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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 B A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

10 10 21 11 10 10 12 10 10

N.S.

1 1.00 2.10 1.10 1.00 1.00 1.20 1.00 1.00

time (sec)

N/A 0.003 0.056 0.085 0.287 0.351 0.038 0.453 0.249

Problem 2

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

25 25 23 27 22 22 46 18 18

N.S.

1 1.00 0.92 1.08 0.88 0.88 1.84 0.72 0.72

time (sec)

N/A 0.006 0.019 0.038 0.272 0.356 0.068 0.490 0.228

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

26 26 26 22 22 21 36 22 24

N.S.

1 1.00 1.00 0.85 0.85 0.81 1.38 0.85 0.92

time (sec)

N/A 0.008 0.006 0.073 0.268 0.354 0.093 0.467 0.071

Problem 4

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

46 46 33 38 33 36 95 32 31

N.S.

1 1.00 0.72 0.83 0.72 0.78 2.07 0.70 0.67

time (sec)

N/A 0.014 0.026 0.080 0.278 0.390 0.156 0.463 0.188

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

41 41 44 32 34 33 58 34 31

N.S.

1 1.00 1.07 0.78 0.83 0.80 1.41 0.83 0.76

time (sec)

N/A 0.011 0.010 0.069 0.277 0.354 0.231 0.460 0.095

Problem 6

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

67 67 43 48 48 46 139 46 42

N.S.

1 1.00 0.64 0.72 0.72 0.69 2.07 0.69 0.63

time (sec)

N/A 0.022 0.023 0.092 0.276 0.378 0.371 0.448 0.222

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

54 54 59 42 44 43 78 44 43

N.S.

1 1.00 1.09 0.78 0.81 0.80 1.44 0.81 0.80

time (sec)

N/A 0.011 0.009 0.065 0.268 0.365 0.551 0.469 0.090

Problem 8

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

88 88 55 58 59 56 184 60 53

N.S.

1 1.00 0.62 0.66 0.67 0.64 2.09 0.68 0.60

time (sec)

N/A 0.031 0.034 0.112 0.273 0.360 0.847 0.451 0.279

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F(-2) F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 51 199 0 80 0 0 42

N.S.

1 1.00 0.78 3.06 0.00 1.23 0.00 0.00 0.65

time (sec)

N/A 0.021 0.176 0.089 0.000 0.121 0.000 0.000 0.294

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F(-2) F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 40 202 0 74 0 0 42

N.S.

1 1.00 0.95 4.81 0.00 1.76 0.00 0.00 1.00

time (sec)

N/A 0.014 0.031 0.033 0.000 0.117 0.000 0.000 0.166

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 36 179 0 68 0 0 35

N.S.

1 1.00 0.86 4.26 0.00 1.62 0.00 0.00 0.83

time (sec)

N/A 0.013 0.026 0.032 0.000 0.092 0.000 0.000 0.078

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 133 0 57 0 0 15

N.S.

1 1.00 1.00 8.31 0.00 3.56 0.00 0.00 0.94

time (sec)

N/A 0.007 0.015 0.100 0.000 0.113 0.000 0.000 0.116

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F C F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 18 0 51 0 0 15

N.S.

1 1.00 1.00 1.12 0.00 3.19 0.00 0.00 0.94

time (sec)

N/A 0.007 0.019 0.029 0.000 0.105 0.000 0.000 0.097

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 38 182 0 93 0 0 42

N.S.

1 1.00 1.00 4.79 0.00 2.45 0.00 0.00 1.11

time (sec)

N/A 0.013 0.037 0.037 0.000 0.111 0.000 0.000 0.246

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 36 213 0 92 0 0 42

N.S.

1 1.00 0.86 5.07 0.00 2.19 0.00 0.00 1.00

time (sec)

N/A 0.013 0.038 0.040 0.000 0.097 0.000 0.000 0.265

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F(-2) F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 59 358 0 110 0 0 42

N.S.

1 1.00 0.91 5.51 0.00 1.69 0.00 0.00 0.65

time (sec)

N/A 0.020 0.062 0.048 0.000 0.105 0.000 0.000 0.309

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 76 210 0 95 0 0 -1

N.S.

1 1.00 0.78 2.14 0.00 0.97 0.00 0.00 -0.01

time (sec)

N/A 0.038 0.058 0.054 0.000 0.105 0.000 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 62 213 0 91 0 0 -1

N.S.

1 1.00 0.89 3.04 0.00 1.30 0.00 0.00 -0.01

time (sec)

N/A 0.024 0.054 0.036 0.000 0.097 0.000 0.000 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 58 190 0 77 0 0 -1

N.S.

1 1.00 0.83 2.71 0.00 1.10 0.00 0.00 -0.01

time (sec)

N/A 0.026 0.029 0.035 0.000 0.098 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 38 142 0 63 0 0 -1

N.S.

1 1.00 1.00 3.74 0.00 1.66 0.00 0.00 -0.03

time (sec)

N/A 0.014 0.014 0.073 0.000 0.091 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F C F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 38 54 0 60 0 0 33

N.S.

1 1.00 1.00 1.42 0.00 1.58 0.00 0.00 0.87

time (sec)

N/A 0.014 0.017 0.043 0.000 0.089 0.000 0.000 0.146

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 50 198 0 104 0 0 -1

N.S.

1 1.00 0.74 2.91 0.00 1.53 0.00 0.00 -0.01

time (sec)

N/A 0.024 0.021 0.041 0.000 0.095 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 51 241 0 103 0 0 -1

N.S.

1 1.00 0.71 3.35 0.00 1.43 0.00 0.00 -0.01

time (sec)

N/A 0.025 0.039 0.041 0.000 0.111 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 68 366 0 121 0 0 -1

N.S.

1 1.00 0.68 3.66 0.00 1.21 0.00 0.00 -0.01

time (sec)

N/A 0.037 0.061 0.056 0.000 0.100 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

53 53 53 0 0 0 0 0 42

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.79

time (sec)

N/A 0.009 0.040 0.017 0.000 0.000 0.000 0.000 0.193

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

53 53 53 0 0 0 0 0 42

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.79

time (sec)

N/A 0.009 0.020 0.014 0.000 0.000 0.000 0.000 0.191

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

53 53 53 0 0 0 0 0 42

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.79

time (sec)

N/A 0.009 0.020 0.015 0.000 0.000 0.000 0.000 0.182

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

53 53 53 0 0 0 0 0 42

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.79

time (sec)

N/A 0.010 0.017 0.015 0.000 0.000 0.000 0.000 0.210

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 51 0 0 0 0 0 42

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.82

time (sec)

N/A 0.010 0.017 0.015 0.000 0.000 0.000 0.000 0.203

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 51 0 0 0 0 0 42

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.82

time (sec)

N/A 0.009 0.017 0.016 0.000 0.000 0.000 0.000 0.227

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 55 0 0 0 0 0 -1

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.011 0.031 0.014 0.000 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 55 0 0 0 0 0 -1

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.011 0.024 0.015 0.000 0.000 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 55 0 0 0 0 0 -1

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.011 0.023 0.013 0.000 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 55 0 0 0 0 0 -1

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.011 0.026 0.012 0.000 0.000 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 53 0 0 0 0 0 -1

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.011 0.026 0.011 0.000 0.000 0.000 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 53 0 0 0 0 0 -1

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.011 0.026 0.013 0.000 0.000 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 64 0 0 0 0 0 57

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.89

time (sec)

N/A 0.011 0.029 0.020 0.000 0.000 0.000 0.000 0.535

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 64 0 0 0 0 0 -1

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.013 0.027 0.020 0.000 0.000 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

53 53 36 32 31 40 0 34 -1

N.S.

1 1.00 0.68 0.60 0.58 0.75 0.00 0.64 -0.02

time (sec)

N/A 0.026 0.013 0.054 0.519 0.372 0.000 0.433 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 26 24 17 26 0 17 -1

N.S.

1 1.00 0.76 0.71 0.50 0.76 0.00 0.50 -0.03

time (sec)

N/A 0.015 0.007 0.033 0.515 0.369 0.000 0.464 0.000

Problem 41

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 15 6 15 15 9 46

N.S.

1 1.00 1.00 1.15 0.46 1.15 1.15 0.69 3.54

time (sec)

N/A 0.007 0.003 0.031 0.513 0.349 0.180 0.530 0.214

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 46 48 38 65 0 0 -1

N.S.

1 1.00 2.88 3.00 2.38 4.06 0.00 0.00 -0.06

time (sec)

N/A 0.008 0.018 0.046 0.529 0.368 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 91 70 304 40 0 57 -1

N.S.

1 1.00 2.17 1.67 7.24 0.95 0.00 1.36 -0.02

time (sec)

N/A 0.014 0.038 0.048 0.540 0.372 0.000 0.560 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

61 61 72 89 933 49 0 35 -1

N.S.

1 1.00 1.18 1.46 15.30 0.80 0.00 0.57 -0.02

time (sec)

N/A 0.025 0.093 0.054 0.799 0.394 0.000 0.453 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 61 114 0 92 0 0 -1

N.S.

1 1.00 0.52 0.97 0.00 0.79 0.00 0.00 -0.01

time (sec)

N/A 0.032 0.071 0.266 0.000 0.143 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 50 198 0 66 0 0 -1

N.S.

1 1.00 0.75 2.96 0.00 0.99 0.00 0.00 -0.01

time (sec)

N/A 0.021 0.045 0.085 0.000 0.123 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

44 44 37 76 0 59 0 0 -1

N.S.

1 1.00 0.84 1.73 0.00 1.34 0.00 0.00 -0.02

time (sec)

N/A 0.015 0.016 0.089 0.000 0.093 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 31 191 0 71 0 0 -1

N.S.

1 1.00 0.74 4.55 0.00 1.69 0.00 0.00 -0.02

time (sec)

N/A 0.015 0.014 0.149 0.000 0.093 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 44 87 0 74 0 0 -1

N.S.

1 1.00 0.62 1.23 0.00 1.04 0.00 0.00 -0.01

time (sec)

N/A 0.021 0.039 0.233 0.000 0.102 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 57 223 0 92 0 0 -1

N.S.

1 1.00 0.49 1.91 0.00 0.79 0.00 0.00 -0.01

time (sec)

N/A 0.032 0.067 0.337 0.000 0.121 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 53 57 85 68 0 57 -1

N.S.

1 1.00 0.40 0.43 0.64 0.52 0.00 0.43 -0.01

time (sec)

N/A 0.035 0.076 0.413 0.495 0.368 0.000 0.443 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 38 41 55 42 0 25 -1

N.S.

1 1.00 0.49 0.53 0.71 0.54 0.00 0.32 -0.01

time (sec)

N/A 0.025 0.044 0.148 0.495 0.369 0.000 0.462 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 36 25 22 22 21 0 13 -1

N.S.

1 1.00 0.69 0.61 0.61 0.58 0.00 0.36 -0.03

time (sec)

N/A 0.011 0.009 0.079 0.514 0.391 0.000 0.440 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

15 15 15 14 6 18 0 6 6

N.S.

1 1.00 1.00 0.93 0.40 1.20 0.00 0.40 0.40

time (sec)

N/A 0.011 0.004 0.076 0.500 0.374 0.000 0.455 0.231

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 30 29 22 33 0 22 36

N.S.

1 1.00 0.45 0.43 0.33 0.49 0.00 0.33 0.54

time (sec)

N/A 0.015 0.017 0.094 0.497 0.373 0.000 0.446 0.541

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 47 41 34 45 0 34 306

N.S.

1 1.00 0.40 0.35 0.29 0.38 0.00 0.29 2.62

time (sec)

N/A 0.021 0.029 0.168 0.488 0.393 0.000 0.457 3.744

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 72 0 0 0 0 0 -1

N.S.

1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.025 0.041 0.053 0.000 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 74 0 0 0 0 0 -1

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.029 0.106 0.053 0.000 0.000 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 72 0 0 0 0 0 -1

N.S.

1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.030 0.076 0.044 0.000 0.000 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 68 0 0 0 0 0 -1

N.S.

1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.027 0.045 0.047 0.000 0.000 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 72 0 0 0 0 0 -1

N.S.

1 1.00 0.90 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.028 0.049 0.043 0.000 0.000 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 72 0 0 0 0 0 -1

N.S.

1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.030 0.067 0.040 0.000 0.000 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 74 0 0 0 0 0 -1

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.029 0.067 0.039 0.000 0.000 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

24 24 24 0 0 15 61 300 40

N.S.

1 1.00 1.00 0.00 0.00 0.62 2.54 12.50 1.67

time (sec)

N/A 0.013 0.018 0.046 0.000 0.368 0.441 1.203 0.404

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 74 0 0 0 0 0 -1

N.S.

1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.029 0.036 0.053 0.000 0.000 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 83 234 0 98 0 0 -1

N.S.

1 1.00 0.67 1.90 0.00 0.80 0.00 0.00 -0.01

time (sec)

N/A 0.060 0.128 0.136 0.000 0.121 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 75 221 0 101 0 0 -1

N.S.

1 1.00 0.77 2.28 0.00 1.04 0.00 0.00 -0.01

time (sec)

N/A 0.043 0.096 0.086 0.000 0.113 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 73 208 0 88 0 0 -1

N.S.

1 1.00 0.77 2.19 0.00 0.93 0.00 0.00 -0.01

time (sec)

N/A 0.042 0.090 0.084 0.000 0.106 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 62 211 0 88 0 0 -1

N.S.

1 1.00 0.90 3.06 0.00 1.28 0.00 0.00 -0.01

time (sec)

N/A 0.028 0.040 0.083 0.000 0.114 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 61 188 0 76 0 0 -1

N.S.

1 1.00 0.91 2.81 0.00 1.13 0.00 0.00 -0.01

time (sec)

N/A 0.029 0.039 0.080 0.000 0.106 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 38 142 0 63 0 0 -1

N.S.

1 1.00 1.00 3.74 0.00 1.66 0.00 0.00 -0.03

time (sec)

N/A 0.015 0.016 0.177 0.000 0.102 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 39 142 0 57 0 0 -1

N.S.

1 1.00 1.00 3.64 0.00 1.46 0.00 0.00 -0.03

time (sec)

N/A 0.020 0.021 0.096 0.000 0.101 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 48 196 0 101 0 0 -1

N.S.

1 1.00 0.76 3.11 0.00 1.60 0.00 0.00 -0.02

time (sec)

N/A 0.035 0.037 0.095 0.000 0.097 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 49 239 0 100 0 0 -1

N.S.

1 1.00 0.70 3.41 0.00 1.43 0.00 0.00 -0.01

time (sec)

N/A 0.037 0.055 0.104 0.000 0.099 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 69 363 0 118 0 0 -1

N.S.

1 1.00 0.73 3.82 0.00 1.24 0.00 0.00 -0.01

time (sec)

N/A 0.054 0.142 0.129 0.000 0.112 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 69 396 0 112 0 0 -1

N.S.

1 1.00 0.70 4.04 0.00 1.14 0.00 0.00 -0.01

time (sec)

N/A 0.050 0.122 0.110 0.000 0.097 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 79 412 0 128 0 0 -1

N.S.

1 1.00 0.64 3.35 0.00 1.04 0.00 0.00 -0.01

time (sec)

N/A 0.066 0.134 0.144 0.000 0.109 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 83 236 0 102 0 0 -1

N.S.

1 1.00 0.66 1.87 0.00 0.81 0.00 0.00 -0.01

time (sec)

N/A 0.059 0.065 0.082 0.000 0.123 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

95 95 75 223 0 103 0 0 -1

N.S.

1 1.00 0.79 2.35 0.00 1.08 0.00 0.00 -0.01

time (sec)

N/A 0.040 0.064 0.082 0.000 0.111 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 73 210 0 91 0 0 -1

N.S.

1 1.00 0.74 2.14 0.00 0.93 0.00 0.00 -0.01

time (sec)

N/A 0.041 0.063 0.080 0.000 0.098 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 65 213 0 89 0 0 -1

N.S.

1 1.00 0.97 3.18 0.00 1.33 0.00 0.00 -0.01

time (sec)

N/A 0.028 0.057 0.079 0.000 0.115 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 58 190 0 77 0 0 -1

N.S.

1 1.00 0.83 2.71 0.00 1.10 0.00 0.00 -0.01

time (sec)

N/A 0.024 0.011 0.070 0.000 0.101 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

39 39 39 144 0 63 0 0 -1

N.S.

1 1.00 1.00 3.69 0.00 1.62 0.00 0.00 -0.03

time (sec)

N/A 0.021 0.011 0.085 0.000 0.101 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 41 144 0 57 0 0 -1

N.S.

1 1.00 1.00 3.51 0.00 1.39 0.00 0.00 -0.02

time (sec)

N/A 0.027 0.015 0.085 0.000 0.119 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 50 198 0 102 0 0 -1

N.S.

1 1.00 0.76 3.00 0.00 1.55 0.00 0.00 -0.02

time (sec)

N/A 0.038 0.035 0.091 0.000 0.117 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 51 241 0 101 0 0 -1

N.S.

1 1.00 0.71 3.35 0.00 1.40 0.00 0.00 -0.01

time (sec)

N/A 0.038 0.043 0.091 0.000 0.096 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 69 364 0 119 0 0 -1

N.S.

1 1.00 0.70 3.71 0.00 1.21 0.00 0.00 -0.01

time (sec)

N/A 0.053 0.075 0.112 0.000 0.117 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 69 398 0 115 0 0 -1

N.S.

1 1.00 0.69 3.98 0.00 1.15 0.00 0.00 -0.01

time (sec)

N/A 0.051 0.085 0.099 0.000 0.118 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 79 414 0 132 0 0 -1

N.S.

1 1.00 0.63 3.29 0.00 1.05 0.00 0.00 -0.01

time (sec)

N/A 0.067 0.115 0.131 0.000 0.119 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

125 125 83 236 0 108 0 0 -1

N.S.

1 1.00 0.66 1.89 0.00 0.86 0.00 0.00 -0.01

time (sec)

N/A 0.062 0.087 0.085 0.000 0.123 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 75 223 0 107 0 0 -1

N.S.

1 1.00 0.77 2.28 0.00 1.09 0.00 0.00 -0.01

time (sec)

N/A 0.044 0.067 0.084 0.000 0.150 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 76 210 0 95 0 0 -1

N.S.

1 1.00 0.78 2.16 0.00 0.98 0.00 0.00 -0.01

time (sec)

N/A 0.044 0.061 0.079 0.000 0.118 0.000 0.000 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B F C F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 62 213 0 91 0 0 -1

N.S.

1 1.00 0.89 3.04 0.00 1.30 0.00 0.00 -0.01

time (sec)

N/A 0.025 0.012 0.069 0.000 0.120 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 59 190 0 79 0 0 -1

N.S.

1 1.00 0.82 2.64 0.00 1.10 0.00 0.00 -0.01

time (sec)

N/A 0.033 0.016 0.079 0.000 0.105 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 41 144 0 63 0 0 -1

N.S.

1 1.00 1.00 3.51 0.00 1.54 0.00 0.00 -0.02

time (sec)

N/A 0.026 0.011 0.091 0.000 0.096 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 38 144 0 57 0 0 -1

N.S.

1 1.00 0.93 3.51 0.00 1.39 0.00 0.00 -0.02

time (sec)

N/A 0.027 0.029 0.089 0.000 0.102 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 50 198 0 104 0 0 -1

N.S.

1 1.00 0.74 2.91 0.00 1.53 0.00 0.00 -0.01

time (sec)

N/A 0.038 0.036 0.095 0.000 0.096 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 51 241 0 103 0 0 -1

N.S.

1 1.00 0.71 3.35 0.00 1.43 0.00 0.00 -0.01

time (sec)

N/A 0.038 0.045 0.093 0.000 0.103 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 69 366 0 123 0 0 -1

N.S.

1 1.00 0.69 3.66 0.00 1.23 0.00 0.00 -0.01

time (sec)

N/A 0.052 0.097 0.117 0.000 0.126 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 69 398 0 119 0 0 -1

N.S.

1 1.00 0.69 3.98 0.00 1.19 0.00 0.00 -0.01

time (sec)

N/A 0.051 0.116 0.098 0.000 0.112 0.000 0.000 0.000

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