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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 B F B F(-2) A F(-2) B B

verified

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

size

31 97 0 63 0 47 0 83 54

N.S.

1 3.13 0.00 2.03 0.00 1.52 0.00 2.68 1.74

time (sec)

N/A 6.036 0.000 4.148 0.000 0.256 0.000 0.328 13.334

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 49 56 13 41 12 10 12 12

N.S.

1 4.08 4.67 1.08 3.42 1.00 0.83 1.00 1.00

time (sec)

N/A 0.378 1.484 1.893 0.312 0.252 0.049 0.268 13.229

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A B A A A A B

verified

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

size

31 0 45 66 35 34 37 55 55

N.S.

1 0.00 1.45 2.13 1.13 1.10 1.19 1.77 1.77

time (sec)

N/A 0.000 0.066 6.899 0.315 0.252 0.276 0.424 13.643

Problem 4

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 8 8 9 8 8 7 8 8

N.S.

1 0.53 0.53 0.60 0.53 0.53 0.47 0.53 0.53

time (sec)

N/A 0.141 0.000 0.041 0.200 0.241 0.019 0.269 0.022

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 86 27 60 59 59 56 59 24

N.S.

1 3.44 1.08 2.40 2.36 2.36 2.24 2.36 0.96

time (sec)

N/A 0.306 0.178 0.134 0.194 0.261 0.072 0.267 13.065

Problem 6

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

31 6 6 5 4 4 5 5 4

N.S.

1 0.19 0.19 0.16 0.13 0.13 0.16 0.16 0.13

time (sec)

N/A 0.115 0.000 0.040 0.190 0.247 0.020 0.278 0.011

Problem 7

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

30 30 30 28 27 29 20 29 27

N.S.

1 1.00 1.00 0.93 0.90 0.97 0.67 0.97 0.90

time (sec)

N/A 2.668 0.086 0.645 0.343 0.262 0.146 0.303 13.733

Problem 8

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

29 22 22 21 22 22 20 24 22

N.S.

1 0.76 0.76 0.72 0.76 0.76 0.69 0.83 0.76

time (sec)

N/A 0.349 0.011 0.051 0.192 0.250 0.053 0.267 0.116

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

22 0 16 24 18 23 22 23 0

N.S.

1 0.00 0.73 1.09 0.82 1.05 1.00 1.05 0.00

time (sec)

N/A 0.000 5.227 1.251 0.312 0.249 0.087 0.329 0.000

Problem 10

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

21 19 20 19 17 18 15 19 17

N.S.

1 0.90 0.95 0.90 0.81 0.86 0.71 0.90 0.81

time (sec)

N/A 0.156 0.009 0.685 0.184 0.231 0.054 0.276 13.612

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 0 36 40 0 39 0 0 69

N.S.

1 0.00 1.20 1.33 0.00 1.30 0.00 0.00 2.30

time (sec)

N/A 0.000 0.298 210.643 0.000 0.251 0.000 0.000 14.020

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

28 0 33 26 33 28 22 33 25

N.S.

1 0.00 1.18 0.93 1.18 1.00 0.79 1.18 0.89

time (sec)

N/A 0.000 0.208 1.023 0.317 0.251 0.176 0.286 13.554

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 109 28 41 30 32 104 30 50

N.S.

1 3.63 0.93 1.37 1.00 1.07 3.47 1.00 1.67

time (sec)

N/A 2.498 1.743 0.454 0.247 0.267 0.154 0.283 13.199

Problem 14

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

24 21 24 23 40 37 29 22 34

N.S.

1 0.88 1.00 0.96 1.67 1.54 1.21 0.92 1.42

time (sec)

N/A 1.574 0.546 0.998 0.341 0.286 0.418 0.385 14.214

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 4620 46 41 304 76 44 83 50

N.S.

1 135.88 1.35 1.21 8.94 2.24 1.29 2.44 1.47

time (sec)

N/A 8.754 0.054 0.292 0.318 0.262 0.093 0.280 14.233

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A F A A A B

verified

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

size

20 0 28 24 0 28 34 32 34

N.S.

1 0.00 1.40 1.20 0.00 1.40 1.70 1.60 1.70

time (sec)

N/A 0.000 1.035 0.559 0.000 0.265 0.142 0.280 13.731

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 32 29 26 27 23 29 0 26

N.S.

1 1.14 1.04 0.93 0.96 0.82 1.04 0.00 0.93

time (sec)

N/A 0.271 3.808 1.006 0.272 0.260 0.097 0.000 0.716

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 62 51 69 76 59 66 76 85

N.S.

1 2.95 2.43 3.29 3.62 2.81 3.14 3.62 4.05

time (sec)

N/A 0.525 2.124 0.296 0.490 0.267 0.103 0.424 13.552

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 22 24 24 41 16 24 21 16

N.S.

1 1.29 1.41 1.41 2.41 0.94 1.41 1.24 0.94

time (sec)

N/A 0.444 0.046 0.513 0.239 0.281 0.151 0.273 13.841

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

17 0 17 16 15 34 0 0 15

N.S.

1 0.00 1.00 0.94 0.88 2.00 0.00 0.00 0.88

time (sec)

N/A 0.000 0.722 0.074 0.435 0.266 0.000 0.000 13.586

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

17 9 9 9 8 8 8 8 9

N.S.

1 0.53 0.53 0.53 0.47 0.47 0.47 0.47 0.53

time (sec)

N/A 0.142 0.025 0.125 0.217 0.246 0.030 0.266 13.422

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 0 46 147 75 45 46 0 45

N.S.

1 0.00 1.44 4.59 2.34 1.41 1.44 0.00 1.41

time (sec)

N/A 0.000 2.181 65.172 0.363 0.254 0.420 0.000 14.176

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

17 12 12 11 10 10 8 11 10

N.S.

1 0.71 0.71 0.65 0.59 0.59 0.47 0.65 0.59

time (sec)

N/A 0.139 0.004 0.424 0.202 0.248 0.032 0.264 0.034

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 41 35 40 0 39 36 0 38

N.S.

1 1.17 1.00 1.14 0.00 1.11 1.03 0.00 1.09

time (sec)

N/A 1.992 0.312 1.761 0.000 0.262 0.183 0.000 14.734

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 20 21 167 20 20 74 24

N.S.

1 1.00 0.87 0.91 7.26 0.87 0.87 3.22 1.04

time (sec)

N/A 0.235 0.032 0.458 0.292 0.241 0.120 0.267 13.159

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A F B

verified

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

size

26 0 27 26 39 23 29 0 26

N.S.

1 0.00 1.04 1.00 1.50 0.88 1.12 0.00 1.00

time (sec)

N/A 0.000 1.142 0.211 0.255 0.260 0.140 0.000 12.888

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 162 29 33 165 21 26 32 21

N.S.

1 7.71 1.38 1.57 7.86 1.00 1.24 1.52 1.00

time (sec)

N/A 0.515 0.147 4.171 0.511 0.264 0.094 0.291 0.371

Problem 28

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

20 12 12 9 8 8 10 9 8

N.S.

1 0.60 0.60 0.45 0.40 0.40 0.50 0.45 0.40

time (sec)

N/A 0.135 0.003 0.073 0.189 0.268 0.032 0.270 0.023

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 32 31 39 689 36 107 1346 38

N.S.

1 0.94 0.91 1.15 20.26 1.06 3.15 39.59 1.12

time (sec)

N/A 1.064 0.079 3.131 0.258 0.279 0.275 0.486 13.791

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 42 28 34 0 52 20 61 27

N.S.

1 1.35 0.90 1.10 0.00 1.68 0.65 1.97 0.87

time (sec)

N/A 1.154 0.216 0.238 0.000 0.257 0.123 0.271 13.287

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

28 0 36 65 1199 63 0 0 59

N.S.

1 0.00 1.29 2.32 42.82 2.25 0.00 0.00 2.11

time (sec)

N/A 0.000 0.154 65.769 1.016 0.259 0.000 0.000 14.733

Problem 32

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

23 22 28 31 32 35 27 32 22

N.S.

1 0.96 1.22 1.35 1.39 1.52 1.17 1.39 0.96

time (sec)

N/A 0.157 0.015 0.107 0.180 0.272 0.065 0.271 0.086

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

25 0 43 39 40 40 0 0 40

N.S.

1 0.00 1.72 1.56 1.60 1.60 0.00 0.00 1.60

time (sec)

N/A 0.000 1.192 4.104 0.382 0.241 0.000 0.000 13.446

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A B B A B B

verified

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

size

28 0 24 25 81 82 37 54 89

N.S.

1 0.00 0.86 0.89 2.89 2.93 1.32 1.93 3.18

time (sec)

N/A 0.000 0.464 0.760 0.299 0.256 0.071 0.289 13.082

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

17 0 17 15 26 25 19 15 14

N.S.

1 0.00 1.00 0.88 1.53 1.47 1.12 0.88 0.82

time (sec)

N/A 0.000 0.187 0.092 0.229 0.260 0.107 0.280 12.848

Problem 36

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

14 21 13 12 23 15 15 24 15

N.S.

1 1.50 0.93 0.86 1.64 1.07 1.07 1.71 1.07

time (sec)

N/A 0.325 0.020 0.500 0.313 0.252 0.060 0.292 13.544

Problem 37

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 27 26 26 24 26 28

N.S.

1 1.00 1.00 1.04 1.00 1.00 0.92 1.00 1.08

time (sec)

N/A 0.450 0.079 25.895 0.356 0.254 0.909 0.444 12.876

Problem 38

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 26 26 25 26 26 22 41 24

N.S.

1 1.18 1.18 1.14 1.18 1.18 1.00 1.86 1.09

time (sec)

N/A 2.085 0.041 0.493 0.326 0.251 0.096 0.300 12.841

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

30 0 75 31 47 47 32 49 0

N.S.

1 0.00 2.50 1.03 1.57 1.57 1.07 1.63 0.00

time (sec)

N/A 0.000 0.279 2.056 0.313 0.271 0.153 0.305 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A F A A A A A B

verified

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

size

27 32 0 33 31 32 39 34 30

N.S.

1 1.19 0.00 1.22 1.15 1.19 1.44 1.26 1.11

time (sec)

N/A 0.495 0.000 1.065 0.302 0.262 0.100 0.281 12.735

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 372 69 48 143 164 151 529 133

N.S.

1 15.50 2.88 2.00 5.96 6.83 6.29 22.04 5.54

time (sec)

N/A 0.945 0.054 0.667 0.186 0.260 2.174 0.306 13.439

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

34 0 27 23 29 29 19 29 22

N.S.

1 0.00 0.79 0.68 0.85 0.85 0.56 0.85 0.65

time (sec)

N/A 0.000 1.453 0.116 0.241 0.257 0.067 0.282 13.179

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

27 0 27 30 31 26 22 53 0

N.S.

1 0.00 1.00 1.11 1.15 0.96 0.81 1.96 0.00

time (sec)

N/A 0.000 2.468 0.799 0.253 0.260 0.102 0.350 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 0 26 266 21 49 0 0 97

N.S.

1 0.00 1.00 10.23 0.81 1.88 0.00 0.00 3.73

time (sec)

N/A 0.000 0.283 0.556 0.408 0.277 0.000 0.000 13.277

Problem 45

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

18 17 17 18 20 21 17 21 19

N.S.

1 0.94 0.94 1.00 1.11 1.17 0.94 1.17 1.06

time (sec)

N/A 0.179 0.005 0.105 0.194 0.238 0.065 0.262 0.041

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

26 0 25 25 23 36 20 23 0

N.S.

1 0.00 0.96 0.96 0.88 1.38 0.77 0.88 0.00

time (sec)

N/A 0.000 0.276 0.616 0.315 0.273 0.085 0.289 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 22 19 22 18 17 21 0

N.S.

1 1.00 1.22 1.06 1.22 1.00 0.94 1.17 0.00

time (sec)

N/A 0.530 0.580 9.306 0.329 0.253 0.330 0.340 0.000

Problem 48

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

28 29 30 24 23 23 26 23 25

N.S.

1 1.04 1.07 0.86 0.82 0.82 0.93 0.82 0.89

time (sec)

N/A 0.164 0.042 0.108 0.215 0.261 0.070 0.271 0.115

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

23 0 21 21 23 23 19 23 20

N.S.

1 0.00 0.91 0.91 1.00 1.00 0.83 1.00 0.87

time (sec)

N/A 0.000 1.275 0.090 0.223 0.247 0.047 0.268 12.932

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

22 0 27 28 27 29 34 29 27

N.S.

1 0.00 1.23 1.27 1.23 1.32 1.55 1.32 1.23

time (sec)

N/A 0.000 0.157 0.098 0.235 0.258 0.149 0.282 13.034

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 19 18 16 0 16 14 33 16

N.S.

1 1.06 1.00 0.89 0.00 0.89 0.78 1.83 0.89

time (sec)

N/A 0.172 0.024 0.331 0.000 0.255 0.103 0.282 0.076

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 18 18 17 137 16 19 137 16

N.S.

1 0.90 0.90 0.85 6.85 0.80 0.95 6.85 0.80

time (sec)

N/A 0.453 0.149 0.444 0.278 0.245 0.055 0.279 13.083

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 44 29 25 24 22 27 24 24

N.S.

1 2.59 1.71 1.47 1.41 1.29 1.59 1.41 1.41

time (sec)

N/A 0.206 0.009 0.132 0.178 0.249 0.064 0.261 14.201

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

15 11 7 8 7 7 5 7 5

N.S.

1 0.73 0.47 0.53 0.47 0.47 0.33 0.47 0.33

time (sec)

N/A 0.126 0.000 0.040 0.192 0.255 0.016 0.268 0.033

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

34 0 32 36 40 40 36 38 44

N.S.

1 0.00 0.94 1.06 1.18 1.18 1.06 1.12 1.29

time (sec)

N/A 0.000 5.155 0.872 0.233 0.259 3.206 0.337 14.418

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

24 0 33 30 32 32 34 32 0

N.S.

1 0.00 1.38 1.25 1.33 1.33 1.42 1.33 0.00

time (sec)

N/A 0.000 5.070 0.257 0.352 0.253 0.092 0.715 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 14 14 0 27 34 31 13

N.S.

1 1.00 0.78 0.78 0.00 1.50 1.89 1.72 0.72

time (sec)

N/A 0.220 0.145 0.207 0.000 0.260 0.081 0.270 13.775

Problem 58

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 13 12 12 11 11 10 11 8

N.S.

1 0.59 0.55 0.55 0.50 0.50 0.45 0.50 0.36

time (sec)

N/A 0.184 0.012 0.079 0.227 0.255 0.091 0.275 13.145

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A F B

verified

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

size

23 0 20 16 15 20 15 0 16

N.S.

1 0.00 0.87 0.70 0.65 0.87 0.65 0.00 0.70

time (sec)

N/A 0.000 0.210 0.246 0.561 0.264 0.161 0.000 0.189

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

19 0 19 17 39 39 17 39 17

N.S.

1 0.00 1.00 0.89 2.05 2.05 0.89 2.05 0.89

time (sec)

N/A 0.000 0.071 0.432 0.388 0.284 82.586 0.301 13.189

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

25 0 24 32 20 28 26 20 21

N.S.

1 0.00 0.96 1.28 0.80 1.12 1.04 0.80 0.84

time (sec)

N/A 0.000 0.937 0.558 0.288 0.254 0.117 0.392 13.417

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A F B

verified

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

size

15 0 15 15 14 14 12 0 14

N.S.

1 0.00 1.00 1.00 0.93 0.93 0.80 0.00 0.93

time (sec)

N/A 0.000 0.391 0.852 0.317 0.257 0.668 0.000 13.628

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 17 17 27 26 26 24 26 0

N.S.

1 0.81 0.81 1.29 1.24 1.24 1.14 1.24 0.00

time (sec)

N/A 0.520 0.106 0.120 0.228 0.264 0.066 0.271 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

32 0 85 62 184 115 0 117 82

N.S.

1 0.00 2.66 1.94 5.75 3.59 0.00 3.66 2.56

time (sec)

N/A 0.000 0.363 3.192 2.974 0.265 0.000 0.996 16.596

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 45 27 23 231 31 26 31 29

N.S.

1 1.61 0.96 0.82 8.25 1.11 0.93 1.11 1.04

time (sec)

N/A 0.321 0.352 0.273 0.324 0.269 0.084 0.285 13.182

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

33 0 26 39 35 40 37 42 32

N.S.

1 0.00 0.79 1.18 1.06 1.21 1.12 1.27 0.97

time (sec)

N/A 0.000 0.168 96.027 0.245 0.257 0.530 0.381 13.084

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A B B

verified

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

size

23 0 21 20 20 18 17 43 18

N.S.

1 0.00 0.91 0.87 0.87 0.78 0.74 1.87 0.78

time (sec)

N/A 0.000 0.467 0.721 0.252 0.262 0.127 0.279 12.791

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 21 22 21 0 20 15 0 21

N.S.

1 0.95 1.00 0.95 0.00 0.91 0.68 0.00 0.95

time (sec)

N/A 0.553 0.149 0.316 0.000 0.249 0.085 0.000 12.966

Problem 69

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

8 8 8 8 7 7 7 7 7

N.S.

1 1.00 1.00 1.00 0.88 0.88 0.88 0.88 0.88

time (sec)

N/A 0.191 0.024 0.133 0.191 0.253 0.053 0.289 13.247

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

26 0 26 22 31 37 20 24 21

N.S.

1 0.00 1.00 0.85 1.19 1.42 0.77 0.92 0.81

time (sec)

N/A 0.000 0.033 0.128 0.253 0.261 0.153 0.293 0.156

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F F B B A B F B

verified

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

size

33 0 0 113 263 53 53 0 53

N.S.

1 0.00 0.00 3.42 7.97 1.61 1.61 0.00 1.61

time (sec)

N/A 0.000 0.000 2.333 0.355 0.266 0.254 0.000 13.838

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F B A A A A A B

verified

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

size

32 0 113 27 28 26 41 39 27

N.S.

1 0.00 3.53 0.84 0.88 0.81 1.28 1.22 0.84

time (sec)

N/A 0.000 5.424 0.697 0.272 0.256 0.652 0.326 13.797

Problem 73

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

10 4 4 5 4 4 3 5 4

N.S.

1 0.40 0.40 0.50 0.40 0.40 0.30 0.50 0.40

time (sec)

N/A 0.135 0.001 0.031 0.193 0.239 0.031 0.287 0.016

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B B C A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 74 62 57 72 55 73 59 51

N.S.

1 2.55 2.14 1.97 2.48 1.90 2.52 2.03 1.76

time (sec)

N/A 0.364 4.039 0.107 0.229 0.250 0.093 0.282 12.681

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A F B

verified

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

size

29 0 42 27 31 34 36 0 37

N.S.

1 0.00 1.45 0.93 1.07 1.17 1.24 0.00 1.28

time (sec)

N/A 0.000 0.540 0.842 0.335 0.265 0.096 0.000 13.130

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A B A F B

verified

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

size

29 0 28 23 22 50 19 0 23

N.S.

1 0.00 0.97 0.79 0.76 1.72 0.66 0.00 0.79

time (sec)

N/A 0.000 0.648 0.266 0.397 0.259 0.263 0.000 13.099

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 19 19 16 56 17 15 17 15

N.S.

1 0.79 0.79 0.67 2.33 0.71 0.62 0.71 0.62

time (sec)

N/A 0.272 0.160 0.349 0.232 0.258 0.064 0.278 12.652

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 23 63 132 48 70 0 36

N.S.

1 1.00 1.00 2.74 5.74 2.09 3.04 0.00 1.57

time (sec)

N/A 0.487 0.026 0.656 0.309 0.253 0.197 0.000 13.297

Problem 79

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 28 19 14 16 28 14 14 13

N.S.

1 1.27 0.86 0.64 0.73 1.27 0.64 0.64 0.59

time (sec)

N/A 0.231 0.012 0.031 0.210 0.230 0.044 0.285 14.090

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 140 51 50 52 56 60 82 48

N.S.

1 5.19 1.89 1.85 1.93 2.07 2.22 3.04 1.78

time (sec)

N/A 1.437 0.049 0.120 0.242 0.250 0.153 0.279 14.390

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 176 20 31 1945 102 56 59 61

N.S.

1 7.65 0.87 1.35 84.57 4.43 2.43 2.57 2.65

time (sec)

N/A 0.897 0.048 0.187 0.326 0.261 0.110 0.275 14.184

Problem 82

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

18 18 18 17 16 16 14 17 16

N.S.

1 1.00 1.00 0.94 0.89 0.89 0.78 0.94 0.89

time (sec)

N/A 0.188 0.008 0.073 0.207 0.245 0.049 0.281 0.081

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A B A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 69 60 56 47 65 58 47 54

N.S.

1 2.30 2.00 1.87 1.57 2.17 1.93 1.57 1.80

time (sec)

N/A 1.267 0.126 1.044 0.582 0.249 0.136 0.295 13.745

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

28 0 36 37 106 31 20 31 0

N.S.

1 0.00 1.29 1.32 3.79 1.11 0.71 1.11 0.00

time (sec)

N/A 0.000 0.136 5.176 0.326 0.253 0.203 0.300 0.000

Problem 85

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

21 16 16 15 16 16 15 18 10

N.S.

1 0.76 0.76 0.71 0.76 0.76 0.71 0.86 0.48

time (sec)

N/A 0.180 0.006 0.773 0.199 0.253 0.050 0.280 0.055

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A B B B B B B

verified

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

size

39 0 47 129 77 129 126 129 77

N.S.

1 0.00 1.21 3.31 1.97 3.31 3.23 3.31 1.97

time (sec)

N/A 0.000 0.188 13.522 0.311 0.270 0.345 4.787 14.267

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 72 73 66 153 60 63 65 65

N.S.

1 3.00 3.04 2.75 6.38 2.50 2.62 2.71 2.71

time (sec)

N/A 0.319 0.032 0.059 0.213 0.263 0.084 0.274 13.610

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 79 19 18 17 20 17 20 18

N.S.

1 4.16 1.00 0.95 0.89 1.05 0.89 1.05 0.95

time (sec)

N/A 0.262 0.024 0.190 0.287 0.259 0.116 0.276 13.820

Problem 89

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

17 17 15 14 13 13 10 14 13

N.S.

1 1.00 0.88 0.82 0.76 0.76 0.59 0.82 0.76

time (sec)

N/A 0.147 0.001 0.029 0.189 0.252 0.029 0.271 0.030

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 124 34 31 29 29 31 0 29

N.S.

1 4.96 1.36 1.24 1.16 1.16 1.24 0.00 1.16

time (sec)

N/A 0.742 0.123 0.335 0.683 0.256 0.097 0.000 14.110

Problem 91

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 16 16 17 16 16 15 16 16

N.S.

1 0.62 0.62 0.65 0.62 0.62 0.58 0.62 0.62

time (sec)

N/A 0.286 0.105 0.168 0.315 0.262 0.095 0.281 14.050

Problem 92

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

6 4 4 5 4 4 3 5 4

N.S.

1 0.67 0.67 0.83 0.67 0.67 0.50 0.83 0.67

time (sec)

N/A 0.118 0.000 0.048 0.180 0.247 0.022 0.285 0.010

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A F A A A A A A B

verified

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

size

26 0 28 28 33 27 24 34 29

N.S.

1 0.00 1.08 1.08 1.27 1.04 0.92 1.31 1.12

time (sec)

N/A 0.000 2.278 0.094 0.226 0.258 0.074 0.279 0.161

Problem 94

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

31 32 32 23 14 47 27 58 23

N.S.

1 1.03 1.03 0.74 0.45 1.52 0.87 1.87 0.74

time (sec)

N/A 1.083 5.079 0.417 0.247 0.256 0.150 0.281 0.356

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

29 0 42 36 33 33 0 33 28

N.S.

1 0.00 1.45 1.24 1.14 1.14 0.00 1.14 0.97

time (sec)

N/A 0.000 0.840 3.187 0.236 0.244 0.000 0.271 14.458

Problem 96

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

23 14 14 28 25 26 27 25 15

N.S.

1 0.61 0.61 1.22 1.09 1.13 1.17 1.09 0.65

time (sec)

N/A 0.151 0.010 0.084 0.190 0.255 0.073 0.264 13.737

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 37 27 24 0 23 20 23 0

N.S.

1 1.68 1.23 1.09 0.00 1.05 0.91 1.05 0.00

time (sec)

N/A 0.626 0.141 1.144 0.000 0.271 5.035 0.287 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 14 28 13 14 28 16

N.S.

1 1.00 1.00 0.78 1.56 0.72 0.78 1.56 0.89

time (sec)

N/A 0.143 0.005 0.115 0.190 0.248 0.050 0.270 13.499

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

25 0 24 29 72 72 70 92 0

N.S.

1 0.00 0.96 1.16 2.88 2.88 2.80 3.68 0.00

time (sec)

N/A 0.000 0.138 0.414 0.379 0.259 0.345 0.302 0.000

Problem 100

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

19 23 19 18 17 17 14 28 17

N.S.

1 1.21 1.00 0.95 0.89 0.89 0.74 1.47 0.89

time (sec)

N/A 0.467 0.256 10.214 0.240 0.248 0.056 0.299 13.354

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