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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

13 13 13 10 9 9 8 9 9

N.S.

1 1.00 1.00 0.77 0.69 0.69 0.62 0.69 0.69

time (sec)

N/A 0.006 0.030 0.098 2.754 0.583 0.007 0.722 0.321

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

27 27 18 20 19 19 39 19 14

N.S.

1 1.00 0.67 0.74 0.70 0.70 1.44 0.70 0.52

time (sec)

N/A 0.004 0.007 0.063 3.710 0.586 0.488 0.682 0.085

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

34 34 21 23 22 22 48 22 19

N.S.

1 1.00 0.62 0.68 0.65 0.65 1.41 0.65 0.56

time (sec)

N/A 0.003 0.050 0.069 4.791 0.606 0.646 0.790 0.069

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 18 20 19 14 60 19 14

N.S.

1 1.00 0.67 0.74 0.70 0.52 2.22 0.70 0.52

time (sec)

N/A 0.003 0.007 0.071 3.825 0.509 0.469 0.721 0.057

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

14 14 14 13 12 22 22 12 12

N.S.

1 1.00 1.00 0.93 0.86 1.57 1.57 0.86 0.86

time (sec)

N/A 0.014 0.018 0.129 2.340 0.589 0.048 0.717 0.065

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

13 13 15 11 11 11 8 11 10

N.S.

1 1.00 1.15 0.85 0.85 0.85 0.62 0.85 0.77

time (sec)

N/A 0.056 0.005 0.089 2.769 0.611 0.010 0.822 0.158

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

23 23 18 16 15 17 92 15 12

N.S.

1 1.00 0.78 0.70 0.65 0.74 4.00 0.65 0.52

time (sec)

N/A 0.003 0.010 0.078 2.648 0.873 0.475 0.810 0.031

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

8 8 8 7 6 10 8 6 6

N.S.

1 1.00 1.00 0.88 0.75 1.25 1.00 0.75 0.75

time (sec)

N/A 0.009 0.036 0.019 4.892 0.697 0.027 0.690 0.418

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 13 12 18 29 12 12

N.S.

1 1.00 1.00 0.81 0.75 1.12 1.81 0.75 0.75

time (sec)

N/A 0.015 0.015 0.072 4.348 0.703 0.093 0.828 0.171

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

6 6 6 7 6 6 5 6 6

N.S.

1 1.00 1.00 1.17 1.00 1.00 0.83 1.00 1.00

time (sec)

N/A 0.011 0.012 0.023 3.615 0.541 0.164 0.811 0.043

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

12 12 12 11 10 12 12 6 9

N.S.

1 1.00 1.00 0.92 0.83 1.00 1.00 0.50 0.75

time (sec)

N/A 0.036 0.090 0.051 3.178 0.494 0.243 0.762 0.199

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

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 0.018 0.018 0.056 3.236 0.445 0.092 0.746 0.171

Problem 13

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

9 9 9 10 9 9 7 9 9

N.S.

1 1.00 1.00 1.11 1.00 1.00 0.78 1.00 1.00

time (sec)

N/A 0.007 0.014 0.055 4.168 0.473 3.520 0.759 0.207

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 12 11 11 10 11 11

N.S.

1 1.00 1.00 0.80 0.73 0.73 0.67 0.73 0.73

time (sec)

N/A 0.002 0.009 0.067 3.777 0.407 0.079 0.868 0.354

Problem 15

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

23 23 18 16 15 15 34 15 12

N.S.

1 1.00 0.78 0.70 0.65 0.65 1.48 0.65 0.52

time (sec)

N/A 0.002 0.009 0.063 11.262 0.588 0.479 0.799 0.034

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

11 11 11 10 9 22 8 9 9

N.S.

1 1.00 1.00 0.91 0.82 2.00 0.73 0.82 0.82

time (sec)

N/A 0.001 0.023 0.062 2.584 0.793 0.343 0.699 0.072

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

15 15 15 12 11 11 27 11 11

N.S.

1 1.00 1.00 0.80 0.73 0.73 1.80 0.73 0.73

time (sec)

N/A 0.002 0.010 0.072 5.546 0.732 0.087 1.078 0.185

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

15 15 15 12 11 11 12 11 15

N.S.

1 1.00 1.00 0.80 0.73 0.73 0.80 0.73 1.00

time (sec)

N/A 0.018 0.038 0.076 4.389 3.361 0.098 0.745 0.239

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

32 32 32 0 0 23 0 15 47

N.S.

1 1.00 1.00 0.00 0.00 0.72 0.00 0.47 1.47

time (sec)

N/A 0.175 1.689 0.019 0.000 0.669 0.000 0.701 0.589

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

17 17 17 14 13 13 14 13 13

N.S.

1 1.00 1.00 0.82 0.76 0.76 0.82 0.76 0.76

time (sec)

N/A 0.071 0.025 0.061 3.776 0.494 0.105 0.585 0.210

Problem 21

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

16 16 13 10 7 12 15 12 9

N.S.

1 1.00 0.81 0.62 0.44 0.75 0.94 0.75 0.56

time (sec)

N/A 0.005 0.008 0.084 3.983 0.418 0.618 0.609 0.156

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

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 0.005 0.002 0.018 3.606 0.465 0.052 0.593 0.064

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

17 17 15 18 15 15 17 15 15

N.S.

1 1.00 0.88 1.06 0.88 0.88 1.00 0.88 0.88

time (sec)

N/A 0.013 0.013 0.017 5.855 0.458 0.081 0.543 0.033

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

23 23 19 24 20 20 26 20 24

N.S.

1 1.00 0.83 1.04 0.87 0.87 1.13 0.87 1.04

time (sec)

N/A 0.023 0.012 0.022 4.803 0.407 0.128 0.546 0.030

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

24 24 20 25 21 21 26 21 23

N.S.

1 1.00 0.83 1.04 0.88 0.88 1.08 0.88 0.96

time (sec)

N/A 0.023 0.011 0.023 1.920 0.426 0.127 0.537 0.030

Problem 26

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

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 0.005 0.001 0.012 4.396 0.451 0.024 0.499 0.019

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

23 23 18 18 14 17 24 14 18

N.S.

1 1.00 0.78 0.78 0.61 0.74 1.04 0.61 0.78

time (sec)

N/A 0.008 0.002 0.013 5.412 0.519 0.082 0.455 0.095

Problem 28

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

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 0.003 0.002 0.032 3.146 0.437 0.009 0.494 0.032

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

13 13 15 11 11 11 8 11 10

N.S.

1 1.00 1.15 0.85 0.85 0.85 0.62 0.85 0.77

time (sec)

N/A 0.004 0.002 0.000 3.095 0.456 0.010 0.469 0.002

Problem 30

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

24 24 22 18 16 19 24 16 16

N.S.

1 1.00 0.92 0.75 0.67 0.79 1.00 0.67 0.67

time (sec)

N/A 0.006 0.002 0.082 2.747 2.666 0.009 0.467 0.036

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

21 21 23 17 17 17 17 17 17

N.S.

1 1.00 1.10 0.81 0.81 0.81 0.81 0.81 0.81

time (sec)

N/A 0.004 0.002 0.101 4.231 1.390 0.012 0.468 0.043

Problem 32

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

34 34 30 24 24 25 36 22 22

N.S.

1 1.00 0.88 0.71 0.71 0.74 1.06 0.65 0.65

time (sec)

N/A 0.010 0.002 0.083 3.179 4.798 0.009 0.470 0.039

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

25 25 25 25 19 19 36 19 19

N.S.

1 1.00 1.00 1.00 0.76 0.76 1.44 0.76 0.76

time (sec)

N/A 0.009 0.009 0.018 2.744 1.922 0.085 0.493 0.093

Problem 34

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

33 33 31 23 23 23 39 23 25

N.S.

1 1.00 0.94 0.70 0.70 0.70 1.18 0.70 0.76

time (sec)

N/A 0.014 0.007 0.038 3.247 1.544 0.131 0.484 0.119

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

41 41 29 37 26 29 56 26 28

N.S.

1 1.00 0.71 0.90 0.63 0.71 1.37 0.63 0.68

time (sec)

N/A 0.018 0.024 0.043 2.515 1.568 0.130 0.508 0.063

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

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 0.004 0.002 0.016 2.257 1.252 0.008 0.504 0.026

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

11 11 15 11 9 10 8 9 9

N.S.

1 1.00 1.36 1.00 0.82 0.91 0.73 0.82 0.82

time (sec)

N/A 0.004 0.002 0.074 4.279 1.534 0.010 0.530 0.033

Problem 38

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

24 24 22 18 16 19 24 16 16

N.S.

1 1.00 0.92 0.75 0.67 0.79 1.00 0.67 0.67

time (sec)

N/A 0.008 0.002 0.101 4.496 1.056 0.008 0.461 0.029

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 84 61 75 60 60 180 50 37

N.S.

1 1.00 0.73 0.89 0.71 0.71 2.14 0.60 0.44

time (sec)

N/A 0.011 0.071 0.073 3.438 0.701 2.328 0.495 0.215

Problem 40

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 25 35 34 21 39 28 20

N.S.

1 1.00 0.66 0.92 0.89 0.55 1.03 0.74 0.53

time (sec)

N/A 0.009 0.012 0.074 2.895 0.612 0.229 0.509 0.029

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F C A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

172 172 34 168 0 17 31 0 301

N.S.

1 1.00 0.20 0.98 0.00 0.10 0.18 0.00 1.75

time (sec)

N/A 0.047 10.034 0.105 0.000 0.311 0.340 0.000 0.075

Problem 42

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

6 6 6 9 6 6 7 6 6

N.S.

1 1.00 1.00 1.50 1.00 1.00 1.17 1.00 1.00

time (sec)

N/A 0.003 0.006 0.010 3.168 0.794 0.012 0.497 0.070

Problem 43

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

14 14 18 15 12 12 19 12 12

N.S.

1 1.00 1.29 1.07 0.86 0.86 1.36 0.86 0.86

time (sec)

N/A 0.005 0.003 0.013 3.183 1.084 0.014 0.444 0.034

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

8 8 8 14 10 20 8 18 8

N.S.

1 1.00 1.00 1.75 1.25 2.50 1.00 2.25 1.00

time (sec)

N/A 0.004 0.005 0.011 2.442 1.213 0.012 0.462 0.057

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

12 12 18 16 16 48 19 34 10

N.S.

1 1.00 1.50 1.33 1.33 4.00 1.58 2.83 0.83

time (sec)

N/A 0.007 0.003 0.028 1.945 1.719 0.015 0.490 0.022

Problem 46

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 26 21 20 18 26 18 20

N.S.

1 1.00 1.18 0.95 0.91 0.82 1.18 0.82 0.91

time (sec)

N/A 0.007 0.014 0.023 1.065 2.308 0.057 0.506 0.103

Problem 47

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

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 0.001 0.001 0.059 2.197 1.652 0.058 0.501 0.025

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

13 13 11 10 9 51 58 9 9

N.S.

1 1.00 0.85 0.77 0.69 3.92 4.46 0.69 0.69

time (sec)

N/A 0.001 0.001 0.064 2.561 0.958 0.009 0.454 0.097

Problem 49

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 16 20 19 19 15 14 14

N.S.

1 1.00 0.89 1.11 1.06 1.06 0.83 0.78 0.78

time (sec)

N/A 0.001 0.003 0.064 1.343 2.029 0.030 0.477 0.042

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

11 11 43 10 9 31 31 9 31

N.S.

1 1.00 3.91 0.91 0.82 2.82 2.82 0.82 2.82

time (sec)

N/A 0.001 0.001 0.056 1.296 1.114 0.007 0.436 0.025

Problem 51

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

56 56 140 107 106 106 131 106 106

N.S.

1 1.00 2.50 1.91 1.89 1.89 2.34 1.89 1.89

time (sec)

N/A 0.023 0.002 0.066 0.772 0.925 0.017 0.458 0.464

Problem 52

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

4 4 4 5 4 4 3 4 4

N.S.

1 1.00 1.00 1.25 1.00 1.00 0.75 1.00 1.00

time (sec)

N/A 0.006 0.008 0.014 1.740 0.694 0.166 0.456 0.096

Problem 53

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

62 62 46 49 37 37 60 37 41

N.S.

1 1.00 0.74 0.79 0.60 0.60 0.97 0.60 0.66

time (sec)

N/A 0.027 0.023 0.012 0.888 1.157 0.350 0.424 0.226

Problem 54

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

10 10 10 9 8 8 8 8 8

N.S.

1 1.00 1.00 0.90 0.80 0.80 0.80 0.80 0.80

time (sec)

N/A 0.005 0.002 0.018 0.946 0.927 0.079 0.444 0.050

Problem 55

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

16 16 16 13 12 12 15 12 12

N.S.

1 1.00 1.00 0.81 0.75 0.75 0.94 0.75 0.75

time (sec)

N/A 0.038 0.010 0.038 0.830 1.193 0.983 0.443 0.193

Problem 56

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

10 10 10 9 8 8 7 9 6

N.S.

1 1.00 1.00 0.90 0.80 0.80 0.70 0.90 0.60

time (sec)

N/A 0.001 0.001 0.061 2.921 0.927 0.006 0.520 0.074

Problem 57

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 12 15 15 15 12

N.S.

1 1.00 1.00 1.07 0.80 1.00 1.00 1.00 0.80

time (sec)

N/A 0.002 0.002 0.018 3.278 1.198 0.028 0.444 0.079

Problem 58

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 9

N.S.

1 1.00 1.00 0.82 0.76 0.76 0.71 0.76 0.53

time (sec)

N/A 0.002 0.001 0.004 2.443 1.111 0.024 0.470 0.032

Problem 59

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

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 0.006 0.002 0.005 1.793 1.682 0.034 0.458 0.030

Problem 60

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

4 4 4 5 4 4 3 5 4

N.S.

1 1.00 1.00 1.25 1.00 1.00 0.75 1.25 1.00

time (sec)

N/A 0.000 0.001 0.058 2.998 1.060 0.005 0.452 0.015

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

3 3 3 4 3 11 3 4 3

N.S.

1 1.00 1.00 1.33 1.00 3.67 1.00 1.33 1.00

time (sec)

N/A 0.002 0.002 0.012 3.586 1.259 0.027 0.440 0.023

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

28 28 21 36 28 32 61 0 38

N.S.

1 1.00 0.75 1.29 1.00 1.14 2.18 0.00 1.36

time (sec)

N/A 0.007 0.005 0.037 0.294 0.935 0.201 0.000 0.205

Problem 63

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

28 28 28 23 17 22 26 22 17

N.S.

1 1.00 1.00 0.82 0.61 0.79 0.93 0.79 0.61

time (sec)

N/A 0.011 0.002 0.005 4.004 0.980 0.035 0.486 0.029

Problem 64

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

3 3 3 4 3 3 3 4 3

N.S.

1 1.00 1.00 1.33 1.00 1.00 1.00 1.33 1.00

time (sec)

N/A 0.008 0.004 0.021 7.557 0.951 0.027 0.436 0.070

Problem 65

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 0.012 0.003 0.066 4.527 1.083 0.026 0.426 0.346

Problem 66

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

23 23 16 18 17 12 20 17 13

N.S.

1 1.00 0.70 0.78 0.74 0.52 0.87 0.74 0.57

time (sec)

N/A 0.026 0.018 0.059 5.802 0.905 2.413 0.477 0.168

Problem 67

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

39 39 39 32 23 31 37 31 23

N.S.

1 1.00 1.00 0.82 0.59 0.79 0.95 0.79 0.59

time (sec)

N/A 0.019 0.002 0.008 3.240 0.964 0.047 0.464 0.036

Problem 68

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

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 0.008 0.010 0.010 2.981 0.898 0.023 0.493 0.076

Problem 69

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

14 14 14 12 12 11 10 11 11

N.S.

1 1.00 1.00 0.86 0.86 0.79 0.71 0.79 0.79

time (sec)

N/A 0.008 0.003 0.019 1.534 1.322 0.047 0.518 0.105

Problem 70

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

10 10 10 8 7 7 7 7 7

N.S.

1 1.00 1.00 0.80 0.70 0.70 0.70 0.70 0.70

time (sec)

N/A 0.006 0.006 0.026 2.150 1.345 0.107 0.512 0.101

Problem 71

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

19 19 14 14 11 13 15 11 11

N.S.

1 1.00 0.74 0.74 0.58 0.68 0.79 0.58 0.58

time (sec)

N/A 0.005 0.010 0.021 2.873 1.397 0.084 0.425 0.018

Problem 72

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

19 19 12 14 9 13 15 9 9

N.S.

1 1.00 0.63 0.74 0.47 0.68 0.79 0.47 0.47

time (sec)

N/A 0.004 0.007 0.023 4.390 1.056 0.081 0.500 0.019

Problem 73

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

10 10 10 12 9 9 7 9 9

N.S.

1 1.00 1.00 1.20 0.90 0.90 0.70 0.90 0.90

time (sec)

N/A 0.004 0.009 0.010 1.473 0.847 0.018 0.471 0.045

Problem 74

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

11 11 7 10 6 6 5 6 6

N.S.

1 1.00 0.64 0.91 0.55 0.55 0.45 0.55 0.55

time (sec)

N/A 0.004 0.005 0.023 2.480 0.901 0.021 0.431 0.018

Problem 75

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

16 16 11 15 9 9 7 9 9

N.S.

1 1.00 0.69 0.94 0.56 0.56 0.44 0.56 0.56

time (sec)

N/A 0.004 0.009 0.010 3.358 0.698 0.022 0.439 0.021

Problem 76

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

19 19 12 17 11 11 10 11 11

N.S.

1 1.00 0.63 0.89 0.58 0.58 0.53 0.58 0.58

time (sec)

N/A 0.009 0.010 0.009 1.425 0.775 0.022 0.452 0.022

Problem 77

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

32 32 19 30 16 16 17 16 16

N.S.

1 1.00 0.59 0.94 0.50 0.50 0.53 0.50 0.50

time (sec)

N/A 0.011 0.012 0.013 2.493 0.782 0.023 0.445 0.075

Problem 78

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

24 24 16 17 11 11 20 11 11

N.S.

1 1.00 0.67 0.71 0.46 0.46 0.83 0.46 0.46

time (sec)

N/A 0.005 0.006 0.005 1.807 0.881 0.061 0.509 0.024

Problem 79

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

26 26 16 21 13 13 12 13 13

N.S.

1 1.00 0.62 0.81 0.50 0.50 0.46 0.50 0.50

time (sec)

N/A 0.013 0.017 0.032 2.141 0.712 0.023 0.643 0.109

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 28 40 27 31 136 36 27

N.S.

1 1.00 0.68 0.98 0.66 0.76 3.32 0.88 0.66

time (sec)

N/A 0.010 0.023 0.049 2.303 0.735 0.266 0.574 0.032

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 29 41 29 33 139 38 29

N.S.

1 1.00 0.69 0.98 0.69 0.79 3.31 0.90 0.69

time (sec)

N/A 0.007 0.023 0.022 1.582 0.821 0.273 0.548 0.021

Problem 82

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 21 13

N.S.

1 1.00 1.00 0.93 0.87 0.87 0.80 1.40 0.87

time (sec)

N/A 0.002 0.002 0.022 3.448 0.997 0.062 0.524 0.105

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A C B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 64 22 35 33 17 37 21

N.S.

1 1.00 3.37 1.16 1.84 1.74 0.89 1.95 1.11

time (sec)

N/A 0.006 0.050 0.006 4.812 0.806 1.105 0.498 0.609

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

17 17 64 20 35 35 17 37 20

N.S.

1 1.00 3.76 1.18 2.06 2.06 1.00 2.18 1.18

time (sec)

N/A 0.006 0.027 0.003 2.946 0.901 1.119 0.481 0.209

Problem 85

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 24 23 23 22 23 22

N.S.

1 1.00 1.00 0.96 0.92 0.92 0.88 0.92 0.88

time (sec)

N/A 0.021 0.006 0.030 3.873 0.941 0.060 0.474 0.032

Problem 86

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 33 39 22 38 20

N.S.

1 1.00 1.00 0.95 1.50 1.77 1.00 1.73 0.91

time (sec)

N/A 0.010 0.003 0.005 2.406 0.910 0.983 0.474 0.021

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 15 6 23 19 28 14

N.S.

1 1.00 1.00 0.94 0.38 1.44 1.19 1.75 0.88

time (sec)

N/A 0.001 0.003 0.076 3.264 0.992 0.442 0.478 0.163

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

10 10 23 10 11 21 0 27 11

N.S.

1 1.00 2.30 1.00 1.10 2.10 0.00 2.70 1.10

time (sec)

N/A 0.009 0.055 0.117 1.239 0.992 0.000 0.460 0.090

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A C A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

10 10 10 11 10 10 20 10 10

N.S.

1 1.00 1.00 1.10 1.00 1.00 2.00 1.00 1.00

time (sec)

N/A 0.083 0.002 0.074 2.190 0.926 0.036 0.461 0.036

Problem 90

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 0.009 0.004 0.077 1.573 0.718 0.048 0.427 0.101

Problem 91

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

19 19 19 17 16 16 26 16 16

N.S.

1 1.00 1.00 0.89 0.84 0.84 1.37 0.84 0.84

time (sec)

N/A 0.009 0.005 0.155 1.430 1.194 0.034 0.434 0.076

Problem 92

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

21 21 21 16 15 13 15 15 14

N.S.

1 1.00 1.00 0.76 0.71 0.62 0.71 0.71 0.67

time (sec)

N/A 0.005 0.003 0.020 2.099 1.008 0.073 0.464 0.023

Problem 93

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

40 40 30 34 33 24 32 33 24

N.S.

1 1.00 0.75 0.85 0.82 0.60 0.80 0.82 0.60

time (sec)

N/A 0.014 0.009 0.013 1.906 1.061 0.093 0.463 0.029

Problem 94

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 26 30 34 25 29 29 29

N.S.

1 1.00 0.74 0.86 0.97 0.71 0.83 0.83 0.83

time (sec)

N/A 0.035 0.007 0.036 1.503 0.818 0.094 0.461 0.124

Problem 95

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 18 17 16 14 19 16 16

N.S.

1 1.00 0.82 0.77 0.73 0.64 0.86 0.73 0.73

time (sec)

N/A 0.004 0.012 0.007 3.529 0.936 0.718 0.519 0.057

Problem 96

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

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 0.023 0.006 0.055 1.890 0.958 0.425 0.498 0.661

Problem 97

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

23 23 37 18 17 31 15 17 17

N.S.

1 1.00 1.61 0.78 0.74 1.35 0.65 0.74 0.74

time (sec)

N/A 0.002 0.035 0.072 1.505 0.839 0.063 0.467 0.078

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A F A A B F

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

22 22 37 16 0 15 31 57 -1

N.S.

1 1.00 1.68 0.73 0.00 0.68 1.41 2.59 -0.05

time (sec)

N/A 0.026 0.008 0.071 0.000 0.946 11.595 0.476 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

20 20 20 16 0 15 31 22 -1

N.S.

1 1.00 1.00 0.80 0.00 0.75 1.55 1.10 -0.05

time (sec)

N/A 0.014 0.005 0.066 0.000 0.896 11.050 0.456 0.000

Problem 100

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

19 19 19 16 15 21 12 15 17

N.S.

1 1.00 1.00 0.84 0.79 1.11 0.63 0.79 0.89

time (sec)

N/A 0.002 0.006 0.084 1.084 0.992 0.032 0.441 0.028

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