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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

19 19 19 16 15 15 14 15 11

N.S.

1 1.00 1.00 0.84 0.79 0.79 0.74 0.79 0.58

time (sec)

N/A 0.145 0.002 0.023 0.197 0.290 0.042 0.296 0.229

Problem 2

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 19 19 16 15 15 14 15 11

N.S.

1 1.00 1.00 0.84 0.79 0.79 0.74 0.79 0.58

time (sec)

N/A 0.145 0.002 0.016 0.186 0.302 0.036 0.293 0.032

Problem 3

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 19 19 16 15 15 14 15 11

N.S.

1 1.00 1.00 0.84 0.79 0.79 0.74 0.79 0.58

time (sec)

N/A 0.141 0.002 0.014 0.189 0.274 0.036 0.291 0.033

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

10 10 10 11 16 10 7 16 8

N.S.

1 1.00 1.00 1.10 1.60 1.00 0.70 1.60 0.80

time (sec)

N/A 0.140 0.002 0.011 0.188 0.305 0.041 0.287 0.024

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

10 10 10 9 8 8 7 8 8

N.S.

1 1.00 1.00 0.90 0.80 0.80 0.70 0.80 0.80

time (sec)

N/A 0.144 0.002 0.027 0.185 0.314 0.036 0.312 0.257

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

15 15 15 13 15 11 10 15 11

N.S.

1 1.00 1.00 0.87 1.00 0.73 0.67 1.00 0.73

time (sec)

N/A 0.146 0.002 0.018 0.198 0.298 0.041 0.335 0.036

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

19 19 19 13 15 13 17 15 11

N.S.

1 1.00 1.00 0.68 0.79 0.68 0.89 0.79 0.58

time (sec)

N/A 0.142 0.002 0.019 0.178 0.292 0.045 0.336 0.025

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

32 37 32 27 21 26 26 26 21

N.S.

1 1.16 1.00 0.84 0.66 0.81 0.81 0.81 0.66

time (sec)

N/A 0.180 0.003 0.021 0.187 0.318 0.046 0.317 0.240

Problem 9

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

32 37 32 27 21 26 29 26 21

N.S.

1 1.16 1.00 0.84 0.66 0.81 0.91 0.81 0.66

time (sec)

N/A 0.182 0.002 0.019 0.186 0.310 0.046 0.320 0.234

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

32 32 32 27 21 26 26 26 21

N.S.

1 1.00 1.00 0.84 0.66 0.81 0.81 0.81 0.66

time (sec)

N/A 0.171 0.002 0.017 0.188 0.297 0.044 0.323 0.291

Problem 11

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 21 19 20 16 19 19 19 16

N.S.

1 1.11 1.00 1.05 0.84 1.00 1.00 1.00 0.84

time (sec)

N/A 0.163 0.002 0.014 0.185 0.313 0.044 0.299 0.250

Problem 12

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 10 10 9 8 8 7 8 8

N.S.

1 1.00 1.00 0.90 0.80 0.80 0.70 0.80 0.80

time (sec)

N/A 0.145 0.002 0.371 0.205 0.286 0.036 0.329 0.246

Problem 13

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 29 26 21 19 19 20 26 19

N.S.

1 1.12 1.00 0.81 0.73 0.73 0.77 1.00 0.73

time (sec)

N/A 0.179 0.002 0.020 0.186 0.296 0.050 0.297 0.297

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

32 32 32 21 21 21 29 26 21

N.S.

1 1.00 1.00 0.66 0.66 0.66 0.91 0.81 0.66

time (sec)

N/A 0.178 0.002 0.025 0.205 0.297 0.061 0.295 0.325

Problem 15

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

45 55 45 38 29 37 42 37 29

N.S.

1 1.22 1.00 0.84 0.64 0.82 0.93 0.82 0.64

time (sec)

N/A 0.221 0.003 0.026 0.192 0.332 0.056 0.299 0.307

Problem 16

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

45 50 45 38 29 37 41 37 29

N.S.

1 1.11 1.00 0.84 0.64 0.82 0.91 0.82 0.64

time (sec)

N/A 0.214 0.003 0.021 0.187 0.331 0.054 0.301 0.250

Problem 17

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

45 50 45 38 29 37 42 37 29

N.S.

1 1.11 1.00 0.84 0.64 0.82 0.93 0.82 0.64

time (sec)

N/A 0.204 0.002 0.017 0.186 0.320 0.053 0.311 0.275

Problem 18

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 32 28 29 24 28 29 28 24

N.S.

1 1.14 1.00 1.04 0.86 1.00 1.04 1.00 0.86

time (sec)

N/A 0.188 0.002 0.017 0.185 0.299 0.049 0.277 0.271

Problem 19

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 10 10 9 8 8 7 8 8

N.S.

1 1.00 1.00 0.90 0.80 0.80 0.70 0.80 0.80

time (sec)

N/A 0.147 0.002 0.218 0.221 0.302 0.036 0.315 0.245

Problem 20

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

37 43 37 29 27 27 31 37 27

N.S.

1 1.16 1.00 0.78 0.73 0.73 0.84 1.00 0.73

time (sec)

N/A 0.218 0.002 0.026 0.191 0.317 0.061 0.300 0.230

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

45 50 45 29 29 29 44 37 29

N.S.

1 1.11 1.00 0.64 0.64 0.64 0.98 0.82 0.64

time (sec)

N/A 0.215 0.002 0.025 0.189 0.313 0.075 0.291 0.252

Problem 22

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

11 11 11 14 11 12 0 11 0

N.S.

1 1.00 1.00 1.27 1.00 1.09 0.00 1.00 0.00

time (sec)

N/A 0.172 0.018 0.031 0.250 0.336 0.000 0.329 0.000

Problem 23

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

11 11 11 14 11 12 0 11 0

N.S.

1 1.00 1.00 1.27 1.00 1.09 0.00 1.00 0.00

time (sec)

N/A 0.173 0.018 0.016 0.243 0.286 0.000 0.298 0.000

Problem 24

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

11 11 11 14 11 12 0 11 0

N.S.

1 1.00 1.00 1.27 1.00 1.09 0.00 1.00 0.00

time (sec)

N/A 0.170 0.017 0.014 0.236 0.289 0.000 0.304 0.000

Problem 25

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 14 9 8 5 9 8

N.S.

1 1.00 1.00 1.75 1.12 1.00 0.62 1.12 1.00

time (sec)

N/A 0.135 0.007 0.016 0.232 0.301 0.162 0.279 0.204

Problem 26

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

5 5 5 6 5 5 5 5 5

N.S.

1 1.00 1.00 1.20 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.145 0.005 0.016 0.188 0.300 0.038 0.283 0.204

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 9 10 9 10 0 0 0

N.S.

1 1.00 1.00 1.11 1.00 1.11 0.00 0.00 0.00

time (sec)

N/A 0.170 0.018 0.019 0.227 0.277 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 14 11 12 0 0 0

N.S.

1 1.00 1.00 1.27 1.00 1.09 0.00 0.00 0.00

time (sec)

N/A 0.173 0.020 0.022 0.232 0.285 0.000 0.000 0.000

Problem 29

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

24 24 24 26 13 33 0 24 0

N.S.

1 1.00 1.00 1.08 0.54 1.38 0.00 1.00 0.00

time (sec)

N/A 0.208 0.019 0.027 0.237 0.290 0.000 0.284 0.000

Problem 30

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

24 24 24 26 13 33 0 24 0

N.S.

1 1.00 1.00 1.08 0.54 1.38 0.00 1.00 0.00

time (sec)

N/A 0.217 0.019 0.024 0.232 0.303 0.000 0.294 0.000

Problem 31

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

24 24 24 26 13 33 0 24 0

N.S.

1 1.00 1.00 1.08 0.54 1.38 0.00 1.00 0.00

time (sec)

N/A 0.200 0.018 0.023 0.232 0.291 0.000 0.325 0.000

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

18 18 18 24 12 25 12 19 18

N.S.

1 1.00 1.00 1.33 0.67 1.39 0.67 1.06 1.00

time (sec)

N/A 0.158 0.007 0.020 0.230 0.288 0.167 0.298 0.254

Problem 33

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 9 8 8 7 8 8

N.S.

1 1.00 1.00 1.12 1.00 1.00 0.88 1.00 1.00

time (sec)

N/A 0.142 0.002 0.018 0.188 0.295 0.032 0.301 0.243

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 22 21 9 28 0 0 0

N.S.

1 1.00 1.00 0.95 0.41 1.27 0.00 0.00 0.00

time (sec)

N/A 0.207 0.021 0.029 0.243 0.310 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 24 26 13 33 0 0 0

N.S.

1 1.00 1.00 1.08 0.54 1.38 0.00 0.00 0.00

time (sec)

N/A 0.213 0.022 0.027 0.242 0.327 0.000 0.000 0.000

Problem 36

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

37 40 37 34 13 47 0 35 0

N.S.

1 1.08 1.00 0.92 0.35 1.27 0.00 0.95 0.00

time (sec)

N/A 0.248 0.021 0.029 0.244 0.305 0.000 0.289 0.000

Problem 37

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

41 42 41 34 13 47 0 35 0

N.S.

1 1.02 1.00 0.83 0.32 1.15 0.00 0.85 0.00

time (sec)

N/A 0.249 0.022 0.028 0.234 0.280 0.000 0.328 0.000

Problem 38

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

37 37 37 34 13 47 0 35 0

N.S.

1 1.00 1.00 0.92 0.35 1.27 0.00 0.95 0.00

time (sec)

N/A 0.235 0.006 0.023 0.231 0.298 0.000 0.301 0.000

Problem 39

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

34 34 34 30 13 34 26 29 29

N.S.

1 1.00 1.00 0.88 0.38 1.00 0.76 0.85 0.85

time (sec)

N/A 0.184 0.010 0.021 0.233 0.268 0.191 0.323 0.287

Problem 40

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 10 10 9 8 8 10 8 8

N.S.

1 1.00 1.00 0.90 0.80 0.80 1.00 0.80 0.80

time (sec)

N/A 0.144 0.002 0.021 0.187 0.319 0.037 0.300 0.229

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 38 39 28 9 34 0 0 0

N.S.

1 0.97 1.00 0.72 0.23 0.87 0.00 0.00 0.00

time (sec)

N/A 0.245 0.020 0.030 0.236 0.319 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 36 34 13 41 0 0 0

N.S.

1 1.00 1.00 0.94 0.36 1.14 0.00 0.00 0.00

time (sec)

N/A 0.244 0.023 0.035 0.231 0.294 0.000 0.000 0.000

Problem 43

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

27 27 32 27 26 30 27 31 25

N.S.

1 1.00 1.19 1.00 0.96 1.11 1.00 1.15 0.93

time (sec)

N/A 0.153 0.003 0.119 0.193 0.311 0.233 0.292 0.299

Problem 44

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

27 27 32 27 26 30 27 31 25

N.S.

1 1.00 1.19 1.00 0.96 1.11 1.00 1.15 0.93

time (sec)

N/A 0.153 0.002 0.069 0.179 0.294 0.161 0.288 0.300

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

27 27 32 27 26 30 27 31 25

N.S.

1 1.00 1.19 1.00 0.96 1.11 1.00 1.15 0.93

time (sec)

N/A 0.147 0.002 0.075 0.178 0.299 0.119 0.331 0.269

Problem 46

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 19 18 22 15 20 18

N.S.

1 1.00 1.00 1.06 1.00 1.22 0.83 1.11 1.00

time (sec)

N/A 0.138 0.002 0.039 0.181 0.313 0.085 0.339 0.258

Problem 47

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

22 22 21 20 20 18 34 19 19

N.S.

1 1.00 0.95 0.91 0.91 0.82 1.55 0.86 0.86

time (sec)

N/A 0.151 0.002 0.094 0.175 0.327 1.536 0.311 0.245

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

23 23 26 19 26 19 19 24 23

N.S.

1 1.00 1.13 0.83 1.13 0.83 0.83 1.04 1.00

time (sec)

N/A 0.151 0.002 0.053 0.184 0.296 0.117 0.365 0.268

Problem 49

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

27 27 32 22 26 23 29 27 26

N.S.

1 1.00 1.19 0.81 0.96 0.85 1.07 1.00 0.96

time (sec)

N/A 0.152 0.002 0.061 0.186 0.312 0.222 0.342 0.295

Problem 50

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

52 53 43 73 71 102 78 111 61

N.S.

1 1.02 0.83 1.40 1.37 1.96 1.50 2.13 1.17

time (sec)

N/A 0.201 0.011 0.180 0.186 0.325 0.322 0.338 0.321

Problem 51

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

52 53 46 73 71 103 85 111 62

N.S.

1 1.02 0.88 1.40 1.37 1.98 1.63 2.13 1.19

time (sec)

N/A 0.203 0.015 0.142 0.181 0.299 0.225 0.319 0.326

Problem 52

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

52 51 41 72 70 102 76 108 60

N.S.

1 0.98 0.79 1.38 1.35 1.96 1.46 2.08 1.15

time (sec)

N/A 0.195 0.010 0.102 0.193 0.306 0.167 0.335 0.304

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

43 37 33 57 57 85 65 88 49

N.S.

1 0.86 0.77 1.33 1.33 1.98 1.51 2.05 1.14

time (sec)

N/A 0.172 0.007 0.102 0.181 0.310 0.126 0.358 0.285

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 22 21 20 51 60 56 37

N.S.

1 1.00 1.00 0.95 0.91 2.32 2.73 2.55 1.68

time (sec)

N/A 0.163 0.004 0.158 0.184 0.300 5.282 0.337 0.290

Problem 55

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

46 45 35 57 70 77 66 86 56

N.S.

1 0.98 0.76 1.24 1.52 1.67 1.43 1.87 1.22

time (sec)

N/A 0.206 0.010 0.109 0.184 0.285 0.127 0.347 0.319

Problem 56

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

52 50 41 59 71 83 78 90 62

N.S.

1 0.96 0.79 1.13 1.37 1.60 1.50 1.73 1.19

time (sec)

N/A 0.203 0.010 0.114 0.182 0.323 0.235 0.419 0.344

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 79 66 141 135 222 167 262 110

N.S.

1 1.03 0.86 1.83 1.75 2.88 2.17 3.40 1.43

time (sec)

N/A 0.265 0.023 0.397 0.189 0.314 0.450 0.303 0.374

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 67 139 134 224 156 256 108

N.S.

1 1.00 0.87 1.81 1.74 2.91 2.03 3.32 1.40

time (sec)

N/A 0.264 0.012 0.313 0.187 0.293 0.320 0.331 0.353

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 77 60 141 135 222 167 262 110

N.S.

1 1.00 0.78 1.83 1.75 2.88 2.17 3.40 1.43

time (sec)

N/A 0.241 0.022 0.243 0.189 0.301 0.237 0.343 0.367

Problem 60

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

66 56 50 119 113 198 133 219 94

N.S.

1 0.85 0.76 1.80 1.71 3.00 2.02 3.32 1.42

time (sec)

N/A 0.216 0.007 0.187 0.189 0.304 0.172 0.325 0.338

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 22 21 20 100 92 114 56

N.S.

1 1.00 1.00 0.95 0.91 4.55 4.18 5.18 2.55

time (sec)

N/A 0.165 0.004 0.384 0.182 0.291 7.271 0.320 0.310

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 67 52 113 133 180 134 197 104

N.S.

1 0.97 0.75 1.64 1.93 2.61 1.94 2.86 1.51

time (sec)

N/A 0.260 0.014 0.257 0.187 0.270 0.170 0.332 0.381

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 76 60 116 135 189 168 203 111

N.S.

1 0.99 0.78 1.51 1.75 2.45 2.18 2.64 1.44

time (sec)

N/A 0.261 0.017 0.276 0.190 0.307 0.251 0.350 0.412

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

77 76 60 116 136 191 158 204 110

N.S.

1 0.99 0.78 1.51 1.77 2.48 2.05 2.65 1.43

time (sec)

N/A 0.261 0.018 0.273 0.186 0.318 0.309 0.345 0.406

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

51 51 51 242 0 42 0 48 0

N.S.

1 1.00 1.00 4.75 0.00 0.82 0.00 0.94 0.00

time (sec)

N/A 0.226 0.047 0.378 0.000 0.288 0.000 0.349 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

51 51 51 242 0 42 0 48 0

N.S.

1 1.00 1.00 4.75 0.00 0.82 0.00 0.94 0.00

time (sec)

N/A 0.231 0.043 0.314 0.000 0.315 0.000 0.326 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

51 51 51 242 0 42 0 48 0

N.S.

1 1.00 1.00 4.75 0.00 0.82 0.00 0.94 0.00

time (sec)

N/A 0.228 0.046 0.283 0.000 0.285 0.000 0.339 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

48 48 48 240 0 39 0 42 0

N.S.

1 1.00 1.00 5.00 0.00 0.81 0.00 0.88 0.00

time (sec)

N/A 0.214 0.035 0.289 0.000 0.313 0.000 0.407 0.000

Problem 69

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

18 18 18 19 18 19 31 45 18

N.S.

1 1.00 1.00 1.06 1.00 1.06 1.72 2.50 1.00

time (sec)

N/A 0.171 0.038 0.091 0.181 0.292 0.363 0.414 0.301

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

48 48 48 236 0 41 0 0 0

N.S.

1 1.00 1.00 4.92 0.00 0.85 0.00 0.00 0.00

time (sec)

N/A 0.230 0.042 0.577 0.000 0.304 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

51 51 51 240 0 42 0 0 0

N.S.

1 1.00 1.00 4.71 0.00 0.82 0.00 0.00 0.00

time (sec)

N/A 0.227 0.042 0.406 0.000 0.293 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

51 51 51 242 0 42 0 0 0

N.S.

1 1.00 1.00 4.75 0.00 0.82 0.00 0.00 0.00

time (sec)

N/A 0.231 0.043 0.456 0.000 0.290 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

76 76 70 354 0 101 0 261 0

N.S.

1 1.00 0.92 4.66 0.00 1.33 0.00 3.43 0.00

time (sec)

N/A 0.292 0.086 0.347 0.000 0.301 0.000 0.375 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

76 76 70 354 0 101 0 261 0

N.S.

1 1.00 0.92 4.66 0.00 1.33 0.00 3.43 0.00

time (sec)

N/A 0.285 0.084 0.347 0.000 0.304 0.000 0.370 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

76 76 70 350 0 101 0 261 0

N.S.

1 1.00 0.92 4.61 0.00 1.33 0.00 3.43 0.00

time (sec)

N/A 0.273 0.084 0.342 0.000 0.289 0.000 0.362 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

70 70 66 350 0 95 0 238 0

N.S.

1 1.00 0.94 5.00 0.00 1.36 0.00 3.40 0.00

time (sec)

N/A 0.248 0.069 0.342 0.000 0.290 0.000 0.327 0.000

Problem 77

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

20 20 20 21 20 25 39 21 20

N.S.

1 1.00 1.00 1.05 1.00 1.25 1.95 1.05 1.00

time (sec)

N/A 0.163 0.005 0.117 0.189 0.299 0.867 0.322 0.269

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

73 73 76 347 0 88 0 0 0

N.S.

1 1.00 1.04 4.75 0.00 1.21 0.00 0.00 0.00

time (sec)

N/A 0.282 0.069 0.475 0.000 0.293 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

76 76 80 352 0 102 0 0 0

N.S.

1 1.00 1.05 4.63 0.00 1.34 0.00 0.00 0.00

time (sec)

N/A 0.281 0.066 0.503 0.000 0.307 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

76 76 80 354 0 102 0 0 0

N.S.

1 1.00 1.05 4.66 0.00 1.34 0.00 0.00 0.00

time (sec)

N/A 0.281 0.070 0.658 0.000 0.305 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

101 110 89 473 0 211 0 1029 0

N.S.

1 1.09 0.88 4.68 0.00 2.09 0.00 10.19 0.00

time (sec)

N/A 0.355 0.095 0.441 0.000 0.308 0.000 0.365 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

105 112 89 477 0 211 0 1029 0

N.S.

1 1.07 0.85 4.54 0.00 2.01 0.00 9.80 0.00

time (sec)

N/A 0.354 0.098 0.358 0.000 0.300 0.000 0.361 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

101 109 89 476 0 211 0 1029 0

N.S.

1 1.08 0.88 4.71 0.00 2.09 0.00 10.19 0.00

time (sec)

N/A 0.335 0.092 0.563 0.000 0.313 0.000 0.458 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

98 104 82 459 0 198 0 982 0

N.S.

1 1.06 0.84 4.68 0.00 2.02 0.00 10.02 0.00

time (sec)

N/A 0.305 0.076 0.388 0.000 0.300 0.000 0.420 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 22 21 20 62 61 21 39

N.S.

1 1.00 1.00 0.95 0.91 2.82 2.77 0.95 1.77

time (sec)

N/A 0.170 0.004 0.134 0.195 0.301 1.874 0.316 0.239

Problem 86

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

102 109 94 449 0 192 0 0 0

N.S.

1 1.07 0.92 4.40 0.00 1.88 0.00 0.00 0.00

time (sec)

N/A 0.357 0.065 0.681 0.000 0.308 0.000 0.000 0.000

Problem 87

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

100 110 89 454 0 221 0 0 0

N.S.

1 1.10 0.89 4.54 0.00 2.21 0.00 0.00 0.00

time (sec)

N/A 0.363 0.084 0.616 0.000 0.329 0.000 0.000 0.000

Problem 88

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

105 112 89 455 0 221 0 0 0

N.S.

1 1.07 0.85 4.33 0.00 2.10 0.00 0.00 0.00

time (sec)

N/A 0.367 0.080 0.854 0.000 0.292 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

41 41 29 128 41 50 48 117 0

N.S.

1 1.00 0.71 3.12 1.00 1.22 1.17 2.85 0.00

time (sec)

N/A 0.170 0.012 0.083 0.243 0.282 13.699 0.365 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

41 41 29 128 41 42 48 108 0

N.S.

1 1.00 0.71 3.12 1.00 1.02 1.17 2.63 0.00

time (sec)

N/A 0.172 0.009 0.033 0.213 0.280 1.846 0.332 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

41 41 29 124 41 32 48 105 0

N.S.

1 1.00 0.71 3.02 1.00 0.78 1.17 2.56 0.00

time (sec)

N/A 0.167 0.006 0.032 0.222 0.286 0.202 0.330 0.000

Problem 92

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

37 37 24 36 41 25 42 41 0

N.S.

1 1.00 0.65 0.97 1.11 0.68 1.14 1.11 0.00

time (sec)

N/A 0.173 0.006 0.027 0.205 0.282 0.235 0.304 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

37 37 24 122 41 28 44 43 0

N.S.

1 1.00 0.65 3.30 1.11 0.76 1.19 1.16 0.00

time (sec)

N/A 0.168 0.007 0.036 0.204 0.279 0.453 0.356 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

41 41 29 128 41 32 49 67 0

N.S.

1 1.00 0.71 3.12 1.00 0.78 1.20 1.63 0.00

time (sec)

N/A 0.170 0.007 0.039 0.203 0.299 2.140 0.329 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

73 74 61 716 102 141 119 425 0

N.S.

1 1.01 0.84 9.81 1.40 1.93 1.63 5.82 0.00

time (sec)

N/A 0.231 0.016 0.207 0.211 0.305 22.490 0.436 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

73 74 61 716 102 121 119 386 0

N.S.

1 1.01 0.84 9.81 1.40 1.66 1.63 5.29 0.00

time (sec)

N/A 0.230 0.014 0.076 0.214 0.298 3.229 0.429 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

73 74 61 710 102 99 119 383 0

N.S.

1 1.01 0.84 9.73 1.40 1.36 1.63 5.25 0.00

time (sec)

N/A 0.226 0.012 0.069 0.217 0.299 0.362 0.580 0.000

Problem 98

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

67 66 54 92 102 87 109 118 0

N.S.

1 0.99 0.81 1.37 1.52 1.30 1.63 1.76 0.00

time (sec)

N/A 0.230 0.011 0.064 0.203 0.295 0.331 0.322 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

67 66 54 707 101 87 110 149 0

N.S.

1 0.99 0.81 10.55 1.51 1.30 1.64 2.22 0.00

time (sec)

N/A 0.228 0.010 0.068 0.201 0.288 0.479 0.332 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

73 74 61 716 102 94 121 213 0

N.S.

1 1.01 0.84 9.81 1.40 1.29 1.66 2.92 0.00

time (sec)

N/A 0.230 0.011 0.072 0.205 0.300 2.126 0.327 0.000

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