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2.2.1 Integrals 1 to 78

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 1

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

415 383 373 508 444 406 0 1539 3993

N.S.

1 0.92 0.90 1.22 1.07 0.98 0.00 3.71 9.62

time (sec)

N/A 0.816 1.670 2.226 0.289 0.290 0.000 0.430 51.668

Problem 2

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

286 271 262 358 307 279 0 1059 2920

N.S.

1 0.95 0.92 1.25 1.07 0.98 0.00 3.70 10.21

time (sec)

N/A 0.643 1.274 1.633 0.283 0.275 0.000 0.412 38.594

Problem 3

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

168 169 159 231 174 170 0 631 736

N.S.

1 1.01 0.95 1.38 1.04 1.01 0.00 3.76 4.38

time (sec)

N/A 0.439 0.701 1.643 0.291 0.291 0.000 0.337 13.443

Problem 4

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

95 91 89 155 93 95 0 284 361

N.S.

1 0.96 0.94 1.63 0.98 1.00 0.00 2.99 3.80

time (sec)

N/A 0.250 0.302 1.646 0.287 0.277 0.000 0.316 7.872

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 127 156 289 0 493 0 0 5803

N.S.

1 1.04 1.28 2.37 0.00 4.04 0.00 0.00 47.57

time (sec)

N/A 0.465 0.610 1.676 0.000 4.253 0.000 0.000 28.855

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 184 197 899 0 1025 0 0 10198

N.S.

1 1.13 1.21 5.52 0.00 6.29 0.00 0.00 62.56

time (sec)

N/A 0.516 0.898 1.671 0.000 16.648 0.000 0.000 57.674

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

248 263 228 1449 0 1580 0 0 9097

N.S.

1 1.06 0.92 5.84 0.00 6.37 0.00 0.00 36.68

time (sec)

N/A 0.583 1.263 1.637 0.000 0.363 0.000 0.000 66.294

Problem 8

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

340 359 259 361 355 286 0 374 2606

N.S.

1 1.06 0.76 1.06 1.04 0.84 0.00 1.10 7.66

time (sec)

N/A 0.802 1.017 1.631 0.287 0.277 0.000 0.337 37.958

Problem 9

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

228 244 178 256 231 192 0 232 1732

N.S.

1 1.07 0.78 1.12 1.01 0.84 0.00 1.02 7.60

time (sec)

N/A 0.640 0.680 1.644 0.281 0.279 0.000 0.319 35.089

Problem 10

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

130 140 107 173 131 114 0 112 492

N.S.

1 1.08 0.82 1.33 1.01 0.88 0.00 0.86 3.78

time (sec)

N/A 0.425 0.463 1.655 0.312 0.283 0.000 0.288 14.683

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 65 64 117 57 67 0 60 232

N.S.

1 1.03 1.02 1.86 0.90 1.06 0.00 0.95 3.68

time (sec)

N/A 0.234 0.251 1.634 0.270 0.264 0.000 0.303 8.146

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 127 156 289 0 493 0 0 5803

N.S.

1 1.04 1.28 2.37 0.00 4.04 0.00 0.00 47.57

time (sec)

N/A 0.470 0.042 1.662 0.000 4.215 0.000 0.000 0.005

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 184 197 899 0 1025 0 0 10198

N.S.

1 1.13 1.21 5.52 0.00 6.29 0.00 0.00 62.56

time (sec)

N/A 0.500 0.101 1.657 0.000 16.955 0.000 0.000 0.010

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

248 263 228 1449 0 1580 0 0 9097

N.S.

1 1.06 0.92 5.84 0.00 6.37 0.00 0.00 36.68

time (sec)

N/A 0.568 0.157 1.652 0.000 0.415 0.000 0.000 0.007

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 95 75 139 87 78 0 76 244

N.S.

1 1.20 0.95 1.76 1.10 0.99 0.00 0.96 3.09

time (sec)

N/A 0.365 0.021 5.667 0.300 0.335 0.000 0.326 8.580

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 65 64 117 57 67 0 60 232

N.S.

1 1.03 1.02 1.86 0.90 1.06 0.00 0.95 3.68

time (sec)

N/A 0.229 0.013 1.635 0.275 0.350 0.000 0.309 8.110

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 73 96 57 81 245 196 122

N.S.

1 1.00 1.52 2.00 1.19 1.69 5.10 4.08 2.54

time (sec)

N/A 0.367 0.017 1.598 0.284 0.300 28.586 0.346 4.514

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 73 97 57 84 221 282 114

N.S.

1 1.00 1.52 2.02 1.19 1.75 4.60 5.88 2.38

time (sec)

N/A 0.361 0.020 1.635 0.287 0.309 28.220 0.376 4.937

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 74 70 108 98 65 0 407 312

N.S.

1 1.04 0.99 1.52 1.38 0.92 0.00 5.73 4.39

time (sec)

N/A 0.387 0.024 1.624 0.264 0.302 0.000 0.365 7.626

Problem 20

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

591 512 402 575 584 1001 0 2671 0

N.S.

1 0.87 0.68 0.97 0.99 1.69 0.00 4.52 0.00

time (sec)

N/A 1.216 0.999 1.691 0.289 0.345 0.000 1.023 0.000

Problem 21

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

451 398 286 401 417 703 0 1868 0

N.S.

1 0.88 0.63 0.89 0.92 1.56 0.00 4.14 0.00

time (sec)

N/A 0.927 0.686 1.673 0.288 0.335 0.000 0.849 0.000

Problem 22

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

300 284 183 253 248 441 0 1142 1765

N.S.

1 0.95 0.61 0.84 0.83 1.47 0.00 3.81 5.88

time (sec)

N/A 0.591 0.394 1.669 0.295 0.330 0.000 0.632 37.004

Problem 23

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

221 153 123 163 140 265 0 527 876

N.S.

1 0.69 0.56 0.74 0.63 1.20 0.00 2.38 3.96

time (sec)

N/A 0.265 0.211 1.658 0.277 0.310 0.000 0.431 19.441

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

278 233 178 299 0 0 0 0 9298

N.S.

1 0.84 0.64 1.08 0.00 0.00 0.00 0.00 33.45

time (sec)

N/A 0.615 0.430 1.719 0.000 0.000 0.000 0.000 56.987

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

322 308 229 1166 0 0 0 526 0

N.S.

1 0.96 0.71 3.62 0.00 0.00 0.00 1.63 0.00

time (sec)

N/A 0.698 0.756 1.703 0.000 0.000 0.000 0.457 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

363 357 252 1794 0 1355 0 1425 9344

N.S.

1 0.98 0.69 4.94 0.00 3.73 0.00 3.93 25.74

time (sec)

N/A 0.786 1.027 1.674 0.000 41.191 0.000 0.711 108.411

Problem 27

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

501 482 283 390 471 700 0 571 4167

N.S.

1 0.96 0.56 0.78 0.94 1.40 0.00 1.14 8.32

time (sec)

N/A 1.207 0.629 1.654 0.275 0.335 0.000 0.354 151.648

Problem 28

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

368 362 200 270 317 482 0 363 2799

N.S.

1 0.98 0.54 0.73 0.86 1.31 0.00 0.99 7.61

time (sec)

N/A 0.919 0.431 1.683 0.284 0.318 0.000 0.327 81.282

Problem 29

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

246 248 128 175 189 302 0 191 1011

N.S.

1 1.01 0.52 0.71 0.77 1.23 0.00 0.78 4.11

time (sec)

N/A 0.562 0.235 1.672 0.273 0.310 0.000 0.330 37.946

Problem 30

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

177 116 90 126 88 196 0 106 489

N.S.

1 0.66 0.51 0.71 0.50 1.11 0.00 0.60 2.76

time (sec)

N/A 0.245 0.135 1.666 0.295 0.282 0.000 0.315 20.546

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

278 233 178 299 0 0 0 0 9298

N.S.

1 0.84 0.64 1.08 0.00 0.00 0.00 0.00 33.45

time (sec)

N/A 0.616 0.161 1.700 0.000 0.000 0.000 0.000 0.008

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

322 308 229 1166 0 0 0 526 0

N.S.

1 0.96 0.71 3.62 0.00 0.00 0.00 1.63 0.00

time (sec)

N/A 0.675 0.267 1.677 0.000 0.000 0.000 0.492 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

363 357 252 1794 0 1355 0 1425 9344

N.S.

1 0.98 0.69 4.94 0.00 3.73 0.00 3.93 25.74

time (sec)

N/A 0.745 0.417 5.677 0.000 40.270 0.000 0.718 0.008

Problem 34

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

87 137 74 108 100 73 0 105 318

N.S.

1 1.57 0.85 1.24 1.15 0.84 0.00 1.21 3.66

time (sec)

N/A 0.382 0.060 1.644 0.201 0.280 0.000 0.309 16.031

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

52 70 63 96 90 61 0 80 312

N.S.

1 1.35 1.21 1.85 1.73 1.17 0.00 1.54 6.00

time (sec)

N/A 0.197 0.043 5.700 0.192 0.280 0.000 0.304 20.382

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A C A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

55 89 69 95 56 73 240 71 118

N.S.

1 1.62 1.25 1.73 1.02 1.33 4.36 1.29 2.15

time (sec)

N/A 0.398 0.047 1.648 0.286 0.281 29.129 0.320 5.821

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

55 89 69 95 56 82 216 83 118

N.S.

1 1.62 1.25 1.73 1.02 1.49 3.93 1.51 2.15

time (sec)

N/A 0.395 0.063 1.651 0.284 0.312 28.633 0.287 5.503

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

83 102 60 76 61 69 0 145 316

N.S.

1 1.23 0.72 0.92 0.73 0.83 0.00 1.75 3.81

time (sec)

N/A 0.398 0.047 5.713 0.287 0.300 0.000 0.316 14.593

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 133 71 89 86 90 0 197 304

N.S.

1 1.15 0.61 0.77 0.74 0.78 0.00 1.70 2.62

time (sec)

N/A 0.417 0.069 1.650 0.315 0.308 0.000 0.325 12.125

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

199 230 185 1095 0 1186 0 0 7235

N.S.

1 1.16 0.93 5.50 0.00 5.96 0.00 0.00 36.36

time (sec)

N/A 0.503 0.602 1.694 0.000 0.323 0.000 0.000 72.885

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1348 815 1253 5734 0 3096 0 4656 0

N.S.

1 0.60 0.93 4.25 0.00 2.30 0.00 3.45 0.00

time (sec)

N/A 1.259 4.434 1.680 0.000 1.577 0.000 0.865 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

721 461 662 3025 0 1620 0 2592 0

N.S.

1 0.64 0.92 4.20 0.00 2.25 0.00 3.60 0.00

time (sec)

N/A 0.652 2.731 1.667 0.000 0.651 0.000 0.619 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

330 249 283 1207 0 840 0 1073 0

N.S.

1 0.75 0.86 3.66 0.00 2.55 0.00 3.25 0.00

time (sec)

N/A 0.342 0.874 1.657 0.000 0.321 0.000 0.432 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

450 481 404 3898 0 0 0 0 0

N.S.

1 1.07 0.90 8.66 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.167 1.544 5.725 0.000 0.000 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

521 546 358 4680 0 0 0 1507 0

N.S.

1 1.05 0.69 8.98 0.00 0.00 0.00 2.89 0.00

time (sec)

N/A 1.257 2.127 1.693 0.000 0.000 0.000 1.539 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

658 695 536 11204 0 0 0 8241 0

N.S.

1 1.06 0.81 17.03 0.00 0.00 0.00 12.52 0.00

time (sec)

N/A 1.508 4.755 1.692 0.000 0.000 0.000 4.811 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1032 778 3220 3958 0 2176 0 1509 0

N.S.

1 0.75 3.12 3.84 0.00 2.11 0.00 1.46 0.00

time (sec)

N/A 1.233 16.915 1.678 0.000 3.084 0.000 0.455 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

540 419 474 2002 0 1114 0 733 0

N.S.

1 0.78 0.88 3.71 0.00 2.06 0.00 1.36 0.00

time (sec)

N/A 0.632 8.633 1.668 0.000 0.921 0.000 0.365 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

246 208 217 763 0 576 0 313 1832

N.S.

1 0.85 0.88 3.10 0.00 2.34 0.00 1.27 7.45

time (sec)

N/A 0.314 3.616 1.672 0.000 0.372 0.000 0.302 98.801

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

290 312 465 1822 0 0 0 0 0

N.S.

1 1.08 1.60 6.28 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.741 11.908 1.689 0.000 0.000 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

364 396 417 3670 0 0 0 1354 0

N.S.

1 1.09 1.15 10.08 0.00 0.00 0.00 3.72 0.00

time (sec)

N/A 0.858 11.283 1.701 0.000 0.000 0.000 1.402 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

484 533 523 9100 0 0 0 7922 0

N.S.

1 1.10 1.08 18.80 0.00 0.00 0.00 16.37 0.00

time (sec)

N/A 1.062 13.010 1.699 0.000 0.000 0.000 23.147 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

685 719 657 15990 0 0 0 25338 0

N.S.

1 1.05 0.96 23.34 0.00 0.00 0.00 36.99 0.00

time (sec)

N/A 1.586 14.908 1.709 0.000 0.000 0.000 60.944 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

718 735 632 2528 0 1436 0 946 0

N.S.

1 1.02 0.88 3.52 0.00 2.00 0.00 1.32 0.00

time (sec)

N/A 1.199 2.224 1.681 0.000 1.120 0.000 0.359 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

371 381 314 1199 0 720 0 441 2621

N.S.

1 1.03 0.85 3.23 0.00 1.94 0.00 1.19 7.06

time (sec)

N/A 0.610 0.958 1.681 0.000 0.486 0.000 0.326 140.157

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

164 167 141 425 0 380 0 190 833

N.S.

1 1.02 0.86 2.59 0.00 2.32 0.00 1.16 5.08

time (sec)

N/A 0.292 0.331 5.701 0.000 0.319 0.000 0.290 50.858

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 204 183 746 0 0 0 0 0

N.S.

1 1.09 0.97 3.97 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.486 0.500 1.692 0.000 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

254 299 249 2973 0 0 0 1319 0

N.S.

1 1.18 0.98 11.70 0.00 0.00 0.00 5.19 0.00

time (sec)

N/A 0.582 1.067 1.693 0.000 0.000 0.000 1.099 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

424 445 420 7119 0 4058 0 7939 0

N.S.

1 1.05 0.99 16.79 0.00 9.57 0.00 18.72 0.00

time (sec)

N/A 0.895 2.400 1.690 0.000 164.611 0.000 38.668 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

826 869 1036 18802 0 0 0 25632 0

N.S.

1 1.05 1.25 22.76 0.00 0.00 0.00 31.03 0.00

time (sec)

N/A 1.645 6.959 1.704 0.000 0.000 0.000 58.083 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1182 1213 1422 2077 0 1916 0 0 0

N.S.

1 1.03 1.20 1.76 0.00 1.62 0.00 0.00 0.00

time (sec)

N/A 2.511 33.212 1.736 0.000 0.167 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

774 789 917 1205 0 1393 0 0 0

N.S.

1 1.02 1.18 1.56 0.00 1.80 0.00 0.00 0.00

time (sec)

N/A 1.706 28.729 1.823 0.000 0.149 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

706 729 633 1163 0 1463 0 0 0

N.S.

1 1.03 0.90 1.65 0.00 2.07 0.00 0.00 0.00

time (sec)

N/A 1.416 25.895 2.279 0.000 0.166 0.000 0.000 0.000

Problem 64

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

687 697 815 1378 0 2588 0 0 0

N.S.

1 1.01 1.19 2.01 0.00 3.77 0.00 0.00 0.00

time (sec)

N/A 1.438 28.992 5.449 0.000 0.267 0.000 0.000 0.000

Problem 65

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

964 996 1444 2292 0 4721 0 0 0

N.S.

1 1.03 1.50 2.38 0.00 4.90 0.00 0.00 0.00

time (sec)

N/A 2.170 33.800 4.641 0.000 0.865 0.000 0.000 0.000

Problem 66

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 Yes Yes TBD TBD TBD TBD TBD

size

1716 1770 2437 3900 0 9150 0 0 0

N.S.

1 1.03 1.42 2.27 0.00 5.33 0.00 0.00 0.00

time (sec)

N/A 4.100 36.937 5.376 0.000 3.015 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1235 1268 1470 2108 0 1931 0 0 0

N.S.

1 1.03 1.19 1.71 0.00 1.56 0.00 0.00 0.00

time (sec)

N/A 2.933 34.132 3.500 0.000 0.159 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

766 792 922 1205 0 1392 0 0 0

N.S.

1 1.03 1.20 1.57 0.00 1.82 0.00 0.00 0.00

time (sec)

N/A 1.539 28.613 1.846 0.000 0.178 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

527 545 562 812 0 1036 0 0 0

N.S.

1 1.03 1.07 1.54 0.00 1.97 0.00 0.00 0.00

time (sec)

N/A 0.935 26.835 1.950 0.000 0.135 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

540 555 551 861 0 1336 0 0 0

N.S.

1 1.03 1.02 1.59 0.00 2.47 0.00 0.00 0.00

time (sec)

N/A 1.057 25.022 3.020 0.000 0.146 0.000 0.000 0.000

Problem 71

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

597 630 724 1269 0 2429 0 0 0

N.S.

1 1.06 1.21 2.13 0.00 4.07 0.00 0.00 0.00

time (sec)

N/A 1.175 28.129 4.205 0.000 0.307 0.000 0.000 0.000

Problem 72

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 Yes Yes TBD TBD TBD TBD TBD

size

1034 1073 1449 2330 0 4867 0 0 0

N.S.

1 1.04 1.40 2.25 0.00 4.71 0.00 0.00 0.00

time (sec)

N/A 2.304 33.497 5.678 0.000 0.999 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

838 857 1000 1233 0 1388 0 0 0

N.S.

1 1.02 1.19 1.47 0.00 1.66 0.00 0.00 0.00

time (sec)

N/A 1.587 29.122 2.923 0.000 0.157 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

528 542 615 812 0 1036 0 0 0

N.S.

1 1.03 1.16 1.54 0.00 1.96 0.00 0.00 0.00

time (sec)

N/A 0.927 25.664 1.884 0.000 0.139 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

387 394 418 615 0 807 0 0 0

N.S.

1 1.02 1.08 1.59 0.00 2.09 0.00 0.00 0.00

time (sec)

N/A 0.630 24.490 2.602 0.000 0.136 0.000 0.000 0.000

Problem 76

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

422 445 477 784 0 1240 0 0 0

N.S.

1 1.05 1.13 1.86 0.00 2.94 0.00 0.00 0.00

time (sec)

N/A 0.779 24.270 3.341 0.000 0.152 0.000 0.000 0.000

Problem 77

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

642 672 699 1249 0 2344 0 0 0

N.S.

1 1.05 1.09 1.95 0.00 3.65 0.00 0.00 0.00

time (sec)

N/A 1.321 27.394 4.564 0.000 0.302 0.000 0.000 0.000

Problem 78

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 Yes Yes TBD TBD TBD TBD TBD

size

1116 1176 1258 2283 0 5108 0 0 0

N.S.

1 1.05 1.13 2.05 0.00 4.58 0.00 0.00 0.00

time (sec)

N/A 2.413 33.536 6.002 0.000 1.049 0.000 0.000 0.000

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