6.822

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

195 195 112 127 213 290 0 146 476

N.S.

1 1.00 0.57 0.65 1.09 1.49 0.00 0.75 2.44

time (sec)

N/A 0.099 0.953 0.322 0.288 0.384 0.000 24.279 10.661

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 50 81 95 102 0 76 172

N.S.

1 1.00 0.38 0.61 0.72 0.77 0.00 0.58 1.30

time (sec)

N/A 0.065 0.074 0.253 0.290 0.359 0.000 16.615 7.508

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

105 105 62 79 121 198 0 91 240

N.S.

1 1.00 0.59 0.75 1.15 1.89 0.00 0.87 2.29

time (sec)

N/A 0.049 0.176 0.323 0.281 0.351 0.000 17.146 10.070

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 73 71 103 196 0 185 228

N.S.

1 1.00 0.69 0.67 0.97 1.85 0.00 1.75 2.15

time (sec)

N/A 0.058 0.547 0.331 0.283 0.401 0.000 7.974 6.610

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 89 89 95 186 0 232 235

N.S.

1 1.00 0.66 0.66 0.70 1.38 0.00 1.72 1.74

time (sec)

N/A 0.060 0.110 0.385 0.284 0.359 0.000 9.920 6.807

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 124 158 356 129 0 146 231

N.S.

1 1.00 0.98 1.24 2.80 1.02 0.00 1.15 1.82

time (sec)

N/A 0.228 0.272 0.271 0.293 0.395 0.000 14.263 7.577

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

108 108 315 119 288 369 0 135 203

N.S.

1 1.00 2.92 1.10 2.67 3.42 0.00 1.25 1.88

time (sec)

N/A 0.249 0.278 0.306 0.301 0.371 0.000 7.343 12.052

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 359 143 285 445 0 179 171

N.S.

1 1.00 2.99 1.19 2.38 3.71 0.00 1.49 1.42

time (sec)

N/A 0.185 4.608 0.294 0.292 0.373 0.000 7.788 7.826

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

133 133 733 165 279 439 0 204 209

N.S.

1 1.00 5.51 1.24 2.10 3.30 0.00 1.53 1.57

time (sec)

N/A 0.197 6.072 0.333 0.301 0.358 0.000 9.178 7.672

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A F F(-2) F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 195 394 172 0 217 0 0 -1

N.S.

1 1.20 2.43 1.06 0.00 1.34 0.00 0.00 -0.01

time (sec)

N/A 0.635 5.384 1.868 0.000 0.387 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 114 89 0 184 0 455 -1

N.S.

1 1.00 1.13 0.88 0.00 1.82 0.00 4.50 -0.01

time (sec)

N/A 0.121 0.232 2.154 0.000 0.390 0.000 10.711 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A F B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 206 125 0 306 0 157 -1

N.S.

1 1.00 2.31 1.40 0.00 3.44 0.00 1.76 -0.01

time (sec)

N/A 0.128 0.666 2.000 0.000 0.388 0.000 3.093 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

163 163 309 170 0 417 0 223 -1

N.S.

1 1.00 1.90 1.04 0.00 2.56 0.00 1.37 -0.01

time (sec)

N/A 0.254 1.074 2.366 0.000 0.394 0.000 3.616 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F(-1) A F(-2) B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

167 195 141 139 0 260 0 974 -1

N.S.

1 1.17 0.84 0.83 0.00 1.56 0.00 5.83 -0.01

time (sec)

N/A 0.655 5.381 1.910 0.000 0.400 0.000 154.082 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 46 55 157 52 0 222 -1

N.S.

1 1.00 0.52 0.62 1.78 0.59 0.00 2.52 -0.01

time (sec)

N/A 0.125 1.978 1.050 0.512 0.355 0.000 42.480 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 233 144 0 344 0 193 -1

N.S.

1 1.00 1.93 1.19 0.00 2.84 0.00 1.60 -0.01

time (sec)

N/A 0.210 0.531 2.319 0.000 0.373 0.000 5.066 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F(-2) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

197 197 334 196 0 463 0 260 -1

N.S.

1 1.00 1.70 0.99 0.00 2.35 0.00 1.32 -0.01

time (sec)

N/A 0.336 1.039 2.275 0.000 0.371 0.000 9.890 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F(-1) B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

151 208 112 87 301 106 0 1580 -1

N.S.

1 1.38 0.74 0.58 1.99 0.70 0.00 10.46 -0.01

time (sec)

N/A 0.671 5.310 1.565 0.549 0.363 0.000 162.755 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F(-2) B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 60 67 207 75 0 1502 -1

N.S.

1 1.00 0.51 0.57 1.75 0.64 0.00 12.73 -0.01

time (sec)

N/A 0.139 5.316 1.356 0.508 0.358 0.000 44.078 0.000

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