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2.2.5 Integrals 401 to 500

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 401

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

197 223 200 611 0 1947 0 856 700

N.S.

1 1.13 1.02 3.10 0.00 9.88 0.00 4.35 3.55

time (sec)

N/A 0.626 0.734 1.723 0.000 0.351 0.000 0.320 32.720

Problem 402

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

292 338 606 1655 0 4069 0 2558 1946

N.S.

1 1.16 2.08 5.67 0.00 13.93 0.00 8.76 6.66

time (sec)

N/A 1.044 1.713 4.406 0.000 0.466 0.000 0.425 29.885

Problem 403

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

185 193 399 821 0 180 0 0 0

N.S.

1 1.04 2.16 4.44 0.00 0.97 0.00 0.00 0.00

time (sec)

N/A 1.003 4.940 2.045 0.000 0.099 0.000 0.000 0.000

Problem 404

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

139 142 349 806 0 159 0 0 0

N.S.

1 1.02 2.51 5.80 0.00 1.14 0.00 0.00 0.00

time (sec)

N/A 0.699 2.856 1.339 0.000 0.095 0.000 0.000 0.000

Problem 405

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 326 461 0 120 0 0 0

N.S.

1 1.00 7.24 10.24 0.00 2.67 0.00 0.00 0.00

time (sec)

N/A 0.238 1.937 2.762 0.000 0.085 0.000 0.000 0.000

Problem 406

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 128 152 0 60 0 0 0

N.S.

1 1.00 2.84 3.38 0.00 1.33 0.00 0.00 0.00

time (sec)

N/A 0.248 0.334 1.592 0.000 0.080 0.000 0.000 0.000

Problem 407

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 94 390 425 0 278 0 0 0

N.S.

1 1.00 4.15 4.52 0.00 2.96 0.00 0.00 0.00

time (sec)

N/A 0.377 4.788 1.348 0.000 0.097 0.000 0.000 0.000

Problem 408

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

187 193 430 586 0 431 0 0 0

N.S.

1 1.03 2.30 3.13 0.00 2.30 0.00 0.00 0.00

time (sec)

N/A 0.944 2.466 1.621 0.000 0.099 0.000 0.000 0.000

Problem 409

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

233 244 436 649 0 577 0 0 0

N.S.

1 1.05 1.87 2.79 0.00 2.48 0.00 0.00 0.00

time (sec)

N/A 1.233 2.998 1.697 0.000 0.109 0.000 0.000 0.000

Problem 410

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

347 359 3767 2270 0 1595 0 0 0

N.S.

1 1.03 10.86 6.54 0.00 4.60 0.00 0.00 0.00

time (sec)

N/A 1.624 6.765 3.022 0.000 0.152 0.000 0.000 0.000

Problem 411

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

283 284 2190 1494 0 1483 0 0 0

N.S.

1 1.00 7.74 5.28 0.00 5.24 0.00 0.00 0.00

time (sec)

N/A 1.066 6.344 1.985 0.000 0.135 0.000 0.000 0.000

Problem 412

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

108 108 1408 691 0 1371 0 0 0

N.S.

1 1.00 13.04 6.40 0.00 12.69 0.00 0.00 0.00

time (sec)

N/A 0.361 6.308 5.309 0.000 0.117 0.000 0.000 0.000

Problem 413

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 108 285 295 0 506 0 0 0

N.S.

1 1.00 2.64 2.73 0.00 4.69 0.00 0.00 0.00

time (sec)

N/A 0.366 0.677 1.348 0.000 0.106 0.000 0.000 0.000

Problem 414

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

186 186 1540 2645 0 1737 0 0 0

N.S.

1 1.00 8.28 14.22 0.00 9.34 0.00 0.00 0.00

time (sec)

N/A 0.547 6.436 2.437 0.000 0.147 0.000 0.000 0.000

Problem 415

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

382 397 2408 3642 0 2805 0 0 0

N.S.

1 1.04 6.30 9.53 0.00 7.34 0.00 0.00 0.00

time (sec)

N/A 1.532 6.694 9.276 0.000 0.213 0.000 0.000 0.000

Problem 416

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

490 526 4116 5028 0 4955 0 0 0

N.S.

1 1.07 8.40 10.26 0.00 10.11 0.00 0.00 0.00

time (sec)

N/A 2.255 6.565 30.194 0.000 0.513 0.000 0.000 0.000

Problem 417

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 142 130 74 0 101 0 0 0

N.S.

1 1.02 0.94 0.53 0.00 0.73 0.00 0.00 0.00

time (sec)

N/A 0.407 6.248 1.062 0.000 0.236 0.000 0.000 0.000

Problem 418

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 93 104 60 0 81 0 0 0

N.S.

1 1.00 1.12 0.65 0.00 0.87 0.00 0.00 0.00

time (sec)

N/A 0.292 1.850 0.668 0.000 0.237 0.000 0.000 0.000

Problem 419

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 75 50 0 61 0 0 39

N.S.

1 1.00 1.70 1.14 0.00 1.39 0.00 0.00 0.89

time (sec)

N/A 0.188 0.037 0.764 0.000 0.239 0.000 0.000 0.416

Problem 420

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 101 77 0 147 0 0 0

N.S.

1 1.00 2.10 1.60 0.00 3.06 0.00 0.00 0.00

time (sec)

N/A 0.260 0.204 2.901 0.000 0.251 0.000 0.000 0.000

Problem 421

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 96 154 117 0 268 0 0 0

N.S.

1 1.00 1.60 1.22 0.00 2.79 0.00 0.00 0.00

time (sec)

N/A 0.364 0.312 0.769 0.000 0.262 0.000 0.000 0.000

Problem 422

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 147 180 190 0 341 0 0 0

N.S.

1 1.04 1.27 1.34 0.00 2.40 0.00 0.00 0.00

time (sec)

N/A 0.502 0.413 0.907 0.000 0.259 0.000 0.000 0.000

Problem 423

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

185 193 151 86 0 121 0 0 0

N.S.

1 1.04 0.82 0.46 0.00 0.65 0.00 0.00 0.00

time (sec)

N/A 0.547 7.295 1.194 0.000 0.245 0.000 0.000 0.000

Problem 424

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 142 127 74 0 101 0 0 0

N.S.

1 1.02 0.91 0.53 0.00 0.73 0.00 0.00 0.00

time (sec)

N/A 0.407 5.842 0.840 0.000 0.254 0.000 0.000 0.000

Problem 425

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 93 103 60 0 80 0 0 0

N.S.

1 1.00 1.11 0.65 0.00 0.86 0.00 0.00 0.00

time (sec)

N/A 0.294 4.045 0.684 0.000 0.238 0.000 0.000 0.000

Problem 426

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 75 50 0 59 0 0 39

N.S.

1 1.00 1.70 1.14 0.00 1.34 0.00 0.00 0.89

time (sec)

N/A 0.190 0.032 0.648 0.000 0.240 0.000 0.000 0.551

Problem 427

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 49 99 77 0 88 0 0 0

N.S.

1 1.00 2.02 1.57 0.00 1.80 0.00 0.00 0.00

time (sec)

N/A 0.256 0.163 2.324 0.000 0.248 0.000 0.000 0.000

Problem 428

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 96 152 118 0 210 0 0 0

N.S.

1 1.00 1.58 1.23 0.00 2.19 0.00 0.00 0.00

time (sec)

N/A 0.364 0.310 0.773 0.000 0.257 0.000 0.000 0.000

Problem 429

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

142 147 178 190 0 280 0 0 0

N.S.

1 1.04 1.25 1.34 0.00 1.97 0.00 0.00 0.00

time (sec)

N/A 0.499 0.441 0.881 0.000 0.251 0.000 0.000 0.000

Problem 430

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

258 272 5490 306 0 268 0 0 0

N.S.

1 1.05 21.28 1.19 0.00 1.04 0.00 0.00 0.00

time (sec)

N/A 0.757 37.941 1.635 0.000 0.261 0.000 0.000 0.000

Problem 431

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

190 199 5377 200 0 189 0 0 0

N.S.

1 1.05 28.30 1.05 0.00 0.99 0.00 0.00 0.00

time (sec)

N/A 0.535 18.056 1.350 0.000 0.256 0.000 0.000 0.000

Problem 432

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

126 126 5279 126 0 125 0 0 0

N.S.

1 1.00 41.90 1.00 0.00 0.99 0.00 0.00 0.00

time (sec)

N/A 0.370 17.981 1.361 0.000 0.256 0.000 0.000 0.000

Problem 433

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 55 565 113 0 80 0 0 0

N.S.

1 1.00 10.27 2.05 0.00 1.45 0.00 0.00 0.00

time (sec)

N/A 0.221 16.601 1.279 0.000 0.247 0.000 0.000 0.000

Problem 434

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

88 88 63264 172 0 349 0 0 0

N.S.

1 1.00 718.91 1.95 0.00 3.97 0.00 0.00 0.00

time (sec)

N/A 0.352 54.766 5.571 0.000 0.425 0.000 0.000 0.000

Problem 435

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

160 160 0 350 0 646 0 0 0

N.S.

1 1.00 0.00 2.19 0.00 4.04 0.00 0.00 0.00

time (sec)

N/A 0.516 0.000 1.540 0.000 0.509 0.000 0.000 0.000

Problem 436

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

226 244 0 350 0 895 0 0 0

N.S.

1 1.08 0.00 1.55 0.00 3.96 0.00 0.00 0.00

time (sec)

N/A 0.739 0.000 1.597 0.000 0.499 0.000 0.000 0.000

Problem 437

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

196 205 5238 204 0 192 0 0 0

N.S.

1 1.05 26.72 1.04 0.00 0.98 0.00 0.00 0.00

time (sec)

N/A 0.560 39.428 1.451 0.000 0.261 0.000 0.000 0.000

Problem 438

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

130 130 5142 130 0 127 0 0 0

N.S.

1 1.00 39.55 1.00 0.00 0.98 0.00 0.00 0.00

time (sec)

N/A 0.372 13.034 1.381 0.000 0.257 0.000 0.000 0.000

Problem 439

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

57 57 5053 117 0 80 0 0 0

N.S.

1 1.00 88.65 2.05 0.00 1.40 0.00 0.00 0.00

time (sec)

N/A 0.226 18.300 1.338 0.000 0.252 0.000 0.000 0.000

Problem 440

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

91 91 61904 175 0 107 0 0 0

N.S.

1 1.00 680.26 1.92 0.00 1.18 0.00 0.00 0.00

time (sec)

N/A 0.345 61.111 4.727 0.000 0.257 0.000 0.000 0.000

Problem 441

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

164 164 0 364 0 442 0 0 0

N.S.

1 1.00 0.00 2.22 0.00 2.70 0.00 0.00 0.00

time (sec)

N/A 0.528 0.000 1.582 0.000 0.305 0.000 0.000 0.000

Problem 442

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

232 250 0 364 0 655 0 0 0

N.S.

1 1.08 0.00 1.57 0.00 2.82 0.00 0.00 0.00

time (sec)

N/A 0.758 0.000 1.629 0.000 0.349 0.000 0.000 0.000

Problem 443

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

101 107 80 176 0 579 0 160 950

N.S.

1 1.06 0.79 1.74 0.00 5.73 0.00 1.58 9.41

time (sec)

N/A 0.333 0.278 0.799 0.000 0.315 0.000 0.285 40.867

Problem 444

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 30 22 20 41 11 22 25 34

N.S.

1 1.36 1.00 0.91 1.86 0.50 1.00 1.14 1.55

time (sec)

N/A 0.227 0.080 0.544 0.296 0.246 0.142 0.292 26.115

Problem 445

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 102 79 171 0 553 0 158 988

N.S.

1 1.05 0.81 1.76 0.00 5.70 0.00 1.63 10.19

time (sec)

N/A 0.386 0.229 0.766 0.000 0.315 0.000 0.272 42.593

Problem 446

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 56 50 53 0 349 0 73 47

N.S.

1 1.10 0.98 1.04 0.00 6.84 0.00 1.43 0.92

time (sec)

N/A 0.274 0.044 0.654 0.000 0.316 0.000 0.289 27.996

Problem 447

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

142 148 120 180 0 663 0 161 977

N.S.

1 1.04 0.85 1.27 0.00 4.67 0.00 1.13 6.88

time (sec)

N/A 0.653 0.341 1.510 0.000 1.620 0.000 0.310 39.084

Problem 448

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

371 337 2490 64069 0 1504 0 0 0

N.S.

1 0.91 6.71 172.69 0.00 4.05 0.00 0.00 0.00

time (sec)

N/A 1.448 6.819 29.328 0.000 0.159 0.000 0.000 0.000

Problem 449

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

118 118 1580 2660 0 1367 0 0 0

N.S.

1 1.00 13.39 22.54 0.00 11.58 0.00 0.00 0.00

time (sec)

N/A 0.506 6.803 26.931 0.000 0.138 0.000 0.000 0.000

Problem 450

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

118 118 339 1018 0 504 0 0 0

N.S.

1 1.00 2.87 8.63 0.00 4.27 0.00 0.00 0.00

time (sec)

N/A 0.498 1.262 25.329 0.000 0.101 0.000 0.000 0.000

Problem 451

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

240 237 1732 40064 0 1724 0 0 0

N.S.

1 0.99 7.22 166.93 0.00 7.18 0.00 0.00 0.00

time (sec)

N/A 0.738 6.943 20.450 0.000 0.158 0.000 0.000 0.000

Problem 452

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

492 443 2708 155460 0 2769 0 0 0

N.S.

1 0.90 5.50 315.98 0.00 5.63 0.00 0.00 0.00

time (sec)

N/A 1.849 7.014 25.615 0.000 0.295 0.000 0.000 0.000

Problem 453

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

371 337 81485 64099 0 1500 0 0 0

N.S.

1 0.91 219.64 172.77 0.00 4.04 0.00 0.00 0.00

time (sec)

N/A 1.315 36.993 26.216 0.000 0.150 0.000 0.000 0.000

Problem 454

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

118 118 54676 2660 0 1371 0 0 0

N.S.

1 1.00 463.36 22.54 0.00 11.62 0.00 0.00 0.00

time (sec)

N/A 0.513 32.799 24.267 0.000 0.136 0.000 0.000 0.000

Problem 455

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

118 118 506 1012 0 506 0 0 0

N.S.

1 1.00 4.29 8.58 0.00 4.29 0.00 0.00 0.00

time (sec)

N/A 0.511 16.024 25.260 0.000 0.101 0.000 0.000 0.000

Problem 456

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

240 237 54829 40403 0 1752 0 0 0

N.S.

1 0.99 228.45 168.35 0.00 7.30 0.00 0.00 0.00

time (sec)

N/A 0.739 32.543 21.589 0.000 0.154 0.000 0.000 0.000

Problem 457

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

492 443 81703 155452 0 2816 0 0 0

N.S.

1 0.90 166.06 315.96 0.00 5.72 0.00 0.00 0.00

time (sec)

N/A 1.790 33.649 25.230 0.000 0.248 0.000 0.000 0.000

Problem 458

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 103 80 176 0 555 0 158 965

N.S.

1 1.05 0.82 1.80 0.00 5.66 0.00 1.61 9.85

time (sec)

N/A 0.377 0.332 0.758 0.000 0.305 0.000 0.283 41.768

Problem 459

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 56 50 53 0 349 0 73 47

N.S.

1 1.10 0.98 1.04 0.00 6.84 0.00 1.43 0.92

time (sec)

N/A 0.270 0.054 0.682 0.000 0.305 0.000 0.276 27.288

Problem 460

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 120 104 123 0 669 0 142 531

N.S.

1 1.00 0.87 1.02 0.00 5.58 0.00 1.18 4.42

time (sec)

N/A 0.599 0.982 1.052 0.000 1.667 0.000 0.286 35.161

Problem 461

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 17 51 10 14 24 0 22 9

N.S.

1 0.81 2.43 0.48 0.67 1.14 0.00 1.05 0.43

time (sec)

N/A 0.240 0.037 0.437 0.317 0.248 0.000 0.271 27.333

Problem 462

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

371 337 2490 21493 0 1511 0 0 0

N.S.

1 0.91 6.71 57.93 0.00 4.07 0.00 0.00 0.00

time (sec)

N/A 1.438 6.813 29.776 0.000 0.149 0.000 0.000 0.000

Problem 463

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

118 118 1580 1862 0 1361 0 0 0

N.S.

1 1.00 13.39 15.78 0.00 11.53 0.00 0.00 0.00

time (sec)

N/A 0.521 6.678 28.197 0.000 0.142 0.000 0.000 0.000

Problem 464

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

118 118 339 644 0 508 0 0 0

N.S.

1 1.00 2.87 5.46 0.00 4.31 0.00 0.00 0.00

time (sec)

N/A 0.508 1.082 31.073 0.000 0.102 0.000 0.000 0.000

Problem 465

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

240 237 1732 12702 0 1711 0 0 0

N.S.

1 0.99 7.22 52.92 0.00 7.13 0.00 0.00 0.00

time (sec)

N/A 0.770 6.876 25.719 0.000 0.161 0.000 0.000 0.000

Problem 466

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

492 443 2708 59351 0 2777 0 0 0

N.S.

1 0.90 5.50 120.63 0.00 5.64 0.00 0.00 0.00

time (sec)

N/A 1.827 7.193 29.434 0.000 0.296 0.000 0.000 0.000

Problem 467

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

371 337 5904 21719 0 1500 0 0 0

N.S.

1 0.91 15.91 58.54 0.00 4.04 0.00 0.00 0.00

time (sec)

N/A 1.358 26.310 28.387 0.000 0.147 0.000 0.000 0.000

Problem 468

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

118 118 5835 1851 0 1371 0 0 0

N.S.

1 1.00 49.45 15.69 0.00 11.62 0.00 0.00 0.00

time (sec)

N/A 0.517 16.941 23.301 0.000 0.136 0.000 0.000 0.000

Problem 469

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

118 118 519 716 0 506 0 0 0

N.S.

1 1.00 4.40 6.07 0.00 4.29 0.00 0.00 0.00

time (sec)

N/A 0.541 18.765 28.566 0.000 0.098 0.000 0.000 0.000

Problem 470

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

240 237 5959 12838 0 1746 0 0 0

N.S.

1 0.99 24.83 53.49 0.00 7.28 0.00 0.00 0.00

time (sec)

N/A 0.786 17.465 26.129 0.000 0.148 0.000 0.000 0.000

Problem 471

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

492 443 6066 60004 0 2798 0 0 0

N.S.

1 0.90 12.33 121.96 0.00 5.69 0.00 0.00 0.00

time (sec)

N/A 1.829 18.635 28.204 0.000 0.253 0.000 0.000 0.000

Problem 472

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1 1 1 2 1 1 10 1 1

N.S.

1 1.00 1.00 2.00 1.00 1.00 10.00 1.00 1.00

time (sec)

N/A 0.150 0.019 0.300 0.305 0.221 0.195 0.285 28.216

Problem 473

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1 1 1 2 1 1 22 1 1

N.S.

1 1.00 1.00 2.00 1.00 1.00 22.00 1.00 1.00

time (sec)

N/A 0.153 0.004 0.241 0.288 0.225 0.326 0.281 27.814

Problem 474

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1 1 1 2 1 1 34 1 1

N.S.

1 1.00 1.00 2.00 1.00 1.00 34.00 1.00 1.00

time (sec)

N/A 0.156 0.001 0.230 0.304 0.217 0.604 0.281 27.169

Problem 475

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 3 9 4 15 23 36 33 3

N.S.

1 0.27 0.82 0.36 1.36 2.09 3.27 3.00 0.27

time (sec)

N/A 0.168 0.049 0.595 0.205 0.243 0.174 0.284 27.891

Problem 476

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 8 13 12 15 48 6 6

N.S.

1 1.00 0.62 1.00 0.92 1.15 3.69 0.46 0.46

time (sec)

N/A 0.177 0.027 0.524 0.205 0.229 0.634 0.279 27.177

Problem 477

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 30 22 48 38 74 765 37 32

N.S.

1 0.94 0.69 1.50 1.19 2.31 23.91 1.16 1.00

time (sec)

N/A 0.193 0.034 0.766 0.225 0.246 1.614 0.276 27.572

Problem 478

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 9 10 9 35 12007 20 9

N.S.

1 1.00 1.00 1.11 1.00 3.89 1334.11 2.22 1.00

time (sec)

N/A 0.181 0.124 1.798 0.284 0.253 8.295 0.278 29.704

Problem 479

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 12 11 31 30189 22 11

N.S.

1 1.00 1.00 1.09 1.00 2.82 2744.45 2.00 1.00

time (sec)

N/A 0.183 0.085 3.571 0.300 0.254 10.340 0.270 27.904

Problem 480

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 16 15 43 71839 26 15

N.S.

1 1.00 1.00 1.07 1.00 2.87 4789.27 1.73 1.00

time (sec)

N/A 0.193 0.074 3.513 0.315 0.255 15.531 0.286 28.071

Problem 481

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

53 25 25 18 17 43 87 61 36

N.S.

1 0.47 0.47 0.34 0.32 0.81 1.64 1.15 0.68

time (sec)

N/A 0.187 0.156 0.677 0.315 0.245 0.321 0.294 28.914

Problem 482

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 45 36 38 35 182 216 48 51

N.S.

1 1.05 0.84 0.88 0.81 4.23 5.02 1.12 1.19

time (sec)

N/A 0.291 0.305 0.530 0.302 0.276 0.583 0.280 27.917

Problem 483

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 45 36 38 35 181 211 48 48

N.S.

1 1.05 0.84 0.88 0.81 4.21 4.91 1.12 1.12

time (sec)

N/A 0.266 0.089 0.516 0.323 0.260 0.594 0.272 27.645

Problem 484

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

36 21 19 18 15 35 0 15 15

N.S.

1 0.58 0.53 0.50 0.42 0.97 0.00 0.42 0.42

time (sec)

N/A 0.191 0.141 3.813 0.282 0.254 0.000 0.264 27.151

Problem 485

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

49 33 42 27 27 68 0 27 27

N.S.

1 0.67 0.86 0.55 0.55 1.39 0.00 0.55 0.55

time (sec)

N/A 0.210 0.255 0.280 0.297 0.252 0.000 0.268 27.224

Problem 486

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

74 64 79 2 45 100 0 39 40

N.S.

1 0.86 1.07 0.03 0.61 1.35 0.00 0.53 0.54

time (sec)

N/A 0.222 0.254 14.445 0.291 0.259 0.000 0.271 28.557

Problem 487

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

1 1 1 2 1 1 0 1 1

N.S.

1 1.00 1.00 2.00 1.00 1.00 0.00 1.00 1.00

time (sec)

N/A 0.157 0.001 0.518 0.297 0.229 0.000 0.263 27.835

Problem 488

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

1 1 1 2 1 1 0 1 1

N.S.

1 1.00 1.00 2.00 1.00 1.00 0.00 1.00 1.00

time (sec)

N/A 0.160 0.003 5.348 0.296 0.224 0.000 0.257 27.109

Problem 489

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

1 1 1 2 1 1 0 1 1

N.S.

1 1.00 1.00 2.00 1.00 1.00 0.00 1.00 1.00

time (sec)

N/A 0.159 0.001 59.677 0.289 0.220 0.000 0.266 28.384

Problem 490

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

37 21 19 19 16 35 0 49 16

N.S.

1 0.57 0.51 0.51 0.43 0.95 0.00 1.32 0.43

time (sec)

N/A 0.187 0.123 3.243 0.288 0.247 0.000 0.278 27.624

Problem 491

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 32 64 28 27 66 0 60 27

N.S.

1 0.68 1.36 0.60 0.57 1.40 0.00 1.28 0.57

time (sec)

N/A 0.200 0.174 0.320 0.311 0.267 0.000 0.263 27.913

Problem 492

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 62 66 2 42 98 0 69 43

N.S.

1 0.86 0.92 0.03 0.58 1.36 0.00 0.96 0.60

time (sec)

N/A 0.238 0.237 11.542 0.312 0.244 0.000 0.269 29.586

Problem 493

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

3 3 3 4 3 3 0 3 3

N.S.

1 1.00 1.00 1.33 1.00 1.00 0.00 1.00 1.00

time (sec)

N/A 0.163 0.001 0.463 0.306 0.230 0.000 0.273 26.306

Problem 494

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1 1 1 2 1 1 0 1 1

N.S.

1 1.00 1.00 2.00 1.00 1.00 0.00 1.00 1.00

time (sec)

N/A 0.162 0.001 3.673 0.310 0.233 0.000 0.279 27.007

Problem 495

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

3 3 3 4 3 3 0 3 3

N.S.

1 1.00 1.00 1.33 1.00 1.00 0.00 1.00 1.00

time (sec)

N/A 0.168 0.001 37.707 0.292 0.226 0.000 0.267 26.513

Problem 496

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

33 33 33 27 26 259 0 61 43

N.S.

1 1.00 1.00 0.82 0.79 7.85 0.00 1.85 1.30

time (sec)

N/A 0.209 0.116 0.598 0.290 0.282 0.000 0.264 27.186

Problem 497

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

239 261 1022 820 0 2869 0 0 0

N.S.

1 1.09 4.28 3.43 0.00 12.00 0.00 0.00 0.00

time (sec)

N/A 0.880 1.229 0.909 0.000 4.762 0.000 0.000 0.000

Problem 498

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

365 369 279 1161 0 4289 0 0 0

N.S.

1 1.01 0.76 3.18 0.00 11.75 0.00 0.00 0.00

time (sec)

N/A 1.292 5.661 0.914 0.000 3.362 0.000 0.000 0.000

Problem 499

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

195 234 149 172 246 150 566 158 456

N.S.

1 1.20 0.76 0.88 1.26 0.77 2.90 0.81 2.34

time (sec)

N/A 0.882 2.400 2.348 0.218 0.258 0.326 0.310 29.601

Problem 500

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 113 77 90 112 76 204 79 88

N.S.

1 1.04 0.71 0.83 1.03 0.70 1.87 0.72 0.81

time (sec)

N/A 0.360 1.125 1.093 0.223 0.258 0.138 0.269 27.241

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