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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 175 247 314 0 7993 0 0 0

N.S.

1 1.14 1.61 2.05 0.00 52.24 0.00 0.00 0.00

time (sec)

N/A 0.377 4.965 2.956 0.000 0.386 0.000 0.000 0.000

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 57 62 92 327 0 108 433

N.S.

1 1.00 1.19 1.29 1.92 6.81 0.00 2.25 9.02

time (sec)

N/A 0.295 0.029 4.524 0.190 0.256 0.000 0.322 2.381

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

49 46 45 49 78 1072 80 119 173

N.S.

1 0.94 0.92 1.00 1.59 21.88 1.63 2.43 3.53

time (sec)

N/A 0.267 0.017 2.523 0.271 0.273 0.285 0.319 0.114

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 38 41 52 42 155 0 72 163

N.S.

1 1.19 1.28 1.62 1.31 4.84 0.00 2.25 5.09

time (sec)

N/A 0.281 0.010 1.976 0.198 0.259 0.000 0.294 2.258

Problem 105

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

29 27 29 28 27 359 42 83 72

N.S.

1 0.93 1.00 0.97 0.93 12.38 1.45 2.86 2.48

time (sec)

N/A 0.226 0.023 0.980 0.180 0.256 0.144 0.300 2.187

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 16 23 36 0 23 23

N.S.

1 1.00 1.00 1.07 1.53 2.40 0.00 1.53 1.53

time (sec)

N/A 0.159 0.001 0.779 0.194 0.252 0.000 0.288 0.059

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 37 44 24 65 69 0 55 167

N.S.

1 1.32 1.57 0.86 2.32 2.46 0.00 1.96 5.96

time (sec)

N/A 0.259 0.039 0.795 0.268 0.261 0.000 0.298 0.162

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 26 41 30 47 39 0 30 25

N.S.

1 1.44 2.28 1.67 2.61 2.17 0.00 1.67 1.39

time (sec)

N/A 0.273 0.018 1.595 0.188 0.261 0.000 0.304 0.102

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 41 52 37 108 378 0 84 76

N.S.

1 1.32 1.68 1.19 3.48 12.19 0.00 2.71 2.45

time (sec)

N/A 0.260 0.170 1.816 0.200 0.273 0.000 0.356 2.142

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 38 49 64 170 140 0 70 161

N.S.

1 1.12 1.44 1.88 5.00 4.12 0.00 2.06 4.74

time (sec)

N/A 0.270 0.023 3.337 0.194 0.259 0.000 0.314 2.185

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 66 62 67 251 1099 0 120 179

N.S.

1 1.29 1.22 1.31 4.92 21.55 0.00 2.35 3.51

time (sec)

N/A 0.281 0.272 4.538 0.189 0.271 0.000 0.354 0.102

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 75 395 93 649 721 0 278 1022

N.S.

1 0.97 5.13 1.21 8.43 9.36 0.00 3.61 13.27

time (sec)

N/A 0.343 2.322 31.116 0.188 0.282 0.000 0.347 0.172

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

77 71 107 81 333 2591 129 244 349

N.S.

1 0.92 1.39 1.05 4.32 33.65 1.68 3.17 4.53

time (sec)

N/A 0.296 0.319 20.833 0.269 0.278 0.664 0.345 2.158

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 61 281 83 325 435 0 196 513

N.S.

1 1.03 4.76 1.41 5.51 7.37 0.00 3.32 8.69

time (sec)

N/A 0.322 1.841 14.876 0.199 0.268 0.000 0.333 0.115

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

48 46 82 42 55 1180 63 162 182

N.S.

1 0.96 1.71 0.88 1.15 24.58 1.31 3.38 3.79

time (sec)

N/A 0.259 0.144 9.357 0.188 0.268 0.338 0.304 2.253

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 44 50 45 120 176 0 79 163

N.S.

1 1.10 1.25 1.12 3.00 4.40 0.00 1.98 4.08

time (sec)

N/A 0.232 0.442 1.097 0.185 0.260 0.000 0.284 0.124

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

53 55 84 50 161 665 0 150 308

N.S.

1 1.04 1.58 0.94 3.04 12.55 0.00 2.83 5.81

time (sec)

N/A 0.283 0.255 6.523 0.270 0.271 0.000 0.326 0.268

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 40 82 64 71 106 0 68 60

N.S.

1 1.11 2.28 1.78 1.97 2.94 0.00 1.89 1.67

time (sec)

N/A 0.322 3.203 7.219 0.188 0.258 0.000 0.323 2.126

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 64 82 64 206 637 0 148 240

N.S.

1 1.16 1.49 1.16 3.75 11.58 0.00 2.69 4.36

time (sec)

N/A 0.296 0.229 10.165 0.280 0.267 0.000 0.363 0.207

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 50 160 94 268 201 0 100 183

N.S.

1 1.09 3.48 2.04 5.83 4.37 0.00 2.17 3.98

time (sec)

N/A 0.327 1.443 15.994 0.194 0.257 0.000 0.325 2.166

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 69 77 84 282 1252 0 150 207

N.S.

1 1.33 1.48 1.62 5.42 24.08 0.00 2.88 3.98

time (sec)

N/A 0.293 0.278 23.417 0.202 0.263 0.000 0.369 2.380

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 66 256 163 613 425 0 170 511

N.S.

1 1.03 4.00 2.55 9.58 6.64 0.00 2.66 7.98

time (sec)

N/A 0.335 4.266 34.228 0.213 0.243 0.000 0.365 2.177

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 105 107 132 696 2548 0 219 377

N.S.

1 1.22 1.24 1.53 8.09 29.63 0.00 2.55 4.38

time (sec)

N/A 0.311 0.544 49.839 0.201 0.277 0.000 0.409 2.207

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 105 301 135 1453 1323 0 475 1834

N.S.

1 0.95 2.74 1.23 13.21 12.03 0.00 4.32 16.67

time (sec)

N/A 0.378 8.129 149.029 0.196 0.257 0.000 0.378 2.315

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

103 94 128 113 652 4658 178 387 573

N.S.

1 0.91 1.24 1.10 6.33 45.22 1.73 3.76 5.56

time (sec)

N/A 0.297 0.783 111.364 0.288 0.299 1.274 0.377 2.293

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 91 479 124 788 881 0 359 1133

N.S.

1 0.99 5.21 1.35 8.57 9.58 0.00 3.90 12.32

time (sec)

N/A 0.356 3.783 84.906 0.203 0.259 0.000 0.347 0.189

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

71 64 100 59 85 2519 87 271 347

N.S.

1 0.90 1.41 0.83 1.20 35.48 1.23 3.82 4.89

time (sec)

N/A 0.260 1.313 60.575 0.188 0.293 0.645 0.322 0.189

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 74 102 83 332 470 0 182 502

N.S.

1 1.01 1.40 1.14 4.55 6.44 0.00 2.49 6.88

time (sec)

N/A 0.261 1.111 1.508 0.194 0.246 0.000 0.292 2.120

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

84 83 114 86 300 2376 0 283 360

N.S.

1 0.99 1.36 1.02 3.57 28.29 0.00 3.37 4.29

time (sec)

N/A 0.306 0.690 46.661 0.280 0.277 0.000 0.319 2.333

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 62 162 111 172 359 0 135 234

N.S.

1 1.02 2.66 1.82 2.82 5.89 0.00 2.21 3.84

time (sec)

N/A 0.353 6.786 47.320 0.200 0.262 0.000 0.341 0.128

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

81 83 110 110 314 1701 0 247 324

N.S.

1 1.02 1.36 1.36 3.88 21.00 0.00 3.05 4.00

time (sec)

N/A 0.317 1.347 46.877 0.285 0.276 0.000 0.398 2.361

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 61 343 149 366 354 0 158 260

N.S.

1 1.02 5.72 2.48 6.10 5.90 0.00 2.63 4.33

time (sec)

N/A 0.344 3.654 67.918 0.203 0.258 0.000 0.378 2.172

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 94 101 119 422 1830 0 227 384

N.S.

1 1.16 1.25 1.47 5.21 22.59 0.00 2.80 4.74

time (sec)

N/A 0.323 0.731 94.218 0.293 0.264 0.000 0.423 2.298

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 71 303 199 826 521 0 213 547

N.S.

1 1.03 4.39 2.88 11.97 7.55 0.00 3.09 7.93

time (sec)

N/A 0.355 2.900 130.205 0.212 0.259 0.000 0.379 2.316

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 94 98 149 727 2632 0 242 411

N.S.

1 1.22 1.27 1.94 9.44 34.18 0.00 3.14 5.34

time (sec)

N/A 0.317 0.855 173.231 0.206 0.275 0.000 0.443 2.316

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 109 175 129 703 941 0 334 1083

N.S.

1 0.98 1.58 1.16 6.33 8.48 0.00 3.01 9.76

time (sec)

N/A 0.286 5.076 1.804 0.196 0.268 0.000 0.300 2.199

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 158 269 185 1277 1652 0 537 1952

N.S.

1 0.97 1.65 1.13 7.83 10.13 0.00 3.29 11.98

time (sec)

N/A 0.329 5.115 2.408 0.201 0.270 0.000 0.317 0.299

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F F B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

70 63 98 183 131 736 0 0 421

N.S.

1 0.90 1.40 2.61 1.87 10.51 0.00 0.00 6.01

time (sec)

N/A 0.298 0.331 4.321 0.269 0.330 0.000 0.000 2.460

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 70 196 184 637 683 0 0 183

N.S.

1 1.19 3.32 3.12 10.80 11.58 0.00 0.00 3.10

time (sec)

N/A 0.358 1.871 2.880 0.356 0.315 0.000 0.000 2.524

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 41 115 77 112 0 0 238

N.S.

1 1.00 0.91 2.56 1.71 2.49 0.00 0.00 5.29

time (sec)

N/A 0.282 0.136 1.741 0.264 0.296 0.000 0.000 2.482

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 54 174 104 291 419 0 0 105

N.S.

1 1.17 3.78 2.26 6.33 9.11 0.00 0.00 2.28

time (sec)

N/A 0.321 0.838 1.219 0.293 0.269 0.000 0.000 0.404

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 26 38 51 76 114 0 51

N.S.

1 1.00 1.13 1.65 2.22 3.30 4.96 0.00 2.22

time (sec)

N/A 0.223 0.216 0.606 0.195 0.257 1.351 0.000 0.317

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 172 108 83 436 0 0 470

N.S.

1 1.00 3.74 2.35 1.80 9.48 0.00 0.00 10.22

time (sec)

N/A 0.270 1.501 0.367 0.281 0.301 0.000 0.000 2.785

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 52 42 119 100 115 0 0 228

N.S.

1 1.13 0.91 2.59 2.17 2.50 0.00 0.00 4.96

time (sec)

N/A 0.292 0.145 1.137 0.198 0.289 0.000 0.000 2.506

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 77 193 133 429 749 0 0 977

N.S.

1 1.24 3.11 2.15 6.92 12.08 0.00 0.00 15.76

time (sec)

N/A 0.360 2.063 1.792 0.295 0.306 0.000 0.000 3.900

Problem 146

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 77 100 171 187 862 0 0 523

N.S.

1 1.05 1.37 2.34 2.56 11.81 0.00 0.00 7.16

time (sec)

N/A 0.315 0.282 2.879 0.200 0.319 0.000 0.000 2.706

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B B B F F B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

87 107 380 192 1435 2705 0 0 779

N.S.

1 1.23 4.37 2.21 16.49 31.09 0.00 0.00 8.95

time (sec)

N/A 0.435 4.373 4.693 0.391 0.309 0.000 0.000 4.209

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 70 109 184 154 853 0 0 0

N.S.

1 0.92 1.43 2.42 2.03 11.22 0.00 0.00 0.00

time (sec)

N/A 0.319 0.495 22.782 0.276 0.323 0.000 0.000 0.000

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

91 105 228 259 1053 1479 0 0 0

N.S.

1 1.15 2.51 2.85 11.57 16.25 0.00 0.00 0.00

time (sec)

N/A 0.375 3.164 15.772 0.464 0.295 0.000 0.000 0.000

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 48 81 115 108 485 0 0 0

N.S.

1 0.94 1.59 2.25 2.12 9.51 0.00 0.00 0.00

time (sec)

N/A 0.286 0.995 9.768 0.199 0.262 0.000 0.000 0.000

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

85 97 326 236 597 1846 0 0 0

N.S.

1 1.14 3.84 2.78 7.02 21.72 0.00 0.00 0.00

time (sec)

N/A 0.346 4.767 6.527 0.346 0.303 0.000 0.000 0.000

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 44 79 60 106 476 0 0 53

N.S.

1 0.90 1.61 1.22 2.16 9.71 0.00 0.00 1.08

time (sec)

N/A 0.260 0.660 6.326 0.189 0.267 0.000 0.000 2.347

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

93 112 221 254 187 1690 0 0 0

N.S.

1 1.20 2.38 2.73 2.01 18.17 0.00 0.00 0.00

time (sec)

N/A 0.279 3.741 0.572 0.298 0.303 0.000 0.000 0.000

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 84 115 206 209 1031 0 0 0

N.S.

1 1.01 1.39 2.48 2.52 12.42 0.00 0.00 0.00

time (sec)

N/A 0.322 0.343 10.170 0.202 0.335 0.000 0.000 0.000

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

121 142 268 288 1070 3624 0 0 0

N.S.

1 1.17 2.21 2.38 8.84 29.95 0.00 0.00 0.00

time (sec)

N/A 0.454 4.116 15.900 0.364 0.307 0.000 0.000 0.000

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 108 130 260 384 3624 0 0 0

N.S.

1 0.98 1.18 2.36 3.49 32.95 0.00 0.00 0.00

time (sec)

N/A 0.354 1.382 23.767 0.224 0.439 0.000 0.000 0.000

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

161 182 350 362 2961 9849 0 0 0

N.S.

1 1.13 2.17 2.25 18.39 61.17 0.00 0.00 0.00

time (sec)

N/A 0.544 6.345 34.979 0.573 0.395 0.000 0.000 0.000

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

148 173 754 389 3239 5463 0 0 0

N.S.

1 1.17 5.09 2.63 21.89 36.91 0.00 0.00 0.00

time (sec)

N/A 0.485 7.975 191.714 1.017 0.337 0.000 0.000 0.000

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 73 136 184 206 1741 0 0 0

N.S.

1 0.95 1.77 2.39 2.68 22.61 0.00 0.00 0.00

time (sec)

N/A 0.306 2.919 145.706 0.225 0.285 0.000 0.000 0.000

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

139 155 1317 343 2201 6464 0 0 0

N.S.

1 1.12 9.47 2.47 15.83 46.50 0.00 0.00 0.00

time (sec)

N/A 0.434 15.010 64.282 0.632 0.343 0.000 0.000 0.000

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 75 131 187 209 1753 0 0 0

N.S.

1 0.93 1.62 2.31 2.58 21.64 0.00 0.00 0.00

time (sec)

N/A 0.316 1.450 46.045 0.210 0.289 0.000 0.000 0.000

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

139 164 1317 335 1255 7158 0 0 0

N.S.

1 1.18 9.47 2.41 9.03 51.50 0.00 0.00 0.00

time (sec)

N/A 0.424 11.778 41.615 0.433 0.355 0.000 0.000 0.000

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 69 129 82 193 1666 0 0 94

N.S.

1 0.95 1.77 1.12 2.64 22.82 0.00 0.00 1.29

time (sec)

N/A 0.292 1.801 43.921 0.231 0.275 0.000 0.000 2.235

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

146 177 301 352 402 6538 0 0 0

N.S.

1 1.21 2.06 2.41 2.75 44.78 0.00 0.00 0.00

time (sec)

N/A 0.373 8.313 1.308 0.310 0.342 0.000 0.000 0.000

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 128 155 292 419 4132 0 0 0

N.S.

1 0.98 1.19 2.25 3.22 31.78 0.00 0.00 0.00

time (sec)

N/A 0.374 1.114 64.557 0.226 0.505 0.000 0.000 0.000

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

182 213 2083 394 1971 11606 0 0 0

N.S.

1 1.17 11.45 2.16 10.83 63.77 0.00 0.00 0.00

time (sec)

N/A 0.565 8.752 136.056 0.463 0.394 0.000 0.000 0.000

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

152 151 172 354 692 10255 0 0 0

N.S.

1 0.99 1.13 2.33 4.55 67.47 0.00 0.00 0.00

time (sec)

N/A 0.413 1.302 191.058 0.268 0.797 0.000 0.000 0.000

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

232 263 3334 468 4920 24263 0 0 0

N.S.

1 1.13 14.37 2.02 21.21 104.58 0.00 0.00 0.00

time (sec)

N/A 0.646 8.501 268.036 0.850 0.558 0.000 0.000 0.000

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

207 248 1405 545 718 17283 0 0 0

N.S.

1 1.20 6.79 2.63 3.47 83.49 0.00 0.00 0.00

time (sec)

N/A 0.458 8.738 3.264 0.341 0.451 0.000 0.000 0.000

Problem 170

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

29 32 25 26 33 183 0 72 0

N.S.

1 1.10 0.86 0.90 1.14 6.31 0.00 2.48 0.00

time (sec)

N/A 0.333 0.022 0.399 0.281 0.264 0.000 0.289 0.000

Problem 171

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

14 14 14 17 13 18 0 26 0

N.S.

1 1.00 1.00 1.21 0.93 1.29 0.00 1.86 0.00

time (sec)

N/A 0.262 0.007 0.355 0.293 0.264 0.000 0.312 0.000

Problem 172

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 18 79 22 18 0 31 0

N.S.

1 1.00 1.29 5.64 1.57 1.29 0.00 2.21 0.00

time (sec)

N/A 0.268 0.017 0.164 0.300 0.258 0.000 0.315 0.000

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 27 95 33 404 0 83 0

N.S.

1 1.00 0.79 2.79 0.97 11.88 0.00 2.44 0.00

time (sec)

N/A 0.329 0.023 0.215 0.279 0.269 0.000 0.286 0.000

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 26 13 70 0 31 0

N.S.

1 1.00 1.00 1.62 0.81 4.38 0.00 1.94 0.00

time (sec)

N/A 0.257 0.007 0.317 0.281 0.258 0.000 0.269 0.000

Problem 175

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 20 33 22 69 0 36 0

N.S.

1 1.00 1.25 2.06 1.38 4.31 0.00 2.25 0.00

time (sec)

N/A 0.268 0.015 0.315 0.285 0.260 0.000 0.294 0.000

Problem 176

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

83 88 108 0 0 4594 0 0 0

N.S.

1 1.06 1.30 0.00 0.00 55.35 0.00 0.00 0.00

time (sec)

N/A 0.327 0.647 0.000 0.000 0.505 0.000 0.000 0.000

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

125 137 192 0 0 8852 0 0 0

N.S.

1 1.10 1.54 0.00 0.00 70.82 0.00 0.00 0.00

time (sec)

N/A 0.472 0.418 0.000 0.000 0.518 0.000 0.000 0.000

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

59 64 56 0 0 2394 0 0 0

N.S.

1 1.08 0.95 0.00 0.00 40.58 0.00 0.00 0.00

time (sec)

N/A 0.271 0.265 0.000 0.000 0.345 0.000 0.000 0.000

Problem 179

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

87 91 150 0 0 4316 0 0 0

N.S.

1 1.05 1.72 0.00 0.00 49.61 0.00 0.00 0.00

time (sec)

N/A 0.389 0.280 0.000 0.000 0.390 0.000 0.000 0.000

Problem 180

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 45 90 43 0 1608 0 0 32

N.S.

1 1.12 2.25 1.08 0.00 40.20 0.00 0.00 0.80

time (sec)

N/A 0.241 0.200 0.132 0.000 0.332 0.000 0.000 2.437

Problem 181

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

59 59 134 0 0 2949 0 0 0

N.S.

1 1.00 2.27 0.00 0.00 49.98 0.00 0.00 0.00

time (sec)

N/A 0.234 0.611 0.000 0.000 0.350 0.000 0.000 0.000

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

56 61 56 0 0 3597 0 0 0

N.S.

1 1.09 1.00 0.00 0.00 64.23 0.00 0.00 0.00

time (sec)

N/A 0.281 0.133 0.000 0.000 0.344 0.000 0.000 0.000

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

48 48 75 0 0 1303 0 0 0

N.S.

1 1.00 1.56 0.00 0.00 27.15 0.00 0.00 0.00

time (sec)

N/A 0.326 0.403 0.000 0.000 0.299 0.000 0.000 0.000

Problem 184

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

83 95 156 0 0 5247 0 0 0

N.S.

1 1.14 1.88 0.00 0.00 63.22 0.00 0.00 0.00

time (sec)

N/A 0.311 0.580 0.000 0.000 0.397 0.000 0.000 0.000

Problem 185

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

84 88 149 0 0 2341 0 0 0

N.S.

1 1.05 1.77 0.00 0.00 27.87 0.00 0.00 0.00

time (sec)

N/A 0.381 0.458 0.000 0.000 0.358 0.000 0.000 0.000

Problem 186

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

125 156 191 0 0 12548 0 0 0

N.S.

1 1.25 1.53 0.00 0.00 100.38 0.00 0.00 0.00

time (sec)

N/A 0.378 0.942 0.000 0.000 0.600 0.000 0.000 0.000

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

76 84 80 0 0 4226 0 0 0

N.S.

1 1.11 1.05 0.00 0.00 55.61 0.00 0.00 0.00

time (sec)

N/A 0.296 0.521 0.000 0.000 0.508 0.000 0.000 0.000

Problem 188

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

125 134 197 0 0 8582 0 0 0

N.S.

1 1.07 1.58 0.00 0.00 68.66 0.00 0.00 0.00

time (sec)

N/A 0.520 0.585 0.000 0.000 0.521 0.000 0.000 0.000

Problem 189

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 65 65 56 0 2312 0 0 45

N.S.

1 1.14 1.14 0.98 0.00 40.56 0.00 0.00 0.79

time (sec)

N/A 0.255 0.093 0.127 0.000 0.349 0.000 0.000 4.005

Problem 190

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

88 91 152 0 0 4140 0 0 0

N.S.

1 1.03 1.73 0.00 0.00 47.05 0.00 0.00 0.00

time (sec)

N/A 0.293 0.195 0.000 0.000 0.380 0.000 0.000 0.000

Problem 191

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

70 76 159 0 0 4123 0 0 0

N.S.

1 1.09 2.27 0.00 0.00 58.90 0.00 0.00 0.00

time (sec)

N/A 0.318 0.520 0.000 0.000 0.381 0.000 0.000 0.000

Problem 192

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

81 81 144 0 0 3349 0 0 0

N.S.

1 1.00 1.78 0.00 0.00 41.35 0.00 0.00 0.00

time (sec)

N/A 0.386 0.328 0.000 0.000 0.377 0.000 0.000 0.000

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

170 170 280 0 0 12452 0 0 0

N.S.

1 1.00 1.65 0.00 0.00 73.25 0.00 0.00 0.00

time (sec)

N/A 0.366 6.957 0.000 0.000 0.736 0.000 0.000 0.000

Problem 194

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

66 72 84 0 0 2678 0 0 0

N.S.

1 1.09 1.27 0.00 0.00 40.58 0.00 0.00 0.00

time (sec)

N/A 0.314 0.453 0.000 0.000 0.386 0.000 0.000 0.000

Problem 195

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

90 97 169 0 0 4569 0 0 0

N.S.

1 1.08 1.88 0.00 0.00 50.77 0.00 0.00 0.00

time (sec)

N/A 0.386 0.445 0.000 0.000 0.403 0.000 0.000 0.000

Problem 196

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

42 48 42 0 0 1650 0 0 0

N.S.

1 1.14 1.00 0.00 0.00 39.29 0.00 0.00 0.00

time (sec)

N/A 0.263 0.225 0.000 0.000 0.319 0.000 0.000 0.000

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

60 60 107 0 0 2856 0 0 0

N.S.

1 1.00 1.78 0.00 0.00 47.60 0.00 0.00 0.00

time (sec)

N/A 0.354 0.221 0.000 0.000 0.342 0.000 0.000 0.000

Problem 198

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 25 30 0 1430 0 0 19

N.S.

1 1.00 1.00 1.20 0.00 57.20 0.00 0.00 0.76

time (sec)

N/A 0.237 0.076 0.242 0.000 0.291 0.000 0.000 2.359

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 29 62 0 0 1059 0 0 0

N.S.

1 1.00 2.14 0.00 0.00 36.52 0.00 0.00 0.00

time (sec)

N/A 0.203 0.037 0.000 0.000 0.285 0.000 0.000 0.000

Problem 200

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

56 61 124 0 0 3663 0 0 0

N.S.

1 1.09 2.21 0.00 0.00 65.41 0.00 0.00 0.00

time (sec)

N/A 0.295 0.345 0.000 0.000 0.361 0.000 0.000 0.000

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