[tail] [up]

2.2.1 Integrals 1 to 84

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

129 129 159 0 0 425 0 0 0

N.S.

1 1.00 1.23 0.00 0.00 3.29 0.00 0.00 0.00

time (sec)

N/A 0.341 0.332 0.000 0.000 0.286 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 16 106 21 15 18 20

N.S.

1 1.00 1.12 1.00 6.62 1.31 0.94 1.12 1.25

time (sec)

N/A 0.173 4.137 0.109 0.249 0.258 2.093 0.359 17.162

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

84 84 118 0 0 288 0 0 0

N.S.

1 1.00 1.40 0.00 0.00 3.43 0.00 0.00 0.00

time (sec)

N/A 0.260 0.163 0.000 0.000 0.262 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 16 106 21 15 18 20

N.S.

1 1.00 1.12 1.00 6.62 1.31 0.94 1.12 1.25

time (sec)

N/A 0.171 3.273 0.111 0.262 0.242 1.827 0.301 17.513

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 57 26 31 44 42 30 69

N.S.

1 1.00 2.19 1.00 1.19 1.69 1.62 1.15 2.65

time (sec)

N/A 0.174 0.086 0.217 0.176 0.242 2.569 0.266 0.563

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 16 108 18 14 18 20

N.S.

1 1.00 1.12 1.00 6.75 1.12 0.88 1.12 1.25

time (sec)

N/A 0.172 3.008 0.110 0.252 0.266 0.618 0.269 18.061

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 16 126 18 15 18 20

N.S.

1 1.00 1.12 1.00 7.88 1.12 0.94 1.12 1.25

time (sec)

N/A 0.172 2.983 0.111 0.245 0.236 0.413 0.398 18.250

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

228 227 639 0 800 687 0 0 0

N.S.

1 1.00 2.80 0.00 3.51 3.01 0.00 0.00 0.00

time (sec)

N/A 0.551 3.300 0.000 0.323 0.282 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 18 310 42 17 20 22

N.S.

1 1.00 1.11 1.00 17.22 2.33 0.94 1.11 1.22

time (sec)

N/A 0.175 22.316 0.198 0.395 0.236 2.492 1.017 17.669

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

125 124 268 0 604 451 0 0 0

N.S.

1 0.99 2.14 0.00 4.83 3.61 0.00 0.00 0.00

time (sec)

N/A 0.360 5.766 0.000 0.306 0.285 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 18 300 42 17 20 22

N.S.

1 1.00 1.11 1.00 16.67 2.33 0.94 1.11 1.22

time (sec)

N/A 0.178 35.070 0.188 0.372 0.249 2.142 0.941 18.882

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 44 86 51 98 94 0 84 102

N.S.

1 0.98 1.91 1.13 2.18 2.09 0.00 1.87 2.27

time (sec)

N/A 0.331 0.998 0.632 0.193 0.257 0.000 0.274 18.321

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 18 360 36 15 20 22

N.S.

1 1.00 1.11 1.00 20.00 2.00 0.83 1.11 1.22

time (sec)

N/A 0.178 86.008 0.205 0.370 0.237 1.946 0.319 17.557

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 18 366 36 17 20 22

N.S.

1 1.00 1.11 1.00 20.33 2.00 0.94 1.11 1.22

time (sec)

N/A 0.179 49.148 0.197 0.403 0.246 0.607 1.139 18.132

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 104 167 73 3543 183 0 211 491

N.S.

1 1.16 1.86 0.81 39.37 2.03 0.00 2.34 5.46

time (sec)

N/A 0.453 0.108 0.706 0.276 0.261 0.000 0.271 28.546

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

396 397 319 0 0 1445 0 0 0

N.S.

1 1.00 0.81 0.00 0.00 3.65 0.00 0.00 0.00

time (sec)

N/A 1.134 1.434 0.000 0.000 0.379 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 18 253 20 15 20 22

N.S.

1 1.00 1.11 1.00 14.06 1.11 0.83 1.11 1.22

time (sec)

N/A 0.181 2.407 0.144 0.399 0.227 0.426 0.311 18.154

Problem 18

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 No N/A TBD TBD TBD TBD TBD

size

271 266 987 0 0 1050 0 0 0

N.S.

1 0.98 3.64 0.00 0.00 3.87 0.00 0.00 0.00

time (sec)

N/A 0.805 5.402 0.000 0.000 0.358 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 18 253 20 15 20 22

N.S.

1 1.00 1.11 1.00 14.06 1.11 0.83 1.11 1.22

time (sec)

N/A 0.179 4.136 0.119 0.396 0.234 0.346 0.313 18.412

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 74 66 73 0 261 0 84 163

N.S.

1 1.17 1.05 1.16 0.00 4.14 0.00 1.33 2.59

time (sec)

N/A 0.336 0.492 0.322 0.000 0.279 0.000 0.274 1.646

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 18 250 19 15 20 22

N.S.

1 1.00 1.11 1.00 13.89 1.06 0.83 1.11 1.22

time (sec)

N/A 0.177 3.330 0.118 0.376 0.246 0.709 0.288 20.828

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 16 126 18 15 18 20

N.S.

1 1.00 1.12 1.00 7.88 1.12 0.94 1.12 1.25

time (sec)

N/A 0.170 0.195 0.010 0.279 0.237 0.379 0.399 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

1124 1123 2033 0 0 3032 0 0 0

N.S.

1 1.00 1.81 0.00 0.00 2.70 0.00 0.00 0.00

time (sec)

N/A 2.530 10.597 0.000 0.000 0.472 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 1286 38 17 20 22

N.S.

1 1.00 1.11 1.00 71.44 2.11 0.94 1.11 1.22

time (sec)

N/A 0.171 12.347 0.164 0.925 0.253 1.118 0.383 21.228

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

616 607 2566 0 0 1906 0 0 0

N.S.

1 0.99 4.17 0.00 0.00 3.09 0.00 0.00 0.00

time (sec)

N/A 1.409 16.929 0.000 0.000 0.419 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 1265 38 17 20 22

N.S.

1 1.00 1.11 1.00 70.28 2.11 0.94 1.11 1.22

time (sec)

N/A 0.177 10.240 0.147 0.808 0.257 0.956 0.395 26.319

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 154 158 179 0 536 0 174 2755

N.S.

1 1.28 1.32 1.49 0.00 4.47 0.00 1.45 22.96

time (sec)

N/A 0.707 1.288 0.503 0.000 0.293 0.000 0.282 22.512

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 4629 38 17 20 22

N.S.

1 1.00 1.11 1.00 257.17 2.11 0.94 1.11 1.22

time (sec)

N/A 0.178 18.418 0.147 5.455 0.252 1.140 0.733 18.556

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 4560 44 19 20 22

N.S.

1 1.00 1.11 1.00 253.33 2.44 1.06 1.11 1.22

time (sec)

N/A 0.180 14.000 0.145 5.412 0.257 1.027 0.388 17.974

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 3530 44 19 20 22

N.S.

1 1.00 1.11 1.00 196.11 2.44 1.06 1.11 1.22

time (sec)

N/A 0.179 15.641 0.149 5.369 0.257 1.092 1.020 17.759

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

432 432 445 0 1498 0 0 0 0

N.S.

1 1.00 1.03 0.00 3.47 0.00 0.00 0.00 0.00

time (sec)

N/A 0.697 0.738 0.000 0.327 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 B F F F F(-1)

verified

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

size

316 316 333 0 956 0 0 0 0

N.S.

1 1.00 1.05 0.00 3.03 0.00 0.00 0.00 0.00

time (sec)

N/A 0.523 0.382 0.000 0.286 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 B F F F F(-1)

verified

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

size

200 200 260 0 534 0 0 0 0

N.S.

1 1.00 1.30 0.00 2.67 0.00 0.00 0.00 0.00

time (sec)

N/A 0.378 0.474 0.000 0.265 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 16 105 18 15 18 20

N.S.

1 1.00 1.11 0.89 5.83 1.00 0.83 1.00 1.11

time (sec)

N/A 0.170 11.763 0.329 0.510 0.247 1.649 0.315 18.570

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 16 111 18 17 18 20

N.S.

1 1.00 1.11 0.89 6.17 1.00 0.94 1.00 1.11

time (sec)

N/A 0.170 16.932 0.322 0.557 0.260 1.575 0.347 18.431

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

695 703 1323 0 6462 0 0 0 0

N.S.

1 1.01 1.90 0.00 9.30 0.00 0.00 0.00 0.00

time (sec)

N/A 1.011 21.468 0.000 0.665 0.000 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

513 517 779 0 3885 0 0 0 0

N.S.

1 1.01 1.52 0.00 7.57 0.00 0.00 0.00 0.00

time (sec)

N/A 0.823 14.591 0.000 0.451 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 B F F F F(-1)

verified

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

size

333 337 449 0 1950 0 0 0 0

N.S.

1 1.01 1.35 0.00 5.86 0.00 0.00 0.00 0.00

time (sec)

N/A 0.649 10.315 0.000 0.320 0.000 0.000 0.000 0.000

Problem 39

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 18 386 36 17 20 22

N.S.

1 1.00 1.10 0.90 19.30 1.80 0.85 1.00 1.10

time (sec)

N/A 0.177 137.819 0.428 0.834 0.262 8.330 0.486 18.794

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 18 388 36 19 20 22

N.S.

1 1.00 1.10 0.90 19.40 1.80 0.95 1.00 1.10

time (sec)

N/A 0.179 85.216 0.445 1.007 0.253 2.444 0.599 18.801

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1075 1077 850 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 1.722 2.077 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(-2) F F F F(-1)

verified

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

size

807 809 644 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 1.373 1.548 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(-2) F F F F(-1)

verified

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

size

539 541 438 0 0 0 0 0 0

N.S.

1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.171 1.503 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 18 242 19 17 20 22

N.S.

1 1.00 1.10 0.90 12.10 0.95 0.85 1.00 1.10

time (sec)

N/A 0.179 4.542 0.373 0.783 0.248 2.060 0.296 18.210

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 16 111 18 17 18 20

N.S.

1 1.00 1.11 0.89 6.17 1.00 0.94 1.00 1.11

time (sec)

N/A 0.173 0.211 0.003 0.585 0.256 1.579 0.358 0.002

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

3205 3207 3831 0 0 0 0 0 0

N.S.

1 1.00 1.20 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 4.473 15.831 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(-2) F F F F(-1)

verified

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

size

2385 2387 2829 0 0 0 0 0 0

N.S.

1 1.00 1.19 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.346 14.549 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(-2) F F F F(-1)

verified

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

size

1565 1567 1752 0 0 0 0 0 0

N.S.

1 1.00 1.12 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.633 15.341 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 4411 38 19 20 22

N.S.

1 1.00 1.10 0.90 220.55 1.90 0.95 1.00 1.10

time (sec)

N/A 0.170 61.389 0.402 13.439 0.269 3.883 0.672 18.146

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 4411 44 20 20 22

N.S.

1 1.00 1.10 0.90 220.55 2.20 1.00 1.00 1.10

time (sec)

N/A 0.176 59.362 0.439 18.932 0.256 8.921 0.976 17.921

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

258 258 286 0 730 0 0 0 0

N.S.

1 1.00 1.11 0.00 2.83 0.00 0.00 0.00 0.00

time (sec)

N/A 0.433 0.548 0.000 0.305 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 B F F F F(-1)

verified

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

size

144 144 191 0 370 0 0 0 0

N.S.

1 1.00 1.33 0.00 2.57 0.00 0.00 0.00 0.00

time (sec)

N/A 0.306 4.266 0.000 0.269 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 A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 52 32 31 43 60 30 73

N.S.

1 1.00 2.00 1.23 1.19 1.65 2.31 1.15 2.81

time (sec)

N/A 0.174 0.205 0.268 0.198 0.254 1.277 0.286 19.859

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 16 113 25 19 18 20

N.S.

1 1.00 1.10 0.80 5.65 1.25 0.95 0.90 1.00

time (sec)

N/A 0.169 25.613 0.314 0.622 0.230 1.014 0.298 18.454

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 16 115 25 19 18 20

N.S.

1 1.00 1.10 0.80 5.75 1.25 0.95 0.90 1.00

time (sec)

N/A 0.166 28.586 0.313 0.615 0.244 6.176 0.342 18.240

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

421 423 749 0 2836 0 0 0 0

N.S.

1 1.00 1.78 0.00 6.74 0.00 0.00 0.00 0.00

time (sec)

N/A 0.753 8.645 0.000 0.375 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 B F F F F(-1)

verified

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

size

241 243 681 0 1217 0 0 0 0

N.S.

1 1.01 2.83 0.00 5.05 0.00 0.00 0.00 0.00

time (sec)

N/A 0.530 5.224 0.000 0.297 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 A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 48 93 51 52 94 88 83 111

N.S.

1 1.02 1.98 1.09 1.11 2.00 1.87 1.77 2.36

time (sec)

N/A 0.331 0.892 0.716 0.205 0.262 7.856 0.301 19.635

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 18 794 46 20 20 22

N.S.

1 1.00 1.09 0.82 36.09 2.09 0.91 0.91 1.00

time (sec)

N/A 0.179 76.763 0.459 1.148 0.252 1.980 0.368 18.061

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 0.179 84.563 0.467 0.000 0.247 7.154 0.394 18.008

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 30 57 24 34 56 0 70 94

N.S.

1 1.25 2.38 1.00 1.42 2.33 0.00 2.92 3.92

time (sec)

N/A 0.246 0.056 0.331 0.249 0.241 0.000 0.264 19.549

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

675 677 539 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 1.266 2.090 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 F F(-2) F F F F(-1)

verified

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

size

407 409 333 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 1.037 3.485 0.000 0.000 0.000 0.000 0.000 0.000

Problem 64

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

66 76 68 73 0 275 0 84 159

N.S.

1 1.15 1.03 1.11 0.00 4.17 0.00 1.27 2.41

time (sec)

N/A 0.334 0.427 0.351 0.000 0.275 0.000 0.275 19.521

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 18 244 27 20 20 22

N.S.

1 1.00 1.09 0.82 11.09 1.23 0.91 0.91 1.00

time (sec)

N/A 0.177 5.100 0.360 0.956 0.258 2.115 0.340 17.956

Problem 66

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 18 245 27 20 20 22

N.S.

1 1.00 1.09 0.82 11.14 1.23 0.91 0.91 1.00

time (sec)

N/A 0.179 5.021 0.361 1.363 0.233 8.638 0.398 17.725

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1977 1979 2316 0 0 0 0 0 0

N.S.

1 1.00 1.17 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 3.078 14.048 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 F F(-2) F F F F(-1)

verified

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

size

1157 1159 846 0 0 0 0 0 0

N.S.

1 1.00 0.73 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.223 9.712 0.000 0.000 0.000 0.000 0.000 0.000

Problem 69

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

125 160 172 179 0 576 0 174 2737

N.S.

1 1.28 1.38 1.43 0.00 4.61 0.00 1.39 21.90

time (sec)

N/A 0.700 1.173 0.391 0.000 0.296 0.000 0.285 22.781

Problem 70

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 48 22 20 22

N.S.

1 1.00 1.09 0.82 0.00 2.18 1.00 0.91 1.00

time (sec)

N/A 0.176 50.492 0.425 0.000 0.254 5.431 1.023 17.893

Problem 71

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 48 22 20 22

N.S.

1 1.00 1.09 0.82 0.00 2.18 1.00 0.91 1.00

time (sec)

N/A 0.182 57.919 0.414 0.000 0.247 39.125 1.767 18.033

Problem 72

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 0.234 4.425 0.375 2.349 0.246 21.909 0.657 17.580

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

45 45 61 158 128 62 0 0 106

N.S.

1 1.00 1.36 3.51 2.84 1.38 0.00 0.00 2.36

time (sec)

N/A 0.211 0.513 1.014 0.291 0.268 0.000 0.000 20.021

Problem 74

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

141 141 185 699 0 384 0 0 0

N.S.

1 1.00 1.31 4.96 0.00 2.72 0.00 0.00 0.00

time (sec)

N/A 0.314 0.487 1.168 0.000 0.271 0.000 0.000 0.000

Problem 75

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

221 221 0 0 0 557 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 2.52 0.00 0.00 0.00

time (sec)

N/A 0.409 0.000 0.000 0.000 0.283 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

80 57 102 275 207 116 0 0 182

N.S.

1 0.71 1.28 3.44 2.59 1.45 0.00 0.00 2.28

time (sec)

N/A 0.429 2.102 1.420 0.264 0.256 0.000 0.000 20.614

Problem 77

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

214 141 286 970 0 568 0 0 0

N.S.

1 0.66 1.34 4.53 0.00 2.65 0.00 0.00 0.00

time (sec)

N/A 0.446 7.769 1.805 0.000 0.279 0.000 0.000 0.000

Problem 78

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

377 250 0 0 0 890 0 0 0

N.S.

1 0.66 0.00 0.00 0.00 2.36 0.00 0.00 0.00

time (sec)

N/A 0.619 0.000 0.000 0.000 0.304 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

85 87 79 315 0 301 0 0 229

N.S.

1 1.02 0.93 3.71 0.00 3.54 0.00 0.00 2.69

time (sec)

N/A 0.422 0.917 1.086 0.000 0.294 0.000 0.000 19.771

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

338 283 1003 769 0 1235 0 0 0

N.S.

1 0.84 2.97 2.28 0.00 3.65 0.00 0.00 0.00

time (sec)

N/A 0.861 6.352 1.342 0.000 0.439 0.000 0.000 0.000

Problem 81

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

499 418 0 0 0 1663 0 0 0

N.S.

1 0.84 0.00 0.00 0.00 3.33 0.00 0.00 0.00

time (sec)

N/A 1.153 0.000 0.000 0.000 0.448 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

156 167 176 646 0 630 0 0 0

N.S.

1 1.07 1.13 4.14 0.00 4.04 0.00 0.00 0.00

time (sec)

N/A 0.791 1.977 6.787 0.000 0.299 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

778 624 2839 3867 0 2435 0 0 0

N.S.

1 0.80 3.65 4.97 0.00 3.13 0.00 0.00 0.00

time (sec)

N/A 1.428 11.168 7.143 0.000 0.519 0.000 0.000 0.000

Problem 84

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

1417 1152 0 0 0 3755 0 0 0

N.S.

1 0.81 0.00 0.00 0.00 2.65 0.00 0.00 0.00

time (sec)

N/A 2.364 0.000 0.000 0.000 0.571 0.000 0.000 0.000

[front] [up]