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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 B A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 73 147 72 72 66 0 69

N.S.

1 1.00 0.85 1.71 0.84 0.84 0.77 0.00 0.80

time (sec)

N/A 0.036 0.032 0.356 0.270 0.370 3.188 0.000 0.309

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 65 120 64 64 58 0 61

N.S.

1 1.00 0.86 1.58 0.84 0.84 0.76 0.00 0.80

time (sec)

N/A 0.031 0.025 0.358 0.262 0.351 1.732 0.000 0.246

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 57 93 56 56 49 0 53

N.S.

1 1.00 0.86 1.41 0.85 0.85 0.74 0.00 0.80

time (sec)

N/A 0.028 0.021 0.375 0.282 0.367 0.892 0.000 0.226

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 48 66 48 48 41 0 46

N.S.

1 1.00 0.86 1.18 0.86 0.86 0.73 0.00 0.82

time (sec)

N/A 0.020 0.021 0.351 0.257 0.360 0.484 0.000 0.341

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

29 29 26 34 29 29 22 0 32

N.S.

1 1.00 0.90 1.17 1.00 1.00 0.76 0.00 1.10

time (sec)

N/A 0.006 0.011 0.288 0.258 0.352 0.251 0.000 0.257

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A F A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

5 5 5 6 5 0 3 0 5

N.S.

1 1.00 1.00 1.20 1.00 0.00 0.60 0.00 1.00

time (sec)

N/A 0.006 0.002 0.087 0.276 0.000 0.401 0.000 0.175

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 36 36 42 28 34 24 0 34

N.S.

1 1.00 1.00 1.17 0.78 0.94 0.67 0.00 0.94

time (sec)

N/A 0.015 0.010 0.386 0.267 0.349 0.365 0.000 0.202

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 50 61 40 47 42 0 51

N.S.

1 1.00 0.86 1.05 0.69 0.81 0.72 0.00 0.88

time (sec)

N/A 0.023 0.017 0.441 0.265 0.360 0.672 0.000 0.298

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 52 76 49 56 51 0 57

N.S.

1 1.00 0.76 1.12 0.72 0.82 0.75 0.00 0.84

time (sec)

N/A 0.026 0.023 0.453 0.269 0.385 1.229 0.000 0.319

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 60 95 58 65 60 0 60

N.S.

1 1.00 0.77 1.22 0.74 0.83 0.77 0.00 0.77

time (sec)

N/A 0.028 0.026 0.442 0.258 0.366 2.285 0.000 0.443

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 86 78 77 77 0 0 71

N.S.

1 1.00 0.98 0.89 0.88 0.88 0.00 0.00 0.81

time (sec)

N/A 0.039 0.009 0.129 0.255 0.358 0.000 0.000 0.819

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 78 69 69 69 0 0 63

N.S.

1 1.00 1.00 0.88 0.88 0.88 0.00 0.00 0.81

time (sec)

N/A 0.034 0.008 0.129 0.260 0.350 0.000 0.000 0.949

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 69 62 61 61 0 0 55

N.S.

1 1.00 1.01 0.91 0.90 0.90 0.00 0.00 0.81

time (sec)

N/A 0.024 0.007 0.139 0.260 0.385 0.000 0.000 0.904

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 39 41 39 39 0 0 37

N.S.

1 1.00 1.15 1.21 1.15 1.15 0.00 0.00 1.09

time (sec)

N/A 0.007 0.009 0.089 0.271 0.333 0.000 0.000 0.844

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A F A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

5 5 5 6 5 0 3 0 -1

N.S.

1 1.00 1.00 1.20 1.00 0.00 0.60 0.00 -0.20

time (sec)

N/A 0.006 0.002 0.128 0.252 0.000 0.194 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 44 57 33 39 0 0 36

N.S.

1 1.00 0.96 1.24 0.72 0.85 0.00 0.00 0.78

time (sec)

N/A 0.021 0.025 0.118 0.262 0.395 0.000 0.000 0.886

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F F B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

70 70 25 90 47 54 0 0 46

N.S.

1 1.00 0.36 1.29 0.67 0.77 0.00 0.00 0.66

time (sec)

N/A 0.030 0.008 0.208 0.254 0.364 0.000 0.000 1.273

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F F B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

80 80 25 106 56 63 0 0 62

N.S.

1 1.00 0.31 1.32 0.70 0.79 0.00 0.00 0.78

time (sec)

N/A 0.031 0.009 0.189 0.264 0.361 0.000 0.000 1.502

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 65 68 62 62 56 0 61

N.S.

1 1.00 0.88 0.92 0.84 0.84 0.76 0.00 0.82

time (sec)

N/A 0.042 0.018 0.056 0.261 0.366 4.648 0.000 0.194

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 56 60 54 54 48 0 53

N.S.

1 1.00 0.88 0.94 0.84 0.84 0.75 0.00 0.83

time (sec)

N/A 0.034 0.015 0.046 0.262 0.349 1.788 0.000 0.270

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 43 45 40 40 39 0 45

N.S.

1 1.00 0.93 0.98 0.87 0.87 0.85 0.00 0.98

time (sec)

N/A 0.018 0.008 0.294 0.250 0.349 0.675 0.000 0.206

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

11 11 11 10 0 0 0 0 9

N.S.

1 1.00 1.00 0.91 0.00 0.00 0.00 0.00 0.82

time (sec)

N/A 0.006 0.002 0.815 0.000 0.000 0.000 0.000 0.173

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 49 43 34 44 37 0 44

N.S.

1 1.00 1.00 0.88 0.69 0.90 0.76 0.00 0.90

time (sec)

N/A 0.027 0.012 0.077 0.265 0.359 0.805 0.000 0.210

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 51 52 46 55 49 0 53

N.S.

1 1.00 0.80 0.81 0.72 0.86 0.77 0.00 0.83

time (sec)

N/A 0.035 0.023 0.104 0.266 0.374 2.154 0.000 0.264

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 60 62 55 64 58 0 61

N.S.

1 1.00 0.81 0.84 0.74 0.86 0.78 0.00 0.82

time (sec)

N/A 0.037 0.027 0.115 0.255 0.419 5.199 0.000 0.278

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 65 63 80 159 94 0 60

N.S.

1 1.00 0.89 0.86 1.10 2.18 1.29 0.00 0.82

time (sec)

N/A 0.033 0.050 0.078 0.467 0.592 48.478 0.000 0.413

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 57 55 68 143 83 0 52

N.S.

1 1.00 0.90 0.87 1.08 2.27 1.32 0.00 0.83

time (sec)

N/A 0.026 0.040 0.070 0.466 0.535 13.127 0.000 0.280

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 39 43 49 107 60 0 39

N.S.

1 1.00 0.98 1.08 1.22 2.68 1.50 0.00 0.98

time (sec)

N/A 0.013 0.021 0.068 0.464 0.478 3.711 0.000 0.239

Problem 29

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

42 42 41 39 49 94 184 0 38

N.S.

1 1.00 0.98 0.93 1.17 2.24 4.38 0.00 0.90

time (sec)

N/A 0.019 0.014 0.069 0.457 0.605 12.264 0.000 0.264

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

56 56 47 47 57 114 275 0 47

N.S.

1 1.00 0.84 0.84 1.02 2.04 4.91 0.00 0.84

time (sec)

N/A 0.022 0.012 0.072 0.469 0.542 43.375 0.000 0.326

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A B F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 47 53 65 132 299 0 58

N.S.

1 1.00 0.71 0.80 0.98 2.00 4.53 0.00 0.88

time (sec)

N/A 0.025 0.013 0.076 0.460 0.516 140.026 0.000 0.336

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 88 80 77 77 0 0 73

N.S.

1 1.00 1.00 0.91 0.88 0.88 0.00 0.00 0.83

time (sec)

N/A 0.051 0.015 0.040 0.269 0.431 0.000 0.000 0.338

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 79 72 69 69 0 0 65

N.S.

1 1.00 1.01 0.92 0.88 0.88 0.00 0.00 0.83

time (sec)

N/A 0.045 0.013 0.043 0.254 0.452 0.000 0.000 0.305

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 52 56 53 53 0 0 57

N.S.

1 1.00 0.87 0.93 0.88 0.88 0.00 0.00 0.95

time (sec)

N/A 0.020 0.010 0.060 0.267 0.463 0.000 0.000 0.378

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F F F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

11 11 11 10 0 0 0 0 9

N.S.

1 1.00 1.00 0.91 0.00 0.00 0.00 0.00 0.82

time (sec)

N/A 0.006 0.003 0.037 0.000 0.000 0.000 0.000 0.202

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 60 68 41 51 0 0 54

N.S.

1 1.00 0.95 1.08 0.65 0.81 0.00 0.00 0.86

time (sec)

N/A 0.033 0.021 0.068 0.264 0.374 0.000 0.000 0.294

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F F B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

78 78 30 98 55 64 0 0 65

N.S.

1 1.00 0.38 1.26 0.71 0.82 0.00 0.00 0.83

time (sec)

N/A 0.042 0.010 0.102 0.253 0.359 0.000 0.000 0.728

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F F B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD

size

88 88 30 115 64 73 0 0 73

N.S.

1 1.00 0.34 1.31 0.73 0.83 0.00 0.00 0.83

time (sec)

N/A 0.046 0.012 0.102 0.268 0.459 0.000 0.000 1.025

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 77 144 95 189 0 0 72

N.S.

1 1.00 0.89 1.66 1.09 2.17 0.00 0.00 0.83

time (sec)

N/A 0.036 0.112 0.114 0.477 0.687 0.000 0.000 0.552

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 69 136 81 173 0 0 64

N.S.

1 1.00 0.90 1.77 1.05 2.25 0.00 0.00 0.83

time (sec)

N/A 0.033 0.103 0.130 0.459 0.450 0.000 0.000 0.487

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 50 119 59 133 0 0 49

N.S.

1 1.00 1.00 2.38 1.18 2.66 0.00 0.00 0.98

time (sec)

N/A 0.016 0.064 0.115 0.480 0.466 0.000 0.000 0.364

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 50 112 58 112 0 0 53

N.S.

1 1.00 0.93 2.07 1.07 2.07 0.00 0.00 0.98

time (sec)

N/A 0.026 0.059 0.116 0.467 0.516 0.000 0.000 0.554

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 61 125 66 132 0 0 59

N.S.

1 1.00 0.87 1.79 0.94 1.89 0.00 0.00 0.84

time (sec)

N/A 0.028 0.063 0.118 0.467 0.365 0.000 0.000 0.771

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 69 138 74 150 0 0 70

N.S.

1 1.00 0.86 1.72 0.92 1.88 0.00 0.00 0.88

time (sec)

N/A 0.032 0.071 0.128 0.473 0.446 0.000 0.000 1.034

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 69 108 0 0 0 0 -1

N.S.

1 1.00 0.97 1.52 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.027 0.032 0.148 0.000 0.000 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 69 108 0 0 0 0 -1

N.S.

1 1.00 0.97 1.52 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.024 0.027 0.112 0.000 0.000 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 51 88 0 0 0 0 -1

N.S.

1 1.00 0.94 1.63 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.017 0.034 0.108 0.000 0.000 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

11 11 11 12 0 11 0 0 -1

N.S.

1 1.00 1.00 1.09 0.00 1.00 0.00 0.00 -0.09

time (sec)

N/A 0.007 0.003 0.234 0.000 0.404 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 60 106 0 0 0 0 -1

N.S.

1 1.00 0.87 1.54 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.028 0.039 0.122 0.000 0.000 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 61 108 0 0 0 0 -1

N.S.

1 1.00 0.78 1.38 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.029 0.040 0.110 0.000 0.000 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 61 108 0 0 0 0 -1

N.S.

1 1.00 0.80 1.42 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.029 0.041 0.116 0.000 0.000 0.000 0.000 0.000

Problem 52

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

88 88 41 132 0 0 0 0 -1

N.S.

1 1.00 0.47 1.50 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.036 0.009 0.200 0.000 0.000 0.000 0.000 0.000

Problem 53

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

88 88 41 132 0 0 0 0 -1

N.S.

1 1.00 0.47 1.50 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.030 0.007 0.199 0.000 0.000 0.000 0.000 0.000

Problem 54

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

69 69 39 105 0 0 0 0 -1

N.S.

1 1.00 0.57 1.52 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.021 0.006 0.194 0.000 0.000 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

11 11 11 12 0 11 0 0 -1

N.S.

1 1.00 1.00 1.09 0.00 1.00 0.00 0.00 -0.09

time (sec)

N/A 0.007 0.003 0.231 0.000 0.374 0.000 0.000 0.000

Problem 56

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

84 84 37 129 0 0 0 0 -1

N.S.

1 1.00 0.44 1.54 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.033 0.008 0.207 0.000 0.000 0.000 0.000 0.000

Problem 57

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

95 95 41 132 0 0 0 0 -1

N.S.

1 1.00 0.43 1.39 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.034 0.008 0.206 0.000 0.000 0.000 0.000 0.000

Problem 58

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

93 93 41 132 0 0 0 0 -1

N.S.

1 1.00 0.44 1.42 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.035 0.009 0.210 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 A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 90 101 128 190 0 0 -1

N.S.

1 1.00 0.77 0.86 1.09 1.62 0.00 0.00 -0.01

time (sec)

N/A 0.050 0.072 0.391 0.554 0.389 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 75 88 109 143 110 0 -1

N.S.

1 1.00 0.74 0.86 1.07 1.40 1.08 0.00 -0.01

time (sec)

N/A 0.035 0.056 0.368 0.467 0.395 30.884 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 63 74 83 135 0 0 -1

N.S.

1 1.00 0.79 0.92 1.04 1.69 0.00 0.00 -0.01

time (sec)

N/A 0.030 0.058 0.421 0.465 0.410 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 51 59 71 132 0 0 -1

N.S.

1 1.00 0.75 0.87 1.04 1.94 0.00 0.00 -0.01

time (sec)

N/A 0.030 0.052 0.377 0.466 0.365 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 57 75 89 150 0 0 -1

N.S.

1 1.00 0.64 0.84 1.00 1.69 0.00 0.00 -0.01

time (sec)

N/A 0.034 0.055 0.353 0.466 0.399 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 65 88 108 170 0 0 -1

N.S.

1 1.00 0.61 0.83 1.02 1.60 0.00 0.00 -0.01

time (sec)

N/A 0.040 0.064 0.374 0.480 0.390 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

153 153 98 149 156 279 0 0 -1

N.S.

1 1.00 0.64 0.97 1.02 1.82 0.00 0.00 -0.01

time (sec)

N/A 0.067 0.178 0.143 0.481 0.392 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

136 136 88 141 143 229 0 0 -1

N.S.

1 1.00 0.65 1.04 1.05 1.68 0.00 0.00 -0.01

time (sec)

N/A 0.057 0.150 0.070 0.484 0.392 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 73 133 122 173 0 0 -1

N.S.

1 1.00 0.60 1.10 1.01 1.43 0.00 0.00 -0.01

time (sec)

N/A 0.047 0.146 0.066 0.493 0.381 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 57 127 94 161 0 0 -1

N.S.

1 1.00 0.59 1.31 0.97 1.66 0.00 0.00 -0.01

time (sec)

N/A 0.041 0.104 0.081 0.486 0.381 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 58 111 78 156 0 0 -1

N.S.

1 1.00 0.68 1.31 0.92 1.84 0.00 0.00 -0.01

time (sec)

N/A 0.040 0.078 0.066 0.470 0.392 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

108 108 64 122 97 175 0 0 -1

N.S.

1 1.00 0.59 1.13 0.90 1.62 0.00 0.00 -0.01

time (sec)

N/A 0.045 0.070 0.069 0.468 0.401 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

125 125 72 135 118 195 0 0 -1

N.S.

1 1.00 0.58 1.08 0.94 1.56 0.00 0.00 -0.01

time (sec)

N/A 0.051 0.098 0.086 0.483 0.426 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 101 145 160 194 0 0 -1

N.S.

1 1.00 0.72 1.04 1.14 1.39 0.00 0.00 -0.01

time (sec)

N/A 0.071 0.073 0.424 0.472 0.425 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

125 125 91 134 139 172 0 0 -1

N.S.

1 1.00 0.73 1.07 1.11 1.38 0.00 0.00 -0.01

time (sec)

N/A 0.058 0.049 0.391 0.472 0.389 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

115 115 57 128 128 156 0 0 -1

N.S.

1 1.00 0.50 1.11 1.11 1.36 0.00 0.00 -0.01

time (sec)

N/A 0.055 0.055 0.411 0.482 0.396 0.000 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 62 114 123 170 0 0 -1

N.S.

1 1.00 0.60 1.11 1.19 1.65 0.00 0.00 -0.01

time (sec)

N/A 0.055 0.051 0.413 0.468 0.404 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 62 116 125 196 0 0 -1

N.S.

1 1.00 0.56 1.05 1.13 1.77 0.00 0.00 -0.01

time (sec)

N/A 0.049 0.049 0.389 0.469 0.453 0.000 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 70 131 151 212 0 0 -1

N.S.

1 1.00 0.56 1.04 1.20 1.68 0.00 0.00 -0.01

time (sec)

N/A 0.058 0.055 0.412 0.480 0.437 0.000 0.000 0.000

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 89 155 178 237 0 0 -1

N.S.

1 1.00 0.55 0.96 1.11 1.47 0.00 0.00 -0.01

time (sec)

N/A 0.087 0.075 0.158 0.475 0.399 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 89 155 175 213 0 0 -1

N.S.

1 1.00 0.55 0.96 1.09 1.32 0.00 0.00 -0.01

time (sec)

N/A 0.082 0.074 0.141 0.474 0.407 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

146 146 68 147 153 187 0 0 -1

N.S.

1 1.00 0.47 1.01 1.05 1.28 0.00 0.00 -0.01

time (sec)

N/A 0.068 0.069 0.142 0.469 0.392 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

134 134 68 147 141 169 0 0 -1

N.S.

1 1.00 0.51 1.10 1.05 1.26 0.00 0.00 -0.01

time (sec)

N/A 0.069 0.066 0.160 0.476 0.384 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 71 131 132 184 0 0 -1

N.S.

1 1.00 0.58 1.07 1.08 1.51 0.00 0.00 -0.01

time (sec)

N/A 0.068 0.063 0.141 0.473 0.437 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

132 132 71 131 134 211 0 0 -1

N.S.

1 1.00 0.54 0.99 1.02 1.60 0.00 0.00 -0.01

time (sec)

N/A 0.071 0.076 0.144 0.475 0.423 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 79 142 163 226 0 0 -1

N.S.

1 1.00 0.54 0.97 1.11 1.54 0.00 0.00 -0.01

time (sec)

N/A 0.074 0.068 0.151 0.474 0.400 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 84 142 168 223 0 0 -1

N.S.

1 1.00 0.57 0.97 1.14 1.52 0.00 0.00 -0.01

time (sec)

N/A 0.073 0.074 0.157 0.482 0.405 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 82 121 0 0 0 0 -1

N.S.

1 1.00 0.81 1.20 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.040 0.088 0.492 0.000 0.000 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 82 121 0 0 0 0 -1

N.S.

1 1.00 0.82 1.21 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.039 0.078 0.522 0.000 0.000 0.000 0.000 0.000

Problem 88

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

93 93 48 109 0 0 0 0 -1

N.S.

1 1.00 0.52 1.17 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.039 0.016 0.517 0.000 0.000 0.000 0.000 0.000

Problem 89

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

97 97 48 121 0 0 0 0 -1

N.S.

1 1.00 0.49 1.25 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.042 0.020 0.520 0.000 0.000 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

105 105 48 121 0 0 0 0 -1

N.S.

1 1.00 0.46 1.15 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.045 0.020 0.510 0.000 0.000 0.000 0.000 0.000

Problem 91

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

125 125 50 145 0 0 0 0 -1

N.S.

1 1.00 0.40 1.16 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.053 0.023 0.250 0.000 0.000 0.000 0.000 0.000

Problem 92

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

124 124 50 145 0 0 0 0 -1

N.S.

1 1.00 0.40 1.17 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.049 0.020 0.254 0.000 0.000 0.000 0.000 0.000

Problem 93

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

115 115 50 133 0 0 0 0 -1

N.S.

1 1.00 0.43 1.16 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.049 0.015 0.257 0.000 0.000 0.000 0.000 0.000

Problem 94

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

119 119 50 145 0 0 0 0 -1

N.S.

1 1.00 0.42 1.22 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.054 0.019 0.244 0.000 0.000 0.000 0.000 0.000

Problem 95

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

129 129 50 145 0 0 0 0 -1

N.S.

1 1.00 0.39 1.12 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.055 0.020 0.242 0.000 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

30 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.005 0.006 0.014 0.000 0.000 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

22 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.004 0.006 0.014 0.000 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

10 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.10

time (sec)

N/A 0.002 0.005 0.012 0.000 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

22 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05

time (sec)

N/A 0.004 0.006 0.015 0.000 0.000 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

N/A N/A N/A TBD TBD TBD TBD TBD TBD

size

30 0 0 0 0 0 0 0 -1

N.S.

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03

time (sec)

N/A 0.005 0.006 0.016 0.000 0.000 0.000 0.000 0.000

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