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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

125 125 143 0 0 256 0 0 0

N.S.

1 1.00 1.14 0.00 0.00 2.05 0.00 0.00 0.00

time (sec)

N/A 0.101 0.274 0.000 0.000 0.267 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 38 21 15 18 20

N.S.

1 1.00 1.12 1.00 2.38 1.31 0.94 1.12 1.25

time (sec)

N/A 0.014 5.382 0.047 0.312 0.252 1.179 0.301 1.978

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

77 77 92 0 0 184 0 0 0

N.S.

1 1.00 1.19 0.00 0.00 2.39 0.00 0.00 0.00

time (sec)

N/A 0.058 0.223 0.000 0.000 0.264 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 38 21 15 18 20

N.S.

1 1.00 1.12 1.00 2.38 1.31 0.94 1.12 1.25

time (sec)

N/A 0.013 4.694 0.058 0.300 0.247 0.708 0.269 1.987

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

26 26 26 23 22 33 39 28 42

N.S.

1 1.00 1.00 0.88 0.85 1.27 1.50 1.08 1.62

time (sec)

N/A 0.019 0.027 0.306 0.197 0.255 0.600 0.275 0.074

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 36 18 14 18 20

N.S.

1 1.00 1.12 1.00 2.25 1.12 0.88 1.12 1.25

time (sec)

N/A 0.013 4.548 0.048 0.306 0.262 1.951 0.288 2.111

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 38 18 15 18 20

N.S.

1 1.00 1.12 1.00 2.38 1.12 0.94 1.12 1.25

time (sec)

N/A 0.014 4.508 0.048 0.303 0.245 0.617 0.329 2.117

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

217 217 320 0 0 1198 0 0 0

N.S.

1 1.00 1.47 0.00 0.00 5.52 0.00 0.00 0.00

time (sec)

N/A 0.272 2.712 0.000 0.000 0.301 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 79 42 17 20 22

N.S.

1 1.00 1.11 1.00 4.39 2.33 0.94 1.11 1.22

time (sec)

N/A 0.017 11.216 0.077 0.413 0.245 1.556 0.670 2.003

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

119 119 324 0 0 782 0 0 0

N.S.

1 1.00 2.72 0.00 0.00 6.57 0.00 0.00 0.00

time (sec)

N/A 0.123 1.942 0.000 0.000 0.280 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 72 42 17 20 22

N.S.

1 1.00 1.11 1.00 4.00 2.33 0.94 1.11 1.22

time (sec)

N/A 0.017 9.295 0.072 0.404 0.256 1.009 0.672 1.992

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

44 44 43 41 46 194 0 55 77

N.S.

1 1.00 0.98 0.93 1.05 4.41 0.00 1.25 1.75

time (sec)

N/A 0.042 0.139 0.701 0.207 0.258 0.000 0.302 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 86 36 15 20 22

N.S.

1 1.00 1.11 1.00 4.78 2.00 0.83 1.11 1.22

time (sec)

N/A 0.017 27.465 0.074 0.399 0.255 6.611 0.310 2.163

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 87 36 17 20 22

N.S.

1 1.00 1.11 1.00 4.83 2.00 0.94 1.11 1.22

time (sec)

N/A 0.017 10.618 0.074 0.434 0.268 1.008 0.818 2.152

Problem 15

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

90 90 90 62 182 1918 0 146 395

N.S.

1 1.00 1.00 0.69 2.02 21.31 0.00 1.62 4.39

time (sec)

N/A 0.061 0.094 1.377 0.287 0.263 0.000 0.277 0.106

Problem 16

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 Yes N/A TBD TBD TBD TBD TBD

size

349 349 272 0 0 731 0 0 0

N.S.

1 1.00 0.78 0.00 0.00 2.09 0.00 0.00 0.00

time (sec)

N/A 0.635 0.762 0.000 0.000 0.303 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 59 20 15 20 22

N.S.

1 1.00 1.11 1.00 3.28 1.11 0.83 1.11 1.22

time (sec)

N/A 0.021 3.845 0.053 0.302 0.265 0.580 0.301 1.975

Problem 18

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 Yes N/A TBD TBD TBD TBD TBD

size

241 241 187 0 0 536 0 0 0

N.S.

1 1.00 0.78 0.00 0.00 2.22 0.00 0.00 0.00

time (sec)

N/A 0.360 0.503 0.000 0.000 0.259 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 59 20 15 20 22

N.S.

1 1.00 1.11 1.00 3.28 1.11 0.83 1.11 1.22

time (sec)

N/A 0.021 3.258 0.051 0.303 0.239 0.486 0.282 1.930

Problem 20

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 66 67 90 0 304 0 61 171

N.S.

1 1.00 1.02 1.36 0.00 4.61 0.00 0.92 2.59

time (sec)

N/A 0.082 0.267 0.204 0.000 0.278 0.000 0.269 0.204

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 58 19 15 20 22

N.S.

1 1.00 1.11 1.00 3.22 1.06 0.83 1.11 1.22

time (sec)

N/A 0.021 2.866 0.052 0.288 0.250 1.133 0.312 2.057

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 38 18 15 18 20

N.S.

1 1.00 1.12 1.00 2.38 1.12 0.94 1.12 1.25

time (sec)

N/A 0.012 0.086 0.010 0.296 0.246 0.703 0.305 0.002

Problem 23

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 Yes N/A TBD TBD TBD TBD TBD

size

994 994 1565 0 0 3918 0 0 0

N.S.

1 1.00 1.57 0.00 0.00 3.94 0.00 0.00 0.00

time (sec)

N/A 1.523 6.717 0.000 0.000 0.326 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 18 312 38 17 20 22

N.S.

1 1.00 1.11 1.00 17.33 2.11 0.94 1.11 1.22

time (sec)

N/A 0.019 20.983 0.057 0.418 0.266 1.002 0.402 2.063

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 Yes N/A TBD TBD TBD TBD TBD

size

555 555 654 0 0 2473 0 0 0

N.S.

1 1.00 1.18 0.00 0.00 4.46 0.00 0.00 0.00

time (sec)

N/A 0.738 5.344 0.000 0.000 0.305 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 18 300 38 17 20 22

N.S.

1 1.00 1.11 1.00 16.67 2.11 0.94 1.11 1.22

time (sec)

N/A 0.019 19.202 0.054 0.432 0.254 0.808 0.401 2.044

Problem 27

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

123 123 220 177 0 1314 0 148 316

N.S.

1 1.00 1.79 1.44 0.00 10.68 0.00 1.20 2.57

time (sec)

N/A 0.189 0.862 0.275 0.000 0.303 0.000 0.275 2.582

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 18 249 38 17 20 22

N.S.

1 1.00 1.11 1.00 13.83 2.11 0.94 1.11 1.22

time (sec)

N/A 0.018 53.753 0.061 0.417 0.250 1.677 0.925 2.547

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 18 318 44 19 20 22

N.S.

1 1.00 1.11 1.00 17.67 2.44 1.06 1.11 1.22

time (sec)

N/A 0.018 26.111 0.057 0.422 0.266 1.442 0.374 2.439

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 18 319 44 19 3 22

N.S.

1 1.00 1.11 1.00 17.72 2.44 1.06 0.17 1.22

time (sec)

N/A 0.018 28.548 0.058 0.412 0.254 1.460 3.003 2.637

Problem 31

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

6 6 6 7 12 28 0 12 12

N.S.

1 1.00 1.00 1.17 2.00 4.67 0.00 2.00 2.00

time (sec)

N/A 0.016 0.027 0.528 0.197 0.260 0.000 0.271 2.016

Problem 32

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

426 426 415 0 0 0 0 0 0

N.S.

1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.312 0.646 0.000 0.000 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 F F F F F(-1)

verified

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

size

310 310 311 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.214 0.516 0.000 0.000 0.000 0.000 0.000 0.000

Problem 34

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

194 194 207 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 0.128 0.456 0.000 0.000 0.000 0.000 0.000 0.000

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 36 18 15 18 20

N.S.

1 1.00 1.11 0.89 2.00 1.00 0.83 1.00 1.11

time (sec)

N/A 0.014 11.138 0.128 0.428 0.268 2.607 0.283 2.150

Problem 36

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 42 18 17 18 20

N.S.

1 1.00 1.11 0.89 2.33 1.00 0.94 1.00 1.11

time (sec)

N/A 0.014 10.482 0.144 0.429 0.252 1.485 0.301 2.200

Problem 37

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

677 677 748 0 0 0 0 0 0

N.S.

1 1.00 1.10 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.594 8.600 0.000 0.000 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 F F F F F(-1)

verified

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

size

497 497 582 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 0.457 7.127 0.000 0.000 0.000 0.000 0.000 0.000

Problem 39

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 No N/A TBD TBD TBD TBD TBD

size

319 319 466 0 0 0 0 0 0

N.S.

1 1.00 1.46 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.312 5.815 0.000 0.000 0.000 0.000 0.000 0.000

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 86 36 17 20 22

N.S.

1 1.00 1.10 0.90 4.30 1.80 0.85 1.00 1.10

time (sec)

N/A 0.018 98.183 0.254 0.574 0.260 13.810 0.380 2.418

Problem 41

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 18 110 36 19 20 22

N.S.

1 1.00 1.10 0.90 5.50 1.80 0.95 1.00 1.10

time (sec)

N/A 0.017 37.837 0.261 0.570 0.282 2.464 0.491 2.375

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

961 961 721 0 0 0 0 0 0

N.S.

1 1.00 0.75 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.986 1.209 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

721 721 547 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 0.792 0.835 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 A A F F(-2) F F F F(-1)

verified

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

size

481 481 373 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 0.615 0.673 0.000 0.000 0.000 0.000 0.000 0.000

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

20 20 22 18 58 19 17 20 22

N.S.

1 1.00 1.10 0.90 2.90 0.95 0.85 1.00 1.10

time (sec)

N/A 0.020 5.432 0.182 0.509 0.251 2.400 0.363 2.041

Problem 46

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 42 18 17 18 20

N.S.

1 1.00 1.11 0.89 2.33 1.00 0.94 1.00 1.11

time (sec)

N/A 0.012 0.105 0.009 0.443 0.261 1.464 0.324 0.002

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

2851 2851 3035 0 0 0 0 0 0

N.S.

1 1.00 1.06 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.778 10.368 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

2123 2123 2247 0 0 0 0 0 0

N.S.

1 1.00 1.06 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 2.119 9.722 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 A A F F(-2) F F F F(-1)

verified

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

size

1395 1395 1393 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.653 8.951 0.000 0.000 0.000 0.000 0.000 0.000

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 18 253 38 19 20 22

N.S.

1 1.00 1.10 0.90 12.65 1.90 0.95 1.00 1.10

time (sec)

N/A 0.018 179.185 0.178 0.977 0.269 4.715 1.375 2.437

Problem 51

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 18 324 44 20 3 22

N.S.

1 1.00 1.10 0.90 16.20 2.20 1.00 0.15 1.10

time (sec)

N/A 0.019 91.963 0.181 1.158 0.274 9.896 3.100 2.477

Problem 52

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

254 254 288 0 0 0 0 0 0

N.S.

1 1.00 1.13 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.165 0.576 0.000 0.000 0.000 0.000 0.000 0.000

Problem 53

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

140 140 172 0 0 0 0 0 0

N.S.

1 1.00 1.23 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.092 0.926 0.000 0.000 0.000 0.000 0.000 0.000

Problem 54

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 26 23 22 33 37 29 43

N.S.

1 1.00 1.00 0.88 0.85 1.27 1.42 1.12 1.65

time (sec)

N/A 0.017 0.058 0.264 0.193 0.259 0.448 0.269 1.978

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 42 25 19 18 20

N.S.

1 1.00 1.10 0.80 2.10 1.25 0.95 0.90 1.00

time (sec)

N/A 0.012 13.992 0.132 0.442 0.264 1.083 0.294 2.195

Problem 56

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 42 25 19 18 20

N.S.

1 1.00 1.10 0.80 2.10 1.25 0.95 0.90 1.00

time (sec)

N/A 0.012 15.408 0.128 0.447 0.247 4.377 0.304 2.279

Problem 57

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

407 407 496 0 0 0 0 0 0

N.S.

1 1.00 1.22 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.381 5.887 0.000 0.000 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

229 229 344 0 0 0 0 0 0

N.S.

1 1.00 1.50 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.236 3.352 0.000 0.000 0.000 0.000 0.000 0.000

Problem 59

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 47 47 42 48 194 0 55 77

N.S.

1 1.00 1.00 0.89 1.02 4.13 0.00 1.17 1.64

time (sec)

N/A 0.044 0.205 0.516 0.199 0.269 0.000 0.283 2.054

Problem 60

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 18 106 46 20 20 22

N.S.

1 1.00 1.09 0.82 4.82 2.09 0.91 0.91 1.00

time (sec)

N/A 0.017 36.169 0.258 0.551 0.259 2.050 0.381 2.375

Problem 61

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 0.018 34.808 0.248 0.000 0.274 5.657 0.436 2.410

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

601 601 460 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 0.703 1.156 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

361 361 286 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 0.554 0.778 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) B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 68 69 90 0 254 0 61 155

N.S.

1 1.00 1.01 1.32 0.00 3.74 0.00 0.90 2.28

time (sec)

N/A 0.071 0.187 0.268 0.000 0.299 0.000 0.276 2.555

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 66 27 20 20 22

N.S.

1 1.00 1.09 0.82 3.00 1.23 0.91 0.91 1.00

time (sec)

N/A 0.018 10.044 0.169 0.493 0.252 2.189 0.343 2.126

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 66 27 20 20 22

N.S.

1 1.00 1.09 0.82 3.00 1.23 0.91 0.91 1.00

time (sec)

N/A 0.020 10.413 0.166 0.550 0.267 6.603 0.428 2.168

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

1755 1755 1769 0 0 0 0 0 0

N.S.

1 1.00 1.01 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.899 8.270 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

1027 1027 986 0 0 0 0 0 0

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.343 5.154 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

127 127 232 177 0 1387 0 148 344

N.S.

1 1.00 1.83 1.39 0.00 10.92 0.00 1.17 2.71

time (sec)

N/A 0.155 0.562 0.273 0.000 0.299 0.000 0.272 2.498

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 18 317 48 22 20 22

N.S.

1 1.00 1.09 0.82 14.41 2.18 1.00 0.91 1.00

time (sec)

N/A 0.018 81.808 0.176 1.022 0.282 5.812 1.384 2.450

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

22 22 24 18 324 48 22 3 22

N.S.

1 1.00 1.09 0.82 14.73 2.18 1.00 0.14 1.00

time (sec)

N/A 0.018 81.059 0.146 1.308 0.286 50.987 3.093 2.507

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 0.037 20.308 0.168 0.329 0.257 44.279 0.782 2.119

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

44 44 41 155 0 122 0 0 110

N.S.

1 1.00 0.93 3.52 0.00 2.77 0.00 0.00 2.50

time (sec)

N/A 0.039 0.335 1.716 0.000 0.253 0.000 0.000 2.108

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

135 135 260 368 0 664 0 0 0

N.S.

1 1.00 1.93 2.73 0.00 4.92 0.00 0.00 0.00

time (sec)

N/A 0.082 0.613 1.698 0.000 0.282 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

217 217 0 0 0 1082 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 4.99 0.00 0.00 0.00

time (sec)

N/A 0.146 0.000 0.000 0.000 0.301 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

79 79 57 271 0 646 0 0 158

N.S.

1 1.00 0.72 3.43 0.00 8.18 0.00 0.00 2.00

time (sec)

N/A 0.074 0.988 17.010 0.000 0.270 0.000 0.000 2.163

Problem 77

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

208 208 501 0 0 2972 0 0 0

N.S.

1 1.00 2.41 0.00 0.00 14.29 0.00 0.00 0.00

time (sec)

N/A 0.161 5.470 0.000 0.000 0.324 0.000 0.000 0.000

Problem 78

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

363 363 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 0.293 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

87 87 80 317 0 511 0 0 409

N.S.

1 1.00 0.92 3.64 0.00 5.87 0.00 0.00 4.70

time (sec)

N/A 0.121 0.648 0.850 0.000 0.298 0.000 0.000 2.685

Problem 80

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

307 307 859 585 0 1286 0 0 0

N.S.

1 1.00 2.80 1.91 0.00 4.19 0.00 0.00 0.00

time (sec)

N/A 0.421 3.704 0.778 0.000 0.298 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

452 452 0 0 0 2005 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 4.44 0.00 0.00 0.00

time (sec)

N/A 0.619 0.000 0.000 0.000 0.318 0.000 0.000 0.000

Problem 82

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

157 157 233 491 0 3547 0 0 0

N.S.

1 1.00 1.48 3.13 0.00 22.59 0.00 0.00 0.00

time (sec)

N/A 0.240 1.267 6.451 0.000 0.320 0.000 0.000 0.000

Problem 83

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

717 717 469 0 0 9020 0 0 0

N.S.

1 1.00 0.65 0.00 0.00 12.58 0.00 0.00 0.00

time (sec)

N/A 0.878 6.458 0.000 0.000 0.422 0.000 0.000 0.000

Problem 84

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

1284 1284 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 1.586 0.000 0.000 0.000 0.000 0.000 0.000 0.000

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