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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 C A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 22 11 16 48 19 34 10

N.S.

1 1.00 1.83 0.92 1.33 4.00 1.58 2.83 0.83

time (sec)

N/A 0.183 0.001 0.058 0.271 0.243 0.025 0.266 0.002

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

13 13 13 12 15 19 14 15 12

N.S.

1 1.00 1.00 0.92 1.15 1.46 1.08 1.15 0.92

time (sec)

N/A 0.124 0.006 0.136 0.277 0.231 0.045 0.256 0.170

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 14 11 11 14 15 11 10

N.S.

1 1.00 0.74 0.58 0.58 0.74 0.79 0.58 0.53

time (sec)

N/A 0.122 0.012 0.073 0.198 0.242 0.074 0.277 0.030

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

2 2 2 3 2 2 2 2 2

N.S.

1 1.00 1.00 1.50 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.128 0.001 0.030 0.208 0.245 0.032 0.261 0.031

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

9 9 9 7 6 6 5 6 6

N.S.

1 1.00 1.00 0.78 0.67 0.67 0.56 0.67 0.67

time (sec)

N/A 0.129 0.001 0.032 0.204 0.235 0.029 0.260 0.019

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

8 8 8 7 6 6 7 6 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.88 0.75 0.75

time (sec)

N/A 0.155 0.007 0.155 0.193 0.261 0.020 0.288 0.024

Problem 7

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

13 13 13 10 9 9 22 9 9

N.S.

1 1.00 1.00 0.77 0.69 0.69 1.69 0.69 0.69

time (sec)

N/A 0.117 0.002 0.103 0.195 0.231 0.068 0.292 0.029

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

19 19 14 12 11 13 15 11 11

N.S.

1 1.00 0.74 0.63 0.58 0.68 0.79 0.58 0.58

time (sec)

N/A 0.146 0.010 0.085 0.201 0.237 0.098 0.280 0.018

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

8 8 8 7 6 14 8 6 6

N.S.

1 1.00 1.00 0.88 0.75 1.75 1.00 0.75 0.75

time (sec)

N/A 0.157 0.007 0.157 0.196 0.232 0.022 0.285 0.054

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

4 4 4 4 15 3 3 3 0

N.S.

1 1.00 1.00 1.00 3.75 0.75 0.75 0.75 0.00

time (sec)

N/A 0.177 0.018 0.147 0.235 0.242 0.281 0.282 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

2 2 2 3 13 2 2 2 0

N.S.

1 1.00 1.00 1.50 6.50 1.00 1.00 1.00 0.00

time (sec)

N/A 0.145 0.019 0.081 0.231 0.254 0.389 0.279 0.000

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

8 8 8 8 7 7 5 7 7

N.S.

1 1.00 1.00 1.00 0.88 0.88 0.62 0.88 0.88

time (sec)

N/A 0.119 0.010 0.104 0.193 0.241 0.032 0.298 0.042

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

7 7 7 7 6 6 5 6 6

N.S.

1 1.00 1.00 1.00 0.86 0.86 0.71 0.86 0.86

time (sec)

N/A 0.134 0.036 0.043 0.201 0.236 0.035 0.309 0.191

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

28 28 26 21 19 19 20 19 21

N.S.

1 1.00 0.93 0.75 0.68 0.68 0.71 0.68 0.75

time (sec)

N/A 0.180 0.044 0.036 0.191 0.237 0.039 0.273 0.056

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

22 22 22 17 16 16 15 16 16

N.S.

1 1.00 1.00 0.77 0.73 0.73 0.68 0.73 0.73

time (sec)

N/A 0.134 0.013 0.031 0.188 0.235 0.037 0.279 0.046

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

8 8 8 7 6 6 5 6 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.62 0.75 0.75

time (sec)

N/A 0.143 0.001 0.049 0.188 0.260 0.034 0.283 0.017

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

9 9 9 7 6 6 5 6 6

N.S.

1 1.00 1.00 0.78 0.67 0.67 0.56 0.67 0.67

time (sec)

N/A 0.130 0.000 0.033 0.191 0.249 0.029 0.272 0.002

Problem 18

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

13 13 13 10 9 9 22 9 9

N.S.

1 1.00 1.00 0.77 0.69 0.69 1.69 0.69 0.69

time (sec)

N/A 0.119 0.001 0.104 0.180 0.256 0.070 0.272 0.002

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

6 6 6 6 5 5 5 5 5

N.S.

1 1.00 1.00 1.00 0.83 0.83 0.83 0.83 0.83

time (sec)

N/A 0.144 0.013 0.029 0.182 0.242 0.030 0.299 0.034

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

9 9 9 6 5 5 7 5 5

N.S.

1 1.00 1.00 0.67 0.56 0.56 0.78 0.56 0.56

time (sec)

N/A 0.110 0.001 0.037 0.183 0.237 0.032 0.281 0.042

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

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 0.142 0.008 0.076 0.184 0.240 0.045 0.263 0.067

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

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 0.130 0.001 0.032 0.190 0.226 0.046 0.251 0.017

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 No Yes Yes TBD TBD TBD TBD TBD

size

10 9 19 8 7 7 8 7 7

N.S.

1 0.90 1.90 0.80 0.70 0.70 0.80 0.70 0.70

time (sec)

N/A 0.187 0.029 0.150 0.201 0.259 0.285 0.261 0.209

Problem 24

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 18 13 15 15 34 15 12

N.S.

1 1.00 0.78 0.57 0.65 0.65 1.48 0.65 0.52

time (sec)

N/A 0.138 0.016 0.109 0.191 0.230 0.555 0.289 0.032

Problem 25

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

13 13 25 10 17 17 17 19 9

N.S.

1 1.00 1.92 0.77 1.31 1.31 1.31 1.46 0.69

time (sec)

N/A 0.129 0.004 0.127 0.275 0.253 0.063 0.268 0.157

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

18 18 18 14 13 13 15 13 13

N.S.

1 1.00 1.00 0.78 0.72 0.72 0.83 0.72 0.72

time (sec)

N/A 0.157 0.038 0.049 0.283 0.251 0.062 0.264 0.090

Problem 27

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 31 31 20 19 76 22 19 19

N.S.

1 1.00 1.00 0.65 0.61 2.45 0.71 0.61 0.61

time (sec)

N/A 0.176 0.039 0.087 0.294 0.245 0.078 0.270 0.235

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

8 8 8 9 8 11 8 8 8

N.S.

1 1.00 1.00 1.12 1.00 1.38 1.00 1.00 1.00

time (sec)

N/A 0.176 0.016 0.041 0.182 0.258 0.040 0.289 0.211

Problem 29

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 15 14 14 10 13 12

N.S.

1 1.00 1.00 1.25 1.17 1.17 0.83 1.08 1.00

time (sec)

N/A 0.137 0.004 0.054 0.186 0.233 0.033 0.266 0.066

Problem 30

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 18 20 17 16 16 15 16 16

N.S.

1 0.90 1.00 0.85 0.80 0.80 0.75 0.80 0.80

time (sec)

N/A 0.218 0.001 0.144 0.186 0.245 0.122 0.267 0.207

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 55 260 41 40 40 46 40 52

N.S.

1 1.12 5.31 0.84 0.82 0.82 0.94 0.82 1.06

time (sec)

N/A 0.195 0.118 0.146 0.280 0.239 0.078 0.275 0.129

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 115 142 41 0 0 54 0 0

N.S.

1 1.00 1.23 0.36 0.00 0.00 0.47 0.00 0.00

time (sec)

N/A 0.243 0.306 0.385 0.000 0.000 1.501 0.000 0.000

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

22 21 22 17 16 16 20 16 16

N.S.

1 0.95 1.00 0.77 0.73 0.73 0.91 0.73 0.73

time (sec)

N/A 0.210 0.018 0.075 0.192 0.250 0.096 0.277 0.248

Problem 34

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 18 13 15 15 34 15 12

N.S.

1 1.00 0.78 0.57 0.65 0.65 1.48 0.65 0.52

time (sec)

N/A 0.134 0.002 0.105 0.198 0.228 0.559 0.282 0.002

Problem 35

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

32 36 33 25 24 24 0 24 24

N.S.

1 1.12 1.03 0.78 0.75 0.75 0.00 0.75 0.75

time (sec)

N/A 0.161 0.006 0.093 0.188 0.240 0.000 0.284 0.002

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 75 75 80 55 0 61 57

N.S.

1 1.00 1.70 1.70 1.82 1.25 0.00 1.39 1.30

time (sec)

N/A 0.154 0.141 0.191 0.284 0.250 0.000 0.290 0.203

Problem 37

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

35 35 44 30 44 63 105 29 91

N.S.

1 1.00 1.26 0.86 1.26 1.80 3.00 0.83 2.60

time (sec)

N/A 0.141 0.106 0.257 0.273 0.250 0.398 0.279 0.169

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 85 52 44 113 44 190 90 0

N.S.

1 1.13 0.69 0.59 1.51 0.59 2.53 1.20 0.00

time (sec)

N/A 0.158 0.091 0.120 0.177 0.241 18.654 0.288 0.000

Problem 39

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

35 35 44 30 44 63 105 29 91

N.S.

1 1.00 1.26 0.86 1.26 1.80 3.00 0.83 2.60

time (sec)

N/A 0.139 0.005 0.165 0.276 0.235 0.391 0.272 0.002

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 51 78 90 114 129 0 295 0

N.S.

1 1.00 1.53 1.76 2.24 2.53 0.00 5.78 0.00

time (sec)

N/A 0.182 1.540 0.566 0.272 0.262 0.000 0.336 0.000

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

14 14 14 11 10 10 10 10 10

N.S.

1 1.00 1.00 0.79 0.71 0.71 0.71 0.71 0.71

time (sec)

N/A 0.145 0.002 0.061 0.191 0.256 0.018 0.269 0.029

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 57 99 149 116 244 0 0 0

N.S.

1 1.16 2.02 3.04 2.37 4.98 0.00 0.00 0.00

time (sec)

N/A 0.264 0.166 1.128 0.274 0.321 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 B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

9 9 6 5 9 9 3 30 4

N.S.

1 1.00 0.67 0.56 1.00 1.00 0.33 3.33 0.44

time (sec)

N/A 0.158 0.003 0.054 0.189 0.249 0.098 0.285 0.184

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

11 11 7 7 6 6 5 6 6

N.S.

1 1.00 0.64 0.64 0.55 0.55 0.45 0.55 0.55

time (sec)

N/A 0.150 0.001 0.026 0.185 0.236 0.028 0.267 0.016

Problem 45

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

9 9 9 9 8 8 5 30 8

N.S.

1 1.00 1.00 1.00 0.89 0.89 0.56 3.33 0.89

time (sec)

N/A 0.151 0.070 0.100 0.188 0.232 0.033 0.287 0.084

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

7 7 7 7 6 6 5 6 6

N.S.

1 1.00 1.00 1.00 0.86 0.86 0.71 0.86 0.86

time (sec)

N/A 0.169 0.002 0.040 0.187 0.239 0.032 0.285 0.162

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 8 9 7 8 9 7

N.S.

1 1.00 1.00 0.73 0.82 0.64 0.73 0.82 0.64

time (sec)

N/A 0.127 0.001 0.018 0.185 0.235 0.081 0.274 0.018

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

2 2 2 8 2 2 2 2 2

N.S.

1 1.00 1.00 4.00 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.130 0.001 0.033 0.221 0.237 0.366 0.269 0.008

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

41 45 40 33 34 34 41 35 46

N.S.

1 1.10 0.98 0.80 0.83 0.83 1.00 0.85 1.12

time (sec)

N/A 0.183 0.010 0.116 0.263 0.240 0.061 0.270 0.112

Problem 50

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

47 79 75 66 65 65 83 67 88

N.S.

1 1.68 1.60 1.40 1.38 1.38 1.77 1.43 1.87

time (sec)

N/A 0.220 0.014 0.112 0.260 0.240 0.127 0.285 0.092

Problem 51

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 30 39 27 70 41 21

N.S.

1 1.00 1.00 1.43 1.86 1.29 3.33 1.95 1.00

time (sec)

N/A 0.134 0.005 0.189 0.195 0.237 0.151 0.270 0.260

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

17 17 17 14 13 13 12 13 9

N.S.

1 1.00 1.00 0.82 0.76 0.76 0.71 0.76 0.53

time (sec)

N/A 0.135 0.000 0.019 0.179 0.243 0.031 0.275 0.035

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

40 43 29 34 33 24 32 38 24

N.S.

1 1.08 0.72 0.85 0.82 0.60 0.80 0.95 0.60

time (sec)

N/A 0.201 0.009 0.012 0.265 0.243 0.093 0.277 0.002

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

7 7 7 8 7 7 5 7 7

N.S.

1 1.00 1.00 1.14 1.00 1.00 0.71 1.00 1.00

time (sec)

N/A 0.122 0.001 0.122 0.206 0.238 0.026 0.265 0.019

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

8 8 8 9 8 8 5 8 8

N.S.

1 1.00 1.00 1.12 1.00 1.00 0.62 1.00 1.00

time (sec)

N/A 0.176 0.016 0.119 0.179 0.231 0.035 0.275 0.272

Problem 56

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

3 3 3 4 3 3 15 3 3

N.S.

1 1.00 1.00 1.33 1.00 1.00 5.00 1.00 1.00

time (sec)

N/A 0.145 0.028 0.095 0.264 0.242 0.069 0.259 0.323

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

2 2 2 9 3 2 2 3 2

N.S.

1 1.00 1.00 4.50 1.50 1.00 1.00 1.50 1.00

time (sec)

N/A 0.124 0.001 0.015 0.200 0.237 0.173 0.261 0.009

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

14 14 14 15 14 14 15 14 14

N.S.

1 1.00 1.00 1.07 1.00 1.00 1.07 1.00 1.00

time (sec)

N/A 0.158 0.006 0.194 0.188 0.261 0.069 0.267 0.061

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

17 17 13 13 11 14 8 11 15

N.S.

1 1.00 0.76 0.76 0.65 0.82 0.47 0.65 0.88

time (sec)

N/A 0.194 0.006 0.030 0.186 0.250 0.044 0.268 0.057

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

38 38 29 25 24 24 26 24 28

N.S.

1 1.00 0.76 0.66 0.63 0.63 0.68 0.63 0.74

time (sec)

N/A 0.179 0.055 0.037 0.189 0.240 0.042 0.276 0.193

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

7 7 7 8 7 7 7 7 7

N.S.

1 1.00 1.00 1.14 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.176 0.003 0.082 0.215 0.233 0.070 0.279 0.019

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

22 21 22 17 16 16 20 16 16

N.S.

1 0.95 1.00 0.77 0.73 0.73 0.91 0.73 0.73

time (sec)

N/A 0.208 0.006 0.066 0.192 0.245 0.107 0.279 0.002

Problem 63

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

7 7 7 8 7 7 7 7 7

N.S.

1 1.00 1.00 1.14 1.00 1.00 1.00 1.00 1.00

time (sec)

N/A 0.180 0.002 0.055 0.180 0.250 0.061 0.274 0.002

Problem 64

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 28 28 23 17 22 22 22 17

N.S.

1 1.00 1.00 0.82 0.61 0.79 0.79 0.79 0.61

time (sec)

N/A 0.158 0.001 0.024 0.180 0.231 0.040 0.278 0.031

Problem 65

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 11 10 9 15 8 9 9

N.S.

1 1.00 1.00 0.91 0.82 1.36 0.73 0.82 0.82

time (sec)

N/A 0.170 0.004 0.190 0.183 0.240 0.121 0.278 0.033

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

3 3 3 4 3 3 15 3 3

N.S.

1 1.00 1.00 1.33 1.00 1.00 5.00 1.00 1.00

time (sec)

N/A 0.141 0.003 0.083 0.283 0.245 0.091 0.282 0.002

Problem 67

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

3 3 3 4 0 3 3 3 43

N.S.

1 1.00 1.00 1.33 0.00 1.00 1.00 1.00 14.33

time (sec)

N/A 0.189 0.103 0.118 0.000 0.251 0.133 0.288 2.835

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 20 53 15 12 21 13

N.S.

1 1.00 1.00 1.25 3.31 0.94 0.75 1.31 0.81

time (sec)

N/A 0.229 0.053 0.257 0.316 0.246 0.055 0.304 0.029

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 73 89 115 128 0 295 0

N.S.

1 1.00 1.38 1.68 2.17 2.42 0.00 5.57 0.00

time (sec)

N/A 0.215 0.194 0.273 0.291 0.257 0.000 0.354 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B B B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 46 35 71 69 67 202 83 360

N.S.

1 2.88 2.19 4.44 4.31 4.19 12.62 5.19 22.50

time (sec)

N/A 0.275 0.268 0.625 0.265 0.265 106.059 0.287 0.512

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B C B A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 44 35 70 68 26 422 82 352

N.S.

1 2.75 2.19 4.38 4.25 1.62 26.38 5.12 22.00

time (sec)

N/A 0.299 0.022 0.178 0.277 0.255 0.991 0.284 0.238

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B C B A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 44 35 40 65 26 422 79 352

N.S.

1 2.75 2.19 2.50 4.06 1.62 26.38 4.94 22.00

time (sec)

N/A 0.159 0.016 0.210 0.263 0.253 1.009 0.274 0.057

Problem 73

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

35 35 44 30 44 63 105 29 91

N.S.

1 1.00 1.26 0.86 1.26 1.80 3.00 0.83 2.60

time (sec)

N/A 0.144 0.016 0.204 0.282 0.241 0.382 0.277 0.002

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 14 16 13 12 26 19 12 12

N.S.

1 1.00 1.14 0.93 0.86 1.86 1.36 0.86 0.86

time (sec)

N/A 0.194 0.007 0.197 0.279 0.244 0.022 0.283 0.073

Problem 75

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 8 11 11

N.S.

1 1.00 1.00 0.92 0.85 0.85 0.62 0.85 0.85

time (sec)

N/A 0.133 0.005 0.132 0.267 0.229 0.032 0.265 0.028

Problem 76

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

7 7 7 7 6 6 5 6 6

N.S.

1 1.00 1.00 1.00 0.86 0.86 0.71 0.86 0.86

time (sec)

N/A 0.163 0.002 0.039 0.188 0.240 0.032 0.276 0.002

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

24 24 19 24 23 23 20 30 24

N.S.

1 1.00 0.79 1.00 0.96 0.96 0.83 1.25 1.00

time (sec)

N/A 0.442 0.379 0.128 0.301 0.239 0.048 0.278 0.247

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

9 9 9 9 8 8 7 8 8

N.S.

1 1.00 1.00 1.00 0.89 0.89 0.78 0.89 0.89

time (sec)

N/A 0.135 0.015 0.026 0.182 0.236 0.029 0.255 0.033

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

25 25 25 20 24 19 19 19 19

N.S.

1 1.00 1.00 0.80 0.96 0.76 0.76 0.76 0.76

time (sec)

N/A 0.192 0.004 0.037 0.185 0.244 0.039 0.257 0.228

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

8 8 8 7 6 6 5 6 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.62 0.75 0.75

time (sec)

N/A 0.127 0.004 0.124 0.266 0.236 0.038 0.271 0.054

Problem 81

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 12 12 10 12 12

N.S.

1 0.88 1.00 0.81 0.75 0.75 0.62 0.75 0.75

time (sec)

N/A 0.134 0.006 0.133 0.273 0.227 0.040 0.252 0.021

Problem 82

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

14 14 14 11 16 20 36 16 10

N.S.

1 1.00 1.00 0.79 1.14 1.43 2.57 1.14 0.71

time (sec)

N/A 0.191 0.003 0.055 0.298 0.238 0.178 0.262 0.190

Problem 83

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

35 35 44 30 44 63 105 29 91

N.S.

1 1.00 1.26 0.86 1.26 1.80 3.00 0.83 2.60

time (sec)

N/A 0.147 0.001 0.176 0.295 0.242 0.391 0.269 0.002

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 35 16 15 45 34 21 37

N.S.

1 1.00 2.06 0.94 0.88 2.65 2.00 1.24 2.18

time (sec)

N/A 0.134 0.074 0.191 0.276 0.255 0.180 0.277 0.175

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

19 19 14 12 11 13 15 11 11

N.S.

1 1.00 0.74 0.63 0.58 0.68 0.79 0.58 0.58

time (sec)

N/A 0.146 0.007 0.074 0.177 0.254 0.088 0.253 0.002

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

2 2 2 3 2 2 2 3 2

N.S.

1 1.00 1.00 1.50 1.00 1.00 1.00 1.50 1.00

time (sec)

N/A 0.113 0.000 0.010 0.178 0.234 0.033 0.262 0.007

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 40 73 31 256 71 0 33 32

N.S.

1 0.89 1.62 0.69 5.69 1.58 0.00 0.73 0.71

time (sec)

N/A 0.276 0.713 1.533 0.357 0.279 0.000 0.283 0.707

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

14 14 14 11 10 10 10 16 10

N.S.

1 1.00 1.00 0.79 0.71 0.71 0.71 1.14 0.71

time (sec)

N/A 0.148 0.002 0.054 0.179 0.237 0.023 0.269 0.003

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 14 11 11 10 14 11 10

N.S.

1 1.00 0.82 0.65 0.65 0.59 0.82 0.65 0.59

time (sec)

N/A 0.131 0.013 0.040 0.182 0.234 0.077 0.254 0.026

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

23 25 31 20 19 27 19 27 27

N.S.

1 1.09 1.35 0.87 0.83 1.17 0.83 1.17 1.17

time (sec)

N/A 0.161 0.069 0.378 0.271 0.239 0.255 0.306 0.101

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

8 8 8 7 6 10 5 6 6

N.S.

1 1.00 1.00 0.88 0.75 1.25 0.62 0.75 0.75

time (sec)

N/A 0.158 0.002 0.079 0.176 0.265 0.034 0.264 0.027

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 6 6 6 5 5 5 5 5

N.S.

1 1.00 1.00 1.00 0.83 0.83 0.83 0.83 0.83

time (sec)

N/A 0.140 0.001 0.023 0.184 0.242 0.032 0.254 0.003

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

12 12 12 11 10 10 8 10 10

N.S.

1 1.00 1.00 0.92 0.83 0.83 0.67 0.83 0.83

time (sec)

N/A 0.160 0.002 0.033 0.191 0.238 0.037 0.280 0.047

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

12 12 8 9 10 10 7 8 6

N.S.

1 1.00 0.67 0.75 0.83 0.83 0.58 0.67 0.50

time (sec)

N/A 0.157 0.006 0.069 0.179 0.247 0.163 0.270 0.208

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

8 8 8 7 6 6 7 6 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.88 0.75 0.75

time (sec)

N/A 0.152 0.002 0.142 0.172 0.239 0.021 0.261 0.003

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

17 17 17 14 13 13 12 13 9

N.S.

1 1.00 1.00 0.82 0.76 0.76 0.71 0.76 0.53

time (sec)

N/A 0.136 0.000 0.019 0.181 0.234 0.038 0.269 0.003

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

8 8 8 7 6 6 5 6 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.62 0.75 0.75

time (sec)

N/A 0.149 0.001 0.036 0.196 0.236 0.032 0.264 0.003

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

24 28 47 21 22 32 15 20 20

N.S.

1 1.17 1.96 0.88 0.92 1.33 0.62 0.83 0.83

time (sec)

N/A 0.153 0.063 0.408 0.265 0.250 0.348 0.278 0.306

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

20 20 20 14 13 19 15 13 13

N.S.

1 1.00 1.00 0.70 0.65 0.95 0.75 0.65 0.65

time (sec)

N/A 0.158 0.006 0.046 0.267 0.232 0.049 0.263 0.106

Problem 100

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

35 35 44 30 44 63 105 29 91

N.S.

1 1.00 1.26 0.86 1.26 1.80 3.00 0.83 2.60

time (sec)

N/A 0.140 0.013 0.180 0.299 0.248 0.403 0.282 0.002

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