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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 B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 104 81 81 192 197 252 73

N.S.

1 1.00 1.02 0.79 0.79 1.88 1.93 2.47 0.72

time (sec)

N/A 0.074 0.328 0.065 0.524 0.894 0.624 1.681 3.813

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 81 68 70 159 168 204 63

N.S.

1 1.00 0.98 0.82 0.84 1.92 2.02 2.46 0.76

time (sec)

N/A 0.061 0.218 0.049 0.523 0.604 0.237 1.104 3.707

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 74 60 59 120 121 156 51

N.S.

1 1.00 1.10 0.90 0.88 1.79 1.81 2.33 0.76

time (sec)

N/A 0.046 0.169 0.047 0.510 0.499 0.195 0.901 3.689

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 53 47 48 85 85 107 39

N.S.

1 1.00 1.08 0.96 0.98 1.73 1.73 2.18 0.80

time (sec)

N/A 0.029 0.116 0.035 0.550 0.444 0.161 0.662 3.748

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

34 34 43 39 37 47 44 58 25

N.S.

1 1.00 1.26 1.15 1.09 1.38 1.29 1.71 0.74

time (sec)

N/A 0.014 0.024 0.031 0.491 0.614 0.125 0.495 3.777

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

19 19 19 23 17 18 24 18 17

N.S.

1 1.00 1.00 1.21 0.89 0.95 1.26 0.95 0.89

time (sec)

N/A 0.006 0.008 0.000 0.289 0.664 0.087 0.461 3.761

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 27 24 37 17 20 34 19

N.S.

1 1.00 1.42 1.26 1.95 0.89 1.05 1.79 1.00

time (sec)

N/A 0.015 0.023 0.152 0.490 0.538 0.086 0.474 3.779

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

32 32 54 35 49 51 46 75 27

N.S.

1 1.00 1.69 1.09 1.53 1.59 1.44 2.34 0.84

time (sec)

N/A 0.032 0.127 0.148 0.490 0.438 0.147 0.605 3.734

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 68 48 58 83 80 102 47

N.S.

1 1.00 1.36 0.96 1.16 1.66 1.60 2.04 0.94

time (sec)

N/A 0.048 0.187 0.210 0.513 0.396 0.157 0.551 3.790

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 72 53 71 125 128 128 57

N.S.

1 1.00 1.12 0.83 1.11 1.95 2.00 2.00 0.89

time (sec)

N/A 0.067 0.208 0.203 0.488 0.547 0.191 0.606 3.872

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 84 61 83 156 158 158 70

N.S.

1 1.00 1.01 0.73 1.00 1.88 1.90 1.90 0.84

time (sec)

N/A 0.081 0.389 0.197 0.514 0.554 0.269 0.675 3.978

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 84 76 93 197 206 186 79

N.S.

1 1.00 0.84 0.76 0.93 1.97 2.06 1.86 0.79

time (sec)

N/A 0.102 0.380 0.188 0.493 0.510 0.296 0.673 4.065

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 108 82 95 217 219 274 86

N.S.

1 1.00 0.96 0.73 0.85 1.94 1.96 2.45 0.77

time (sec)

N/A 0.098 0.331 0.051 0.502 0.428 0.320 1.141 3.702

Problem 14

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

93 93 73 70 82 174 168 222 73

N.S.

1 1.00 0.78 0.75 0.88 1.87 1.81 2.39 0.78

time (sec)

N/A 0.080 0.223 0.044 0.503 0.423 0.397 0.888 3.802

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 76 61 68 137 136 170 60

N.S.

1 1.00 1.19 0.95 1.06 2.14 2.12 2.66 0.94

time (sec)

N/A 0.042 0.262 0.043 0.500 0.423 0.219 0.658 3.787

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 51 49 55 93 88 116 40

N.S.

1 1.00 0.82 0.79 0.89 1.50 1.42 1.87 0.65

time (sec)

N/A 0.034 0.174 0.044 0.492 0.450 0.165 0.608 3.742

Problem 17

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

38 38 100 40 41 56 53 66 29

N.S.

1 1.00 2.63 1.05 1.08 1.47 1.39 1.74 0.76

time (sec)

N/A 0.014 0.633 0.017 0.635 0.431 0.143 0.466 3.679

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

37 37 30 39 42 19 22 68 30

N.S.

1 1.00 0.81 1.05 1.14 0.51 0.59 1.84 0.81

time (sec)

N/A 0.030 0.050 0.193 0.501 0.509 0.129 0.600 3.733

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 100 49 56 58 51 85 29

N.S.

1 1.00 2.63 1.29 1.47 1.53 1.34 2.24 0.76

time (sec)

N/A 0.046 0.563 0.137 0.520 0.426 0.162 0.629 3.826

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 64 64 68 94 87 116 53

N.S.

1 1.00 1.10 1.10 1.17 1.62 1.50 2.00 0.91

time (sec)

N/A 0.065 0.224 0.208 0.512 0.397 0.260 0.818 3.840

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 105 78 83 139 136 146 68

N.S.

1 1.00 1.42 1.05 1.12 1.88 1.84 1.97 0.92

time (sec)

N/A 0.083 0.495 0.209 0.493 0.471 0.226 0.860 3.812

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 79 90 97 174 168 180 80

N.S.

1 1.00 0.85 0.97 1.04 1.87 1.81 1.94 0.86

time (sec)

N/A 0.103 0.406 0.217 0.497 0.417 0.983 0.954 3.915

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 124 106 109 219 218 212 92

N.S.

1 1.00 1.11 0.95 0.97 1.96 1.95 1.89 0.82

time (sec)

N/A 0.122 0.830 0.199 0.666 0.432 0.328 1.134 4.156

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 296 83 95 214 207 274 87

N.S.

1 1.00 2.35 0.66 0.75 1.70 1.64 2.17 0.69

time (sec)

N/A 0.121 1.333 0.052 0.869 0.450 0.369 0.915 3.792

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

90 90 228 72 82 177 173 222 73

N.S.

1 1.00 2.53 0.80 0.91 1.97 1.92 2.47 0.81

time (sec)

N/A 0.053 1.283 0.047 0.493 0.449 0.289 0.700 3.804

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 178 62 69 134 131 170 59

N.S.

1 1.00 2.09 0.73 0.81 1.58 1.54 2.00 0.69

time (sec)

N/A 0.044 0.891 0.051 0.495 0.478 0.224 0.590 3.728

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 119 51 76 97 94 118 41

N.S.

1 1.00 1.89 0.81 1.21 1.54 1.49 1.87 0.65

time (sec)

N/A 0.025 0.774 0.023 0.504 0.424 0.170 0.497 3.683

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 95 60 53 83 66 123 39

N.S.

1 1.00 1.58 1.00 0.88 1.38 1.10 2.05 0.65

time (sec)

N/A 0.074 0.895 0.198 0.540 0.474 0.209 0.743 3.771

Problem 29

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

69 69 144 62 56 91 71 119 38

N.S.

1 1.00 2.09 0.90 0.81 1.32 1.03 1.72 0.55

time (sec)

N/A 0.080 1.110 0.195 0.513 0.463 0.256 0.846 3.809

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

71 71 126 75 68 94 87 116 53

N.S.

1 1.00 1.77 1.06 0.96 1.32 1.23 1.63 0.75

time (sec)

N/A 0.076 0.785 0.220 0.503 0.493 0.220 1.019 3.782

Problem 31

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

101 101 251 91 83 139 136 146 68

N.S.

1 1.00 2.49 0.90 0.82 1.38 1.35 1.45 0.67

time (sec)

N/A 0.107 0.926 0.217 0.577 0.465 0.278 1.075 3.794

Problem 32

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

108 108 254 112 94 174 165 180 80

N.S.

1 1.00 2.35 1.04 0.87 1.61 1.53 1.67 0.74

time (sec)

N/A 0.131 0.965 0.202 0.548 0.460 0.416 1.289 3.905

Problem 33

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

126 126 359 132 109 219 218 212 92

N.S.

1 1.00 2.85 1.05 0.87 1.74 1.73 1.68 0.73

time (sec)

N/A 0.150 1.649 0.204 0.590 0.442 0.365 1.612 4.105

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

160 160 349 93 108 254 246 326 100

N.S.

1 1.00 2.18 0.58 0.68 1.59 1.54 2.04 0.62

time (sec)

N/A 0.185 1.738 0.055 0.501 0.404 1.090 1.015 3.764

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 294 82 95 217 218 274 87

N.S.

1 1.00 2.53 0.71 0.82 1.87 1.88 2.36 0.75

time (sec)

N/A 0.064 2.182 0.050 0.615 0.424 0.330 0.847 3.732

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

108 108 231 72 82 174 170 222 72

N.S.

1 1.00 2.14 0.67 0.76 1.61 1.57 2.06 0.67

time (sec)

N/A 0.060 0.957 0.056 0.535 0.439 0.320 0.594 3.722

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 176 61 108 137 138 170 59

N.S.

1 1.00 1.98 0.69 1.21 1.54 1.55 1.91 0.66

time (sec)

N/A 0.039 0.908 0.042 0.572 0.433 0.209 0.505 3.691

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

86 86 159 82 67 137 105 157 64

N.S.

1 1.00 1.85 0.95 0.78 1.59 1.22 1.83 0.74

time (sec)

N/A 0.127 1.272 0.201 0.516 0.412 0.328 0.914 3.800

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 151 80 67 58 51 163 63

N.S.

1 1.00 2.13 1.13 0.94 0.82 0.72 2.30 0.89

time (sec)

N/A 0.063 1.545 0.176 0.499 0.404 0.193 1.020 4.000

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

103 103 133 87 68 138 107 150 65

N.S.

1 1.00 1.29 0.84 0.66 1.34 1.04 1.46 0.63

time (sec)

N/A 0.152 1.325 0.214 0.505 0.390 0.598 1.206 3.966

Problem 41

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

103 103 240 100 83 139 136 146 68

N.S.

1 1.00 2.33 0.97 0.81 1.35 1.32 1.42 0.66

time (sec)

N/A 0.107 0.826 0.213 0.501 0.358 0.268 1.409 3.977

Problem 42

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

134 134 245 123 96 174 168 180 80

N.S.

1 1.00 1.83 0.92 0.72 1.30 1.25 1.34 0.60

time (sec)

N/A 0.140 0.746 0.201 0.515 0.364 1.728 1.466 4.009

Problem 43

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

142 142 359 152 109 219 218 212 92

N.S.

1 1.00 2.53 1.07 0.77 1.54 1.54 1.49 0.65

time (sec)

N/A 0.211 2.831 0.213 0.489 0.372 0.409 0.850 4.271

Problem 44

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

162 162 363 176 123 254 246 245 107

N.S.

1 1.00 2.24 1.09 0.76 1.57 1.52 1.51 0.66

time (sec)

N/A 0.223 1.389 0.233 0.505 0.364 6.052 0.905 4.680

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

130 130 840 88 0 221 219 116 125

N.S.

1 1.00 6.46 0.68 0.00 1.70 1.68 0.89 0.96

time (sec)

N/A 0.104 6.580 0.133 0.000 0.381 0.353 2.430 4.070

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

109 109 235 77 0 175 197 104 106

N.S.

1 1.00 2.16 0.71 0.00 1.61 1.81 0.95 0.97

time (sec)

N/A 0.086 3.812 0.098 0.000 0.383 0.303 1.903 3.979

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

90 90 196 65 0 138 134 87 91

N.S.

1 1.00 2.18 0.72 0.00 1.53 1.49 0.97 1.01

time (sec)

N/A 0.066 1.984 0.095 0.000 0.379 0.230 0.966 4.006

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 174 56 0 93 114 70 73

N.S.

1 1.00 2.35 0.76 0.00 1.26 1.54 0.95 0.99

time (sec)

N/A 0.049 1.237 0.101 0.000 0.378 0.207 0.725 4.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 86 48 0 55 88 60 61

N.S.

1 1.00 1.72 0.96 0.00 1.10 1.76 1.20 1.22

time (sec)

N/A 0.039 0.362 0.093 0.000 0.369 0.173 0.657 3.947

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 45 47 0 32 65 58 29

N.S.

1 1.00 1.36 1.42 0.00 0.97 1.97 1.76 0.88

time (sec)

N/A 0.018 0.113 0.074 0.000 0.367 0.097 0.502 3.942

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

33 33 45 48 0 32 60 60 29

N.S.

1 1.00 1.36 1.45 0.00 0.97 1.82 1.82 0.88

time (sec)

N/A 0.011 0.123 0.001 0.000 0.383 0.092 0.457 3.951

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 87 54 0 55 92 72 72

N.S.

1 1.00 1.85 1.15 0.00 1.17 1.96 1.53 1.53

time (sec)

N/A 0.042 0.362 0.300 0.000 0.372 0.161 0.522 4.042

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 286 68 0 99 116 91 96

N.S.

1 1.00 4.09 0.97 0.00 1.41 1.66 1.30 1.37

time (sec)

N/A 0.066 0.708 0.244 0.000 0.381 0.190 0.585 3.986

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

90 90 414 77 0 134 138 105 110

N.S.

1 1.00 4.60 0.86 0.00 1.49 1.53 1.17 1.22

time (sec)

N/A 0.086 0.946 0.282 0.000 0.363 0.231 0.797 3.973

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

108 108 365 89 0 181 196 116 126

N.S.

1 1.00 3.38 0.82 0.00 1.68 1.81 1.07 1.17

time (sec)

N/A 0.104 3.397 0.283 0.000 0.379 0.269 0.791 4.091

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

142 142 882 91 0 198 262 111 132

N.S.

1 1.00 6.21 0.64 0.00 1.39 1.85 0.78 0.93

time (sec)

N/A 0.158 6.526 0.147 0.000 0.374 0.350 2.089 4.061

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

124 124 300 79 0 151 214 98 114

N.S.

1 1.00 2.42 0.64 0.00 1.22 1.73 0.79 0.92

time (sec)

N/A 0.137 1.822 0.114 0.000 0.377 1.004 1.652 4.032

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

104 104 273 70 0 113 177 79 100

N.S.

1 1.00 2.62 0.67 0.00 1.09 1.70 0.76 0.96

time (sec)

N/A 0.114 1.672 0.129 0.000 0.382 0.288 1.049 4.026

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

79 79 135 60 0 66 148 69 84

N.S.

1 1.00 1.71 0.76 0.00 0.84 1.87 0.87 1.06

time (sec)

N/A 0.098 0.430 0.112 0.000 0.369 0.304 0.902 4.015

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 68 62 0 43 117 72 39

N.S.

1 1.00 1.15 1.05 0.00 0.73 1.98 1.22 0.66

time (sec)

N/A 0.057 0.220 0.126 0.000 0.402 0.161 0.680 3.969

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 66 60 0 32 73 70 46

N.S.

1 1.00 1.12 1.02 0.00 0.54 1.24 1.19 0.78

time (sec)

N/A 0.030 0.110 0.089 0.000 0.357 0.126 0.532 3.969

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

61 61 68 62 0 43 117 72 39

N.S.

1 1.00 1.11 1.02 0.00 0.70 1.92 1.18 0.64

time (sec)

N/A 0.023 0.194 0.000 0.000 0.354 0.135 0.460 3.944

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 135 67 0 66 150 81 97

N.S.

1 1.00 1.90 0.94 0.00 0.93 2.11 1.14 1.37

time (sec)

N/A 0.102 0.383 0.276 0.000 0.373 0.250 0.750 3.941

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 276 82 0 114 180 109 125

N.S.

1 1.00 2.85 0.85 0.00 1.18 1.86 1.12 1.29

time (sec)

N/A 0.141 1.982 0.301 0.000 0.377 0.278 0.881 3.958

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

122 122 319 90 0 151 216 109 135

N.S.

1 1.00 2.61 0.74 0.00 1.24 1.77 0.89 1.11

time (sec)

N/A 0.162 1.624 0.296 0.000 0.381 0.457 1.612 4.007

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 264 94 0 167 257 111 140

N.S.

1 1.00 1.64 0.58 0.00 1.04 1.60 0.69 0.87

time (sec)

N/A 0.210 4.264 0.187 0.000 0.377 0.423 2.665 3.949

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

143 143 239 83 0 120 214 91 122

N.S.

1 1.00 1.67 0.58 0.00 0.84 1.50 0.64 0.85

time (sec)

N/A 0.190 2.697 0.158 0.000 0.368 0.495 2.217 3.809

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 118 75 0 77 184 80 110

N.S.

1 1.00 0.99 0.63 0.00 0.65 1.55 0.67 0.92

time (sec)

N/A 0.163 0.483 0.158 0.000 0.363 0.326 1.391 3.851

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

92 92 91 74 0 54 156 81 49

N.S.

1 1.00 0.99 0.80 0.00 0.59 1.70 0.88 0.53

time (sec)

N/A 0.088 0.277 0.130 0.000 0.359 0.241 1.073 3.769

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 91 75 0 54 151 80 49

N.S.

1 1.00 1.03 0.85 0.00 0.61 1.72 0.91 0.56

time (sec)

N/A 0.069 0.454 0.124 0.000 0.377 0.213 0.959 3.757

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 84 91 74 0 54 153 81 49

N.S.

1 1.00 1.08 0.88 0.00 0.64 1.82 0.96 0.58

time (sec)

N/A 0.044 0.381 0.120 0.000 0.364 0.221 0.836 3.775

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 93 75 0 54 155 80 50

N.S.

1 1.00 1.06 0.85 0.00 0.61 1.76 0.91 0.57

time (sec)

N/A 0.035 0.252 0.122 0.000 0.357 0.177 0.597 3.752

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 118 81 0 77 187 93 120

N.S.

1 1.00 1.20 0.83 0.00 0.79 1.91 0.95 1.22

time (sec)

N/A 0.154 0.470 0.342 0.000 0.383 0.301 1.012 3.868

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

133 133 379 95 0 125 218 119 145

N.S.

1 1.00 2.85 0.71 0.00 0.94 1.64 0.89 1.09

time (sec)

N/A 0.215 4.992 0.329 0.000 0.372 0.356 0.954 4.054

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 429 95 0 135 248 100 132

N.S.

1 1.00 2.51 0.56 0.00 0.79 1.45 0.58 0.77

time (sec)

N/A 0.259 0.906 0.214 0.000 0.387 0.460 4.517 3.911

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 126 87 0 88 219 89 128

N.S.

1 1.00 0.86 0.59 0.00 0.60 1.49 0.61 0.87

time (sec)

N/A 0.236 0.502 0.182 0.000 0.386 1.829 2.079 3.980

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

128 128 98 89 0 65 189 92 59

N.S.

1 1.00 0.77 0.70 0.00 0.51 1.48 0.72 0.46

time (sec)

N/A 0.125 0.266 0.158 0.000 0.365 0.270 1.392 3.937

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

126 126 95 87 0 54 156 88 60

N.S.

1 1.00 0.75 0.69 0.00 0.43 1.24 0.70 0.48

time (sec)

N/A 0.127 0.487 0.146 0.000 0.365 0.607 1.173 3.898

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 69 89 0 43 117 87 92

N.S.

1 1.00 0.59 0.77 0.00 0.37 1.01 0.75 0.79

time (sec)

N/A 0.083 0.373 0.152 0.000 0.370 0.202 1.099 3.899

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 94 87 0 54 156 88 60

N.S.

1 1.00 0.85 0.79 0.00 0.49 1.42 0.80 0.55

time (sec)

N/A 0.058 0.356 0.164 0.000 0.359 0.295 1.016 3.897

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

116 116 98 89 0 65 189 92 60

N.S.

1 1.00 0.84 0.77 0.00 0.56 1.63 0.79 0.52

time (sec)

N/A 0.051 0.255 0.000 0.000 0.363 0.218 0.780 3.894

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 123 94 0 88 221 101 142

N.S.

1 1.00 1.02 0.78 0.00 0.73 1.84 0.84 1.18

time (sec)

N/A 0.218 0.446 0.332 0.000 0.392 0.438 1.274 3.839

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 159 444 109 0 136 252 129 165

N.S.

1 1.00 2.79 0.69 0.00 0.86 1.58 0.81 1.04

time (sec)

N/A 0.303 2.957 0.390 0.000 0.381 0.375 1.244 4.163

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

168 168 105 94 120 330 0 0 109

N.S.

1 1.00 0.62 0.56 0.71 1.96 0.00 0.00 0.65

time (sec)

N/A 0.230 2.380 0.263 0.493 0.490 0.000 0.000 0.338

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 95 92 120 285 0 0 100

N.S.

1 1.00 0.75 0.72 0.94 2.24 0.00 0.00 0.79

time (sec)

N/A 0.142 1.798 0.203 0.479 0.457 0.000 0.000 4.147

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

76 76 97 58 84 233 0 0 63

N.S.

1 1.00 1.28 0.76 1.11 3.07 0.00 0.00 0.83

time (sec)

N/A 0.055 0.768 0.168 0.492 0.413 0.000 0.000 0.221

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 77 53 83 187 0 0 54

N.S.

1 1.00 1.15 0.79 1.24 2.79 0.00 0.00 0.81

time (sec)

N/A 0.040 0.471 0.163 0.497 0.423 0.000 0.000 4.037

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 64 36 60 159 0 0 39

N.S.

1 1.00 1.39 0.78 1.30 3.46 0.00 0.00 0.85

time (sec)

N/A 0.017 0.201 0.151 0.496 0.464 0.000 0.000 3.948

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A F B A B F F B

verified

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

size

78 78 0 230 107 336 0 0 61

N.S.

1 1.00 0.00 2.95 1.37 4.31 0.00 0.00 0.78

time (sec)

N/A 0.132 0.709 4.585 0.486 0.559 0.000 0.000 0.171

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 197 586 134 476 0 0 97

N.S.

1 1.00 1.77 5.28 1.21 4.29 0.00 0.00 0.87

time (sec)

N/A 0.172 4.477 0.899 0.503 0.454 0.000 0.000 4.016

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 144 904 179 519 0 0 124

N.S.

1 1.00 0.99 6.23 1.23 3.58 0.00 0.00 0.86

time (sec)

N/A 0.292 2.161 0.899 0.493 0.474 0.000 0.000 4.070

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

199 199 166 111 138 354 0 0 120

N.S.

1 1.00 0.83 0.56 0.69 1.78 0.00 0.00 0.60

time (sec)

N/A 0.334 2.826 0.204 0.498 0.395 0.000 0.000 4.231

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 162 76 102 315 0 0 84

N.S.

1 1.00 1.60 0.75 1.01 3.12 0.00 0.00 0.83

time (sec)

N/A 0.069 1.516 0.189 0.488 0.384 0.000 0.000 0.301

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

92 92 148 70 102 258 0 0 74

N.S.

1 1.00 1.61 0.76 1.11 2.80 0.00 0.00 0.80

time (sec)

N/A 0.058 1.003 0.169 0.486 0.386 0.000 0.000 4.059

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 79 54 83 215 0 0 61

N.S.

1 1.00 1.10 0.75 1.15 2.99 0.00 0.00 0.85

time (sec)

N/A 0.028 0.528 0.153 0.485 0.474 0.000 0.000 0.184

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B A B F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

79 79 201 231 107 357 0 0 76

N.S.

1 1.00 2.54 2.92 1.35 4.52 0.00 0.00 0.96

time (sec)

N/A 0.121 1.248 0.770 0.528 0.466 0.000 0.000 4.087

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

141 141 178 631 132 501 0 0 112

N.S.

1 1.00 1.26 4.48 0.94 3.55 0.00 0.00 0.79

time (sec)

N/A 0.275 1.447 0.837 0.506 0.463 0.000 0.000 4.197

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

184 184 190 1142 178 546 0 0 136

N.S.

1 1.00 1.03 6.21 0.97 2.97 0.00 0.00 0.74

time (sec)

N/A 0.394 2.083 0.867 0.491 0.461 0.000 0.000 4.072

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

204 204 176 131 156 412 0 0 142

N.S.

1 1.00 0.86 0.64 0.76 2.02 0.00 0.00 0.70

time (sec)

N/A 0.334 2.355 0.194 0.486 0.496 0.000 0.000 4.295

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

130 130 170 96 120 371 0 0 107

N.S.

1 1.00 1.31 0.74 0.92 2.85 0.00 0.00 0.82

time (sec)

N/A 0.082 2.823 0.187 0.491 0.486 0.000 0.000 4.209

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