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2.2.1 Integrals 1 to 83

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 F F B F F F(-1)

verified

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

size

104 104 133 0 0 209 0 0 0

N.S.

1 1.00 1.28 0.00 0.00 2.01 0.00 0.00 0.00

time (sec)

N/A 0.319 0.139 0.000 0.000 0.270 0.000 0.000 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 40 21 15 18 20

N.S.

1 1.00 1.12 1.00 2.50 1.31 0.94 1.12 1.25

time (sec)

N/A 0.184 10.011 0.088 0.313 0.248 0.383 0.327 2.193

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

68 68 97 0 0 144 0 0 0

N.S.

1 1.00 1.43 0.00 0.00 2.12 0.00 0.00 0.00

time (sec)

N/A 0.259 0.124 0.000 0.000 0.282 0.000 0.000 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 40 21 15 18 20

N.S.

1 1.00 1.12 1.00 2.50 1.31 0.94 1.12 1.25

time (sec)

N/A 0.185 8.350 0.076 0.311 0.240 0.369 0.312 2.229

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 57 26 25 55 37 49 47

N.S.

1 1.00 2.19 1.00 0.96 2.12 1.42 1.88 1.81

time (sec)

N/A 0.189 0.072 0.222 0.202 0.268 0.428 0.291 0.104

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 38 18 14 18 20

N.S.

1 1.00 1.12 1.00 2.38 1.12 0.88 1.12 1.25

time (sec)

N/A 0.182 7.209 0.066 0.297 0.251 0.853 0.300 2.347

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 40 18 15 18 20

N.S.

1 1.00 1.12 1.00 2.50 1.12 0.94 1.12 1.25

time (sec)

N/A 0.186 8.175 0.071 0.304 0.246 0.346 0.340 2.472

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

196 194 595 0 271 1031 0 0 0

N.S.

1 0.99 3.04 0.00 1.38 5.26 0.00 0.00 0.00

time (sec)

N/A 0.609 2.230 0.000 0.355 0.276 0.000 0.000 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 108 42 17 20 22

N.S.

1 1.00 1.11 1.00 6.00 2.33 0.94 1.11 1.22

time (sec)

N/A 0.195 22.467 0.103 0.418 0.258 0.492 0.811 2.288

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

108 108 276 0 0 683 0 0 0

N.S.

1 1.00 2.56 0.00 0.00 6.32 0.00 0.00 0.00

time (sec)

N/A 0.394 0.734 0.000 0.000 0.275 0.000 0.000 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 98 42 17 20 22

N.S.

1 1.00 1.11 1.00 5.44 2.33 0.94 1.11 1.22

time (sec)

N/A 0.193 20.545 0.103 0.417 0.270 0.473 0.547 2.253

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 44 85 44 49 271 0 75 81

N.S.

1 0.98 1.89 0.98 1.09 6.02 0.00 1.67 1.80

time (sec)

N/A 0.368 0.505 0.936 0.222 0.279 0.000 0.274 0.114

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 112 36 15 20 22

N.S.

1 1.00 1.11 1.00 6.22 2.00 0.83 1.11 1.22

time (sec)

N/A 0.189 58.644 0.108 0.424 0.270 3.291 0.322 2.389

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 118 36 17 20 22

N.S.

1 1.00 1.11 1.00 6.56 2.00 0.94 1.11 1.22

time (sec)

N/A 0.194 33.333 0.102 0.439 0.254 0.591 0.869 2.387

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 114 167 62 205 2590 0 158 399

N.S.

1 1.27 1.86 0.69 2.28 28.78 0.00 1.76 4.43

time (sec)

N/A 0.514 0.084 0.914 0.226 0.271 0.000 0.275 0.135

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

325 326 256 0 0 686 0 0 0

N.S.

1 1.00 0.79 0.00 0.00 2.11 0.00 0.00 0.00

time (sec)

N/A 1.066 0.243 0.000 0.000 0.274 0.000 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 61 20 15 20 22

N.S.

1 1.00 1.11 1.00 3.39 1.11 0.83 1.11 1.22

time (sec)

N/A 0.197 2.702 0.088 0.290 0.273 0.291 0.313 2.115

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

225 219 175 0 0 505 0 0 0

N.S.

1 0.97 0.78 0.00 0.00 2.24 0.00 0.00 0.00

time (sec)

N/A 0.746 0.170 0.000 0.000 0.282 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 61 20 15 20 22

N.S.

1 1.00 1.11 1.00 3.39 1.11 0.83 1.11 1.22

time (sec)

N/A 0.195 2.286 0.084 0.293 0.260 0.298 0.295 2.077

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

60 61 71 89 92 213 0 92 175

N.S.

1 1.02 1.18 1.48 1.53 3.55 0.00 1.53 2.92

time (sec)

N/A 0.366 0.123 0.261 0.277 0.271 0.000 0.309 2.776

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 59 19 15 20 22

N.S.

1 1.00 1.11 1.00 3.28 1.06 0.83 1.11 1.22

time (sec)

N/A 0.197 2.055 0.078 0.279 0.261 0.783 0.324 2.255

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

16 16 18 16 40 18 15 18 20

N.S.

1 1.00 1.12 1.00 2.50 1.12 0.94 1.12 1.25

time (sec)

N/A 0.186 0.141 0.014 0.320 0.258 0.354 0.328 0.002

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

922 924 1502 0 0 3756 0 0 0

N.S.

1 1.00 1.63 0.00 0.00 4.07 0.00 0.00 0.00

time (sec)

N/A 2.298 4.079 0.000 0.000 0.325 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 304 38 17 20 22

N.S.

1 1.00 1.11 1.00 16.89 2.11 0.94 1.11 1.22

time (sec)

N/A 0.181 14.953 0.070 0.428 0.256 0.492 0.382 2.282

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

519 510 735 0 0 2383 0 0 0

N.S.

1 0.98 1.42 0.00 0.00 4.59 0.00 0.00 0.00

time (sec)

N/A 1.285 3.906 0.000 0.000 0.315 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 292 38 17 20 22

N.S.

1 1.00 1.11 1.00 16.22 2.11 0.94 1.11 1.22

time (sec)

N/A 0.189 15.012 0.082 0.411 0.258 0.490 0.360 2.280

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

113 133 161 189 200 711 0 177 290

N.S.

1 1.18 1.42 1.67 1.77 6.29 0.00 1.57 2.57

time (sec)

N/A 0.744 0.782 0.336 0.279 0.272 0.000 0.296 2.723

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 246 38 17 20 22

N.S.

1 1.00 1.11 1.00 13.67 2.11 0.94 1.11 1.22

time (sec)

N/A 0.198 32.770 0.075 0.408 0.274 1.061 0.941 2.603

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 313 44 19 20 22

N.S.

1 1.00 1.11 1.00 17.39 2.44 1.06 1.11 1.22

time (sec)

N/A 0.205 19.243 0.077 0.443 0.253 0.829 0.356 2.494

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 315 44 19 3 22

N.S.

1 1.00 1.11 1.00 17.50 2.44 1.06 0.17 1.22

time (sec)

N/A 0.205 19.371 0.076 0.435 0.273 0.726 2.849 2.696

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

356 356 365 0 349 0 0 0 0

N.S.

1 1.00 1.03 0.00 0.98 0.00 0.00 0.00 0.00

time (sec)

N/A 0.697 0.250 0.000 0.377 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

260 260 273 0 261 0 0 0 0

N.S.

1 1.00 1.05 0.00 1.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.517 0.161 0.000 0.380 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

164 164 181 0 173 0 0 0 0

N.S.

1 1.00 1.10 0.00 1.05 0.00 0.00 0.00 0.00

time (sec)

N/A 0.380 0.131 0.000 0.400 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 16 43 18 15 18 20

N.S.

1 1.00 1.11 0.89 2.39 1.00 0.83 1.00 1.11

time (sec)

N/A 0.179 34.834 0.178 0.435 0.256 1.591 0.302 2.182

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 16 53 18 17 18 20

N.S.

1 1.00 1.11 0.89 2.94 1.00 0.94 1.00 1.11

time (sec)

N/A 0.185 32.926 0.164 0.471 0.258 0.540 0.306 2.264

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

597 605 1289 0 648 0 0 0 0

N.S.

1 1.01 2.16 0.00 1.09 0.00 0.00 0.00 0.00

time (sec)

N/A 1.130 7.404 0.000 0.375 0.000 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

441 445 1017 0 496 0 0 0 0

N.S.

1 1.01 2.31 0.00 1.12 0.00 0.00 0.00 0.00

time (sec)

N/A 0.881 7.154 0.000 0.404 0.000 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

287 291 382 0 343 0 0 0 0

N.S.

1 1.01 1.33 0.00 1.20 0.00 0.00 0.00 0.00

time (sec)

N/A 0.688 3.981 0.000 0.394 0.000 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 0 18 117 36 17 20 22

N.S.

1 1.00 0.00 0.90 5.85 1.80 0.85 1.00 1.10

time (sec)

N/A 0.192 0.000 0.329 0.595 0.265 9.162 0.407 2.500

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 18 143 36 19 20 22

N.S.

1 1.00 1.10 0.90 7.15 1.80 0.95 1.00 1.10

time (sec)

N/A 0.195 127.543 0.324 0.630 0.260 1.530 0.507 2.494

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

897 898 685 0 0 0 0 0 0

N.S.

1 1.00 0.76 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.693 0.784 0.000 0.000 0.000 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

673 674 519 0 0 0 0 0 0

N.S.

1 1.00 0.77 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.353 0.542 0.000 0.000 0.000 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

449 450 353 0 0 0 0 0 0

N.S.

1 1.00 0.79 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.119 0.462 0.000 0.000 0.000 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 18 59 19 17 20 22

N.S.

1 1.00 1.10 0.90 2.95 0.95 0.85 1.00 1.10

time (sec)

N/A 0.196 3.764 0.232 0.527 0.264 1.970 0.336 2.225

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 16 53 18 17 18 20

N.S.

1 1.00 1.11 0.89 2.94 1.00 0.94 1.00 1.11

time (sec)

N/A 0.182 0.149 0.013 0.444 0.253 0.667 0.308 0.003

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

2663 2664 2841 0 0 0 0 0 0

N.S.

1 1.00 1.07 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 4.223 8.522 0.000 0.000 0.000 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1983 1984 2085 0 0 0 0 0 0

N.S.

1 1.00 1.05 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.197 6.118 0.000 0.000 0.000 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1303 1304 1333 0 0 0 0 0 0

N.S.

1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.518 7.777 0.000 0.000 0.000 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 18 249 38 19 20 22

N.S.

1 1.00 1.10 0.90 12.45 1.90 0.95 1.00 1.10

time (sec)

N/A 0.184 103.453 0.226 0.987 0.274 2.957 1.705 2.564

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 18 318 44 20 3 22

N.S.

1 1.00 1.10 0.90 15.90 2.20 1.00 0.15 1.10

time (sec)

N/A 0.186 69.896 0.233 1.150 0.278 2.333 2.696 2.657

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

214 214 238 0 217 0 0 0 0

N.S.

1 1.00 1.11 0.00 1.01 0.00 0.00 0.00 0.00

time (sec)

N/A 0.436 0.239 0.000 0.386 0.000 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

120 120 142 0 129 0 0 0 0

N.S.

1 1.00 1.18 0.00 1.08 0.00 0.00 0.00 0.00

time (sec)

N/A 0.312 0.138 0.000 0.395 0.000 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 52 26 25 55 36 49 47

N.S.

1 1.00 2.00 1.00 0.96 2.12 1.38 1.88 1.81

time (sec)

N/A 0.185 0.096 0.265 0.187 0.281 0.298 0.281 2.224

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 16 53 25 19 18 20

N.S.

1 1.00 1.10 0.80 2.65 1.25 0.95 0.90 1.00

time (sec)

N/A 0.177 55.211 0.160 0.449 0.267 0.505 0.282 2.443

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 16 53 25 19 18 20

N.S.

1 1.00 1.10 0.80 2.65 1.25 0.95 0.90 1.00

time (sec)

N/A 0.179 55.876 0.188 0.449 0.261 0.573 0.302 2.433

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

363 365 875 0 422 0 0 0 0

N.S.

1 1.01 2.41 0.00 1.16 0.00 0.00 0.00 0.00

time (sec)

N/A 0.812 7.019 0.000 0.347 0.000 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

209 210 637 0 264 0 0 0 0

N.S.

1 1.00 3.05 0.00 1.26 0.00 0.00 0.00 0.00

time (sec)

N/A 0.566 2.341 0.000 0.336 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 48 93 44 51 271 0 76 81

N.S.

1 1.02 1.98 0.94 1.09 5.77 0.00 1.62 1.72

time (sec)

N/A 0.365 0.307 0.841 0.192 0.282 0.000 0.302 2.235

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

22 22 24 18 138 46 20 20 22

N.S.

1 1.00 1.09 0.82 6.27 2.09 0.91 0.91 1.00

time (sec)

N/A 0.189 126.542 0.329 0.626 0.267 1.464 0.388 2.531

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

22 22 24 18 0 46 20 20 22

N.S.

1 1.00 1.09 0.82 0.00 2.09 0.91 0.91 1.00

time (sec)

N/A 0.192 125.544 0.321 0.000 0.272 1.640 0.471 2.586

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

561 562 436 0 0 0 0 0 0

N.S.

1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.201 0.799 0.000 0.000 0.000 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

337 338 270 0 0 0 0 0 0

N.S.

1 1.00 0.80 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.993 0.520 0.000 0.000 0.000 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

63 63 73 89 92 123 0 92 145

N.S.

1 1.00 1.16 1.41 1.46 1.95 0.00 1.46 2.30

time (sec)

N/A 0.374 0.158 0.352 0.276 0.270 0.000 0.321 2.571

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

22 22 24 18 67 27 20 20 22

N.S.

1 1.00 1.09 0.82 3.05 1.23 0.91 0.91 1.00

time (sec)

N/A 0.194 5.551 0.230 0.491 0.260 1.599 0.360 2.230

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

22 22 24 18 67 27 20 20 22

N.S.

1 1.00 1.09 0.82 3.05 1.23 0.91 0.91 1.00

time (sec)

N/A 0.197 5.759 0.240 0.582 0.268 1.595 0.441 2.236

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1639 1640 1696 0 0 0 0 0 0

N.S.

1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.073 6.350 0.000 0.000 0.000 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

959 960 948 0 0 0 0 0 0

N.S.

1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.077 3.172 0.000 0.000 0.000 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

118 139 175 189 200 670 0 178 319

N.S.

1 1.18 1.48 1.60 1.69 5.68 0.00 1.51 2.70

time (sec)

N/A 0.740 0.363 0.347 0.284 0.315 0.000 0.354 2.823

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

22 22 24 18 311 48 22 20 22

N.S.

1 1.00 1.09 0.82 14.14 2.18 1.00 0.91 1.00

time (sec)

N/A 0.201 59.997 0.218 1.037 0.276 2.369 2.207 2.907

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

22 22 24 18 318 48 22 3 22

N.S.

1 1.00 1.09 0.82 14.45 2.18 1.00 0.14 1.00

time (sec)

N/A 0.203 61.459 0.224 1.364 0.279 2.304 3.037 2.702

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 20 22 22 19 22 24

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.95 1.10 1.20

time (sec)

N/A 0.273 14.634 0.172 0.376 0.273 0.308 0.761 2.218

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A B F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

45 45 61 155 75 180 0 0 112

N.S.

1 1.00 1.36 3.44 1.67 4.00 0.00 0.00 2.49

time (sec)

N/A 0.235 0.227 0.794 0.200 0.285 0.000 0.000 5.040

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

124 124 175 326 0 555 0 0 0

N.S.

1 1.00 1.41 2.63 0.00 4.48 0.00 0.00 0.00

time (sec)

N/A 0.323 0.550 0.800 0.000 0.299 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

197 197 0 0 0 951 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 4.83 0.00 0.00 0.00

time (sec)

N/A 0.417 0.000 0.000 0.000 0.285 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A B F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

80 57 103 271 109 854 0 0 160

N.S.

1 0.71 1.29 3.39 1.36 10.68 0.00 0.00 2.00

time (sec)

N/A 0.486 0.917 1.903 0.209 0.275 0.000 0.000 2.321

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

198 125 488 0 0 2678 0 0 0

N.S.

1 0.63 2.46 0.00 0.00 13.53 0.00 0.00 0.00

time (sec)

N/A 0.506 2.748 0.000 0.000 0.325 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

344 217 0 0 0 4967 0 0 0

N.S.

1 0.63 0.00 0.00 0.00 14.44 0.00 0.00 0.00

time (sec)

N/A 0.675 0.000 0.000 0.000 0.342 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B F F B

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

82 74 84 319 0 248 0 0 410

N.S.

1 0.90 1.02 3.89 0.00 3.02 0.00 0.00 5.00

time (sec)

N/A 0.481 0.544 0.880 0.000 0.280 0.000 0.000 8.675

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

291 236 1181 577 0 1183 0 0 0

N.S.

1 0.81 4.06 1.98 0.00 4.07 0.00 0.00 0.00

time (sec)

N/A 0.895 4.648 0.885 0.000 0.299 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

428 347 0 0 0 1850 0 0 0

N.S.

1 0.81 0.00 0.00 0.00 4.32 0.00 0.00 0.00

time (sec)

N/A 1.144 0.000 0.000 0.000 0.310 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B F F B

verified

N/A No Yes No TBD TBD TBD TBD TBD

size

149 146 167 490 0 1729 0 0 1449

N.S.

1 0.98 1.12 3.29 0.00 11.60 0.00 0.00 9.72

time (sec)

N/A 0.876 0.925 5.430 0.000 0.291 0.000 0.000 17.956

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

681 527 3219 0 0 8453 0 0 0

N.S.

1 0.77 4.73 0.00 0.00 12.41 0.00 0.00 0.00

time (sec)

N/A 1.530 20.681 0.000 0.000 0.415 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1218 953 0 0 0 0 0 0 0

N.S.

1 0.78 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.259 0.000 0.000 0.000 0.000 0.000 0.000 0.000

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