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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

143 143 146 0 0 495 0 0 0

N.S.

1 1.00 1.02 0.00 0.00 3.46 0.00 0.00 0.00

time (sec)

N/A 0.204 0.054 0.000 0.000 0.312 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 16 115 21 15 18 20

N.S.

1 1.00 1.12 1.00 7.19 1.31 0.94 1.12 1.25

time (sec)

N/A 0.021 1.180 0.191 0.360 0.280 2.144 0.379 13.236

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

92 92 95 0 0 346 0 0 0

N.S.

1 1.00 1.03 0.00 0.00 3.76 0.00 0.00 0.00

time (sec)

N/A 0.117 0.027 0.000 0.000 0.306 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 16 115 21 15 18 20

N.S.

1 1.00 1.12 1.00 7.19 1.31 0.94 1.12 1.25

time (sec)

N/A 0.022 0.888 0.148 0.331 0.260 1.844 0.310 13.910

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 26 32 31 42 42 50 67

N.S.

1 1.00 1.00 1.23 1.19 1.62 1.62 1.92 2.58

time (sec)

N/A 0.030 0.017 0.247 0.220 0.275 2.543 0.303 0.553

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 0.023 1.019 0.189 0.346 0.279 0.644 0.279 14.500

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 16 118 18 15 18 20

N.S.

1 1.00 1.12 1.00 7.38 1.12 0.94 1.12 1.25

time (sec)

N/A 0.023 0.872 0.152 0.334 0.261 0.420 0.398 13.262

Problem 8

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

242 242 229 0 0 799 0 0 0

N.S.

1 1.00 0.95 0.00 0.00 3.30 0.00 0.00 0.00

time (sec)

N/A 0.468 0.664 0.000 0.000 0.316 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 18 256 42 17 20 22

N.S.

1 1.00 1.11 1.00 14.22 2.33 0.94 1.11 1.22

time (sec)

N/A 0.029 12.322 0.295 0.490 0.259 2.762 1.211 14.046

Problem 10

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

133 133 123 0 0 525 0 0 0

N.S.

1 1.00 0.92 0.00 0.00 3.95 0.00 0.00 0.00

time (sec)

N/A 0.202 0.528 0.000 0.000 0.334 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 18 251 42 17 20 22

N.S.

1 1.00 1.11 1.00 13.94 2.33 0.94 1.11 1.22

time (sec)

N/A 0.028 9.074 0.245 0.509 0.274 2.185 1.012 13.183

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

44 44 41 50 96 91 0 88 100

N.S.

1 1.00 0.93 1.14 2.18 2.07 0.00 2.00 2.27

time (sec)

N/A 0.067 0.254 0.387 0.229 0.269 0.000 0.319 13.780

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 18 286 36 15 20 22

N.S.

1 1.00 1.11 1.00 15.89 2.00 0.83 1.11 1.22

time (sec)

N/A 0.027 29.803 0.245 0.495 0.272 2.025 0.376 13.583

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 18 289 36 17 20 22

N.S.

1 1.00 1.11 1.00 16.06 2.00 0.94 1.11 1.22

time (sec)

N/A 0.026 12.103 0.302 0.517 0.275 0.657 1.293 13.361

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 90 90 72 2838 100 0 85 496

N.S.

1 1.00 1.00 0.80 31.53 1.11 0.00 0.94 5.51

time (sec)

N/A 0.094 0.079 0.528 0.453 0.278 0.000 0.290 25.416

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

382 382 305 0 0 1457 0 0 0

N.S.

1 1.00 0.80 0.00 0.00 3.81 0.00 0.00 0.00

time (sec)

N/A 1.098 1.101 0.000 0.000 0.442 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 18 252 20 15 20 22

N.S.

1 1.00 1.11 1.00 14.00 1.11 0.83 1.11 1.22

time (sec)

N/A 0.031 1.769 0.153 0.437 0.270 0.457 0.335 13.063

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 Yes N/A TBD TBD TBD TBD TBD

size

261 261 845 0 0 1060 0 0 0

N.S.

1 1.00 3.24 0.00 0.00 4.06 0.00 0.00 0.00

time (sec)

N/A 0.662 1.614 0.000 0.000 0.402 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 18 252 20 15 20 22

N.S.

1 1.00 1.11 1.00 14.00 1.11 0.83 1.11 1.22

time (sec)

N/A 0.033 1.537 0.181 0.438 0.272 0.369 0.327 13.057

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 67 70 7945 251 0 278 157

N.S.

1 1.00 1.02 1.06 120.38 3.80 0.00 4.21 2.38

time (sec)

N/A 0.125 0.338 0.294 28.612 0.288 0.000 0.288 15.088

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 18 249 19 15 20 22

N.S.

1 1.00 1.11 1.00 13.83 1.06 0.83 1.11 1.22

time (sec)

N/A 0.030 1.779 0.182 0.612 0.257 0.750 0.305 13.059

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 16 118 18 15 18 20

N.S.

1 1.00 1.12 1.00 7.38 1.12 0.94 1.12 1.25

time (sec)

N/A 0.016 0.068 0.002 0.440 0.265 0.443 0.428 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

1092 1092 895 0 0 3050 0 0 0

N.S.

1 1.00 0.82 0.00 0.00 2.79 0.00 0.00 0.00

time (sec)

N/A 2.673 6.730 0.000 0.000 0.512 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 1284 38 17 20 22

N.S.

1 1.00 1.11 1.00 71.33 2.11 0.94 1.11 1.22

time (sec)

N/A 0.027 6.946 0.207 1.158 0.267 1.233 0.389 12.906

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

596 596 1118 0 0 1928 0 0 0

N.S.

1 1.00 1.88 0.00 0.00 3.23 0.00 0.00 0.00

time (sec)

N/A 1.342 11.656 0.000 0.000 0.442 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 1261 38 17 20 22

N.S.

1 1.00 1.11 1.00 70.06 2.11 0.94 1.11 1.22

time (sec)

N/A 0.029 6.732 0.167 0.886 0.270 1.017 0.402 13.464

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 123 153 162 8871 525 0 195 340

N.S.

1 1.00 1.24 1.32 72.12 4.27 0.00 1.59 2.76

time (sec)

N/A 0.294 1.064 0.292 25.253 0.304 0.000 0.299 17.646

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 0.026 10.514 0.200 6.023 0.273 1.256 0.812 14.004

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 4550 44 19 20 22

N.S.

1 1.00 1.11 1.00 252.78 2.44 1.06 1.11 1.22

time (sec)

N/A 0.025 6.986 0.175 5.773 0.291 1.195 0.416 14.692

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 3521 44 19 20 22

N.S.

1 1.00 1.11 1.00 195.61 2.44 1.06 1.11 1.22

time (sec)

N/A 0.027 9.394 0.175 5.741 0.291 1.382 1.065 13.855

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

476 476 479 0 1512 0 0 0 0

N.S.

1 1.00 1.01 0.00 3.18 0.00 0.00 0.00 0.00

time (sec)

N/A 0.532 0.149 0.000 0.508 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

348 348 351 0 966 0 0 0 0

N.S.

1 1.00 1.01 0.00 2.78 0.00 0.00 0.00 0.00

time (sec)

N/A 0.376 0.087 0.000 0.466 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

220 220 223 0 540 0 0 0 0

N.S.

1 1.00 1.01 0.00 2.45 0.00 0.00 0.00 0.00

time (sec)

N/A 0.232 0.062 0.000 0.406 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 16 106 18 15 18 20

N.S.

1 1.00 1.11 0.89 5.89 1.00 0.83 1.00 1.11

time (sec)

N/A 0.021 3.043 0.527 0.666 0.263 1.609 0.323 13.804

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 16 110 18 17 18 20

N.S.

1 1.00 1.11 0.89 6.11 1.00 0.94 1.00 1.11

time (sec)

N/A 0.022 12.006 0.531 0.702 0.258 1.282 0.360 13.753

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

749 749 739 0 6347 0 0 0 0

N.S.

1 1.00 0.99 0.00 8.47 0.00 0.00 0.00 0.00

time (sec)

N/A 1.066 2.145 0.000 0.687 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

551 551 543 0 3879 0 0 0 0

N.S.

1 1.00 0.99 0.00 7.04 0.00 0.00 0.00 0.00

time (sec)

N/A 0.747 1.264 0.000 0.614 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

355 355 347 0 1991 0 0 0 0

N.S.

1 1.00 0.98 0.00 5.61 0.00 0.00 0.00 0.00

time (sec)

N/A 0.524 0.752 0.000 0.445 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 18 319 36 17 20 22

N.S.

1 1.00 1.10 0.90 15.95 1.80 0.85 1.00 1.10

time (sec)

N/A 0.024 109.927 0.707 0.892 0.270 8.294 0.456 13.429

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 18 321 36 19 20 22

N.S.

1 1.00 1.10 0.90 16.05 1.80 0.95 1.00 1.10

time (sec)

N/A 0.025 74.353 0.784 1.090 0.266 2.171 0.585 13.485

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

1041 1041 802 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 1.886 1.661 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

781 781 608 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 2.037 1.192 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

521 521 414 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 1.318 1.106 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 18 241 19 17 20 22

N.S.

1 1.00 1.10 0.90 12.05 0.95 0.85 1.00 1.10

time (sec)

N/A 0.032 3.497 0.563 0.826 0.267 2.133 0.304 13.865

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 16 110 18 17 18 20

N.S.

1 1.00 1.11 0.89 6.11 1.00 0.94 1.00 1.11

time (sec)

N/A 0.019 0.074 0.002 0.702 0.266 1.270 0.365 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 Yes N/A TBD TBD TBD TBD TBD

size

3123 3123 3702 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 5.088 15.373 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 Yes N/A TBD TBD TBD TBD TBD

size

2323 2323 2777 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 4.034 13.737 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 Yes N/A TBD TBD TBD TBD TBD

size

1523 1523 1767 0 0 0 0 0 0

N.S.

1 1.00 1.16 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.986 15.265 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 4405 38 19 20 22

N.S.

1 1.00 1.10 0.90 220.25 1.90 0.95 1.00 1.10

time (sec)

N/A 0.027 64.798 0.560 13.785 0.270 4.112 0.738 13.597

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 4406 44 20 20 22

N.S.

1 1.00 1.10 0.90 220.30 2.20 1.00 1.00 1.10

time (sec)

N/A 0.028 49.629 0.603 20.356 0.286 9.593 0.946 13.185

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

284 284 281 0 738 0 0 0 0

N.S.

1 1.00 0.99 0.00 2.60 0.00 0.00 0.00 0.00

time (sec)

N/A 0.288 0.233 0.000 0.439 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

158 158 155 0 374 0 0 0 0

N.S.

1 1.00 0.98 0.00 2.37 0.00 0.00 0.00 0.00

time (sec)

N/A 0.161 0.130 0.000 0.414 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 B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 26 32 31 41 58 50 71

N.S.

1 1.00 1.00 1.23 1.19 1.58 2.23 1.92 2.73

time (sec)

N/A 0.030 0.073 0.325 0.232 0.290 1.242 0.352 15.745

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 16 112 25 19 18 20

N.S.

1 1.00 1.10 0.80 5.60 1.25 0.95 0.90 1.00

time (sec)

N/A 0.019 22.507 0.530 0.745 0.260 0.875 0.303 13.258

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 16 113 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 0.019 22.476 0.541 0.781 0.271 3.856 0.362 13.139

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

451 451 443 0 2869 0 0 0 0

N.S.

1 1.00 0.98 0.00 6.36 0.00 0.00 0.00 0.00

time (sec)

N/A 0.700 1.487 0.000 0.535 0.000 0.000 0.000 0.000

Problem 57

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

255 255 247 0 1272 0 0 0 0

N.S.

1 1.00 0.97 0.00 4.99 0.00 0.00 0.00 0.00

time (sec)

N/A 0.412 0.772 0.000 0.449 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 47 45 51 50 91 88 88 109

N.S.

1 1.00 0.96 1.09 1.06 1.94 1.87 1.87 2.32

time (sec)

N/A 0.069 0.288 0.669 0.244 0.279 8.777 0.349 14.972

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 18 718 46 20 20 22

N.S.

1 1.00 1.09 0.82 32.64 2.09 0.91 0.91 1.00

time (sec)

N/A 0.027 72.660 0.795 1.580 0.283 1.961 0.370 13.541

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 0.028 72.340 0.816 0.000 0.277 5.518 0.407 14.012

Problem 61

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

653 653 513 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 1.334 1.625 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(-2) F F F F(-1)

verified

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

size

393 393 319 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 1.002 3.035 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 F(-2) A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 68 69 70 0 274 0 278 153

N.S.

1 1.00 1.01 1.03 0.00 4.03 0.00 4.09 2.25

time (sec)

N/A 0.118 0.369 0.342 0.000 0.329 0.000 0.289 14.629

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 18 243 27 20 20 22

N.S.

1 1.00 1.09 0.82 11.05 1.23 0.91 0.91 1.00

time (sec)

N/A 0.031 5.084 0.569 0.861 0.265 2.221 0.366 13.163

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 0.031 5.167 0.483 1.091 0.271 6.474 0.405 13.336

Problem 66

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

1925 1925 2254 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 3.582 14.041 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(-2) F F F F(-1)

verified

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

size

1125 1125 1210 0 0 0 0 0 0

N.S.

1 1.00 1.08 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.435 9.273 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 F(-2) B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 127 163 162 0 574 0 196 330

N.S.

1 1.00 1.28 1.28 0.00 4.52 0.00 1.54 2.60

time (sec)

N/A 0.268 0.996 0.343 0.000 0.328 0.000 0.305 18.695

Problem 69

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 0.027 44.623 0.565 0.000 0.280 5.915 1.040 13.754

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 0.029 47.706 0.490 0.000 0.302 45.723 1.802 13.182

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 0.062 4.199 0.927 2.363 0.269 47.827 0.757 12.910

Problem 72

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

44 44 38 159 0 60 0 0 104

N.S.

1 1.00 0.86 3.61 0.00 1.36 0.00 0.00 2.36

time (sec)

N/A 0.064 0.110 0.977 0.000 0.298 0.000 0.000 14.717

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

149 149 188 829 0 470 0 0 0

N.S.

1 1.00 1.26 5.56 0.00 3.15 0.00 0.00 0.00

time (sec)

N/A 0.140 0.866 0.928 0.000 0.300 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

235 235 0 0 0 655 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 2.79 0.00 0.00 0.00

time (sec)

N/A 0.256 0.000 0.000 0.000 0.343 0.000 0.000 0.000

Problem 75

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

79 79 54 276 0 113 0 0 180

N.S.

1 1.00 0.68 3.49 0.00 1.43 0.00 0.00 2.28

time (sec)

N/A 0.125 0.487 4.020 0.000 0.307 0.000 0.000 15.510

Problem 76

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

221 221 347 1100 0 656 0 0 0

N.S.

1 1.00 1.57 4.98 0.00 2.97 0.00 0.00 0.00

time (sec)

N/A 0.242 5.784 4.271 0.000 0.324 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

390 390 0 0 0 1032 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 2.65 0.00 0.00 0.00

time (sec)

N/A 0.472 0.000 0.000 0.000 0.362 0.000 0.000 0.000

Problem 78

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

87 87 80 314 0 300 0 0 223

N.S.

1 1.00 0.92 3.61 0.00 3.45 0.00 0.00 2.56

time (sec)

N/A 0.178 0.853 0.497 0.000 0.320 0.000 0.000 15.280

Problem 79

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 Yes No TBD TBD TBD TBD TBD

size

328 328 861 752 0 1268 0 0 0

N.S.

1 1.00 2.62 2.29 0.00 3.87 0.00 0.00 0.00

time (sec)

N/A 0.732 2.362 0.659 0.000 0.529 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

485 485 0 0 0 1711 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 3.53 0.00 0.00 0.00

time (sec)

N/A 1.105 0.000 0.000 0.000 0.510 0.000 0.000 0.000

Problem 81

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

157 157 191 638 0 628 0 0 461

N.S.

1 1.00 1.22 4.06 0.00 4.00 0.00 0.00 2.94

time (sec)

N/A 0.418 1.687 1.716 0.000 0.322 0.000 0.000 18.234

Problem 82

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

757 757 2450 3010 0 2503 0 0 0

N.S.

1 1.00 3.24 3.98 0.00 3.31 0.00 0.00 0.00

time (sec)

N/A 1.684 10.692 1.736 0.000 0.569 0.000 0.000 0.000

Problem 83

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

1384 1384 0 0 0 3831 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 2.77 0.00 0.00 0.00

time (sec)

N/A 2.867 0.000 0.000 0.000 0.675 0.000 0.000 0.000

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