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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 B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 18 19 24 29 61 26 18

N.S.

1 1.00 0.82 0.86 1.09 1.32 2.77 1.18 0.82

time (sec)

N/A 0.137 0.004 0.124 0.236 0.272 0.814 0.276 5.779

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

16 16 16 13 15 12 12 10 10

N.S.

1 1.00 1.00 0.81 0.94 0.75 0.75 0.62 0.62

time (sec)

N/A 0.131 0.002 0.065 0.225 0.260 0.099 0.282 5.870

Problem 3

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

16 16 16 13 13 12 12 10 0

N.S.

1 1.00 1.00 0.81 0.81 0.75 0.75 0.62 0.00

time (sec)

N/A 0.131 0.001 0.051 0.220 0.234 0.082 0.291 0.000

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

16 16 16 13 12 12 12 10 10

N.S.

1 1.00 1.00 0.81 0.75 0.75 0.75 0.62 0.62

time (sec)

N/A 0.130 0.001 0.073 0.207 0.232 0.071 0.266 5.522

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

14 14 14 11 10 10 10 10 8

N.S.

1 1.00 1.00 0.79 0.71 0.71 0.71 0.71 0.57

time (sec)

N/A 0.126 0.001 0.044 0.200 0.255 0.062 0.266 5.772

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 9 8 0 7 7 7 6

N.S.

1 1.00 1.00 0.89 0.00 0.78 0.78 0.78 0.67

time (sec)

N/A 0.130 0.002 0.050 0.000 0.270 0.062 0.277 5.742

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 14 14 14 0 13 12 9 0

N.S.

1 0.93 0.93 0.93 0.00 0.87 0.80 0.60 0.00

time (sec)

N/A 0.128 0.001 0.048 0.000 0.268 0.260 0.293 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 12 14 13 0 12 12 10 10

N.S.

1 0.86 1.00 0.93 0.00 0.86 0.86 0.71 0.71

time (sec)

N/A 0.129 0.002 0.050 0.000 0.266 0.160 0.282 5.804

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 17 16 13 0 12 14 10 13

N.S.

1 1.06 1.00 0.81 0.00 0.75 0.88 0.62 0.81

time (sec)

N/A 0.127 0.001 0.047 0.000 0.269 0.163 0.263 5.797

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 13 0 12 14 10 10

N.S.

1 1.00 1.00 0.81 0.00 0.75 0.88 0.62 0.62

time (sec)

N/A 0.130 0.002 0.054 0.000 0.266 0.175 0.304 5.768

Problem 11

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

14 12 12 8 8 5 10 7 0

N.S.

1 0.86 0.86 0.57 0.57 0.36 0.71 0.50 0.00

time (sec)

N/A 0.121 0.003 0.048 0.240 0.252 0.079 0.283 0.000

Problem 12

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

17 16 16 13 13 13 12 10 0

N.S.

1 0.94 0.94 0.76 0.76 0.76 0.71 0.59 0.00

time (sec)

N/A 0.126 0.001 0.054 0.205 0.250 0.152 0.277 0.000

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

17 16 16 13 12 13 12 10 10

N.S.

1 0.94 0.94 0.76 0.71 0.76 0.71 0.59 0.59

time (sec)

N/A 0.130 0.001 0.079 0.277 0.259 0.128 0.268 5.427

Problem 14

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

17 14 14 11 10 13 10 10 0

N.S.

1 0.82 0.82 0.65 0.59 0.76 0.59 0.59 0.00

time (sec)

N/A 0.123 0.001 0.048 0.216 0.240 0.113 0.291 0.000

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

17 13 17 10 9 13 8 10 10

N.S.

1 0.76 1.00 0.59 0.53 0.76 0.47 0.59 0.59

time (sec)

N/A 0.126 0.001 0.059 0.224 0.252 0.104 0.283 5.680

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 12 0 11 10 10 8

N.S.

1 1.00 1.00 0.80 0.00 0.73 0.67 0.67 0.53

time (sec)

N/A 0.126 0.001 0.049 0.000 0.238 0.106 0.282 5.641

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 10 0 9 10 7 6

N.S.

1 1.00 1.00 0.91 0.00 0.82 0.91 0.64 0.55

time (sec)

N/A 0.134 0.013 0.054 0.000 0.237 0.197 0.283 5.701

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 15 14 0 14 14 9 0

N.S.

1 1.00 0.94 0.88 0.00 0.88 0.88 0.56 0.00

time (sec)

N/A 0.127 0.001 0.051 0.000 0.252 0.323 0.277 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 14 14 13 0 13 12 10 10

N.S.

1 0.93 0.93 0.87 0.00 0.87 0.80 0.67 0.67

time (sec)

N/A 0.130 0.001 0.052 0.000 0.260 0.212 0.285 5.573

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 16 13 0 13 14 10 13

N.S.

1 1.00 0.94 0.76 0.00 0.76 0.82 0.59 0.76

time (sec)

N/A 0.137 0.001 0.052 0.000 0.240 0.239 0.272 5.551

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 16 16 13 0 13 14 10 10

N.S.

1 0.94 0.94 0.76 0.00 0.76 0.82 0.59 0.59

time (sec)

N/A 0.137 0.001 0.057 0.000 0.242 0.269 0.297 5.405

Problem 22

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

14 12 12 9 8 5 8 7 0

N.S.

1 0.86 0.86 0.64 0.57 0.36 0.57 0.50 0.00

time (sec)

N/A 0.124 0.003 0.037 0.214 0.248 0.199 0.279 0.000

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

19 16 16 13 12 15 12 10 10

N.S.

1 0.84 0.84 0.68 0.63 0.79 0.63 0.53 0.53

time (sec)

N/A 0.128 0.001 0.085 0.231 0.261 0.226 0.275 5.742

Problem 24

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

19 14 14 11 10 15 10 10 0

N.S.

1 0.74 0.74 0.58 0.53 0.79 0.53 0.53 0.00

time (sec)

N/A 0.128 0.001 0.050 0.204 0.269 0.198 0.302 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

19 13 17 10 9 15 8 10 10

N.S.

1 0.68 0.89 0.53 0.47 0.79 0.42 0.53 0.53

time (sec)

N/A 0.130 0.001 0.063 0.203 0.251 0.188 0.295 5.618

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

19 15 15 13 12 15 10 10 13

N.S.

1 0.79 0.79 0.68 0.63 0.79 0.53 0.53 0.68

time (sec)

N/A 0.128 0.001 0.055 0.199 0.234 0.191 0.287 5.585

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 14 16 13 0 15 12 10 10

N.S.

1 0.74 0.84 0.68 0.00 0.79 0.63 0.53 0.53

time (sec)

N/A 0.131 0.002 0.065 0.000 0.239 0.259 0.284 5.578

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 17 13 0 13 12 10 8

N.S.

1 1.00 1.00 0.76 0.00 0.76 0.71 0.59 0.47

time (sec)

N/A 0.130 0.001 0.061 0.000 0.281 0.253 0.279 5.580

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 13 12 0 11 10 7 6

N.S.

1 1.00 1.00 0.92 0.00 0.85 0.77 0.54 0.46

time (sec)

N/A 0.132 0.015 0.064 0.000 0.247 0.257 0.286 5.584

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 16 15 14 0 16 14 9 0

N.S.

1 0.89 0.83 0.78 0.00 0.89 0.78 0.50 0.00

time (sec)

N/A 0.133 0.001 0.068 0.000 0.240 0.442 0.268 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 14 14 13 0 15 12 10 10

N.S.

1 0.82 0.82 0.76 0.00 0.88 0.71 0.59 0.59

time (sec)

N/A 0.135 0.002 0.076 0.000 0.244 0.317 0.263 5.513

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 17 16 13 0 15 14 10 13

N.S.

1 0.89 0.84 0.68 0.00 0.79 0.74 0.53 0.68

time (sec)

N/A 0.126 0.001 0.087 0.000 0.236 0.345 0.263 5.553

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 16 16 13 0 15 14 10 10

N.S.

1 0.84 0.84 0.68 0.00 0.79 0.74 0.53 0.53

time (sec)

N/A 0.132 0.002 0.103 0.000 0.267 0.388 0.285 5.439

Problem 34

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

14 12 12 9 8 5 8 7 0

N.S.

1 0.86 0.86 0.64 0.57 0.36 0.57 0.50 0.00

time (sec)

N/A 0.119 0.002 0.039 0.206 0.255 0.334 0.283 0.000

Problem 35

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

16 16 16 13 15 15 12 12 10

N.S.

1 1.00 1.00 0.81 0.94 0.94 0.75 0.75 0.62

time (sec)

N/A 0.135 0.001 0.056 0.185 0.248 0.194 0.260 5.487

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

13 13 13 12 11 11 10 9 6

N.S.

1 1.00 1.00 0.92 0.85 0.85 0.77 0.69 0.46

time (sec)

N/A 0.131 0.001 0.071 0.192 0.235 0.179 0.268 5.478

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

11 11 15 10 8 15 10 12 10

N.S.

1 1.00 1.36 0.91 0.73 1.36 0.91 1.09 0.91

time (sec)

N/A 0.132 0.002 0.053 0.195 0.239 0.184 0.297 5.426

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

16 14 16 13 8 15 15 12 10

N.S.

1 0.88 1.00 0.81 0.50 0.94 0.94 0.75 0.62

time (sec)

N/A 0.134 0.002 0.053 0.188 0.475 0.216 0.273 5.442

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

16 17 16 13 8 13 12 12 11

N.S.

1 1.06 1.00 0.81 0.50 0.81 0.75 0.75 0.69

time (sec)

N/A 0.127 0.001 0.322 0.189 0.263 0.180 0.267 5.560

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

13 13 13 12 6 16 12 19 10

N.S.

1 1.00 1.00 0.92 0.46 1.23 0.92 1.46 0.77

time (sec)

N/A 0.128 0.000 0.043 0.195 0.241 0.205 0.284 5.753

Problem 41

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

16 16 15 13 8 15 14 12 13

N.S.

1 1.00 0.94 0.81 0.50 0.94 0.88 0.75 0.81

time (sec)

N/A 0.133 0.001 0.046 0.201 0.235 0.200 0.293 6.187

Problem 42

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 16 16 13 15 15 12 12 10

N.S.

1 0.84 0.84 0.68 0.79 0.79 0.63 0.63 0.53

time (sec)

N/A 0.132 0.001 0.057 0.194 0.257 0.228 0.302 6.045

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

16 13 13 12 14 11 10 9 6

N.S.

1 0.81 0.81 0.75 0.88 0.69 0.62 0.56 0.38

time (sec)

N/A 0.134 0.011 0.049 0.223 0.264 0.199 0.297 6.129

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

14 14 14 13 12 15 12 12 10

N.S.

1 1.00 1.00 0.93 0.86 1.07 0.86 0.86 0.71

time (sec)

N/A 0.130 0.001 0.143 0.211 0.235 0.195 0.298 5.992

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

19 13 17 10 8 15 12 12 10

N.S.

1 0.68 0.89 0.53 0.42 0.79 0.63 0.63 0.53

time (sec)

N/A 0.129 0.002 0.064 0.200 0.246 0.212 0.307 5.819

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

19 14 16 13 8 15 15 12 10

N.S.

1 0.74 0.84 0.68 0.42 0.79 0.79 0.63 0.53

time (sec)

N/A 0.133 0.002 0.057 0.207 0.245 0.242 0.282 5.741

Problem 47

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

19 17 16 13 15 15 12 12 0

N.S.

1 0.89 0.84 0.68 0.79 0.79 0.63 0.63 0.00

time (sec)

N/A 0.131 0.002 0.055 0.224 0.236 0.245 0.284 0.000

Problem 48

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

19 17 16 13 15 13 12 12 0

N.S.

1 0.89 0.84 0.68 0.79 0.68 0.63 0.63 0.00

time (sec)

N/A 0.134 0.001 0.049 0.198 0.235 0.218 0.294 0.000

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

16 16 15 14 6 16 14 11 37

N.S.

1 1.00 0.94 0.88 0.38 1.00 0.88 0.69 2.31

time (sec)

N/A 0.137 0.001 0.045 0.199 0.277 0.270 0.286 0.061

Problem 50

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 14 14 11 8 15 12 12 13

N.S.

1 0.74 0.74 0.58 0.42 0.79 0.63 0.63 0.68

time (sec)

N/A 0.130 0.000 0.045 0.189 0.252 0.206 0.283 5.707

Problem 51

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 16 15 13 8 15 14 12 13

N.S.

1 0.84 0.79 0.68 0.42 0.79 0.74 0.63 0.68

time (sec)

N/A 0.130 0.001 0.057 0.189 0.235 0.234 0.274 5.814

Problem 52

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 16 16 13 15 15 12 12 10

N.S.

1 0.84 0.84 0.68 0.79 0.79 0.63 0.63 0.53

time (sec)

N/A 0.133 0.001 0.060 0.194 0.254 0.291 0.272 5.641

Problem 53

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

16 13 13 12 14 11 10 9 6

N.S.

1 0.81 0.81 0.75 0.88 0.69 0.62 0.56 0.38

time (sec)

N/A 0.132 0.012 0.052 0.194 0.254 0.242 0.277 5.757

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

14 14 14 13 15 15 12 12 10

N.S.

1 1.00 1.00 0.93 1.07 1.07 0.86 0.86 0.71

time (sec)

N/A 0.133 0.001 0.053 0.194 0.252 0.249 0.269 5.793

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

19 16 16 13 12 15 14 12 10

N.S.

1 0.84 0.84 0.68 0.63 0.79 0.74 0.63 0.53

time (sec)

N/A 0.133 0.001 0.074 0.197 0.267 0.239 0.273 5.765

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

19 13 17 10 8 15 12 12 10

N.S.

1 0.68 0.89 0.53 0.42 0.79 0.63 0.63 0.53

time (sec)

N/A 0.131 0.002 0.062 0.189 0.257 0.264 0.262 5.867

Problem 57

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

19 17 16 13 15 13 12 12 0

N.S.

1 0.89 0.84 0.68 0.79 0.68 0.63 0.63 0.00

time (sec)

N/A 0.126 0.001 0.054 0.202 0.248 0.260 0.267 0.000

Problem 58

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

16 16 15 14 6 16 14 11 0

N.S.

1 1.00 0.94 0.88 0.38 1.00 0.88 0.69 0.00

time (sec)

N/A 0.125 0.001 0.051 0.195 0.252 0.330 0.279 0.000

Problem 59

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 17 16 13 8 15 14 12 13

N.S.

1 0.89 0.84 0.68 0.42 0.79 0.74 0.63 0.68

time (sec)

N/A 0.130 0.004 0.049 0.199 0.283 0.242 0.268 5.435

Problem 60

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 14 14 11 8 15 12 12 13

N.S.

1 0.74 0.74 0.58 0.42 0.79 0.63 0.63 0.68

time (sec)

N/A 0.126 0.000 0.049 0.197 0.406 0.244 0.276 5.421

Problem 61

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 16 15 13 8 15 14 12 13

N.S.

1 0.84 0.79 0.68 0.42 0.79 0.74 0.63 0.68

time (sec)

N/A 0.128 0.002 0.053 0.205 0.273 0.284 0.288 5.401

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 21 20 18 22 37 0 22

N.S.

1 1.00 0.72 0.69 0.62 0.76 1.28 0.00 0.76

time (sec)

N/A 0.144 0.003 0.022 0.204 0.275 0.994 0.000 5.449

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 28 21 20 18 19 36 0 20

N.S.

1 1.00 0.75 0.71 0.64 0.68 1.29 0.00 0.71

time (sec)

N/A 0.143 0.003 0.021 0.207 0.277 0.397 0.000 5.311

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 19 18 13 22 29 0 18

N.S.

1 1.00 1.00 0.95 0.68 1.16 1.53 0.00 0.95

time (sec)

N/A 0.138 0.003 0.025 0.212 0.289 0.411 0.000 5.336

Problem 65

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

32 32 21 20 18 29 44 0 22

N.S.

1 1.00 0.66 0.62 0.56 0.91 1.38 0.00 0.69

time (sec)

N/A 0.144 0.005 0.030 0.204 0.296 0.595 0.000 5.370

Problem 66

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

21 21 21 21 24 24 42 24 21

N.S.

1 1.00 1.00 1.00 1.14 1.14 2.00 1.14 1.00

time (sec)

N/A 0.141 0.004 0.095 0.215 0.265 0.472 0.297 5.416

Problem 67

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 26 22 23 27 32 46 29 22

N.S.

1 1.18 1.00 1.05 1.23 1.45 2.09 1.32 1.00

time (sec)

N/A 0.146 0.002 0.116 0.205 0.259 0.468 0.284 5.295

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 13 13 21 2 2 17 0 0

N.S.

1 1.00 1.00 1.62 0.15 0.15 1.31 0.00 0.00

time (sec)

N/A 0.137 0.008 0.069 0.198 0.289 0.337 0.000 0.000

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

19 21 18 18 18 17 22 17 18

N.S.

1 1.11 0.95 0.95 0.95 0.89 1.16 0.89 0.95

time (sec)

N/A 0.151 0.002 0.036 0.211 0.266 0.122 0.276 5.344

Problem 70

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

18 18 18 19 19 18 32 18 18

N.S.

1 1.00 1.00 1.06 1.06 1.00 1.78 1.00 1.00

time (sec)

N/A 0.143 0.002 0.031 0.194 0.261 0.334 0.279 5.338

Problem 71

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 18 18 19 17 20 19 18

N.S.

1 1.11 0.95 0.95 1.00 0.89 1.05 1.00 0.95

time (sec)

N/A 0.147 0.002 0.030 0.192 0.291 0.087 0.274 5.434

Problem 72

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

16 16 16 17 17 16 29 16 16

N.S.

1 1.00 1.00 1.06 1.06 1.00 1.81 1.00 1.00

time (sec)

N/A 0.139 0.001 0.023 0.205 0.364 0.257 0.279 5.394

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

14 14 14 13 13 12 12 12 12

N.S.

1 1.00 1.00 0.93 0.93 0.86 0.86 0.86 0.86

time (sec)

N/A 0.137 0.001 0.030 0.199 0.268 0.081 0.275 5.290

Problem 74

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

19 19 18 19 19 18 27 0 18

N.S.

1 1.00 0.95 1.00 1.00 0.95 1.42 0.00 0.95

time (sec)

N/A 0.139 0.003 0.034 0.200 0.282 0.391 0.000 5.401

Problem 75

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

21 21 18 18 18 17 22 0 18

N.S.

1 1.00 0.86 0.86 0.86 0.81 1.05 0.00 0.86

time (sec)

N/A 0.147 0.002 0.039 0.195 0.255 0.180 0.000 5.432

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 18 19 19 18 34 0 18

N.S.

1 1.00 0.95 1.00 1.00 0.95 1.79 0.00 0.95

time (sec)

N/A 0.142 0.002 0.043 0.195 0.248 0.528 0.000 5.428

Problem 77

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 14 14 9 10 10 12 12 10

N.S.

1 1.00 1.00 0.64 0.71 0.71 0.86 0.86 0.71

time (sec)

N/A 0.136 0.002 0.109 0.217 0.237 0.066 0.269 5.814

Problem 78

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 14 14 11 10 10 10 10 8

N.S.

1 1.00 1.00 0.79 0.71 0.71 0.71 0.71 0.57

time (sec)

N/A 0.141 0.000 0.039 0.195 0.247 0.063 0.285 0.002

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

14 14 12 9 10 8 10 8 10

N.S.

1 1.00 0.86 0.64 0.71 0.57 0.71 0.57 0.71

time (sec)

N/A 0.134 0.001 0.043 0.202 0.244 0.018 0.267 0.024

Problem 80

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

12 12 12 11 10 10 8 9 10

N.S.

1 1.00 1.00 0.92 0.83 0.83 0.67 0.75 0.83

time (sec)

N/A 0.138 0.001 0.045 0.202 0.259 0.065 0.276 5.307

Problem 81

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

13 13 13 12 11 11 12 9 0

N.S.

1 1.00 1.00 0.92 0.85 0.85 0.92 0.69 0.00

time (sec)

N/A 0.138 0.001 0.045 0.200 0.348 0.247 0.265 0.000

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

12 12 12 11 10 10 12 8 10

N.S.

1 1.00 1.00 0.92 0.83 0.83 1.00 0.67 0.83

time (sec)

N/A 0.130 0.001 0.046 0.199 0.256 0.133 0.267 5.464

Problem 83

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 14 14 11 10 13 12 13 10

N.S.

1 0.82 0.82 0.65 0.59 0.76 0.71 0.76 0.59

time (sec)

N/A 0.128 0.001 0.099 0.208 0.261 0.118 0.279 5.432

Problem 84

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

17 14 14 11 10 13 10 10 0

N.S.

1 0.82 0.82 0.65 0.59 0.76 0.59 0.59 0.00

time (sec)

N/A 0.129 0.000 0.043 0.192 0.264 0.111 0.281 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

14 14 12 9 10 11 10 11 10

N.S.

1 1.00 0.86 0.64 0.71 0.79 0.71 0.79 0.71

time (sec)

N/A 0.130 0.001 0.041 0.197 0.248 0.016 0.277 0.015

Problem 86

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

12 12 12 11 10 10 10 12 10

N.S.

1 1.00 1.00 0.92 0.83 0.83 0.83 1.00 0.83

time (sec)

N/A 0.129 0.001 0.031 0.194 0.323 0.110 0.276 5.396

Problem 87

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 14 14 11 10 13 12 10 13

N.S.

1 0.82 0.82 0.65 0.59 0.76 0.71 0.59 0.76

time (sec)

N/A 0.130 0.001 0.033 0.208 0.249 0.189 0.267 5.360

Problem 88

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 14 14 11 10 13 14 13 13

N.S.

1 0.82 0.82 0.65 0.59 0.76 0.82 0.76 0.76

time (sec)

N/A 0.132 0.001 0.040 0.227 0.253 0.174 0.283 5.277

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

12 12 12 11 10 15 12 11 15

N.S.

1 1.00 1.00 0.92 0.83 1.25 1.00 0.92 1.25

time (sec)

N/A 0.129 0.001 0.094 0.201 0.264 0.176 0.269 5.306

Problem 90

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

13 13 13 12 6 16 12 19 10

N.S.

1 1.00 1.00 0.92 0.46 1.23 0.92 1.46 0.77

time (sec)

N/A 0.135 0.001 0.036 0.196 0.336 0.202 0.283 0.002

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

12 12 10 9 10 10 8 10 10

N.S.

1 1.00 0.83 0.75 0.83 0.83 0.67 0.83 0.83

time (sec)

N/A 0.129 0.001 0.041 0.201 0.283 0.017 0.277 0.014

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

14 14 14 11 10 15 10 15 15

N.S.

1 1.00 1.00 0.79 0.71 1.07 0.71 1.07 1.07

time (sec)

N/A 0.131 0.001 0.035 0.192 0.261 0.180 0.281 5.390

Problem 93

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 14 14 11 10 15 10 12 13

N.S.

1 1.00 1.00 0.79 0.71 1.07 0.71 0.86 0.93

time (sec)

N/A 0.133 0.001 0.033 0.191 0.276 0.181 0.265 5.462

Problem 94

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 14 14 11 10 15 12 13 15

N.S.

1 1.00 1.00 0.79 0.71 1.07 0.86 0.93 1.07

time (sec)

N/A 0.133 0.001 0.034 0.193 0.257 0.184 0.272 5.391

Problem 95

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 14 14 11 10 15 14 17 15

N.S.

1 0.74 0.74 0.58 0.53 0.79 0.74 0.89 0.79

time (sec)

N/A 0.131 0.001 0.095 0.200 0.324 0.201 0.272 5.378

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

19 14 14 11 8 15 12 12 13

N.S.

1 0.74 0.74 0.58 0.42 0.79 0.63 0.63 0.68

time (sec)

N/A 0.129 0.000 0.038 0.188 0.271 0.199 0.279 0.002

Problem 97

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

12 12 10 9 10 13 10 10 10

N.S.

1 1.00 0.83 0.75 0.83 1.08 0.83 0.83 0.83

time (sec)

N/A 0.127 0.001 0.044 0.179 0.279 0.018 0.264 0.018

Problem 98

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 14 14 11 10 15 10 17 15

N.S.

1 0.74 0.74 0.58 0.53 0.79 0.53 0.89 0.79

time (sec)

N/A 0.126 0.001 0.035 0.196 0.278 0.195 0.264 5.360

Problem 99

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 14 14 11 10 15 10 12 13

N.S.

1 0.74 0.74 0.58 0.53 0.79 0.53 0.63 0.68

time (sec)

N/A 0.129 0.001 0.039 0.210 0.249 0.199 0.269 5.462

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 14 14 11 10 15 12 13 15

N.S.

1 0.74 0.74 0.58 0.53 0.79 0.63 0.68 0.79

time (sec)

N/A 0.136 0.001 0.040 0.204 0.275 0.203 0.278 5.516

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