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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 A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

172 172 172 176 175 179 236 210 182

N.S.

1 1.00 1.00 1.02 1.02 1.04 1.37 1.22 1.06

time (sec)

N/A 0.135 0.064 0.154 0.264 0.968 0.022 1.430 0.102

Problem 2

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

130 130 130 135 135 139 173 161 143

N.S.

1 1.00 1.00 1.04 1.04 1.07 1.33 1.24 1.10

time (sec)

N/A 0.087 0.048 0.157 0.268 0.835 0.018 1.348 0.838

Problem 3

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

94 94 96 94 95 99 121 114 99

N.S.

1 1.00 1.02 1.00 1.01 1.05 1.29 1.21 1.05

time (sec)

N/A 0.056 0.027 0.146 0.272 0.988 0.015 0.966 0.047

Problem 4

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

56 56 56 53 55 59 63 66 54

N.S.

1 1.00 1.00 0.95 0.98 1.05 1.12 1.18 0.96

time (sec)

N/A 0.026 0.010 0.127 0.260 0.921 0.009 1.321 0.048

Problem 5

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

81 81 72 74 73 191 206 80 108

N.S.

1 1.00 0.89 0.91 0.90 2.36 2.54 0.99 1.33

time (sec)

N/A 0.053 0.039 0.138 0.519 0.954 0.387 1.181 0.115

Problem 6

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

108 108 95 97 96 313 190 95 95

N.S.

1 1.00 0.88 0.90 0.89 2.90 1.76 0.88 0.88

time (sec)

N/A 0.057 0.047 0.133 0.476 0.668 0.735 1.279 0.167

Problem 7

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

130 130 130 132 140 469 246 135 136

N.S.

1 1.00 1.00 1.02 1.08 3.61 1.89 1.04 1.05

time (sec)

N/A 0.074 0.058 0.139 0.560 0.961 1.623 1.148 0.968

Problem 8

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

171 171 171 163 189 647 313 184 176

N.S.

1 1.00 1.00 0.95 1.11 3.78 1.83 1.08 1.03

time (sec)

N/A 0.109 0.073 0.139 0.518 0.937 3.554 0.690 0.177

Problem 9

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

226 226 226 237 240 242 304 283 233

N.S.

1 1.00 1.00 1.05 1.06 1.07 1.35 1.25 1.03

time (sec)

N/A 0.144 0.060 0.167 0.268 0.882 0.027 0.982 0.857

Problem 10

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

158 158 158 169 172 175 216 202 158

N.S.

1 1.00 1.00 1.07 1.09 1.11 1.37 1.28 1.00

time (sec)

N/A 0.114 0.044 0.158 0.358 1.191 0.024 1.158 0.069

Problem 11

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

94 94 96 101 104 108 121 120 99

N.S.

1 1.00 1.02 1.07 1.11 1.15 1.29 1.28 1.05

time (sec)

N/A 0.055 0.022 0.148 0.271 1.422 0.014 1.244 0.047

Problem 12

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

142 142 115 170 161 364 347 178 203

N.S.

1 1.00 0.81 1.20 1.13 2.56 2.44 1.25 1.43

time (sec)

N/A 0.141 0.046 0.135 0.509 0.781 0.580 0.636 0.857

Problem 13

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

164 164 134 182 186 552 483 195 257

N.S.

1 1.00 0.82 1.11 1.13 3.37 2.95 1.19 1.57

time (sec)

N/A 0.152 0.066 0.155 0.492 1.003 1.501 0.672 0.167

Problem 14

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

207 207 183 230 233 776 400 238 243

N.S.

1 1.00 0.88 1.11 1.13 3.75 1.93 1.15 1.17

time (sec)

N/A 0.160 0.088 0.167 0.504 2.478 7.023 0.633 0.976

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

240 240 242 289 301 1033 0 311 303

N.S.

1 1.00 1.01 1.20 1.25 4.30 0.00 1.30 1.26

time (sec)

N/A 0.183 0.114 0.163 0.515 1.223 0.000 0.633 0.976

Problem 16

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

310 310 310 339 333 337 423 401 335

N.S.

1 1.00 1.00 1.09 1.07 1.09 1.36 1.29 1.08

time (sec)

N/A 0.215 0.089 0.169 0.280 0.808 0.033 0.548 0.116

Problem 17

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

226 226 226 244 246 245 304 289 233

N.S.

1 1.00 1.00 1.08 1.09 1.08 1.35 1.28 1.03

time (sec)

N/A 0.146 0.059 0.168 0.279 1.063 0.026 0.581 0.846

Problem 18

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

130 130 130 149 152 153 173 173 143

N.S.

1 1.00 1.00 1.15 1.17 1.18 1.33 1.33 1.10

time (sec)

N/A 0.092 0.036 0.148 0.271 1.133 0.018 0.769 0.815

Problem 19

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

227 227 179 300 272 581 508 307 312

N.S.

1 1.00 0.79 1.32 1.20 2.56 2.24 1.35 1.37

time (sec)

N/A 0.252 0.067 0.137 0.501 1.872 0.919 1.003 0.849

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

242 242 176 308 298 824 661 321 389

N.S.

1 1.00 0.73 1.27 1.23 3.40 2.73 1.33 1.61

time (sec)

N/A 0.275 0.089 0.166 0.487 1.182 2.654 1.246 0.977

Problem 21

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

291 291 219 344 345 1104 865 371 495

N.S.

1 1.00 0.75 1.18 1.19 3.79 2.97 1.27 1.70

time (sec)

N/A 0.270 0.109 0.171 0.570 1.470 59.616 1.681 0.223

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

348 348 295 417 416 1424 0 447 444

N.S.

1 1.00 0.85 1.20 1.20 4.09 0.00 1.28 1.28

time (sec)

N/A 0.286 0.143 0.181 0.493 1.448 0.000 1.264 1.187

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

544 544 373 1332 0 0 0 0 -1

N.S.

1 1.00 0.69 2.45 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.453 3.365 0.176 0.000 0.000 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

381 381 267 865 0 0 0 0 -1

N.S.

1 1.00 0.70 2.27 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.243 1.704 0.132 0.000 0.000 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

283 283 212 394 0 0 0 0 -1

N.S.

1 1.00 0.75 1.39 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.123 1.530 0.127 0.000 0.000 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

271 271 192 328 0 0 0 0 -1

N.S.

1 1.00 0.71 1.21 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.116 2.677 0.127 0.000 0.000 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

274 274 297 1237 0 0 0 0 -1

N.S.

1 1.00 1.08 4.51 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.137 3.738 0.140 0.000 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

385 385 379 2861 0 0 0 0 -1

N.S.

1 1.00 0.98 7.43 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.261 4.135 0.154 0.000 0.000 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

543 543 372 1331 0 0 0 0 -1

N.S.

1 1.00 0.69 2.45 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.429 3.345 0.139 0.000 0.000 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

400 400 275 870 0 0 0 0 -1

N.S.

1 1.00 0.69 2.18 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.287 3.273 0.147 0.000 0.000 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

369 369 248 671 0 0 0 0 -1

N.S.

1 1.00 0.67 1.82 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.269 5.056 0.173 0.000 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

373 373 296 1225 0 0 0 0 -1

N.S.

1 1.00 0.79 3.28 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.260 5.855 0.143 0.000 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

376 376 382 2860 0 0 0 0 -1

N.S.

1 1.00 1.02 7.61 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.275 6.238 0.138 0.000 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

531 531 545 5113 0 0 0 0 -1

N.S.

1 1.00 1.03 9.63 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.423 6.714 0.159 0.000 0.000 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

551 551 386 1386 0 0 0 0 -1

N.S.

1 1.00 0.70 2.52 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.431 4.275 0.142 0.000 0.000 0.000 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

396 396 279 924 0 0 0 0 -1

N.S.

1 1.00 0.70 2.33 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.299 3.302 0.136 0.000 0.000 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

282 282 215 501 0 0 0 0 -1

N.S.

1 1.00 0.76 1.78 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.125 1.590 0.127 0.000 0.000 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

206 206 131 158 0 0 0 0 -1

N.S.

1 1.00 0.64 0.77 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.069 2.953 0.115 0.000 0.000 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

209 209 206 334 0 0 0 0 -1

N.S.

1 1.00 0.99 1.60 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.057 7.296 0.120 0.000 0.000 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

284 284 302 1352 0 0 0 0 -1

N.S.

1 1.00 1.06 4.76 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.139 9.826 0.125 0.000 0.000 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

401 401 393 3039 0 0 0 0 -1

N.S.

1 1.00 0.98 7.58 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.279 10.920 0.133 0.000 0.000 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

501 501 369 1169 0 0 0 0 -1

N.S.

1 1.00 0.74 2.33 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.403 6.194 0.180 0.000 0.000 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

358 358 260 750 0 0 0 0 -1

N.S.

1 1.00 0.73 2.09 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.251 5.213 0.149 0.000 0.000 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

258 258 208 393 0 0 0 0 -1

N.S.

1 1.00 0.81 1.52 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.114 2.751 0.123 0.000 0.000 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

209 209 212 349 0 0 0 0 -1

N.S.

1 1.00 1.01 1.67 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.058 7.029 0.136 0.000 0.000 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

272 272 262 581 0 0 0 0 -1

N.S.

1 1.00 0.96 2.14 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.146 10.510 0.131 0.000 0.000 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

375 375 428 1742 0 0 0 0 -1

N.S.

1 1.00 1.14 4.65 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.265 11.492 0.141 0.000 0.000 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

209 209 212 349 0 0 0 0 -1

N.S.

1 1.00 1.01 1.67 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.060 7.326 0.129 0.000 0.000 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

247 247 220 349 0 0 0 0 -1

N.S.

1 1.00 0.89 1.41 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.157 7.537 0.125 0.000 0.000 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

237 237 213 333 0 0 0 0 -1

N.S.

1 1.00 0.90 1.41 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.146 7.380 0.125 0.000 0.000 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

242 242 221 338 0 0 0 0 -1

N.S.

1 1.00 0.91 1.40 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.162 7.436 0.117 0.000 0.000 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

191 191 81 105 0 0 0 0 -1

N.S.

1 1.00 0.42 0.55 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.067 2.740 0.130 0.000 0.000 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

262 262 142 367 0 0 0 0 -1

N.S.

1 1.00 0.54 1.40 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.115 1.253 0.141 0.000 0.000 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

356 356 186 775 0 0 0 0 -1

N.S.

1 1.00 0.52 2.18 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.214 1.261 0.134 0.000 0.000 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 113 104 2538 0 0 0 0 -1

N.S.

1 1.00 0.92 22.46 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.151 2.564 0.470 0.000 0.000 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

526 526 203 2477 0 0 0 0 -1

N.S.

1 1.00 0.39 4.71 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.427 2.600 0.318 0.000 0.000 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

128 128 141 707 0 786 0 0 -1

N.S.

1 1.00 1.10 5.52 0.00 6.14 0.00 0.00 -0.01

time (sec)

N/A 0.101 0.382 0.175 0.000 2.253 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

304 304 214 591 0 1772 0 0 -1

N.S.

1 1.00 0.70 1.94 0.00 5.83 0.00 0.00 -0.00

time (sec)

N/A 0.211 0.590 0.175 0.000 10.185 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

166 166 151 449 0 1166 0 0 -1

N.S.

1 1.00 0.91 2.70 0.00 7.02 0.00 0.00 -0.01

time (sec)

N/A 0.076 0.315 0.136 0.000 2.525 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 111 352 0 782 0 0 -1

N.S.

1 1.00 1.22 3.87 0.00 8.59 0.00 0.00 -0.01

time (sec)

N/A 0.035 0.250 0.109 0.000 1.727 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 70 306 0 258 0 74 -1

N.S.

1 1.00 1.43 6.24 0.00 5.27 0.00 1.51 -0.02

time (sec)

N/A 0.014 0.085 0.112 0.000 0.954 0.000 1.029 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 153 782 0 1377 0 173 -1

N.S.

1 1.00 1.25 6.41 0.00 11.29 0.00 1.42 -0.01

time (sec)

N/A 0.078 0.381 0.123 0.000 58.266 0.000 1.267 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

203 203 531 1400 0 0 0 479 -1

N.S.

1 1.00 2.62 6.90 0.00 0.00 0.00 2.36 -0.00

time (sec)

N/A 0.189 14.002 0.118 0.000 0.000 0.000 7.963 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

608 776 456 1891 0 0 0 0 -1

N.S.

1 1.28 0.75 3.11 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.521 5.621 0.228 0.000 0.000 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

400 400 346 1059 0 0 0 0 -1

N.S.

1 1.00 0.86 2.65 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.195 4.058 0.194 0.000 0.000 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

321 321 184 340 0 0 0 0 -1

N.S.

1 1.00 0.57 1.06 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.123 1.725 0.139 0.000 0.000 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 143 191 0 0 0 0 -1

N.S.

1 1.00 1.40 1.87 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.022 1.847 0.133 0.000 0.000 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

209 209 347 390 0 0 0 0 -1

N.S.

1 1.00 1.66 1.87 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.069 3.790 0.156 0.000 0.000 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

401 401 427 2068 0 0 0 0 -1

N.S.

1 1.00 1.06 5.16 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.247 6.451 0.156 0.000 0.000 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

630 630 584 6245 0 0 0 0 -1

N.S.

1 1.00 0.93 9.91 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.484 6.062 0.175 0.000 0.000 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

659 784 445 1939 0 0 0 0 -1

N.S.

1 1.19 0.68 2.94 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.504 6.816 0.233 0.000 0.000 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

403 403 739 1028 0 0 0 0 -1

N.S.

1 1.00 1.83 2.55 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.194 3.710 0.179 0.000 0.000 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

328 328 184 300 0 0 0 0 -1

N.S.

1 1.00 0.56 0.91 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.125 3.440 0.141 0.000 0.000 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

224 224 492 630 0 0 0 0 -1

N.S.

1 1.00 2.20 2.81 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.073 6.354 0.155 0.000 0.000 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

391 391 999 1876 0 0 0 0 -1

N.S.

1 1.00 2.55 4.80 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.262 7.219 0.160 0.000 0.000 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

639 639 570 6211 0 0 0 0 -1

N.S.

1 1.00 0.89 9.72 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.512 7.900 0.164 0.000 0.000 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

621 621 350 988 0 0 0 0 -1

N.S.

1 1.00 0.56 1.59 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.307 4.976 0.189 0.000 0.000 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

319 319 197 341 0 0 0 0 -1

N.S.

1 1.00 0.62 1.07 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.119 3.511 0.141 0.000 0.000 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 143 191 0 0 0 0 -1

N.S.

1 1.00 1.40 1.87 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.023 1.822 0.139 0.000 0.000 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 101 118 0 0 0 0 -1

N.S.

1 1.00 1.01 1.18 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.078 2.250 0.134 0.000 0.000 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

344 344 365 413 0 0 0 0 -1

N.S.

1 1.00 1.06 1.20 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.147 4.404 0.145 0.000 0.000 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

435 435 433 2062 0 0 0 0 -1

N.S.

1 1.00 1.00 4.74 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.371 6.688 0.155 0.000 0.000 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

980 980 352 1063 0 0 0 0 -1

N.S.

1 1.00 0.36 1.08 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.752 7.094 0.160 0.000 0.000 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

223 223 304 594 0 0 0 0 -1

N.S.

1 1.00 1.36 2.66 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.079 6.169 0.151 0.000 0.000 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

209 209 207 285 0 0 0 0 -1

N.S.

1 1.00 0.99 1.36 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.068 3.600 0.144 0.000 0.000 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

344 344 221 303 0 0 0 0 -1

N.S.

1 1.00 0.64 0.88 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.147 4.283 0.146 0.000 0.000 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

539 539 418 956 0 0 0 0 -1

N.S.

1 1.00 0.78 1.77 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.320 8.419 0.172 0.000 0.000 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

814 814 1645 4115 0 0 0 0 -1

N.S.

1 1.00 2.02 5.06 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.631 10.037 0.189 0.000 0.000 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

242 239 204 370 0 0 0 0 -1

N.S.

1 0.99 0.84 1.53 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.095 2.223 0.219 0.000 0.000 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

192 192 71 121 0 0 0 0 -1

N.S.

1 1.00 0.37 0.63 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.058 0.900 0.131 0.000 0.000 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 50 64 0 0 0 0 -1

N.S.

1 1.00 0.86 1.10 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.013 0.874 0.141 0.000 0.000 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 122 147 0 0 0 0 -1

N.S.

1 1.00 1.01 1.21 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.041 2.219 0.146 0.000 0.000 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

215 215 357 477 0 0 0 0 -1

N.S.

1 1.00 1.66 2.22 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.093 3.077 0.156 0.000 0.000 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

298 298 134 293 0 0 0 0 -1

N.S.

1 1.00 0.45 0.98 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.118 1.566 0.131 0.000 0.000 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 94 133 0 0 0 0 -1

N.S.

1 1.00 1.01 1.43 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.024 1.630 0.138 0.000 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 49 53 0 0 0 0 -1

N.S.

1 1.00 1.00 1.08 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.028 1.862 0.137 0.000 0.000 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 36 37 35 0 13 19 0 -1

N.S.

1 1.00 1.03 0.97 0.00 0.36 0.53 0.00 -0.03

time (sec)

N/A 0.017 0.488 0.165 0.000 0.380 2.067 0.000 0.000

Problem 98

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

113 113 131 848 0 523 0 336 -1

N.S.

1 1.00 1.16 7.50 0.00 4.63 0.00 2.97 -0.01

time (sec)

N/A 0.078 0.552 0.120 0.000 3.918 0.000 2.320 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

359 359 422 773 0 0 0 0 -1

N.S.

1 1.00 1.18 2.15 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.210 3.424 0.161 0.000 0.000 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

381 381 401 765 0 0 0 0 -1

N.S.

1 1.00 1.05 2.01 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.192 3.100 0.155 0.000 0.000 0.000 0.000 0.000

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