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2.2.1 Integrals 1 to 100

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 A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

163 163 164 165 166 166 187 182 158

N.S.

1 1.00 1.01 1.01 1.02 1.02 1.15 1.12 0.97

time (sec)

N/A 0.365 0.046 0.875 0.204 0.247 0.035 0.306 0.052

Problem 2

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

135 135 135 134 135 135 151 147 130

N.S.

1 1.00 1.00 0.99 1.00 1.00 1.12 1.09 0.96

time (sec)

N/A 0.328 0.028 0.676 0.202 0.260 0.029 0.291 0.034

Problem 3

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

103 103 104 103 102 102 117 112 102

N.S.

1 1.00 1.01 1.00 0.99 0.99 1.14 1.09 0.99

time (sec)

N/A 0.287 0.021 0.644 0.202 0.267 0.028 0.312 0.027

Problem 4

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

73 73 73 70 69 69 75 76 70

N.S.

1 1.00 1.00 0.96 0.95 0.95 1.03 1.04 0.96

time (sec)

N/A 0.239 0.016 0.674 0.202 0.260 0.027 0.288 0.023

Problem 5

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

42 42 42 37 36 36 39 40 38

N.S.

1 1.00 1.00 0.88 0.86 0.86 0.93 0.95 0.90

time (sec)

N/A 0.196 0.008 0.101 0.200 0.255 0.020 0.295 0.026

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 162 176 67 0 465 175 191 165

N.S.

1 0.86 0.94 0.36 0.00 2.47 0.93 1.02 0.88

time (sec)

N/A 0.361 0.112 0.709 0.000 0.276 0.416 0.297 0.172

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

213 183 199 88 0 697 206 211 187

N.S.

1 0.86 0.93 0.41 0.00 3.27 0.97 0.99 0.88

time (sec)

N/A 0.391 0.131 0.651 0.000 0.299 0.818 0.292 10.843

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

242 218 209 114 0 941 246 236 221

N.S.

1 0.90 0.86 0.47 0.00 3.89 1.02 0.98 0.91

time (sec)

N/A 0.424 0.189 0.645 0.000 0.325 11.306 0.333 0.174

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

132 131 126 136 0 430 0 125 3586

N.S.

1 0.99 0.95 1.03 0.00 3.26 0.00 0.95 27.17

time (sec)

N/A 0.348 0.049 0.270 0.000 0.522 0.000 0.366 11.115

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 95 93 98 0 305 434 91 2624

N.S.

1 0.98 0.96 1.01 0.00 3.14 4.47 0.94 27.05

time (sec)

N/A 0.280 0.076 0.160 0.000 0.364 101.949 0.357 11.310

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 74 71 66 0 216 287 68 1632

N.S.

1 1.03 0.99 0.92 0.00 3.00 3.99 0.94 22.67

time (sec)

N/A 0.235 0.040 0.122 0.000 0.326 10.297 0.430 11.273

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 81 80 75 0 240 0 75 4149

N.S.

1 1.04 1.03 0.96 0.00 3.08 0.00 0.96 53.19

time (sec)

N/A 0.277 0.028 0.097 0.000 0.414 0.000 0.449 13.612

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 114 130 126 0 385 0 124 7282

N.S.

1 1.02 1.16 1.12 0.00 3.44 0.00 1.11 65.02

time (sec)

N/A 0.340 0.036 0.125 0.000 0.677 0.000 0.401 15.505

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

723 577 88 70 0 13535 0 0 13112

N.S.

1 0.80 0.12 0.10 0.00 18.72 0.00 0.00 18.14

time (sec)

N/A 1.081 0.037 0.079 0.000 52.228 0.000 0.000 38.703

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

718 550 88 67 0 8705 0 0 11453

N.S.

1 0.77 0.12 0.09 0.00 12.12 0.00 0.00 15.95

time (sec)

N/A 0.981 0.033 0.062 0.000 4.249 0.000 0.000 29.746

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

634 532 59 49 0 8268 0 0 7457

N.S.

1 0.84 0.09 0.08 0.00 13.04 0.00 0.00 11.76

time (sec)

N/A 0.842 0.033 0.061 0.000 14.503 0.000 0.000 26.698

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

634 512 61 47 0 6748 0 0 7469

N.S.

1 0.81 0.10 0.07 0.00 10.64 0.00 0.00 11.78

time (sec)

N/A 0.786 0.023 0.056 0.000 1.872 0.000 0.000 21.637

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

653 547 85 71 0 11285 0 0 11174

N.S.

1 0.84 0.13 0.11 0.00 17.28 0.00 0.00 17.11

time (sec)

N/A 0.918 0.033 0.102 0.000 37.035 0.000 0.000 36.131

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

655 529 89 68 0 11459 0 0 13466

N.S.

1 0.81 0.14 0.10 0.00 17.49 0.00 0.00 20.56

time (sec)

N/A 0.896 0.032 0.099 0.000 18.760 0.000 0.000 35.790

Problem 20

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

46 48 46 38 37 37 42 37 39

N.S.

1 1.04 1.00 0.83 0.80 0.80 0.91 0.80 0.85

time (sec)

N/A 0.217 0.028 0.048 0.290 0.279 0.063 0.383 10.137

Problem 21

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

31 31 31 25 24 24 32 24 26

N.S.

1 1.00 1.00 0.81 0.77 0.77 1.03 0.77 0.84

time (sec)

N/A 0.196 0.008 0.045 0.286 0.284 0.057 0.367 0.027

Problem 22

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

39 40 39 33 32 32 37 32 34

N.S.

1 1.03 1.00 0.85 0.82 0.82 0.95 0.82 0.87

time (sec)

N/A 0.207 0.009 0.042 0.292 0.296 0.058 0.325 0.035

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 44 44 33 38 34 41 35 36

N.S.

1 1.07 1.07 0.80 0.93 0.83 1.00 0.85 0.88

time (sec)

N/A 0.214 0.017 0.054 0.289 0.326 0.069 0.315 10.153

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 31 45 25 24 28 36 24 26

N.S.

1 1.00 1.45 0.81 0.77 0.90 1.16 0.77 0.84

time (sec)

N/A 0.202 0.012 0.059 0.347 0.302 0.062 0.301 10.004

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

418 356 47 46 0 266 31 645 332

N.S.

1 0.85 0.11 0.11 0.00 0.64 0.07 1.54 0.79

time (sec)

N/A 0.610 0.012 0.046 0.000 0.317 0.082 0.319 0.396

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

382 362 48 44 0 300 32 820 309

N.S.

1 0.95 0.13 0.12 0.00 0.79 0.08 2.15 0.81

time (sec)

N/A 0.594 0.012 0.046 0.000 0.327 0.084 0.350 10.566

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

378 340 46 41 0 288 24 635 330

N.S.

1 0.90 0.12 0.11 0.00 0.76 0.06 1.68 0.87

time (sec)

N/A 0.518 0.011 0.040 0.000 0.316 0.079 0.366 10.547

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

411 367 55 44 0 237 22 824 281

N.S.

1 0.89 0.13 0.11 0.00 0.58 0.05 2.00 0.68

time (sec)

N/A 0.530 0.010 0.043 0.000 0.293 0.086 0.374 10.351

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

411 349 57 44 0 299 26 640 319

N.S.

1 0.85 0.14 0.11 0.00 0.73 0.06 1.56 0.78

time (sec)

N/A 0.501 0.011 0.045 0.000 0.299 0.084 0.436 10.351

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

416 372 47 40 0 313 31 832 313

N.S.

1 0.89 0.11 0.10 0.00 0.75 0.07 2.00 0.75

time (sec)

N/A 0.551 0.013 0.055 0.000 0.299 0.098 0.318 0.255

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

418 356 47 38 0 299 32 645 332

N.S.

1 0.85 0.11 0.09 0.00 0.72 0.08 1.54 0.79

time (sec)

N/A 0.528 0.012 0.057 0.000 0.298 0.090 0.319 10.538

Problem 32

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

36 41 37 33 32 32 37 32 34

N.S.

1 1.14 1.03 0.92 0.89 0.89 1.03 0.89 0.94

time (sec)

N/A 0.208 0.008 0.046 0.276 0.294 0.063 0.304 0.029

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 45 55 33 38 34 41 35 36

N.S.

1 1.15 1.41 0.85 0.97 0.87 1.05 0.90 0.92

time (sec)

N/A 0.212 0.011 0.052 0.260 0.286 0.067 0.298 8.860

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 45 55 33 0 34 41 35 36

N.S.

1 1.15 1.41 0.85 0.00 0.87 1.05 0.90 0.92

time (sec)

N/A 0.224 0.008 0.053 0.000 0.292 0.066 0.283 0.024

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

396 356 103 434 0 169 400 0 0

N.S.

1 0.90 0.26 1.10 0.00 0.43 1.01 0.00 0.00

time (sec)

N/A 0.416 8.031 2.217 0.000 0.092 3.679 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

356 334 101 398 0 137 257 0 0

N.S.

1 0.94 0.28 1.12 0.00 0.38 0.72 0.00 0.00

time (sec)

N/A 0.382 6.722 0.894 0.000 0.099 2.534 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

316 312 98 362 0 104 124 0 0

N.S.

1 0.99 0.31 1.15 0.00 0.33 0.39 0.00 0.00

time (sec)

N/A 0.365 4.947 0.893 0.000 0.092 1.411 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

278 287 98 333 0 72 119 0 0

N.S.

1 1.03 0.35 1.20 0.00 0.26 0.43 0.00 0.00

time (sec)

N/A 0.335 10.065 0.855 0.000 0.095 1.300 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

289 295 102 382 0 125 119 0 0

N.S.

1 1.02 0.35 1.32 0.00 0.43 0.41 0.00 0.00

time (sec)

N/A 0.371 10.072 1.293 0.000 0.096 6.245 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

309 317 129 401 0 190 119 0 0

N.S.

1 1.03 0.42 1.30 0.00 0.61 0.39 0.00 0.00

time (sec)

N/A 0.367 10.086 1.000 0.000 0.105 34.982 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

349 344 166 437 0 268 119 0 0

N.S.

1 0.99 0.48 1.25 0.00 0.77 0.34 0.00 0.00

time (sec)

N/A 0.426 10.121 0.898 0.000 0.101 146.823 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

389 371 200 484 0 346 0 0 0

N.S.

1 0.95 0.51 1.24 0.00 0.89 0.00 0.00 0.00

time (sec)

N/A 0.431 10.144 0.906 0.000 0.109 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

433 366 88 67 0 12866 0 0 50213

N.S.

1 0.85 0.20 0.15 0.00 29.71 0.00 0.00 115.97

time (sec)

N/A 0.632 0.054 0.073 0.000 7.770 0.000 0.000 13.574

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 74 71 66 0 216 287 68 3704

N.S.

1 1.03 0.99 0.92 0.00 3.00 3.99 0.94 51.44

time (sec)

N/A 0.238 0.040 0.154 0.000 0.421 119.858 1.827 10.386

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

375 330 59 51 0 15561 0 0 29445

N.S.

1 0.88 0.16 0.14 0.00 41.50 0.00 0.00 78.52

time (sec)

N/A 0.470 0.034 0.066 0.000 49.644 0.000 0.000 14.129

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

184 182 179 168 0 1535 0 1402 4501

N.S.

1 0.99 0.97 0.91 0.00 8.34 0.00 7.62 24.46

time (sec)

N/A 0.316 0.106 0.119 0.000 0.408 0.000 2.356 12.415

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

375 328 61 47 0 9245 0 0 36707

N.S.

1 0.87 0.16 0.13 0.00 24.65 0.00 0.00 97.89

time (sec)

N/A 0.452 0.033 0.062 0.000 2.697 0.000 0.000 13.406

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 81 80 74 0 240 0 77 8454

N.S.

1 1.04 1.03 0.95 0.00 3.08 0.00 0.99 108.38

time (sec)

N/A 0.273 0.026 0.123 0.000 0.755 0.000 1.875 10.971

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

392 345 85 73 0 21400 0 0 39028

N.S.

1 0.88 0.22 0.19 0.00 54.59 0.00 0.00 99.56

time (sec)

N/A 0.549 0.091 0.112 0.000 137.794 0.000 0.000 13.320

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

199 195 89 177 0 2772 0 3003 15013

N.S.

1 0.98 0.45 0.89 0.00 13.93 0.00 15.09 75.44

time (sec)

N/A 0.375 0.030 0.151 0.000 1.058 0.000 2.112 12.123

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

394 345 86 68 0 20184 0 0 65350

N.S.

1 0.88 0.22 0.17 0.00 51.23 0.00 0.00 165.86

time (sec)

N/A 0.524 0.049 0.119 0.000 52.641 0.000 0.000 13.454

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

278 414 46 34 0 104 170 208 56

N.S.

1 1.49 0.17 0.12 0.00 0.37 0.61 0.75 0.20

time (sec)

N/A 0.634 0.022 0.066 0.000 0.277 0.105 0.348 0.061

Problem 53

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

39 40 39 33 32 32 37 32 34

N.S.

1 1.03 1.00 0.85 0.82 0.82 0.95 0.82 0.87

time (sec)

N/A 0.200 0.010 0.070 0.263 0.285 0.063 0.346 0.027

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

355 360 55 46 0 545 27 253 248

N.S.

1 1.01 0.15 0.13 0.00 1.54 0.08 0.71 0.70

time (sec)

N/A 0.635 0.015 0.078 0.000 0.296 1.354 0.361 0.094

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 54 44 39 0 41 42 31 20

N.S.

1 1.08 0.88 0.78 0.00 0.82 0.84 0.62 0.40

time (sec)

N/A 0.218 0.016 0.076 0.000 0.262 0.063 0.344 8.478

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

355 347 57 44 0 417 26 253 208

N.S.

1 0.98 0.16 0.12 0.00 1.17 0.07 0.71 0.59

time (sec)

N/A 0.616 0.012 0.065 0.000 0.305 1.350 0.312 0.001

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 44 44 33 38 34 41 38 36

N.S.

1 1.07 1.07 0.80 0.93 0.83 1.00 0.93 0.88

time (sec)

N/A 0.214 0.012 0.081 0.263 0.262 0.074 0.352 8.504

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

280 418 47 38 0 111 168 210 58

N.S.

1 1.49 0.17 0.14 0.00 0.40 0.60 0.75 0.21

time (sec)

N/A 0.599 0.015 0.091 0.000 0.260 0.105 0.326 8.549

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 95 49 40 0 169 76 81 56

N.S.

1 1.07 0.55 0.45 0.00 1.90 0.85 0.91 0.63

time (sec)

N/A 0.322 0.013 0.105 0.000 0.257 0.111 0.314 0.058

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

370 370 47 38 0 419 32 258 479

N.S.

1 1.00 0.13 0.10 0.00 1.13 0.09 0.70 1.29

time (sec)

N/A 0.559 0.014 0.102 0.000 0.294 1.543 0.365 0.041

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

280 280 283 286 0 1027 0 295 2490

N.S.

1 1.00 1.01 1.02 0.00 3.67 0.00 1.05 8.89

time (sec)

N/A 0.684 0.151 0.671 0.000 18.156 0.000 0.336 11.488

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

218 218 218 208 0 798 0 221 2051

N.S.

1 1.00 1.00 0.95 0.00 3.66 0.00 1.01 9.41

time (sec)

N/A 0.527 0.109 0.709 0.000 9.547 0.000 0.331 10.700

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

176 176 178 164 0 596 0 185 1367

N.S.

1 1.00 1.01 0.93 0.00 3.39 0.00 1.05 7.77

time (sec)

N/A 0.428 0.113 0.822 0.000 3.159 0.000 0.327 10.179

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 149 132 130 0 405 0 147 966

N.S.

1 1.00 0.89 0.87 0.00 2.72 0.00 0.99 6.48

time (sec)

N/A 0.366 0.077 0.743 0.000 1.066 0.000 0.341 9.718

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 122 107 105 0 305 0 125 801

N.S.

1 0.98 0.86 0.85 0.00 2.46 0.00 1.01 6.46

time (sec)

N/A 0.331 0.045 0.690 0.000 0.431 0.000 0.322 9.902

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 106 105 104 0 305 0 125 521

N.S.

1 0.86 0.85 0.85 0.00 2.48 0.00 1.02 4.24

time (sec)

N/A 0.308 0.047 0.681 0.000 0.453 0.000 0.305 10.160

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

158 159 152 160 0 504 0 162 2399

N.S.

1 1.01 0.96 1.01 0.00 3.19 0.00 1.03 15.18

time (sec)

N/A 0.444 0.111 0.769 0.000 184.148 0.000 0.355 11.089

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 193 194 207 0 0 0 206 2388

N.S.

1 1.00 1.01 1.07 0.00 0.00 0.00 1.07 12.37

time (sec)

N/A 0.512 0.109 0.871 0.000 0.000 0.000 0.325 22.980

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

252 252 252 277 0 0 0 274 3530

N.S.

1 1.00 1.00 1.10 0.00 0.00 0.00 1.09 14.01

time (sec)

N/A 0.597 0.138 0.742 0.000 0.000 0.000 0.319 28.669

Problem 70

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

343 343 338 360 0 2703 0 576 3503

N.S.

1 1.00 0.99 1.05 0.00 7.88 0.00 1.68 10.21

time (sec)

N/A 0.862 0.231 0.749 0.000 64.455 0.000 0.311 12.481

Problem 71

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

274 274 269 290 0 2139 0 483 2495

N.S.

1 1.00 0.98 1.06 0.00 7.81 0.00 1.76 9.11

time (sec)

N/A 0.659 0.186 0.742 0.000 26.472 0.000 0.319 11.200

Problem 72

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

246 246 207 228 0 1465 0 420 2037

N.S.

1 1.00 0.84 0.93 0.00 5.96 0.00 1.71 8.28

time (sec)

N/A 0.550 0.152 0.846 0.000 11.045 0.000 0.314 10.578

Problem 73

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

194 194 159 188 0 1120 0 339 1585

N.S.

1 1.00 0.82 0.97 0.00 5.77 0.00 1.75 8.17

time (sec)

N/A 0.460 0.143 0.858 0.000 3.638 0.000 0.297 11.246

Problem 74

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

183 183 148 187 0 1059 0 328 1768

N.S.

1 1.00 0.81 1.02 0.00 5.79 0.00 1.79 9.66

time (sec)

N/A 0.434 0.141 0.713 0.000 3.324 0.000 0.288 12.946

Problem 75

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

189 209 151 197 0 1079 0 336 1782

N.S.

1 1.11 0.80 1.04 0.00 5.71 0.00 1.78 9.43

time (sec)

N/A 0.499 0.129 0.741 0.000 1.860 0.000 0.309 12.751

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

248 249 246 281 0 0 0 401 3510

N.S.

1 1.00 0.99 1.13 0.00 0.00 0.00 1.62 14.15

time (sec)

N/A 0.592 0.162 0.955 0.000 0.000 0.000 0.303 27.771

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

291 291 287 346 0 0 0 493 4948

N.S.

1 1.00 0.99 1.19 0.00 0.00 0.00 1.69 17.00

time (sec)

N/A 0.692 0.218 0.998 0.000 0.000 0.000 0.300 34.253

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

372 372 370 455 0 0 0 598 7144

N.S.

1 1.00 0.99 1.22 0.00 0.00 0.00 1.61 19.20

time (sec)

N/A 0.920 0.265 0.818 0.000 0.000 0.000 0.354 47.165

Problem 79

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

981 1021 10904 5004 0 920 0 0 0

N.S.

1 1.04 11.12 5.10 0.00 0.94 0.00 0.00 0.00

time (sec)

N/A 3.101 35.469 2.698 0.000 0.116 0.000 0.000 0.000

Problem 80

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

778 799 7531 3661 0 734 0 0 0

N.S.

1 1.03 9.68 4.71 0.00 0.94 0.00 0.00 0.00

time (sec)

N/A 2.198 34.884 2.061 0.000 0.127 0.000 0.000 0.000

Problem 81

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

636 636 1314 2662 0 598 0 0 0

N.S.

1 1.00 2.07 4.19 0.00 0.94 0.00 0.00 0.00

time (sec)

N/A 0.991 34.034 1.835 0.000 0.107 0.000 0.000 0.000

Problem 82

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

550 555 1051 1711 0 490 0 0 0

N.S.

1 1.01 1.91 3.11 0.00 0.89 0.00 0.00 0.00

time (sec)

N/A 0.784 32.189 1.669 0.000 0.099 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

955 857 1258 3023 0 0 0 0 0

N.S.

1 0.90 1.32 3.17 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.680 28.320 0.451 0.000 0.000 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

929 843 1207 1400 0 0 0 0 0

N.S.

1 0.91 1.30 1.51 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.542 30.801 1.605 0.000 0.000 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

1287 1486 1392 1597 0 0 0 0 0

N.S.

1 1.15 1.08 1.24 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.931 32.614 1.972 0.000 0.000 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 26 28 26 28 28 0 28 28

N.S.

1 1.00 1.08 1.00 1.08 1.08 0.00 1.08 1.08

time (sec)

N/A 0.183 0.604 0.349 0.258 0.323 0.000 0.348 8.786

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

358 358 249 0 0 0 0 0 0

N.S.

1 1.00 0.70 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.548 0.316 0.000 0.000 0.000 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

262 262 189 0 0 0 0 0 0

N.S.

1 1.00 0.72 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.430 0.197 0.000 0.000 0.000 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

166 166 136 0 0 0 0 0 0

N.S.

1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.326 0.096 0.000 0.000 0.000 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

194 200 0 0 0 0 0 0 0

N.S.

1 1.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.414 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

302 304 0 0 0 0 0 0 0

N.S.

1 1.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.522 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

412 410 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.651 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 201 15 14 1234 1326 216 1203

N.S.

1 1.00 12.56 0.94 0.88 77.12 82.88 13.50 75.19

time (sec)

N/A 0.179 0.119 0.789 0.192 0.273 0.156 0.323 9.422

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 233 17 1240 1240 1384 246 1210

N.S.

1 1.00 12.94 0.94 68.89 68.89 76.89 13.67 67.22

time (sec)

N/A 0.188 0.117 0.171 0.208 0.261 0.144 0.323 9.433

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 233 17 1240 1240 1394 246 1210

N.S.

1 1.00 12.94 0.94 68.89 68.89 77.44 13.67 67.22

time (sec)

N/A 0.187 0.110 0.217 0.199 0.270 0.154 0.321 9.605

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 22 2042 2041 1297 0 1693 1395

N.S.

1 1.00 0.96 88.78 88.74 56.39 0.00 73.61 60.65

time (sec)

N/A 0.180 0.077 0.025 0.269 0.293 0.000 0.380 11.021

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 201 17 16 1238 1326 218 1208

N.S.

1 1.00 11.17 0.94 0.89 68.78 73.67 12.11 67.11

time (sec)

N/A 0.184 0.108 0.817 0.189 0.258 0.146 0.314 0.931

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 233 19 1242 1242 1384 246 1214

N.S.

1 1.00 11.65 0.95 62.10 62.10 69.20 12.30 60.70

time (sec)

N/A 0.226 0.120 0.172 0.204 0.259 0.141 0.324 9.465

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 233 19 1242 1242 1394 246 1214

N.S.

1 1.00 11.65 0.95 62.10 62.10 69.70 12.30 60.70

time (sec)

N/A 0.194 0.113 0.220 0.209 0.281 0.140 0.322 9.572

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 24 2046 2045 1299 0 1693 1401

N.S.

1 1.00 0.96 81.84 81.80 51.96 0.00 67.72 56.04

time (sec)

N/A 0.187 0.063 0.025 0.268 0.332 0.000 0.370 11.073

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