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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.

In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 14 13 13 12 13 13

N.S.

1 1.00 1.00 0.93 0.87 0.87 0.80 0.87 0.87

time (sec)

N/A 0.118 0.002 0.315 0.195 0.242 0.017 0.300 0.029

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C C C B F A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 49 37 34 41 0 42 41 43

N.S.

1 3.27 2.47 2.27 2.73 0.00 2.80 2.73 2.87

time (sec)

N/A 0.238 0.019 0.342 0.187 0.000 4.721 0.283 0.547

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 82 60 73 0 100 0 177 204

N.S.

1 1.00 0.73 0.89 0.00 1.22 0.00 2.16 2.49

time (sec)

N/A 0.251 0.188 0.201 0.000 0.247 0.000 0.292 0.568

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 71 52 0 80 0 94 0

N.S.

1 1.00 1.65 1.21 0.00 1.86 0.00 2.19 0.00

time (sec)

N/A 0.155 0.074 0.460 0.000 0.243 0.000 0.299 0.000

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 73 115 0 105 0 133 82

N.S.

1 1.00 0.99 1.55 0.00 1.42 0.00 1.80 1.11

time (sec)

N/A 0.239 0.065 0.024 0.000 0.240 0.000 0.323 1.773

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 70 65 53 89 0 84 0

N.S.

1 1.00 1.09 1.02 0.83 1.39 0.00 1.31 0.00

time (sec)

N/A 0.184 0.186 0.424 0.272 0.243 0.000 0.286 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 55 37 0 83 0 101 0

N.S.

1 1.00 1.15 0.77 0.00 1.73 0.00 2.10 0.00

time (sec)

N/A 0.150 0.104 0.416 0.000 0.238 0.000 0.298 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 26 21 0 18 53 20 21

N.S.

1 1.00 0.87 0.70 0.00 0.60 1.77 0.67 0.70

time (sec)

N/A 0.242 0.181 0.329 0.000 0.235 0.292 0.281 0.438

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

220 365 195 1206 0 450 0 367 0

N.S.

1 1.66 0.89 5.48 0.00 2.05 0.00 1.67 0.00

time (sec)

N/A 0.694 6.105 0.324 0.000 0.245 0.000 1.489 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

220 541 195 1637 0 450 0 358 0

N.S.

1 2.46 0.89 7.44 0.00 2.05 0.00 1.63 0.00

time (sec)

N/A 0.954 6.314 0.485 0.000 0.250 0.000 1.649 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 138 126 146 0 161 0 547 0

N.S.

1 1.00 0.91 1.06 0.00 1.17 0.00 3.96 0.00

time (sec)

N/A 0.221 3.633 0.366 0.000 0.252 0.000 0.331 0.000

Problem 12

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

125 151 272 0 0 502 0 0 0

N.S.

1 1.21 2.18 0.00 0.00 4.02 0.00 0.00 0.00

time (sec)

N/A 0.334 2.366 0.000 0.000 1.171 0.000 0.000 0.000

Problem 13

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

81 81 205 0 0 504 0 0 0

N.S.

1 1.00 2.53 0.00 0.00 6.22 0.00 0.00 0.00

time (sec)

N/A 0.287 1.074 0.000 0.000 3.271 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

31 31 44 0 0 60 15 0 0

N.S.

1 1.00 1.42 0.00 0.00 1.94 0.48 0.00 0.00

time (sec)

N/A 0.190 0.134 0.000 0.000 0.368 0.986 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 57 22 0 29 15 0 0

N.S.

1 1.00 1.73 0.67 0.00 0.88 0.45 0.00 0.00

time (sec)

N/A 0.196 0.158 0.358 0.000 0.385 0.444 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 19 16 15 28 56 15 15

N.S.

1 1.00 1.00 0.84 0.79 1.47 2.95 0.79 0.79

time (sec)

N/A 0.370 0.009 0.411 0.189 0.240 0.820 0.308 0.476

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 51 43 120 0 32 2236 0 0

N.S.

1 0.98 0.83 2.31 0.00 0.62 43.00 0.00 0.00

time (sec)

N/A 0.186 0.144 0.040 0.000 0.248 1.264 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

56 55 50 0 0 33 0 0 0

N.S.

1 0.98 0.89 0.00 0.00 0.59 0.00 0.00 0.00

time (sec)

N/A 0.184 0.140 0.000 0.000 0.255 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 17 16 0 15 311 15 15

N.S.

1 1.00 1.00 0.94 0.00 0.88 18.29 0.88 0.88

time (sec)

N/A 0.183 0.022 0.332 0.000 0.240 1.365 0.303 0.343

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 19 0 18 41 18 18

N.S.

1 1.00 1.00 0.95 0.00 0.90 2.05 0.90 0.90

time (sec)

N/A 0.186 0.023 0.356 0.000 0.245 0.666 0.286 0.342

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 45 39 43 40 52 36 47 58

N.S.

1 1.07 0.93 1.02 0.95 1.24 0.86 1.12 1.38

time (sec)

N/A 0.187 0.040 0.056 0.192 0.239 0.068 0.280 0.534

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 22 20 20 19 20 19 24

N.S.

1 1.00 1.00 0.91 0.91 0.86 0.91 0.86 1.09

time (sec)

N/A 0.169 0.022 0.046 0.190 0.254 0.055 0.292 0.436

Problem 23

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

62 62 49 50 51 58 51 74 47

N.S.

1 1.00 0.79 0.81 0.82 0.94 0.82 1.19 0.76

time (sec)

N/A 0.281 0.071 0.104 0.202 0.267 0.081 0.294 0.454

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 94 239 158 0 285 0 304 0

N.S.

1 1.09 2.78 1.84 0.00 3.31 0.00 3.53 0.00

time (sec)

N/A 0.291 0.299 1.065 0.000 0.256 0.000 0.322 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 19 16 0 15 15 15 15

N.S.

1 1.00 1.00 0.84 0.00 0.79 0.79 0.79 0.79

time (sec)

N/A 0.199 0.048 0.435 0.000 0.243 0.090 0.292 0.484

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 26 23 0 22 27 22 22

N.S.

1 1.00 1.00 0.88 0.00 0.85 1.04 0.85 0.85

time (sec)

N/A 0.221 0.068 0.343 0.000 0.242 0.454 0.294 0.546

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

63 69 56 0 0 198 46 0 0

N.S.

1 1.10 0.89 0.00 0.00 3.14 0.73 0.00 0.00

time (sec)

N/A 0.336 0.105 0.000 0.000 0.258 1.072 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 92 82 25 0 216 51 0 0

N.S.

1 1.12 1.00 0.30 0.00 2.63 0.62 0.00 0.00

time (sec)

N/A 0.224 0.013 0.023 0.000 0.261 1.760 0.000 0.000

Problem 29

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

606 741 412 0 518 0 0 0 0

N.S.

1 1.22 0.68 0.00 0.85 0.00 0.00 0.00 0.00

time (sec)

N/A 4.520 0.295 0.000 0.208 0.000 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 17 16 0 15 311 15 15

N.S.

1 1.00 1.00 0.94 0.00 0.88 18.29 0.88 0.88

time (sec)

N/A 0.184 0.043 0.367 0.000 0.245 1.246 0.305 0.355

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 51 46 120 0 32 2236 0 0

N.S.

1 0.98 0.88 2.31 0.00 0.62 43.00 0.00 0.00

time (sec)

N/A 0.184 0.209 0.036 0.000 0.259 1.270 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 33 44 48 48 0 0 0

N.S.

1 1.00 0.97 1.29 1.41 1.41 0.00 0.00 0.00

time (sec)

N/A 0.212 0.196 0.723 0.276 0.246 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 61 77 63 62 64 36 64 86

N.S.

1 1.05 1.33 1.09 1.07 1.10 0.62 1.10 1.48

time (sec)

N/A 0.171 0.069 1.300 0.283 0.242 0.447 0.287 0.603

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 62 77 48 62 64 37 64 76

N.S.

1 1.07 1.33 0.83 1.07 1.10 0.64 1.10 1.31

time (sec)

N/A 0.173 0.054 1.234 0.279 0.244 0.472 0.298 0.557

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A B C F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 49 86 12 78 82 29 0 10

N.S.

1 1.00 1.76 0.24 1.59 1.67 0.59 0.00 0.20

time (sec)

N/A 0.141 0.043 1.540 0.278 0.241 0.436 0.000 0.367

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 61 79 63 62 64 32 63 80

N.S.

1 1.11 1.44 1.15 1.13 1.16 0.58 1.15 1.45

time (sec)

N/A 0.173 0.056 1.997 0.272 0.245 0.453 0.289 0.575

Problem 37

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

97 97 148 769 0 301 0 0 0

N.S.

1 1.00 1.53 7.93 0.00 3.10 0.00 0.00 0.00

time (sec)

N/A 0.197 1.271 6.006 0.000 1.929 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

145 145 0 1878 0 0 0 0 0

N.S.

1 1.00 0.00 12.95 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.305 0.000 13.997 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 C F B F F F(-1)

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

110 120 162 1593 0 277 0 0 0

N.S.

1 1.09 1.47 14.48 0.00 2.52 0.00 0.00 0.00

time (sec)

N/A 0.187 0.294 6.433 0.000 1.226 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

81 86 85 653 0 120 0 0 0

N.S.

1 1.06 1.05 8.06 0.00 1.48 0.00 0.00 0.00

time (sec)

N/A 0.215 0.015 0.950 0.000 0.404 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

66 86 130 92 0 415 0 67 37

N.S.

1 1.30 1.97 1.39 0.00 6.29 0.00 1.02 0.56

time (sec)

N/A 0.210 0.818 0.849 0.000 0.898 0.000 0.319 0.483

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

79 94 145 0 0 665 0 0 0

N.S.

1 1.19 1.84 0.00 0.00 8.42 0.00 0.00 0.00

time (sec)

N/A 0.213 0.968 0.000 0.000 0.783 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

118 0 189 0 0 1496 0 0 0

N.S.

1 0.00 1.60 0.00 0.00 12.68 0.00 0.00 0.00

time (sec)

N/A 0.000 2.966 0.000 0.000 13.441 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

111 0 128 111 0 0 0 0 0

N.S.

1 0.00 1.15 1.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.000 15.299 1.215 0.000 0.000 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

176 0 0 0 0 932 0 0 0

N.S.

1 0.00 0.00 0.00 0.00 5.30 0.00 0.00 0.00

time (sec)

N/A 0.000 0.000 0.000 0.000 54.282 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

493 570 0 0 0 0 0 0 0

N.S.

1 1.16 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.778 0.000 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 C A F C F(-1) B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

407 506 178 277 0 555 0 795 343

N.S.

1 1.24 0.44 0.68 0.00 1.36 0.00 1.95 0.84

time (sec)

N/A 0.874 7.416 3.160 0.000 0.272 0.000 0.623 0.554

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

648 0 610 352 0 1005 0 1000 567

N.S.

1 0.00 0.94 0.54 0.00 1.55 0.00 1.54 0.88

time (sec)

N/A 0.000 16.413 3.783 0.000 0.284 0.000 0.765 0.614

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

1058 0 1100 502 0 1905 0 1410 1017

N.S.

1 0.00 1.04 0.47 0.00 1.80 0.00 1.33 0.96

time (sec)

N/A 0.000 17.330 7.409 0.000 2.036 0.000 1.091 1.060

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

378 424 733 452 0 869 0 2509 0

N.S.

1 1.12 1.94 1.20 0.00 2.30 0.00 6.64 0.00

time (sec)

N/A 1.341 3.996 3.310 0.000 0.285 0.000 35.108 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

638 0 1431 552 0 1569 0 0 0

N.S.

1 0.00 2.24 0.87 0.00 2.46 0.00 0.00 0.00

time (sec)

N/A 0.000 21.655 6.780 0.000 0.322 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

66 429 99 787 0 546 0 0 0

N.S.

1 6.50 1.50 11.92 0.00 8.27 0.00 0.00 0.00

time (sec)

N/A 1.220 2.110 1.605 0.000 0.297 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

198 203 145 0 0 0 0 0 0

N.S.

1 1.03 0.73 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.291 10.240 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 C F F F(-2) F F F(-1)

verified

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

size

198 198 153 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 0.271 10.270 0.000 0.000 0.000 0.000 0.000 0.000

Problem 55

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 Yes TBD TBD TBD TBD TBD

size

97 97 168 2395 0 171 0 0 0

N.S.

1 1.00 1.73 24.69 0.00 1.76 0.00 0.00 0.00

time (sec)

N/A 0.172 0.312 9.443 0.000 1.244 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 76 99 15 105 96 32 0 0

N.S.

1 1.04 1.36 0.21 1.44 1.32 0.44 0.00 0.00

time (sec)

N/A 0.168 0.240 1.189 0.276 0.257 0.568 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 75 88 49 71 73 37 72 83

N.S.

1 1.12 1.31 0.73 1.06 1.09 0.55 1.07 1.24

time (sec)

N/A 0.196 0.074 1.553 0.277 0.245 0.561 0.295 0.407

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

482 482 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 0.665 0.000 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 F C F C F F F(-1)

verified

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

size

280 408 0 1410 0 3880 0 0 0

N.S.

1 1.46 0.00 5.04 0.00 13.86 0.00 0.00 0.00

time (sec)

N/A 0.546 0.000 21.318 0.000 5.355 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

232 232 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 0.397 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

168 168 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 0.343 0.000 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 A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 25 22 23 23 22 23 23

N.S.

1 1.00 1.00 0.88 0.92 0.92 0.88 0.92 0.92

time (sec)

N/A 0.172 0.009 0.022 0.196 0.264 0.038 0.304 0.071

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 86 52 0 43 73 40 53

N.S.

1 1.00 1.46 0.88 0.00 0.73 1.24 0.68 0.90

time (sec)

N/A 0.184 0.025 0.046 0.000 0.249 0.067 0.311 0.389

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 85 99 70 0 66 100 64 76

N.S.

1 1.09 1.27 0.90 0.00 0.85 1.28 0.82 0.97

time (sec)

N/A 0.257 0.027 0.036 0.000 0.247 0.078 0.302 0.096

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 49 57 55 0 56 0 0 0

N.S.

1 1.00 1.16 1.12 0.00 1.14 0.00 0.00 0.00

time (sec)

N/A 0.149 0.289 0.904 0.000 0.280 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 44 62 0 61 0 0 0

N.S.

1 1.00 0.83 1.17 0.00 1.15 0.00 0.00 0.00

time (sec)

N/A 0.159 0.291 0.862 0.000 0.285 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 101 79 89 0 359 0 0 0

N.S.

1 1.35 1.05 1.19 0.00 4.79 0.00 0.00 0.00

time (sec)

N/A 0.265 0.399 1.347 0.000 0.313 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 171 92 149 0 229 0 0 0

N.S.

1 1.00 0.54 0.87 0.00 1.34 0.00 0.00 0.00

time (sec)

N/A 0.263 0.380 0.925 0.000 0.328 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

80 88 157 0 0 0 0 0 0

N.S.

1 1.10 1.96 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.207 10.301 0.000 0.000 0.000 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

88 96 162 0 0 0 0 0 0

N.S.

1 1.09 1.84 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.213 10.183 0.000 0.000 0.000 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

149 151 144 0 0 0 0 0 0

N.S.

1 1.01 0.97 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.223 10.184 0.000 0.000 0.000 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

135 137 152 0 0 0 0 0 0

N.S.

1 1.01 1.13 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.210 10.138 0.000 0.000 0.000 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 127 28 164 0 1116 0 0 653

N.S.

1 1.00 0.22 1.29 0.00 8.79 0.00 0.00 5.14

time (sec)

N/A 0.187 10.018 5.903 0.000 0.338 0.000 0.000 0.515

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

157 157 54 240 0 1669 0 0 331

N.S.

1 1.00 0.34 1.53 0.00 10.63 0.00 0.00 2.11

time (sec)

N/A 0.206 10.025 0.665 0.000 0.391 0.000 0.000 15.033

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F C F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 48 421 0 723 0 0 533

N.S.

1 1.00 0.65 5.69 0.00 9.77 0.00 0.00 7.20

time (sec)

N/A 0.429 10.017 3.015 0.000 0.348 0.000 0.000 0.208

Problem 76

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

103 103 32 383 0 497 0 0 0

N.S.

1 1.00 0.31 3.72 0.00 4.83 0.00 0.00 0.00

time (sec)

N/A 0.650 10.022 1.086 0.000 0.423 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

81 81 126 538 0 1210 0 0 0

N.S.

1 1.00 1.56 6.64 0.00 14.94 0.00 0.00 0.00

time (sec)

N/A 0.161 4.134 7.796 0.000 1.301 0.000 0.000 0.000

Problem 78

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 No Yes TBD TBD TBD TBD TBD

size

81 81 126 443 0 345 0 0 0

N.S.

1 1.00 1.56 5.47 0.00 4.26 0.00 0.00 0.00

time (sec)

N/A 0.165 4.070 1.669 0.000 1.009 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

113 113 118 938 0 1232 0 0 0

N.S.

1 1.00 1.04 8.30 0.00 10.90 0.00 0.00 0.00

time (sec)

N/A 0.172 4.047 9.519 0.000 0.681 0.000 0.000 0.000

Problem 80

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

109 109 124 0 0 1103 0 0 0

N.S.

1 1.00 1.14 0.00 0.00 10.12 0.00 0.00 0.00

time (sec)

N/A 0.169 4.032 0.000 0.000 0.739 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 87 29 33 0 85 0 0 217

N.S.

1 1.00 0.33 0.38 0.00 0.98 0.00 0.00 2.49

time (sec)

N/A 0.499 10.362 0.759 0.000 0.253 0.000 0.000 0.163

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A C F C F F B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

71 546 46 317 0 70 0 0 207

N.S.

1 7.69 0.65 4.46 0.00 0.99 0.00 0.00 2.92

time (sec)

N/A 1.173 10.372 0.506 0.000 0.264 0.000 0.000 0.490

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 233 52 367 0 63 0 0 0

N.S.

1 5.07 1.13 7.98 0.00 1.37 0.00 0.00 0.00

time (sec)

N/A 0.818 10.879 0.655 0.000 0.276 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 34 111 0 0 0 0 67

N.S.

1 1.00 1.06 3.47 0.00 0.00 0.00 0.00 2.09

time (sec)

N/A 0.228 1.217 2.957 0.000 0.000 0.000 0.000 1.770

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 31 42 0 44 0 0 204

N.S.

1 1.00 1.35 1.83 0.00 1.91 0.00 0.00 8.87

time (sec)

N/A 0.186 0.879 0.817 0.000 0.268 0.000 0.000 0.567

Problem 86

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 Yes TBD TBD TBD TBD TBD

size

218 218 47 355 0 1569 0 0 0

N.S.

1 1.00 0.22 1.63 0.00 7.20 0.00 0.00 0.00

time (sec)

N/A 0.232 10.046 48.349 0.000 0.426 0.000 0.000 0.000

Problem 87

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 Yes TBD TBD TBD TBD TBD

size

210 210 50 352 0 1702 0 0 0

N.S.

1 1.00 0.24 1.68 0.00 8.10 0.00 0.00 0.00

time (sec)

N/A 0.216 10.051 48.707 0.000 0.393 0.000 0.000 0.000

Problem 88

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 Yes TBD TBD TBD TBD TBD

size

222 222 65 351 0 1718 0 0 0

N.S.

1 1.00 0.29 1.58 0.00 7.74 0.00 0.00 0.00

time (sec)

N/A 0.218 10.053 41.432 0.000 0.396 0.000 0.000 0.000

Problem 89

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 Yes TBD TBD TBD TBD TBD

size

214 214 68 352 0 1538 0 0 0

N.S.

1 1.00 0.32 1.64 0.00 7.19 0.00 0.00 0.00

time (sec)

N/A 0.222 10.045 41.404 0.000 0.391 0.000 0.000 0.000

Problem 90

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 Yes TBD TBD TBD TBD TBD

size

65 73 77 327 0 323 0 0 0

N.S.

1 1.12 1.18 5.03 0.00 4.97 0.00 0.00 0.00

time (sec)

N/A 0.265 8.275 2.295 0.000 0.360 0.000 0.000 0.000

Problem 91

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 Yes TBD TBD TBD TBD TBD

size

63 70 77 311 0 112 0 0 0

N.S.

1 1.11 1.22 4.94 0.00 1.78 0.00 0.00 0.00

time (sec)

N/A 0.269 8.204 2.308 0.000 0.380 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 92 816 0 0 0 0 0

N.S.

1 1.00 1.74 15.40 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.201 0.757 2.089 0.000 0.000 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

108 111 0 1421 0 267 0 0 0

N.S.

1 1.03 0.00 13.16 0.00 2.47 0.00 0.00 0.00

time (sec)

N/A 0.275 0.000 4.127 0.000 1.044 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 98 189 111 0 1252 0 0 0

N.S.

1 1.00 1.93 1.13 0.00 12.78 0.00 0.00 0.00

time (sec)

N/A 0.178 0.882 1.293 0.000 108.172 0.000 0.000 0.000

Problem 95

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

154 154 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 0.385 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 100 182 92 110 387 0 113 157

N.S.

1 1.04 1.90 0.96 1.15 4.03 0.00 1.18 1.64

time (sec)

N/A 0.207 0.370 0.911 0.286 0.263 0.000 3.121 0.611

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 88 114 95 0 253 0 0 0

N.S.

1 1.00 1.30 1.08 0.00 2.88 0.00 0.00 0.00

time (sec)

N/A 0.160 0.258 3.221 0.000 1.607 0.000 0.000 0.000

Problem 98

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

233 249 283 0 0 373 0 0 0

N.S.

1 1.07 1.21 0.00 0.00 1.60 0.00 0.00 0.00

time (sec)

N/A 0.369 0.775 0.000 0.000 1.485 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 86 104 80 86 90 0 87 100

N.S.

1 1.05 1.27 0.98 1.05 1.10 0.00 1.06 1.22

time (sec)

N/A 0.185 0.097 3.605 0.287 0.245 0.000 0.315 0.558

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

135 383 145 677 0 318 0 0 0

N.S.

1 2.84 1.07 5.01 0.00 2.36 0.00 0.00 0.00

time (sec)

N/A 0.540 1.163 6.457 0.000 5.537 0.000 0.000 0.000

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