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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

17 17 17 14 13 13 12 13 13

N.S.

1 1.00 1.00 0.82 0.76 0.76 0.71 0.76 0.76

time (sec)

N/A 0.003 0.002 0.084 0.306 1.945 0.006 1.499 0.022

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

17 17 17 14 13 13 12 13 13

N.S.

1 1.00 1.00 0.82 0.76 0.76 0.71 0.76 0.76

time (sec)

N/A 0.003 0.001 0.049 0.280 1.132 0.009 1.412 0.022

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

17 17 17 15 13 13 12 13 13

N.S.

1 1.00 1.00 0.88 0.76 0.76 0.71 0.76 0.76

time (sec)

N/A 0.002 0.000 0.046 0.282 2.011 0.010 1.360 0.019

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD 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 0.002 0.000 0.015 0.289 1.743 0.005 1.466 0.017

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

13 13 13 12 11 11 10 14 11

N.S.

1 1.00 1.00 0.92 0.85 0.85 0.77 1.08 0.85

time (sec)

N/A 0.003 0.001 0.018 0.281 1.699 0.021 1.576 0.024

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 30 25 24 24 26 24 24

N.S.

1 1.00 1.00 0.83 0.80 0.80 0.87 0.80 0.80

time (sec)

N/A 0.010 0.001 0.343 0.290 1.416 0.011 1.161 0.041

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 30 25 24 24 24 24 24

N.S.

1 1.00 1.00 0.83 0.80 0.80 0.80 0.80 0.80

time (sec)

N/A 0.013 0.001 0.373 0.287 2.168 0.008 1.616 0.033

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

30 30 30 25 24 24 26 24 24

N.S.

1 1.00 1.00 0.83 0.80 0.80 0.87 0.80 0.80

time (sec)

N/A 0.007 0.002 0.365 0.295 1.307 0.007 1.732 0.030

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 15 24 24 24 24 24

N.S.

1 1.00 1.00 0.94 1.50 1.50 1.50 1.50 1.50

time (sec)

N/A 0.005 0.001 0.348 0.281 1.822 0.009 1.005 0.031

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 25 22 21 21 22 21 21

N.S.

1 1.00 1.00 0.88 0.84 0.84 0.88 0.84 0.84

time (sec)

N/A 0.008 0.001 0.331 0.276 1.288 0.008 1.316 0.030

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 46 37 36 36 42 36 36

N.S.

1 1.00 1.00 0.80 0.78 0.78 0.91 0.78 0.78

time (sec)

N/A 0.010 0.002 0.376 0.292 2.267 0.011 1.234 0.039

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 27 24 23 22 20 24 22

N.S.

1 1.00 1.00 0.89 0.85 0.81 0.74 0.89 0.81

time (sec)

N/A 0.015 0.004 0.351 0.285 1.368 0.050 1.256 0.040

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 31 27 26 82 56 26 23

N.S.

1 1.00 1.00 0.87 0.84 2.65 1.81 0.84 0.74

time (sec)

N/A 0.011 0.006 0.355 0.511 2.239 0.058 1.169 4.913

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 15 14 13 13 10 14 13

N.S.

1 1.00 1.00 0.93 0.87 0.87 0.67 0.93 0.87

time (sec)

N/A 0.005 0.002 0.408 0.281 1.356 0.036 1.147 4.916

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

24 24 24 16 15 67 53 15 16

N.S.

1 1.00 1.00 0.67 0.62 2.79 2.21 0.62 0.67

time (sec)

N/A 0.005 0.003 0.368 0.502 3.543 0.049 1.036 0.045

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 22 21 20 18 15 24 18

N.S.

1 1.00 1.00 0.95 0.91 0.82 0.68 1.09 0.82

time (sec)

N/A 0.008 0.003 0.337 0.285 2.147 0.084 2.205 0.063

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 34 30 29 82 65 29 26

N.S.

1 1.00 1.00 0.88 0.85 2.41 1.91 0.85 0.76

time (sec)

N/A 0.010 0.009 0.353 0.509 1.337 0.069 2.572 4.956

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

35 35 35 32 31 33 31 43 31

N.S.

1 1.00 1.00 0.91 0.89 0.94 0.89 1.23 0.89

time (sec)

N/A 0.018 0.005 0.346 0.277 1.667 0.121 1.363 0.060

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

43 43 43 39 40 106 87 40 37

N.S.

1 1.00 1.00 0.91 0.93 2.47 2.02 0.93 0.86

time (sec)

N/A 0.015 0.014 0.368 0.513 1.292 0.100 0.918 4.937

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 49 44 44 45 42 57 46

N.S.

1 1.00 1.00 0.90 0.90 0.92 0.86 1.16 0.94

time (sec)

N/A 0.023 0.005 0.345 0.298 1.453 0.138 0.886 0.062

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 45 36 35 120 78 35 33

N.S.

1 1.00 1.00 0.80 0.78 2.67 1.73 0.78 0.73

time (sec)

N/A 0.010 0.018 0.374 0.512 3.026 0.114 1.432 4.955

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 33 42 34 47 34 47 34

N.S.

1 1.00 0.87 1.11 0.89 1.24 0.89 1.24 0.89

time (sec)

N/A 0.021 0.012 0.359 0.289 2.394 0.134 1.462 0.049

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

57 57 54 45 49 136 92 47 44

N.S.

1 1.00 0.95 0.79 0.86 2.39 1.61 0.82 0.77

time (sec)

N/A 0.012 0.024 0.354 0.509 1.823 0.145 1.174 4.975

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 41 55 50 73 51 51 51

N.S.

1 1.00 0.84 1.12 1.02 1.49 1.04 1.04 1.04

time (sec)

N/A 0.028 0.024 0.359 0.287 1.349 0.176 1.371 0.053

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 67 55 64 172 114 59 58

N.S.

1 1.00 0.99 0.81 0.94 2.53 1.68 0.87 0.85

time (sec)

N/A 0.020 0.028 0.358 0.508 1.764 0.159 1.783 5.026

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

13 13 29 22 21 21 19 23 11

N.S.

1 1.00 2.23 1.69 1.62 1.62 1.46 1.77 0.85

time (sec)

N/A 0.008 0.004 0.350 0.295 1.599 0.030 1.081 4.977

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

20 20 18 19 18 14 14 15 14

N.S.

1 1.00 0.90 0.95 0.90 0.70 0.70 0.75 0.70

time (sec)

N/A 0.010 0.003 0.345 0.283 2.103 0.019 1.019 0.036

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

6 6 22 17 16 16 14 18 6

N.S.

1 1.00 3.67 2.83 2.67 2.67 2.33 3.00 1.00

time (sec)

N/A 0.005 0.002 0.352 0.298 1.162 0.026 1.717 0.058

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

12 12 12 14 13 8 8 15 8

N.S.

1 1.00 1.00 1.17 1.08 0.67 0.67 1.25 0.67

time (sec)

N/A 0.004 0.002 0.374 0.286 1.710 0.021 1.256 0.029

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

2 2 19 3 13 13 12 15 2

N.S.

1 1.00 9.50 1.50 6.50 6.50 6.00 7.50 1.00

time (sec)

N/A 0.003 0.002 0.362 0.278 1.352 0.027 1.151 0.033

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 15 16 15 11 10 16 11

N.S.

1 1.00 1.00 1.07 1.00 0.73 0.67 1.07 0.73

time (sec)

N/A 0.006 0.002 0.360 0.279 3.929 0.029 1.262 4.960

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

8 8 24 19 18 20 15 20 8

N.S.

1 1.00 3.00 2.38 2.25 2.50 1.88 2.50 1.00

time (sec)

N/A 0.005 0.002 0.351 0.289 2.496 0.035 1.316 0.033

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 22 21 20 24 17 26 16

N.S.

1 1.00 1.00 0.95 0.91 1.09 0.77 1.18 0.73

time (sec)

N/A 0.010 0.003 0.372 0.279 2.805 0.033 0.995 0.033

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 31 24 25 30 24 27 13

N.S.

1 1.00 2.07 1.60 1.67 2.00 1.60 1.80 0.87

time (sec)

N/A 0.007 0.003 0.355 0.279 2.565 0.039 1.038 4.924

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

29 29 29 26 27 30 22 33 23

N.S.

1 1.00 1.00 0.90 0.93 1.03 0.76 1.14 0.79

time (sec)

N/A 0.012 0.003 0.361 0.291 2.703 0.040 1.552 0.033

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 15 14 13 13 12 18 14

N.S.

1 1.00 1.00 0.93 0.87 0.87 0.80 1.20 0.93

time (sec)

N/A 0.007 0.003 0.348 0.267 2.405 0.055 1.797 4.950

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

18 18 18 16 15 15 12 18 16

N.S.

1 1.00 1.00 0.89 0.83 0.83 0.67 1.00 0.89

time (sec)

N/A 0.007 0.003 0.346 0.274 1.609 0.052 1.089 0.052

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

163 163 95 168 0 59 0 0 -1

N.S.

1 1.00 0.58 1.03 0.00 0.36 0.00 0.00 -0.01

time (sec)

N/A 0.125 10.044 0.347 0.000 0.492 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

281 281 80 197 0 57 0 0 -1

N.S.

1 1.00 0.28 0.70 0.00 0.20 0.00 0.00 -0.00

time (sec)

N/A 0.187 10.028 0.358 0.000 0.410 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

137 137 79 146 0 49 0 0 -1

N.S.

1 1.00 0.58 1.07 0.00 0.36 0.00 0.00 -0.01

time (sec)

N/A 0.084 9.562 0.346 0.000 0.369 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

255 255 51 175 0 43 0 0 40

N.S.

1 1.00 0.20 0.69 0.00 0.17 0.00 0.00 0.16

time (sec)

N/A 0.125 7.781 0.351 0.000 0.847 0.000 0.000 5.051

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

113 113 48 124 0 34 0 0 -1

N.S.

1 1.00 0.42 1.10 0.00 0.30 0.00 0.00 -0.01

time (sec)

N/A 0.060 6.860 0.347 0.000 0.591 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

248 248 51 177 0 40 0 0 -1

N.S.

1 1.00 0.21 0.71 0.00 0.16 0.00 0.00 -0.00

time (sec)

N/A 0.146 10.013 0.353 0.000 0.421 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 53 123 0 36 0 0 -1

N.S.

1 1.00 0.46 1.06 0.00 0.31 0.00 0.00 -0.01

time (sec)

N/A 0.063 10.019 0.388 0.000 0.470 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

283 283 53 201 0 54 0 0 -1

N.S.

1 1.00 0.19 0.71 0.00 0.19 0.00 0.00 -0.00

time (sec)

N/A 0.183 10.014 0.363 0.000 0.452 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

186 186 94 188 0 70 0 0 -1

N.S.

1 1.00 0.51 1.01 0.00 0.38 0.00 0.00 -0.01

time (sec)

N/A 0.163 10.038 0.365 0.000 0.661 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

304 304 84 217 0 68 0 0 -1

N.S.

1 1.00 0.28 0.71 0.00 0.22 0.00 0.00 -0.00

time (sec)

N/A 0.217 10.041 0.364 0.000 0.358 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

158 158 83 166 0 60 0 0 40

N.S.

1 1.00 0.53 1.05 0.00 0.38 0.00 0.00 0.25

time (sec)

N/A 0.093 10.033 0.368 0.000 0.542 0.000 0.000 5.005

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

275 275 52 195 0 58 0 0 -1

N.S.

1 1.00 0.19 0.71 0.00 0.21 0.00 0.00 -0.00

time (sec)

N/A 0.318 10.015 0.349 0.000 0.574 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 49 144 0 47 0 0 -1

N.S.

1 1.00 0.37 1.07 0.00 0.35 0.00 0.00 -0.01

time (sec)

N/A 0.186 9.205 0.346 0.000 0.441 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

274 274 52 194 0 52 0 0 -1

N.S.

1 1.00 0.19 0.71 0.00 0.19 0.00 0.00 -0.00

time (sec)

N/A 0.267 10.012 0.347 0.000 0.386 0.000 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 54 139 0 45 0 0 -1

N.S.

1 1.00 0.40 1.04 0.00 0.34 0.00 0.00 -0.01

time (sec)

N/A 0.089 10.015 0.348 0.000 0.422 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

277 277 54 196 0 51 0 0 -1

N.S.

1 1.00 0.19 0.71 0.00 0.18 0.00 0.00 -0.00

time (sec)

N/A 0.178 10.017 0.350 0.000 0.388 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

137 137 54 142 0 44 0 0 -1

N.S.

1 1.00 0.39 1.04 0.00 0.32 0.00 0.00 -0.01

time (sec)

N/A 0.088 10.015 0.356 0.000 0.429 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

306 306 54 223 0 67 0 0 -1

N.S.

1 1.00 0.18 0.73 0.00 0.22 0.00 0.00 -0.00

time (sec)

N/A 0.215 10.022 0.371 0.000 0.833 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

163 163 54 169 0 59 0 0 -1

N.S.

1 1.00 0.33 1.04 0.00 0.36 0.00 0.00 -0.01

time (sec)

N/A 0.124 10.013 0.352 0.000 0.508 0.000 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 80 149 0 48 0 0 -1

N.S.

1 1.00 0.57 1.06 0.00 0.34 0.00 0.00 -0.01

time (sec)

N/A 0.101 10.028 0.352 0.000 0.388 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

258 258 66 178 0 43 0 0 -1

N.S.

1 1.00 0.26 0.69 0.00 0.17 0.00 0.00 -0.00

time (sec)

N/A 0.151 10.034 0.343 0.000 0.539 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 64 127 0 34 0 0 -1

N.S.

1 1.00 0.55 1.09 0.00 0.29 0.00 0.00 -0.01

time (sec)

N/A 0.065 10.030 0.391 0.000 0.316 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

229 229 53 158 0 22 0 0 -1

N.S.

1 1.00 0.23 0.69 0.00 0.10 0.00 0.00 -0.00

time (sec)

N/A 0.111 10.023 0.381 0.000 0.485 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

92 92 49 108 0 14 0 0 40

N.S.

1 1.00 0.53 1.17 0.00 0.15 0.00 0.00 0.43

time (sec)

N/A 0.035 10.011 0.351 0.000 0.293 0.000 0.000 5.035

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

253 253 48 182 0 42 0 0 -1

N.S.

1 1.00 0.19 0.72 0.00 0.17 0.00 0.00 -0.00

time (sec)

N/A 0.145 10.012 0.352 0.000 0.390 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 53 129 0 36 0 0 -1

N.S.

1 1.00 0.45 1.08 0.00 0.30 0.00 0.00 -0.01

time (sec)

N/A 0.063 10.023 0.359 0.000 0.381 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

286 286 53 204 0 56 0 0 -1

N.S.

1 1.00 0.19 0.71 0.00 0.20 0.00 0.00 -0.00

time (sec)

N/A 0.180 10.013 0.368 0.000 0.452 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 80 172 0 80 0 0 -1

N.S.

1 1.00 0.50 1.07 0.00 0.50 0.00 0.00 -0.01

time (sec)

N/A 0.129 10.036 0.410 0.000 0.297 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

279 279 68 200 0 76 0 0 -1

N.S.

1 1.00 0.24 0.72 0.00 0.27 0.00 0.00 -0.00

time (sec)

N/A 0.191 10.019 0.397 0.000 0.507 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

137 137 67 147 0 68 0 0 -1

N.S.

1 1.00 0.49 1.07 0.00 0.50 0.00 0.00 -0.01

time (sec)

N/A 0.095 10.021 0.385 0.000 0.334 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

253 253 57 182 0 61 0 0 -1

N.S.

1 1.00 0.23 0.72 0.00 0.24 0.00 0.00 -0.00

time (sec)

N/A 0.152 10.036 0.354 0.000 0.506 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 54 130 0 51 0 0 -1

N.S.

1 1.00 0.47 1.13 0.00 0.44 0.00 0.00 -0.01

time (sec)

N/A 0.068 10.020 0.345 0.000 0.409 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

254 254 56 184 0 60 0 0 -1

N.S.

1 1.00 0.22 0.72 0.00 0.24 0.00 0.00 -0.00

time (sec)

N/A 0.152 10.018 0.345 0.000 0.398 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

114 114 54 132 0 51 0 0 -1

N.S.

1 1.00 0.47 1.16 0.00 0.45 0.00 0.00 -0.01

time (sec)

N/A 0.058 9.989 0.342 0.000 0.648 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

273 273 51 206 0 72 0 0 40

N.S.

1 1.00 0.19 0.75 0.00 0.26 0.00 0.00 0.15

time (sec)

N/A 0.162 10.024 0.497 0.000 0.506 0.000 0.000 5.168

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 56 150 0 68 0 0 -1

N.S.

1 1.00 0.40 1.08 0.00 0.49 0.00 0.00 -0.01

time (sec)

N/A 0.097 10.018 0.408 0.000 0.413 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

306 306 56 228 0 90 0 0 -1

N.S.

1 1.00 0.18 0.75 0.00 0.29 0.00 0.00 -0.00

time (sec)

N/A 0.221 10.017 0.406 0.000 0.306 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F(-1) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 159 122 212 0 376 0 100 -1

N.S.

1 1.00 0.77 1.33 0.00 2.36 0.00 0.63 -0.01

time (sec)

N/A 0.163 0.203 0.421 0.000 2.843 0.000 1.513 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F(-1) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 68 72 0 108 0 80 -1

N.S.

1 1.00 0.54 0.57 0.00 0.86 0.00 0.63 -0.01

time (sec)

N/A 0.134 0.038 0.394 0.000 2.137 0.000 1.487 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F(-1) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

130 130 110 198 0 348 0 86 -1

N.S.

1 1.00 0.85 1.52 0.00 2.68 0.00 0.66 -0.01

time (sec)

N/A 0.136 0.164 0.346 0.000 3.429 0.000 1.455 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F(-1) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 64 61 0 97 0 64 -1

N.S.

1 1.00 0.63 0.60 0.00 0.96 0.00 0.63 -0.01

time (sec)

N/A 0.108 0.038 0.346 0.000 1.846 0.000 1.294 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F(-1) A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 25 29 0 61 0 17 -1

N.S.

1 1.00 1.00 1.16 0.00 2.44 0.00 0.68 -0.04

time (sec)

N/A 0.027 0.082 0.352 0.000 1.256 0.000 1.391 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 46 50 0 86 0 50 -1

N.S.

1 1.00 0.61 0.66 0.00 1.13 0.00 0.66 -0.01

time (sec)

N/A 0.080 0.033 0.373 0.000 2.228 0.000 1.528 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 38 39 0 76 0 29 -1

N.S.

1 1.00 0.75 0.76 0.00 1.49 0.00 0.57 -0.02

time (sec)

N/A 0.051 0.080 0.364 0.000 1.267 0.000 1.365 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 35 39 0 75 0 33 -1

N.S.

1 1.00 0.69 0.76 0.00 1.47 0.00 0.65 -0.02

time (sec)

N/A 0.051 0.029 0.358 0.000 1.750 0.000 1.619 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 56 50 0 87 0 43 -1

N.S.

1 1.00 0.74 0.66 0.00 1.14 0.00 0.57 -0.01

time (sec)

N/A 0.075 0.077 0.363 0.000 1.024 0.000 0.990 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F B F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

25 25 25 29 0 63 0 23 -1

N.S.

1 1.00 1.00 1.16 0.00 2.52 0.00 0.92 -0.04

time (sec)

N/A 0.025 0.010 0.369 0.000 1.624 0.000 0.956 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 58 61 0 95 0 55 -1

N.S.

1 1.00 0.57 0.60 0.00 0.94 0.00 0.54 -0.01

time (sec)

N/A 0.106 0.072 0.363 0.000 1.363 0.000 0.972 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

130 130 106 217 0 360 0 114 -1

N.S.

1 1.00 0.82 1.67 0.00 2.77 0.00 0.88 -0.01

time (sec)

N/A 0.135 0.092 0.498 0.000 1.437 0.000 0.798 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 68 72 0 110 0 90 -1

N.S.

1 1.00 0.54 0.57 0.00 0.87 0.00 0.71 -0.01

time (sec)

N/A 0.134 0.093 0.456 0.000 1.571 0.000 0.675 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 159 122 234 0 396 0 104 -1

N.S.

1 1.00 0.77 1.47 0.00 2.49 0.00 0.65 -0.01

time (sec)

N/A 0.166 0.153 0.439 0.000 1.551 0.000 1.189 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

152 152 79 83 0 121 0 147 -1

N.S.

1 1.00 0.52 0.55 0.00 0.80 0.00 0.97 -0.01

time (sec)

N/A 0.159 0.101 0.389 0.000 1.758 0.000 0.846 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

189 189 134 247 0 422 0 138 -1

N.S.

1 1.00 0.71 1.31 0.00 2.23 0.00 0.73 -0.01

time (sec)

N/A 0.199 0.162 0.447 0.000 1.510 0.000 0.769 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

180 180 90 94 0 132 0 202 -1

N.S.

1 1.00 0.50 0.52 0.00 0.73 0.00 1.12 -0.01

time (sec)

N/A 0.195 0.118 0.404 0.000 1.970 0.000 0.866 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

55 55 81 997 0 133 0 45 -1

N.S.

1 1.00 1.47 18.13 0.00 2.42 0.00 0.82 -0.02

time (sec)

N/A 0.050 0.170 0.370 0.000 1.522 0.000 0.820 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

32 32 61 979 0 94 0 23 -1

N.S.

1 1.00 1.91 30.59 0.00 2.94 0.00 0.72 -0.03

time (sec)

N/A 0.021 0.125 0.346 0.000 2.075 0.000 0.692 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

23 23 23 20 26 19 0 14 19

N.S.

1 1.00 1.00 0.87 1.13 0.83 0.00 0.61 0.83

time (sec)

N/A 0.022 0.142 0.356 0.294 1.635 0.000 0.862 5.134

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

48 48 31 41 38 29 0 30 27

N.S.

1 1.00 0.65 0.85 0.79 0.60 0.00 0.62 0.56

time (sec)

N/A 0.045 0.179 0.357 0.292 1.418 0.000 0.886 5.129

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 44 63 50 40 0 47 40

N.S.

1 1.00 0.59 0.85 0.68 0.54 0.00 0.64 0.54

time (sec)

N/A 0.072 1.216 0.359 0.300 1.805 0.000 0.813 5.266

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

224 224 64 688 0 0 0 0 -1

N.S.

1 1.00 0.29 3.07 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.159 10.036 0.365 0.000 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

197 197 49 671 0 16 0 39 40

N.S.

1 1.00 0.25 3.41 0.00 0.08 0.00 0.20 0.20

time (sec)

N/A 0.102 10.015 0.342 0.000 0.287 0.000 0.483 5.157

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

225 225 53 696 0 43 0 0 -1

N.S.

1 1.00 0.24 3.09 0.00 0.19 0.00 0.00 -0.00

time (sec)

N/A 0.140 10.015 0.357 0.000 0.552 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

503 503 66 1079 0 0 0 0 -1

N.S.

1 1.00 0.13 2.15 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.390 10.035 0.356 0.000 0.000 0.000 0.000 0.000

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