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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 A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

162 164 162 169 167 170 197 212 166

N.S.

1 1.01 1.00 1.04 1.03 1.05 1.22 1.31 1.02

time (sec)

N/A 0.345 0.054 0.049 0.185 0.276 0.196 0.296 0.032

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 132 126 136 0 421 0 126 1343

N.S.

1 0.99 0.95 1.02 0.00 3.17 0.00 0.95 10.10

time (sec)

N/A 0.335 0.045 0.203 0.000 0.290 0.000 0.616 7.875

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 96 93 98 0 312 434 91 979

N.S.

1 0.99 0.96 1.01 0.00 3.22 4.47 0.94 10.09

time (sec)

N/A 0.283 0.046 0.142 0.000 0.284 72.994 0.616 8.008

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 72 71 65 0 219 287 67 606

N.S.

1 1.01 1.00 0.92 0.00 3.08 4.04 0.94 8.54

time (sec)

N/A 0.245 0.033 0.096 0.000 0.276 5.220 0.686 7.711

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 81 128 76 0 249 0 78 2424

N.S.

1 1.04 1.64 0.97 0.00 3.19 0.00 1.00 31.08

time (sec)

N/A 0.279 0.074 0.067 0.000 0.279 0.000 0.726 10.104

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 114 186 126 0 385 0 124 3729

N.S.

1 1.02 1.66 1.12 0.00 3.44 0.00 1.11 33.29

time (sec)

N/A 0.358 0.146 0.090 0.000 0.392 0.000 0.629 10.265

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

261 272 327 95 0 5140 0 4391 10177

N.S.

1 1.04 1.25 0.36 0.00 19.69 0.00 16.82 38.99

time (sec)

N/A 0.563 0.255 0.101 0.000 2.570 0.000 1.073 8.400

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

208 212 251 65 0 2632 0 3179 6366

N.S.

1 1.02 1.21 0.31 0.00 12.65 0.00 15.28 30.61

time (sec)

N/A 0.416 0.105 0.070 0.000 0.618 0.000 0.958 8.233

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

172 172 173 45 0 1569 0 1402 4109

N.S.

1 1.00 1.01 0.26 0.00 9.12 0.00 8.15 23.89

time (sec)

N/A 0.305 0.062 0.059 0.000 0.438 0.000 0.783 8.071

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 187 206 173 0 2914 0 2805 6335

N.S.

1 0.99 1.09 0.92 0.00 15.42 0.00 14.84 33.52

time (sec)

N/A 0.392 0.187 0.093 0.000 0.786 0.000 1.051 0.779

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

271 0 267 232 0 5442 0 2870 10101

N.S.

1 0.00 0.99 0.86 0.00 20.08 0.00 10.59 37.27

time (sec)

N/A 0.000 0.206 0.108 0.000 2.886 0.000 0.908 8.694

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

212 220 208 282 0 1323 0 239 2282

N.S.

1 1.04 0.98 1.33 0.00 6.24 0.00 1.13 10.76

time (sec)

N/A 0.488 0.193 0.227 0.000 0.347 0.000 0.647 8.065

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 169 160 211 0 849 0 194 1527

N.S.

1 1.15 1.09 1.44 0.00 5.78 0.00 1.32 10.39

time (sec)

N/A 0.362 0.122 0.175 0.000 0.296 0.000 0.614 8.163

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 109 111 126 0 538 394 120 283

N.S.

1 1.02 1.04 1.18 0.00 5.03 3.68 1.12 2.64

time (sec)

N/A 0.268 0.057 0.118 0.000 0.258 4.227 0.586 7.612

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 96 101 95 0 474 374 102 264

N.S.

1 1.02 1.07 1.01 0.00 5.04 3.98 1.09 2.81

time (sec)

N/A 0.241 0.056 0.102 0.000 0.258 2.279 0.560 7.675

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 180 243 212 0 1014 0 201 7119

N.S.

1 1.20 1.62 1.41 0.00 6.76 0.00 1.34 47.46

time (sec)

N/A 0.444 0.226 0.118 0.000 0.596 0.000 0.613 12.299

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

223 0 379 300 0 1635 0 250 10034

N.S.

1 0.00 1.70 1.35 0.00 7.33 0.00 1.12 45.00

time (sec)

N/A 0.000 0.340 0.155 0.000 1.149 0.000 0.562 13.332

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

425 400 455 217 0 7252 0 5675 16604

N.S.

1 0.94 1.07 0.51 0.00 17.06 0.00 13.35 39.07

time (sec)

N/A 0.759 0.761 0.131 0.000 7.531 0.000 1.513 10.139

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

336 318 362 178 0 4658 0 4538 12396

N.S.

1 0.95 1.08 0.53 0.00 13.86 0.00 13.51 36.89

time (sec)

N/A 0.585 0.586 0.130 0.000 2.308 0.000 1.397 10.982

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

276 265 298 152 0 3467 0 3776 9444

N.S.

1 0.96 1.08 0.55 0.00 12.56 0.00 13.68 34.22

time (sec)

N/A 0.441 0.422 0.106 0.000 1.158 0.000 1.140 10.412

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

293 279 304 178 0 4885 0 4426 12349

N.S.

1 0.95 1.04 0.61 0.00 16.67 0.00 15.11 42.15

time (sec)

N/A 0.544 0.510 0.179 0.000 3.281 0.000 1.378 10.668

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

389 379 382 379 0 7583 0 5408 17591

N.S.

1 0.97 0.98 0.97 0.00 19.49 0.00 13.90 45.22

time (sec)

N/A 0.703 0.698 0.160 0.000 8.891 0.000 1.358 11.087

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

522 518 487 484 0 10190 0 6327 21554

N.S.

1 0.99 0.93 0.93 0.00 19.52 0.00 12.12 41.29

time (sec)

N/A 0.916 0.795 0.187 0.000 21.405 0.000 1.489 11.357

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

365 391 435 624 0 3196 0 598 4501

N.S.

1 1.07 1.19 1.71 0.00 8.76 0.00 1.64 12.33

time (sec)

N/A 1.087 0.428 0.311 0.000 0.535 0.000 1.418 10.379

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

254 297 354 495 0 2167 0 466 3062

N.S.

1 1.17 1.39 1.95 0.00 8.53 0.00 1.83 12.06

time (sec)

N/A 0.574 0.301 0.228 0.000 0.395 0.000 1.525 10.737

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

146 154 261 343 0 1378 0 318 593

N.S.

1 1.05 1.79 2.35 0.00 9.44 0.00 2.18 4.06

time (sec)

N/A 0.316 0.200 0.146 0.000 0.304 0.000 1.453 7.846

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

185 203 233 303 0 1369 0 268 625

N.S.

1 1.10 1.26 1.64 0.00 7.40 0.00 1.45 3.38

time (sec)

N/A 0.408 0.165 0.150 0.000 0.334 0.000 1.416 7.852

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

170 172 172 273 0 1226 0 228 587

N.S.

1 1.01 1.01 1.61 0.00 7.21 0.00 1.34 3.45

time (sec)

N/A 0.328 0.148 0.149 0.000 0.314 0.000 1.548 7.818

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 148 142 147 0 1109 661 208 517

N.S.

1 1.06 1.02 1.06 0.00 7.98 4.76 1.50 3.72

time (sec)

N/A 0.294 0.089 0.138 0.000 0.296 165.164 1.445 7.741

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

252 306 396 442 0 2494 0 421 11674

N.S.

1 1.21 1.57 1.75 0.00 9.90 0.00 1.67 46.33

time (sec)

N/A 0.635 0.417 0.187 0.000 1.950 0.000 1.510 14.337

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

363 405 642 616 0 3956 0 648 16265

N.S.

1 1.12 1.77 1.70 0.00 10.90 0.00 1.79 44.81

time (sec)

N/A 0.837 0.903 0.282 0.000 3.981 0.000 1.427 18.347

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

554 544 644 445 0 9636 0 3987 22911

N.S.

1 0.98 1.16 0.80 0.00 17.39 0.00 7.20 41.36

time (sec)

N/A 1.052 1.520 0.169 0.000 18.804 0.000 2.019 10.325

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

461 458 543 375 0 7060 0 7578 19041

N.S.

1 0.99 1.18 0.81 0.00 15.31 0.00 16.44 41.30

time (sec)

N/A 0.817 1.269 0.155 0.000 6.011 0.000 2.353 9.742

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

380 386 447 328 0 5650 0 3164 16688

N.S.

1 1.02 1.18 0.86 0.00 14.87 0.00 8.33 43.92

time (sec)

N/A 0.710 1.080 0.160 0.000 4.207 0.000 1.745 9.432

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

438 403 436 374 0 7270 0 7267 18992

N.S.

1 0.92 1.00 0.85 0.00 16.60 0.00 16.59 43.36

time (sec)

N/A 0.809 1.013 0.147 0.000 8.330 0.000 2.183 9.694

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

460 464 516 447 0 9909 0 4605 22914

N.S.

1 1.01 1.12 0.97 0.00 21.54 0.00 10.01 49.81

time (sec)

N/A 0.872 1.297 0.389 0.000 21.044 0.000 1.787 10.184

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

25 23 25 18 17 17 17 19 17

N.S.

1 0.92 1.00 0.72 0.68 0.68 0.68 0.76 0.68

time (sec)

N/A 0.190 0.008 0.042 0.196 0.256 0.052 0.273 0.033

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 23 25 18 25 17 17 19 17

N.S.

1 0.92 1.00 0.72 1.00 0.68 0.68 0.76 0.68

time (sec)

N/A 0.213 0.004 0.035 0.184 0.254 0.049 0.277 0.017

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

37 38 37 31 30 30 37 30 32

N.S.

1 1.03 1.00 0.84 0.81 0.81 1.00 0.81 0.86

time (sec)

N/A 0.200 0.010 0.047 0.271 0.262 0.056 0.263 7.558

Problem 140

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 38 37 31 53 30 37 30 32

N.S.

1 1.03 1.00 0.84 1.43 0.81 1.00 0.81 0.86

time (sec)

N/A 0.217 0.005 0.034 0.264 0.257 0.051 0.261 0.020

Problem 141

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

45 54 45 38 0 47 44 38 41

N.S.

1 1.20 1.00 0.84 0.00 1.04 0.98 0.84 0.91

time (sec)

N/A 0.219 0.023 0.053 0.000 0.255 0.062 0.409 0.031

Problem 142

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

102 116 69 58 104 61 105 102 102

N.S.

1 1.14 0.68 0.57 1.02 0.60 1.03 1.00 1.00

time (sec)

N/A 0.265 0.107 0.334 0.201 0.252 0.776 0.307 0.272

Problem 143

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

81 90 64 53 87 56 94 88 85

N.S.

1 1.11 0.79 0.65 1.07 0.69 1.16 1.09 1.05

time (sec)

N/A 0.231 0.083 0.203 0.186 0.254 0.735 0.287 7.680

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

74 79 59 48 70 51 80 74 67

N.S.

1 1.07 0.80 0.65 0.95 0.69 1.08 1.00 0.91

time (sec)

N/A 0.213 0.081 0.179 0.189 0.263 0.703 0.271 7.666

Problem 145

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

94 99 88 83 89 95 0 98 86

N.S.

1 1.05 0.94 0.88 0.95 1.01 0.00 1.04 0.91

time (sec)

N/A 0.269 0.132 0.521 0.276 0.272 0.000 0.294 0.245

Problem 146

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

97 102 91 83 89 112 0 138 84

N.S.

1 1.05 0.94 0.86 0.92 1.15 0.00 1.42 0.87

time (sec)

N/A 0.286 0.153 0.503 0.268 0.268 0.000 0.305 8.006

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 104 91 86 106 112 0 169 0

N.S.

1 1.05 0.92 0.87 1.07 1.13 0.00 1.71 0.00

time (sec)

N/A 0.283 0.182 0.480 0.268 0.260 0.000 0.322 0.000

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 99 70 66 99 90 0 189 0

N.S.

1 1.10 0.78 0.73 1.10 1.00 0.00 2.10 0.00

time (sec)

N/A 0.242 0.219 0.409 0.273 0.249 0.000 0.309 0.000

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 125 80 71 116 95 0 233 0

N.S.

1 1.13 0.72 0.64 1.05 0.86 0.00 2.10 0.00

time (sec)

N/A 0.275 0.245 0.398 0.276 0.266 0.000 0.290 0.000

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 151 80 76 133 100 0 255 0

N.S.

1 1.14 0.61 0.58 1.01 0.76 0.00 1.93 0.00

time (sec)

N/A 0.305 0.307 0.435 0.283 0.260 0.000 0.314 0.000

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

322 344 237 226 0 139 0 0 0

N.S.

1 1.07 0.74 0.70 0.00 0.43 0.00 0.00 0.00

time (sec)

N/A 0.494 6.063 5.582 0.000 0.085 0.000 0.000 0.000

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

305 316 234 221 0 134 0 0 0

N.S.

1 1.04 0.77 0.72 0.00 0.44 0.00 0.00 0.00

time (sec)

N/A 0.398 5.090 1.998 0.000 0.097 0.000 0.000 0.000

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

279 292 229 216 0 129 0 0 0

N.S.

1 1.05 0.82 0.77 0.00 0.46 0.00 0.00 0.00

time (sec)

N/A 0.347 5.058 1.745 0.000 0.093 0.000 0.000 0.000

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

284 287 231 225 0 0 0 0 0

N.S.

1 1.01 0.81 0.79 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.349 4.815 1.407 0.000 0.000 0.000 0.000 0.000

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

305 320 237 228 0 0 0 0 0

N.S.

1 1.05 0.78 0.75 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.406 9.679 2.151 0.000 0.000 0.000 0.000 0.000

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 146 79 68 135 71 218 207 0

N.S.

1 1.15 0.62 0.54 1.06 0.56 1.72 1.63 0.00

time (sec)

N/A 0.289 0.184 0.237 0.194 0.267 1.206 0.298 0.000

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

106 120 74 63 118 66 190 179 0

N.S.

1 1.13 0.70 0.59 1.11 0.62 1.79 1.69 0.00

time (sec)

N/A 0.268 0.143 0.214 0.191 0.267 1.160 0.324 0.000

Problem 158

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

99 113 69 58 101 61 165 151 127

N.S.

1 1.14 0.70 0.59 1.02 0.62 1.67 1.53 1.28

time (sec)

N/A 0.247 0.132 0.192 0.182 0.275 1.100 0.293 7.785

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 131 99 87 120 106 0 113 0

N.S.

1 1.10 0.83 0.73 1.01 0.89 0.00 0.95 0.00

time (sec)

N/A 0.321 0.201 0.475 0.276 0.270 0.000 0.303 0.000

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 132 102 96 120 122 0 153 0

N.S.

1 1.08 0.84 0.79 0.98 1.00 0.00 1.25 0.00

time (sec)

N/A 0.322 0.227 0.527 0.264 0.292 0.000 0.313 0.000

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 135 101 96 137 122 0 190 0

N.S.

1 1.06 0.80 0.76 1.08 0.96 0.00 1.50 0.00

time (sec)

N/A 0.324 0.255 0.532 0.286 0.280 0.000 0.309 0.000

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 135 101 96 154 122 0 227 0

N.S.

1 1.06 0.80 0.76 1.21 0.96 0.00 1.79 0.00

time (sec)

N/A 0.321 0.344 0.548 0.275 0.268 0.000 0.319 0.000

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

356 375 249 236 0 149 0 0 0

N.S.

1 1.05 0.70 0.66 0.00 0.42 0.00 0.00 0.00

time (sec)

N/A 0.513 9.168 4.206 0.000 0.083 0.000 0.000 0.000

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

331 351 244 231 0 144 0 0 0

N.S.

1 1.06 0.74 0.70 0.00 0.44 0.00 0.00 0.00

time (sec)

N/A 0.454 7.622 2.783 0.000 0.085 0.000 0.000 0.000

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

308 314 239 226 0 139 0 0 0

N.S.

1 1.02 0.78 0.73 0.00 0.45 0.00 0.00 0.00

time (sec)

N/A 0.395 6.662 1.405 0.000 0.104 0.000 0.000 0.000

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

312 325 235 233 0 0 0 0 0

N.S.

1 1.04 0.75 0.75 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.410 6.508 1.456 0.000 0.000 0.000 0.000 0.000

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

314 325 247 238 0 0 0 0 0

N.S.

1 1.04 0.79 0.76 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.407 10.248 2.127 0.000 0.000 0.000 0.000 0.000

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

331 353 244 238 0 0 0 0 0

N.S.

1 1.07 0.74 0.72 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.462 10.270 4.088 0.000 0.000 0.000 0.000 0.000

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 165 135 125 0 315 325 136 0

N.S.

1 1.08 0.88 0.82 0.00 2.06 2.12 0.89 0.00

time (sec)

N/A 0.350 0.524 0.186 0.000 0.273 1.052 0.334 0.000

Problem 170

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 104 104 88 0 233 233 96 0

N.S.

1 1.04 1.04 0.88 0.00 2.33 2.33 0.96 0.00

time (sec)

N/A 0.247 0.329 0.121 0.000 0.274 0.920 0.309 0.000

Problem 171

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 77 77 65 0 178 165 67 92

N.S.

1 1.01 1.01 0.86 0.00 2.34 2.17 0.88 1.21

time (sec)

N/A 0.215 0.290 0.087 0.000 0.264 0.834 0.294 8.168

Problem 172

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 89 85 76 0 517 0 0 81

N.S.

1 0.99 0.94 0.84 0.00 5.74 0.00 0.00 0.90

time (sec)

N/A 0.265 0.245 0.097 0.000 0.319 0.000 0.000 8.000

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 82 81 71 0 197 0 124 103

N.S.

1 1.02 1.01 0.89 0.00 2.46 0.00 1.55 1.29

time (sec)

N/A 0.234 0.334 0.123 0.000 0.305 0.000 0.300 8.149

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 134 145 98 0 255 0 339 0

N.S.

1 1.08 1.17 0.79 0.00 2.06 0.00 2.73 0.00

time (sec)

N/A 0.311 0.572 0.135 0.000 0.348 0.000 0.306 0.000

Problem 175

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

177 195 186 138 0 339 0 571 0

N.S.

1 1.10 1.05 0.78 0.00 1.92 0.00 3.23 0.00

time (sec)

N/A 0.416 0.808 0.163 0.000 0.407 0.000 0.310 0.000

Problem 176

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

403 400 532 448 0 431 0 0 0

N.S.

1 0.99 1.32 1.11 0.00 1.07 0.00 0.00 0.00

time (sec)

N/A 0.562 11.508 5.782 0.000 0.094 0.000 0.000 0.000

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

336 333 479 395 0 346 0 0 0

N.S.

1 0.99 1.43 1.18 0.00 1.03 0.00 0.00 0.00

time (sec)

N/A 0.411 11.006 2.403 0.000 0.097 0.000 0.000 0.000

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

283 285 302 362 0 300 0 0 0

N.S.

1 1.01 1.07 1.28 0.00 1.06 0.00 0.00 0.00

time (sec)

N/A 0.332 10.184 0.987 0.000 0.097 0.000 0.000 0.000

Problem 179

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

312 316 448 385 0 294 0 0 0

N.S.

1 1.01 1.44 1.23 0.00 0.94 0.00 0.00 0.00

time (sec)

N/A 0.396 10.707 1.938 0.000 0.086 0.000 0.000 0.000

Problem 180

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

376 374 373 418 0 347 0 0 0

N.S.

1 0.99 0.99 1.11 0.00 0.92 0.00 0.00 0.00

time (sec)

N/A 0.511 10.467 3.381 0.000 0.094 0.000 0.000 0.000

Problem 181

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 112 64 53 90 56 65 60 0

N.S.

1 1.14 0.65 0.54 0.92 0.57 0.66 0.61 0.00

time (sec)

N/A 0.271 0.115 0.206 0.184 0.248 0.912 0.291 0.000

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 83 59 48 73 51 54 53 0

N.S.

1 1.08 0.77 0.62 0.95 0.66 0.70 0.69 0.00

time (sec)

N/A 0.234 0.102 0.195 0.239 0.241 0.871 0.270 0.000

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 60 54 43 56 46 51 46 0

N.S.

1 1.07 0.96 0.77 1.00 0.82 0.91 0.82 0.00

time (sec)

N/A 0.200 0.097 0.181 0.193 0.240 0.816 0.273 0.000

Problem 184

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

49 51 47 36 39 39 42 39 35

N.S.

1 1.04 0.96 0.73 0.80 0.80 0.86 0.80 0.71

time (sec)

N/A 0.192 0.091 0.165 0.192 0.252 0.796 0.275 8.098

Problem 185

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

69 71 63 52 58 75 0 78 56

N.S.

1 1.03 0.91 0.75 0.84 1.09 0.00 1.13 0.81

time (sec)

N/A 0.235 0.121 0.448 0.270 0.264 0.000 0.283 8.203

Problem 186

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

62 66 58 49 51 78 0 101 83

N.S.

1 1.06 0.94 0.79 0.82 1.26 0.00 1.63 1.34

time (sec)

N/A 0.206 0.141 0.332 0.273 0.257 0.000 0.292 0.277

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 90 63 64 68 83 0 145 0

N.S.

1 1.08 0.76 0.77 0.82 1.00 0.00 1.75 0.00

time (sec)

N/A 0.242 0.177 0.355 0.273 0.269 0.000 0.294 0.000

Problem 188

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 116 75 66 85 90 0 167 0

N.S.

1 1.12 0.72 0.63 0.82 0.87 0.00 1.61 0.00

time (sec)

N/A 0.274 0.240 0.375 0.283 0.264 0.000 0.301 0.000

Problem 189

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

298 309 229 216 0 129 0 0 0

N.S.

1 1.04 0.77 0.72 0.00 0.43 0.00 0.00 0.00

time (sec)

N/A 0.390 10.226 3.891 0.000 0.099 0.000 0.000 0.000

Problem 190

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

270 277 222 208 0 122 0 0 0

N.S.

1 1.03 0.82 0.77 0.00 0.45 0.00 0.00 0.00

time (sec)

N/A 0.341 10.228 2.597 0.000 0.093 0.000 0.000 0.000

Problem 191

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

257 260 159 194 0 117 0 0 0

N.S.

1 1.01 0.62 0.75 0.00 0.46 0.00 0.00 0.00

time (sec)

N/A 0.306 10.125 0.840 0.000 0.086 0.000 0.000 0.000

Problem 192

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

278 287 224 211 0 124 0 0 0

N.S.

1 1.03 0.81 0.76 0.00 0.45 0.00 0.00 0.00

time (sec)

N/A 0.356 10.233 1.400 0.000 0.082 0.000 0.000 0.000

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

302 311 237 228 0 140 0 0 0

N.S.

1 1.03 0.78 0.75 0.00 0.46 0.00 0.00 0.00

time (sec)

N/A 0.397 10.241 2.114 0.000 0.081 0.000 0.000 0.000

Problem 194

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 84 59 48 73 86 0 52 0

N.S.

1 1.09 0.77 0.62 0.95 1.12 0.00 0.68 0.00

time (sec)

N/A 0.232 0.179 0.216 0.196 0.246 0.000 0.273 0.000

Problem 195

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

56 58 54 43 56 81 0 46 52

N.S.

1 1.04 0.96 0.77 1.00 1.45 0.00 0.82 0.93

time (sec)

N/A 0.206 0.144 0.199 0.197 0.259 0.000 0.292 7.849

Problem 196

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

25 25 25 22 32 46 0 21 21

N.S.

1 1.00 1.00 0.88 1.28 1.84 0.00 0.84 0.84

time (sec)

N/A 0.166 0.144 0.065 0.185 0.260 0.000 0.292 7.578

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 70 62 53 65 107 0 78 0

N.S.

1 1.06 0.94 0.80 0.98 1.62 0.00 1.18 0.00

time (sec)

N/A 0.212 0.206 0.339 0.277 0.266 0.000 0.295 0.000

Problem 198

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 97 70 61 82 124 0 122 0

N.S.

1 1.08 0.78 0.68 0.91 1.38 0.00 1.36 0.00

time (sec)

N/A 0.252 0.229 0.370 0.286 0.247 0.000 0.311 0.000

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

307 318 219 216 0 184 0 0 0

N.S.

1 1.04 0.71 0.70 0.00 0.60 0.00 0.00 0.00

time (sec)

N/A 0.404 10.230 4.031 0.000 0.082 0.000 0.000 0.000

Problem 200

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

286 292 219 216 0 179 0 0 0

N.S.

1 1.02 0.77 0.76 0.00 0.63 0.00 0.00 0.00

time (sec)

N/A 0.374 10.251 2.625 0.000 0.080 0.000 0.000 0.000

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