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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 F F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

373 373 248 0 0 0 0 0 -1

N.S.

1 1.00 0.66 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.603 1.615 0.828 0.000 0.000 0.000 0.000 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

277 277 204 0 0 0 0 0 -1

N.S.

1 1.00 0.74 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.346 1.056 1.424 0.000 0.000 0.000 0.000 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F F F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

191 191 392 0 0 0 0 0 -1

N.S.

1 1.00 2.05 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.157 3.384 1.203 0.000 0.000 0.000 0.000 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

202 202 157 0 0 0 0 0 -1

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.153 0.598 0.335 0.000 0.000 0.000 0.000 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

279 279 212 0 0 0 0 0 -1

N.S.

1 1.00 0.76 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.336 0.875 1.699 0.000 0.000 0.000 0.000 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

362 362 260 0 0 0 0 0 -1

N.S.

1 1.00 0.72 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.589 2.915 1.872 0.000 0.000 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

336 336 596 0 0 0 0 0 -1

N.S.

1 1.00 1.77 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.607 29.705 0.227 0.000 0.000 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

229 229 478 0 0 0 0 0 -1

N.S.

1 1.00 2.09 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.336 26.739 0.213 0.000 0.000 0.000 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

137 137 409 0 0 0 0 0 -1

N.S.

1 1.00 2.99 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.141 44.824 0.241 0.000 0.000 0.000 0.000 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

152 152 250 0 0 0 0 0 -1

N.S.

1 1.00 1.64 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.259 24.220 0.286 0.000 0.000 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

226 226 523 0 0 0 0 0 -1

N.S.

1 1.00 2.31 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.452 55.883 0.286 0.000 0.000 0.000 0.000 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F F F F F F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

221 221 5918 0 0 0 0 0 -1

N.S.

1 1.00 26.78 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.315 20.990 0.235 0.000 0.000 0.000 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F F F F F F F

verified

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

size

114 114 0 0 0 0 0 0 -1

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.101 9.808 0.268 0.000 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 107 0 0 41 0 9496 61

N.S.

1 1.00 2.89 0.00 0.00 1.11 0.00 256.65 1.65

time (sec)

N/A 0.084 4.146 0.460 0.000 0.612 0.000 56.537 12.982

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

35 35 35 0 0 41 0 5502 38

N.S.

1 1.00 1.00 0.00 0.00 1.17 0.00 157.20 1.09

time (sec)

N/A 0.063 0.269 0.367 0.000 0.377 0.000 26.689 12.848

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

153 153 147 212 0 823 0 371 2500

N.S.

1 1.00 0.96 1.39 0.00 5.38 0.00 2.42 16.34

time (sec)

N/A 0.273 0.595 0.415 0.000 0.445 0.000 0.460 17.182

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

182 182 131 342 363 129 853 184 454

N.S.

1 1.00 0.72 1.88 1.99 0.71 4.69 1.01 2.49

time (sec)

N/A 0.208 0.644 0.260 0.280 0.387 0.565 0.471 14.833

Problem 18

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

142 142 95 208 216 107 486 145 389

N.S.

1 1.00 0.67 1.46 1.52 0.75 3.42 1.02 2.74

time (sec)

N/A 0.168 0.572 0.179 0.283 0.376 0.365 0.417 13.800

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 105 74 185 193 86 396 114 345

N.S.

1 1.08 0.76 1.91 1.99 0.89 4.08 1.18 3.56

time (sec)

N/A 0.112 0.422 0.154 0.356 0.363 0.238 0.413 13.381

Problem 20

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

49 49 48 74 79 46 138 58 122

N.S.

1 1.00 0.98 1.51 1.61 0.94 2.82 1.18 2.49

time (sec)

N/A 0.047 0.112 0.094 0.272 0.369 0.133 0.409 14.329

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 125 67 287 122 828 124 111

N.S.

1 1.00 2.23 1.20 5.12 2.18 14.79 2.21 1.98

time (sec)

N/A 0.113 0.633 0.227 0.528 0.390 1.209 0.406 12.636

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 160 87 494 170 700 92 132

N.S.

1 1.00 2.22 1.21 6.86 2.36 9.72 1.28 1.83

time (sec)

N/A 0.154 0.429 0.273 0.515 0.374 2.438 0.436 12.506

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 147 115 801 195 1035 139 172

N.S.

1 1.00 1.41 1.11 7.70 1.88 9.95 1.34 1.65

time (sec)

N/A 0.164 0.499 0.345 0.302 0.363 5.360 0.454 12.981

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 174 159 1176 267 1831 187 228

N.S.

1 1.00 1.23 1.12 8.28 1.88 12.89 1.32 1.61

time (sec)

N/A 0.195 0.587 0.403 0.326 0.356 10.560 0.436 13.223

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

176 176 200 203 1553 325 3232 267 310

N.S.

1 1.00 1.14 1.15 8.82 1.85 18.36 1.52 1.76

time (sec)

N/A 0.215 0.583 0.507 0.405 0.361 20.035 0.463 13.345

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

229 229 219 569 615 165 1586 278 661

N.S.

1 1.00 0.96 2.48 2.69 0.72 6.93 1.21 2.89

time (sec)

N/A 0.247 1.242 0.356 0.308 0.378 1.171 0.492 15.132

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

189 189 163 463 495 141 1210 244 553

N.S.

1 1.00 0.86 2.45 2.62 0.75 6.40 1.29 2.93

time (sec)

N/A 0.205 0.985 0.269 0.293 0.389 0.811 0.467 14.888

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 137 365 387 119 910 208 542

N.S.

1 1.00 0.93 2.48 2.63 0.81 6.19 1.41 3.69

time (sec)

N/A 0.146 0.676 0.210 0.297 0.366 0.566 0.470 14.154

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 54 166 176 79 372 118 238

N.S.

1 1.00 0.61 1.87 1.98 0.89 4.18 1.33 2.67

time (sec)

N/A 0.097 0.103 0.128 0.277 0.368 0.334 0.456 14.205

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 67 186 193 81 396 111 339

N.S.

1 1.00 0.68 1.90 1.97 0.83 4.04 1.13 3.46

time (sec)

N/A 0.106 0.578 0.129 0.273 0.374 0.237 0.395 13.705

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 191 123 678 185 2365 163 244

N.S.

1 1.00 1.63 1.05 5.79 1.58 20.21 1.39 2.09

time (sec)

N/A 0.196 0.836 0.264 0.511 0.371 2.378 0.508 14.701

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

109 109 238 107 909 247 2474 135 246

N.S.

1 1.00 2.18 0.98 8.34 2.27 22.70 1.24 2.26

time (sec)

N/A 0.193 0.418 0.322 0.530 0.373 4.866 0.435 14.150

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 278 126 1237 289 1647 159 233

N.S.

1 1.00 2.48 1.12 11.04 2.58 14.71 1.42 2.08

time (sec)

N/A 0.185 0.475 0.398 0.526 0.370 9.578 0.485 14.679

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 191 161 1709 279 2008 229 269

N.S.

1 1.00 2.55 2.15 22.79 3.72 26.77 3.05 3.59

time (sec)

N/A 0.151 0.646 0.459 0.365 0.350 18.235 0.448 13.351

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 261 205 2273 355 3262 301 331

N.S.

1 1.00 2.27 1.78 19.77 3.09 28.37 2.62 2.88

time (sec)

N/A 0.192 0.779 0.565 0.363 0.366 33.150 0.500 13.358

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

156 156 285 249 2838 431 4816 373 423

N.S.

1 1.00 1.83 1.60 18.19 2.76 30.87 2.39 2.71

time (sec)

N/A 0.232 1.002 0.648 0.398 0.394 56.210 0.484 13.544

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

197 197 313 293 3402 503 6669 445 500

N.S.

1 1.00 1.59 1.49 17.27 2.55 33.85 2.26 2.54

time (sec)

N/A 0.275 2.317 0.545 0.425 0.369 93.867 0.509 14.053

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

265 265 255 651 713 189 1948 347 812

N.S.

1 1.00 0.96 2.46 2.69 0.71 7.35 1.31 3.06

time (sec)

N/A 0.265 2.623 0.492 0.303 0.400 2.132 0.493 14.869

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

222 222 232 611 665 165 1753 301 705

N.S.

1 1.00 1.05 2.75 3.00 0.74 7.90 1.36 3.18

time (sec)

N/A 0.218 1.609 0.434 0.300 0.410 1.576 0.480 14.929

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

181 181 209 568 615 143 1579 273 661

N.S.

1 1.00 1.15 3.14 3.40 0.79 8.72 1.51 3.65

time (sec)

N/A 0.166 1.204 0.348 0.301 0.393 1.167 0.483 14.782

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 64 263 284 97 682 162 325

N.S.

1 1.00 0.55 2.25 2.43 0.83 5.83 1.38 2.78

time (sec)

N/A 0.107 0.152 0.201 0.294 0.380 0.720 0.492 14.288

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

138 138 133 364 387 111 910 204 536

N.S.

1 1.00 0.96 2.64 2.80 0.80 6.59 1.48 3.88

time (sec)

N/A 0.140 0.670 0.213 0.287 0.381 0.567 0.532 14.166

Problem 43

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

140 140 95 208 216 105 486 145 390

N.S.

1 1.00 0.68 1.49 1.54 0.75 3.47 1.04 2.79

time (sec)

N/A 0.153 0.560 0.167 0.279 0.361 0.359 0.574 13.664

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

156 156 223 152 1241 228 4255 234 323

N.S.

1 1.00 1.43 0.97 7.96 1.46 27.28 1.50 2.07

time (sec)

N/A 0.210 0.919 0.287 0.517 0.373 4.619 0.522 14.120

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

163 163 280 166 1504 298 4665 233 341

N.S.

1 1.00 1.72 1.02 9.23 1.83 28.62 1.43 2.09

time (sec)

N/A 0.236 0.612 0.333 0.549 0.365 8.977 0.557 14.005

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

153 153 316 157 1831 351 4665 226 336

N.S.

1 1.00 2.07 1.03 11.97 2.29 30.49 1.48 2.20

time (sec)

N/A 0.240 0.734 0.444 0.612 0.370 17.182 0.583 14.002

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

151 151 356 177 2304 379 2951 213 316

N.S.

1 1.00 2.36 1.17 15.26 2.51 19.54 1.41 2.09

time (sec)

N/A 0.229 0.807 0.520 0.566 0.342 30.300 0.663 15.978

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 283 205 2941 351 3262 301 346

N.S.

1 1.00 3.68 2.66 38.19 4.56 42.36 3.91 4.49

time (sec)

N/A 0.157 1.635 0.602 0.380 0.532 51.282 0.651 13.392

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 313 249 3694 429 4816 373 408

N.S.

1 1.00 2.65 2.11 31.31 3.64 40.81 3.16 3.46

time (sec)

N/A 0.189 1.841 0.437 0.490 0.587 85.306 0.676 13.544

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

156 156 339 293 4446 503 6669 445 500

N.S.

1 1.00 2.17 1.88 28.50 3.22 42.75 2.85 3.21

time (sec)

N/A 0.240 3.345 0.542 0.472 0.591 135.346 0.680 13.794

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

197 197 365 337 5197 573 8821 517 577

N.S.

1 1.00 1.85 1.71 26.38 2.91 44.78 2.62 2.93

time (sec)

N/A 0.279 4.584 0.623 0.538 0.389 211.770 0.669 13.963

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

190 190 274 209 1962 273 6690 343 397

N.S.

1 1.00 1.44 1.10 10.33 1.44 35.21 1.81 2.09

time (sec)

N/A 0.253 1.539 0.321 0.525 0.366 8.623 0.568 14.778

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

157 157 220 152 1222 228 4255 235 319

N.S.

1 1.00 1.40 0.97 7.78 1.45 27.10 1.50 2.03

time (sec)

N/A 0.222 0.913 0.289 0.579 0.358 4.656 0.525 14.012

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 188 119 662 187 2365 164 241

N.S.

1 1.00 1.59 1.01 5.61 1.58 20.04 1.39 2.04

time (sec)

N/A 0.192 0.882 0.261 0.526 0.372 2.451 0.511 14.577

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

57 57 127 67 278 123 828 122 110

N.S.

1 1.00 2.23 1.18 4.88 2.16 14.53 2.14 1.93

time (sec)

N/A 0.110 0.402 0.224 0.493 0.377 1.253 0.499 12.941

Problem 56

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

35 35 35 57 37 30 83 41 39

N.S.

1 1.00 1.00 1.63 1.06 0.86 2.37 1.17 1.11

time (sec)

N/A 0.099 0.024 0.168 0.286 0.334 0.801 0.511 12.554

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 108 93 288 78 578 102 118

N.S.

1 1.00 1.71 1.48 4.57 1.24 9.17 1.62 1.87

time (sec)

N/A 0.139 0.409 0.232 0.302 0.345 2.698 0.486 12.323

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 157 145 459 114 1236 177 178

N.S.

1 1.00 1.54 1.42 4.50 1.12 12.12 1.74 1.75

time (sec)

N/A 0.184 0.586 0.322 0.297 0.346 5.573 0.554 12.469

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 240 189 673 150 2468 237 239

N.S.

1 1.00 1.69 1.33 4.74 1.06 17.38 1.67 1.68

time (sec)

N/A 0.222 0.756 0.358 0.304 0.363 11.821 0.521 13.233

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

240 240 354 252 3244 386 10608 412 500

N.S.

1 1.00 1.48 1.05 13.52 1.61 44.20 1.72 2.08

time (sec)

N/A 0.299 1.318 0.447 0.575 0.389 28.336 0.537 14.825

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

180 180 311 193 2276 336 7337 369 414

N.S.

1 1.00 1.73 1.07 12.64 1.87 40.76 2.05 2.30

time (sec)

N/A 0.254 0.842 0.407 0.552 0.364 16.258 0.534 14.952

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 274 162 1496 303 4665 233 336

N.S.

1 1.00 1.69 1.00 9.23 1.87 28.80 1.44 2.07

time (sec)

N/A 0.234 0.589 0.375 0.521 0.384 9.145 0.530 14.341

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

108 108 234 107 903 252 2474 136 242

N.S.

1 1.00 2.17 0.99 8.36 2.33 22.91 1.26 2.24

time (sec)

N/A 0.188 0.402 0.325 0.596 0.365 4.956 0.539 14.527

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 156 86 490 174 702 92 133

N.S.

1 1.00 2.17 1.19 6.81 2.42 9.75 1.28 1.85

time (sec)

N/A 0.144 0.397 0.266 0.565 0.400 2.506 0.482 12.826

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 110 97 287 74 578 102 117

N.S.

1 1.00 1.77 1.56 4.63 1.19 9.32 1.65 1.89

time (sec)

N/A 0.142 0.352 0.227 0.292 0.356 2.670 0.447 12.286

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 53 145 50 44 469 87 82

N.S.

1 1.00 0.85 2.34 0.81 0.71 7.56 1.40 1.32

time (sec)

N/A 0.098 0.090 0.205 0.285 0.362 2.420 0.460 12.383

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 237 183 705 123 2674 235 183

N.S.

1 1.00 2.55 1.97 7.58 1.32 28.75 2.53 1.97

time (sec)

N/A 0.152 0.696 0.336 0.304 0.362 11.352 0.496 12.450

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

135 135 285 233 905 160 4228 295 197

N.S.

1 1.00 2.11 1.73 6.70 1.19 31.32 2.19 1.46

time (sec)

N/A 0.187 0.660 0.450 0.336 0.353 22.302 0.469 12.749

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

175 175 329 277 1082 198 5868 355 337

N.S.

1 1.00 1.88 1.58 6.18 1.13 33.53 2.03 1.93

time (sec)

N/A 0.229 0.758 0.542 0.326 0.363 45.129 0.512 12.883

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

243 243 388 240 3572 447 10608 376 501

N.S.

1 1.00 1.60 0.99 14.70 1.84 43.65 1.55 2.06

time (sec)

N/A 0.296 1.777 0.513 0.691 0.376 48.373 0.514 14.754

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

201 201 348 201 2604 408 7337 305 419

N.S.

1 1.00 1.73 1.00 12.96 2.03 36.50 1.52 2.08

time (sec)

N/A 0.274 1.058 0.441 0.561 0.381 30.036 0.456 14.711

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

153 153 308 157 1825 352 4665 226 333

N.S.

1 1.00 2.01 1.03 11.93 2.30 30.49 1.48 2.18

time (sec)

N/A 0.228 0.721 0.410 0.550 0.365 17.511 0.473 14.365

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 272 127 1232 291 1647 159 230

N.S.

1 1.00 2.47 1.15 11.20 2.65 14.97 1.45 2.09

time (sec)

N/A 0.183 0.456 0.362 0.524 0.557 9.637 0.474 15.081

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 139 115 797 203 1035 138 172

N.S.

1 1.00 1.35 1.12 7.74 1.97 10.05 1.34 1.67

time (sec)

N/A 0.154 0.563 0.328 0.296 0.668 5.433 0.516 13.026

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 156 145 459 113 1236 175 178

N.S.

1 1.00 1.53 1.42 4.50 1.11 12.12 1.72 1.75

time (sec)

N/A 0.178 0.565 0.339 0.306 0.338 5.526 0.440 12.429

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

90 90 237 185 704 115 2674 235 183

N.S.

1 1.00 2.63 2.06 7.82 1.28 29.71 2.61 2.03

time (sec)

N/A 0.144 0.680 0.336 0.301 0.357 11.269 0.489 12.469

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 84 65 227 64 60 1098 134 126

N.S.

1 1.00 0.77 2.70 0.76 0.71 13.07 1.60 1.50

time (sec)

N/A 0.107 0.143 0.319 0.285 0.370 7.449 0.442 14.421

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 325 271 1105 159 6135 355 217

N.S.

1 1.00 2.69 2.24 9.13 1.31 50.70 2.93 1.79

time (sec)

N/A 0.159 0.764 0.497 0.332 0.363 44.453 0.497 13.158

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 373 321 1303 196 8396 415 231

N.S.

1 1.00 2.30 1.98 8.04 1.21 51.83 2.56 1.43

time (sec)

N/A 0.199 0.910 0.628 0.344 0.379 78.502 0.531 13.139

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

205 205 401 365 1505 234 11011 475 474

N.S.

1 1.00 1.96 1.78 7.34 1.14 53.71 2.32 2.31

time (sec)

N/A 0.241 2.246 0.450 0.368 0.377 136.236 0.485 14.522

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

198 198 149 119 0 302 0 312 -1

N.S.

1 1.00 0.75 0.60 0.00 1.53 0.00 1.58 -0.01

time (sec)

N/A 0.335 1.878 6.213 0.000 0.356 0.000 0.697 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

157 157 123 103 0 256 0 276 -1

N.S.

1 1.00 0.78 0.66 0.00 1.63 0.00 1.76 -0.01

time (sec)

N/A 0.278 0.979 5.451 0.000 0.371 0.000 0.700 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 104 81 0 195 0 205 -1

N.S.

1 1.00 0.90 0.70 0.00 1.68 0.00 1.77 -0.01

time (sec)

N/A 0.209 0.662 5.247 0.000 0.362 0.000 0.583 0.000

Problem 84

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

73 73 87 63 0 139 0 125 -1

N.S.

1 1.00 1.19 0.86 0.00 1.90 0.00 1.71 -0.01

time (sec)

N/A 0.168 0.281 5.184 0.000 0.348 0.000 0.543 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 166 159 0 274 0 314 -1

N.S.

1 1.00 1.36 1.30 0.00 2.25 0.00 2.57 -0.01

time (sec)

N/A 0.228 0.884 8.148 0.000 0.378 0.000 0.466 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 157 227 0 342 0 409 -1

N.S.

1 1.00 1.37 1.97 0.00 2.97 0.00 3.56 -0.01

time (sec)

N/A 0.222 1.128 6.365 0.000 0.373 0.000 0.514 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 199 268 0 422 0 440 -1

N.S.

1 1.00 1.58 2.13 0.00 3.35 0.00 3.49 -0.01

time (sec)

N/A 0.233 1.526 8.109 0.000 0.383 0.000 0.571 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

163 163 217 352 0 524 0 659 -1

N.S.

1 1.00 1.33 2.16 0.00 3.21 0.00 4.04 -0.01

time (sec)

N/A 0.264 2.249 10.470 0.000 0.371 0.000 0.614 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

210 210 1355 121 0 375 0 392 -1

N.S.

1 1.00 6.45 0.58 0.00 1.79 0.00 1.87 -0.00

time (sec)

N/A 0.374 6.451 6.194 0.000 0.385 0.000 0.782 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

167 167 1173 105 0 328 0 357 -1

N.S.

1 1.00 7.02 0.63 0.00 1.96 0.00 2.14 -0.01

time (sec)

N/A 0.294 6.357 5.744 0.000 0.356 0.000 0.661 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 106 83 0 241 0 251 -1

N.S.

1 1.00 0.88 0.69 0.00 2.01 0.00 2.09 -0.01

time (sec)

N/A 0.251 2.831 6.938 0.000 0.371 0.000 0.661 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

81 81 89 65 0 204 0 211 -1

N.S.

1 1.00 1.10 0.80 0.00 2.52 0.00 2.60 -0.01

time (sec)

N/A 0.209 0.382 4.940 0.000 0.357 0.000 0.580 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 175 197 0 332 0 502 -1

N.S.

1 1.00 1.09 1.22 0.00 2.06 0.00 3.12 -0.01

time (sec)

N/A 0.303 0.796 6.417 0.000 0.374 0.000 0.508 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

176 176 355 282 0 411 0 592 -1

N.S.

1 1.00 2.02 1.60 0.00 2.34 0.00 3.36 -0.01

time (sec)

N/A 0.317 0.623 6.725 0.000 0.382 0.000 0.586 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

175 175 344 386 0 479 0 630 -1

N.S.

1 1.00 1.97 2.21 0.00 2.74 0.00 3.60 -0.01

time (sec)

N/A 0.320 0.798 10.194 0.000 0.493 0.000 0.591 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

175 175 342 354 0 555 0 689 -1

N.S.

1 1.00 1.95 2.02 0.00 3.17 0.00 3.94 -0.01

time (sec)

N/A 0.326 1.219 9.523 0.000 0.593 0.000 0.630 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

222 222 357 440 0 694 0 781 -1

N.S.

1 1.00 1.61 1.98 0.00 3.13 0.00 3.52 -0.00

time (sec)

N/A 0.359 1.672 9.960 0.000 0.867 0.000 0.638 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

210 210 1569 121 0 424 0 481 -1

N.S.

1 1.00 7.47 0.58 0.00 2.02 0.00 2.29 -0.00

time (sec)

N/A 0.368 6.544 6.131 0.000 0.366 0.000 0.728 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 143 105 0 351 0 391 -1

N.S.

1 1.00 0.89 0.65 0.00 2.18 0.00 2.43 -0.01

time (sec)

N/A 0.317 5.923 6.063 0.000 0.369 0.000 0.751 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A F B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

124 124 1157 83 0 302 0 310 -1

N.S.

1 1.00 9.33 0.67 0.00 2.44 0.00 2.50 -0.01

time (sec)

N/A 0.271 6.346 6.022 0.000 0.356 0.000 0.681 0.000

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