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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

149 149 149 126 131 124 151 131 125

N.S.

1 1.00 1.00 0.85 0.88 0.83 1.01 0.88 0.84

time (sec)

N/A 0.143 0.003 0.123 0.292 0.409 0.015 3.695 0.306

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

149 149 149 126 131 124 155 131 125

N.S.

1 1.00 1.00 0.85 0.88 0.83 1.04 0.88 0.84

time (sec)

N/A 0.061 0.003 0.125 0.270 0.334 0.015 6.341 0.069

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

89 89 146 125 130 122 150 130 124

N.S.

1 1.00 1.64 1.40 1.46 1.37 1.69 1.46 1.39

time (sec)

N/A 0.052 0.003 0.132 0.281 0.341 0.015 3.637 0.071

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

141 141 141 122 127 120 148 127 121

N.S.

1 1.00 1.00 0.87 0.90 0.85 1.05 0.90 0.86

time (sec)

N/A 0.049 0.003 0.138 0.274 0.335 0.015 4.129 0.070

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

142 142 142 123 131 122 150 131 122

N.S.

1 1.00 1.00 0.87 0.92 0.86 1.06 0.92 0.86

time (sec)

N/A 0.068 0.006 0.109 0.268 0.377 0.075 4.148 0.109

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

139 139 139 122 127 126 143 127 121

N.S.

1 1.00 1.00 0.88 0.91 0.91 1.03 0.91 0.87

time (sec)

N/A 0.047 0.006 0.131 0.282 0.367 0.067 4.192 0.094

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

142 142 142 123 131 130 150 142 122

N.S.

1 1.00 1.00 0.87 0.92 0.92 1.06 1.00 0.86

time (sec)

N/A 0.074 0.006 0.141 0.283 0.369 0.087 4.333 0.072

Problem 8

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

67 67 54 53 102 48 97 54 42

N.S.

1 1.00 0.81 0.79 1.52 0.72 1.45 0.81 0.63

time (sec)

N/A 0.033 0.073 0.157 0.493 0.370 3.249 4.326 0.370

Problem 9

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

51 51 49 46 93 43 70 45 37

N.S.

1 1.00 0.96 0.90 1.82 0.84 1.37 0.88 0.73

time (sec)

N/A 0.019 0.061 0.131 0.482 0.351 2.501 2.901 0.392

Problem 10

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

44 44 40 34 67 34 53 38 32

N.S.

1 1.00 0.91 0.77 1.52 0.77 1.20 0.86 0.73

time (sec)

N/A 0.013 0.062 0.125 0.493 0.357 1.603 3.283 0.137

Problem 11

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

58 58 67 49 99 56 83 76 45

N.S.

1 1.00 1.16 0.84 1.71 0.97 1.43 1.31 0.78

time (sec)

N/A 0.034 0.100 0.260 0.487 0.354 7.858 3.176 0.146

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

59 59 67 61 88 72 83 91 51

N.S.

1 1.00 1.14 1.03 1.49 1.22 1.41 1.54 0.86

time (sec)

N/A 0.033 0.112 0.270 0.496 0.348 3.764 3.860 0.787

Problem 13

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 70 75 91 72 76 129 56

N.S.

1 1.00 1.11 1.19 1.44 1.14 1.21 2.05 0.89

time (sec)

N/A 0.033 0.163 0.270 0.502 0.363 2.988 4.083 0.423

Problem 14

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

58 58 60 52 59 59 63 116 43

N.S.

1 1.00 1.03 0.90 1.02 1.02 1.09 2.00 0.74

time (sec)

N/A 0.029 0.154 0.204 0.500 0.388 2.899 4.243 0.681

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

208 208 82 192 0 0 78 0 -1

N.S.

1 1.00 0.39 0.92 0.00 0.00 0.38 0.00 -0.00

time (sec)

N/A 0.079 4.496 0.155 0.000 0.000 1.106 0.000 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

192 192 68 180 0 0 78 0 -1

N.S.

1 1.00 0.35 0.94 0.00 0.00 0.41 0.00 -0.01

time (sec)

N/A 0.065 3.888 0.145 0.000 0.000 1.022 0.000 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

176 176 48 168 0 0 76 0 -1

N.S.

1 1.00 0.27 0.95 0.00 0.00 0.43 0.00 -0.01

time (sec)

N/A 0.043 3.464 0.125 0.000 0.000 0.944 0.000 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F F C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 108 167 0 0 78 0 61

N.S.

1 1.00 0.63 0.98 0.00 0.00 0.46 0.00 0.36

time (sec)

N/A 0.045 3.416 0.151 0.000 0.000 1.107 0.000 0.410

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

192 192 98 170 0 0 83 0 -1

N.S.

1 1.00 0.51 0.89 0.00 0.00 0.43 0.00 -0.01

time (sec)

N/A 0.059 7.827 0.141 0.000 0.000 1.177 0.000 0.000

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

83 83 64 73 127 58 131 80 52

N.S.

1 1.00 0.77 0.88 1.53 0.70 1.58 0.96 0.63

time (sec)

N/A 0.042 0.102 0.139 0.496 0.339 8.971 3.617 0.319

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 59 58 118 53 124 71 47

N.S.

1 1.00 0.88 0.87 1.76 0.79 1.85 1.06 0.70

time (sec)

N/A 0.025 0.087 0.131 0.481 0.385 7.972 4.133 0.430

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 54 46 95 48 109 57 42

N.S.

1 1.00 0.90 0.77 1.58 0.80 1.82 0.95 0.70

time (sec)

N/A 0.021 0.085 0.129 0.496 0.384 4.249 4.850 0.177

Problem 23

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

78 78 77 75 138 67 114 90 55

N.S.

1 1.00 0.99 0.96 1.77 0.86 1.46 1.15 0.71

time (sec)

N/A 0.049 0.132 0.259 0.488 0.350 16.339 4.035 0.180

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

81 81 76 75 122 78 114 102 64

N.S.

1 1.00 0.94 0.93 1.51 0.96 1.41 1.26 0.79

time (sec)

N/A 0.048 0.147 0.280 0.487 0.365 5.436 4.685 0.765

Problem 25

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

86 86 81 73 123 82 133 146 71

N.S.

1 1.00 0.94 0.85 1.43 0.95 1.55 1.70 0.83

time (sec)

N/A 0.050 0.189 0.273 0.490 0.402 6.473 2.731 0.552

Problem 26

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

82 82 79 73 112 82 148 158 82

N.S.

1 1.00 0.96 0.89 1.37 1.00 1.80 1.93 1.00

time (sec)

N/A 0.048 0.204 0.267 0.505 0.361 6.581 4.811 0.946

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

235 235 74 216 0 0 160 0 -1

N.S.

1 1.00 0.31 0.92 0.00 0.00 0.68 0.00 -0.00

time (sec)

N/A 0.088 6.945 0.141 0.000 0.000 1.926 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

219 219 68 204 0 0 160 0 -1

N.S.

1 1.00 0.31 0.93 0.00 0.00 0.73 0.00 -0.00

time (sec)

N/A 0.080 5.652 0.137 0.000 0.000 1.770 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

197 197 49 192 0 0 158 0 -1

N.S.

1 1.00 0.25 0.97 0.00 0.00 0.80 0.00 -0.01

time (sec)

N/A 0.055 4.888 0.128 0.000 0.000 1.650 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F F C F B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

199 199 125 192 0 0 160 0 48

N.S.

1 1.00 0.63 0.96 0.00 0.00 0.80 0.00 0.24

time (sec)

N/A 0.058 4.778 0.155 0.000 0.000 1.930 0.000 0.533

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

201 201 124 192 0 0 163 0 -1

N.S.

1 1.00 0.62 0.96 0.00 0.00 0.81 0.00 -0.00

time (sec)

N/A 0.058 9.404 0.140 0.000 0.000 1.981 0.000 0.000

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

67 67 49 51 104 43 85 46 38

N.S.

1 1.00 0.73 0.76 1.55 0.64 1.27 0.69 0.57

time (sec)

N/A 0.038 0.074 0.135 0.498 0.339 3.914 4.127 0.590

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

51 51 40 39 76 34 66 37 32

N.S.

1 1.00 0.78 0.76 1.49 0.67 1.29 0.73 0.63

time (sec)

N/A 0.026 0.078 0.137 0.489 0.348 2.704 5.044 0.309

Problem 34

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

35 35 39 32 65 33 53 33 27

N.S.

1 1.00 1.11 0.91 1.86 0.94 1.51 0.94 0.77

time (sec)

N/A 0.017 0.067 0.128 0.487 0.363 1.997 4.221 0.491

Problem 35

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

24 24 28 20 42 26 22 26 19

N.S.

1 1.00 1.17 0.83 1.75 1.08 0.92 1.08 0.79

time (sec)

N/A 0.011 0.067 0.132 0.487 0.332 0.947 3.693 0.294

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 38 48 30 67 41 31 61 30

N.S.

1 1.00 1.26 0.79 1.76 1.08 0.82 1.61 0.79

time (sec)

N/A 0.026 0.080 0.245 0.500 0.358 2.928 3.615 0.615

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

42 42 46 31 47 47 31 66 31

N.S.

1 1.00 1.10 0.74 1.12 1.12 0.74 1.57 0.74

time (sec)

N/A 0.025 0.088 0.181 0.491 0.374 1.760 4.778 0.329

Problem 38

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

58 58 55 43 59 50 88 114 43

N.S.

1 1.00 0.95 0.74 1.02 0.86 1.52 1.97 0.74

time (sec)

N/A 0.033 0.138 0.199 0.505 0.343 5.662 5.760 0.694

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

185 185 74 168 0 0 75 0 -1

N.S.

1 1.00 0.40 0.91 0.00 0.00 0.41 0.00 -0.01

time (sec)

N/A 0.056 10.028 0.128 0.000 0.000 1.169 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

166 166 66 155 0 0 75 0 -1

N.S.

1 1.00 0.40 0.93 0.00 0.00 0.45 0.00 -0.01

time (sec)

N/A 0.046 10.034 0.131 0.000 0.000 1.083 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

155 155 48 146 0 0 73 0 -1

N.S.

1 1.00 0.31 0.94 0.00 0.00 0.47 0.00 -0.01

time (sec)

N/A 0.033 10.035 0.129 0.000 0.000 0.767 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

173 173 81 158 0 0 75 0 48

N.S.

1 1.00 0.47 0.91 0.00 0.00 0.43 0.00 0.28

time (sec)

N/A 0.044 10.124 0.136 0.000 0.000 0.853 0.000 0.504

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

189 189 97 170 0 0 80 0 -1

N.S.

1 1.00 0.51 0.90 0.00 0.00 0.42 0.00 -0.01

time (sec)

N/A 0.062 10.101 0.135 0.000 0.000 0.973 0.000 0.000

Problem 44

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

58 58 49 50 89 62 66 45 97

N.S.

1 1.00 0.84 0.86 1.53 1.07 1.14 0.78 1.67

time (sec)

N/A 0.031 0.111 0.143 0.483 0.382 6.497 3.866 1.108

Problem 45

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

45 45 40 37 63 58 48 39 89

N.S.

1 1.00 0.89 0.82 1.40 1.29 1.07 0.87 1.98

time (sec)

N/A 0.026 0.118 0.155 0.487 0.374 5.372 3.567 0.894

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

35 35 39 34 54 52 39 33 82

N.S.

1 1.00 1.11 0.97 1.54 1.49 1.11 0.94 2.34

time (sec)

N/A 0.017 0.108 0.148 0.507 0.384 4.416 3.322 0.841

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

20 20 20 23 22 31 31 16 16

N.S.

1 1.00 1.00 1.15 1.10 1.55 1.55 0.80 0.80

time (sec)

N/A 0.010 0.098 0.128 0.484 0.347 3.208 3.785 0.164

Problem 48

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 52 40 56 61 212 61 40

N.S.

1 1.00 1.13 0.87 1.22 1.33 4.61 1.33 0.87

time (sec)

N/A 0.028 0.130 0.203 0.484 0.346 8.372 4.310 0.475

Problem 49

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

65 65 59 47 68 77 228 82 47

N.S.

1 1.00 0.91 0.72 1.05 1.18 3.51 1.26 0.72

time (sec)

N/A 0.037 0.140 0.200 0.517 0.357 5.561 6.059 0.537

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

196 196 70 168 0 0 75 0 -1

N.S.

1 1.00 0.36 0.86 0.00 0.00 0.38 0.00 -0.01

time (sec)

N/A 0.058 10.031 0.139 0.000 0.000 2.417 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

177 177 68 168 0 0 75 0 -1

N.S.

1 1.00 0.38 0.95 0.00 0.00 0.42 0.00 -0.01

time (sec)

N/A 0.050 10.026 0.138 0.000 0.000 2.236 0.000 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

180 180 66 168 0 0 73 0 -1

N.S.

1 1.00 0.37 0.93 0.00 0.00 0.41 0.00 -0.01

time (sec)

N/A 0.042 10.023 0.133 0.000 0.000 2.126 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

196 196 108 180 0 0 75 0 48

N.S.

1 1.00 0.55 0.92 0.00 0.00 0.38 0.00 0.24

time (sec)

N/A 0.057 10.087 0.180 0.000 0.000 3.013 0.000 0.456

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

214 214 119 192 0 0 80 0 -1

N.S.

1 1.00 0.56 0.90 0.00 0.00 0.37 0.00 -0.00

time (sec)

N/A 0.077 10.101 0.135 0.000 0.000 3.447 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

269 269 189 2295 405 1495 21612 3752 1539

N.S.

1 1.00 0.70 8.53 1.51 5.56 80.34 13.95 5.72

time (sec)

N/A 0.108 0.708 0.036 0.339 0.376 3.438 3.966 1.777

Problem 56

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

63 63 153 130 140 127 134 143 121

N.S.

1 1.00 2.43 2.06 2.22 2.02 2.13 2.27 1.92

time (sec)

N/A 0.127 0.020 0.087 0.271 0.337 0.026 4.029 0.094

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

153 153 153 130 140 127 141 144 123

N.S.

1 1.00 1.00 0.85 0.92 0.83 0.92 0.94 0.80

time (sec)

N/A 0.076 0.015 0.079 0.297 0.367 0.017 4.397 0.121

Problem 58

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

45 45 151 130 140 127 136 144 123

N.S.

1 1.00 3.36 2.89 3.11 2.82 3.02 3.20 2.73

time (sec)

N/A 0.081 0.013 0.079 0.268 0.355 0.025 4.986 0.078

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

153 153 153 130 140 127 139 144 123

N.S.

1 1.00 1.00 0.85 0.92 0.83 0.91 0.94 0.80

time (sec)

N/A 0.056 0.012 0.079 0.280 0.349 0.016 4.171 0.081

Problem 60

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

29 29 149 130 140 127 133 144 123

N.S.

1 1.00 5.14 4.48 4.83 4.38 4.59 4.97 4.24

time (sec)

N/A 0.030 0.008 0.081 0.274 0.369 0.030 4.320 0.077

Problem 61

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

143 143 143 127 136 124 134 141 120

N.S.

1 1.00 1.00 0.89 0.95 0.87 0.94 0.99 0.84

time (sec)

N/A 0.046 0.011 0.122 0.280 0.347 0.025 3.682 0.079

Problem 62

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

93 93 149 132 141 123 131 145 121

N.S.

1 1.00 1.60 1.42 1.52 1.32 1.41 1.56 1.30

time (sec)

N/A 0.033 0.019 0.022 0.277 0.557 0.111 3.510 0.129

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

141 141 141 129 136 128 124 139 119

N.S.

1 1.00 1.00 0.91 0.96 0.91 0.88 0.99 0.84

time (sec)

N/A 0.052 0.019 0.040 0.282 0.442 0.105 3.750 0.081

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

147 147 147 130 141 134 131 156 120

N.S.

1 1.00 1.00 0.88 0.96 0.91 0.89 1.06 0.82

time (sec)

N/A 0.091 0.026 0.026 0.279 0.427 0.142 3.572 0.084

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

203 203 122 1121 192 759 11387 1848 1483

N.S.

1 1.00 0.60 5.52 0.95 3.74 56.09 9.10 7.31

time (sec)

N/A 0.049 0.076 0.024 0.307 0.600 2.750 3.874 1.251

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 85 29 61 61 76 61 61

N.S.

1 1.00 2.50 0.85 1.79 1.79 2.24 1.79 1.79

time (sec)

N/A 0.029 0.002 0.062 0.277 0.495 0.012 3.702 0.062

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

83 83 83 62 61 61 75 61 61

N.S.

1 1.00 1.00 0.75 0.73 0.73 0.90 0.73 0.73

time (sec)

N/A 0.019 0.002 0.061 0.281 0.377 0.011 3.988 0.059

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

23 23 83 20 61 61 75 61 61

N.S.

1 1.00 3.61 0.87 2.65 2.65 3.26 2.65 2.65

time (sec)

N/A 0.014 0.001 0.034 0.270 0.448 0.012 3.688 0.060

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

83 83 83 62 61 61 75 61 61

N.S.

1 1.00 1.00 0.75 0.73 0.73 0.90 0.73 0.73

time (sec)

N/A 0.015 0.001 0.060 0.275 0.378 0.011 4.048 0.059

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

11 11 11 10 61 61 71 76 61

N.S.

1 1.00 1.00 0.91 5.55 5.55 6.45 6.91 5.55

time (sec)

N/A 0.002 0.001 0.036 0.284 0.421 0.012 4.300 0.058

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

73 73 73 58 57 57 68 57 57

N.S.

1 1.00 1.00 0.79 0.78 0.78 0.93 0.78 0.78

time (sec)

N/A 0.013 0.001 0.073 0.285 0.642 0.013 3.813 0.058

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

80 80 80 59 62 58 75 62 58

N.S.

1 1.00 1.00 0.74 0.78 0.72 0.94 0.78 0.72

time (sec)

N/A 0.021 0.003 0.015 0.283 0.399 0.036 3.874 0.061

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

73 73 73 60 59 62 66 59 59

N.S.

1 1.00 1.00 0.82 0.81 0.85 0.90 0.81 0.81

time (sec)

N/A 0.015 0.003 0.023 0.270 0.418 0.032 5.976 0.060

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

80 80 80 61 62 64 75 69 60

N.S.

1 1.00 1.00 0.76 0.78 0.80 0.94 0.86 0.75

time (sec)

N/A 0.024 0.002 0.029 0.284 0.345 0.032 5.063 0.061

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 80 91 57 133 90 101 -1

N.S.

1 1.00 0.55 0.63 0.39 0.92 0.62 0.70 -0.01

time (sec)

N/A 0.056 0.036 0.132 0.478 0.384 0.184 5.120 0.000

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

83 83 51 55 33 31 27 42 103

N.S.

1 1.00 0.61 0.66 0.40 0.37 0.33 0.51 1.24

time (sec)

N/A 0.046 0.015 0.122 0.271 0.363 0.123 5.056 0.876

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 69 62 35 102 82 59 -1

N.S.

1 1.00 0.71 0.64 0.36 1.05 0.85 0.61 -0.01

time (sec)

N/A 0.030 0.020 0.129 0.476 0.452 0.140 5.171 0.000

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

92 92 54 57 36 34 26 61 83

N.S.

1 1.00 0.59 0.62 0.39 0.37 0.28 0.66 0.90

time (sec)

N/A 0.047 0.015 0.122 0.282 0.547 0.392 4.973 0.766

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

101 101 72 67 38 110 82 62 -1

N.S.

1 1.00 0.71 0.66 0.38 1.09 0.81 0.61 -0.01

time (sec)

N/A 0.040 0.022 0.141 0.499 0.355 0.170 3.628 0.000

Problem 80

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

137 137 70 78 50 56 41 131 125

N.S.

1 1.00 0.51 0.57 0.36 0.41 0.30 0.96 0.91

time (sec)

N/A 0.063 0.024 0.131 0.269 0.448 0.396 4.072 0.810

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

153 153 108 188 126 308 0 101 -1

N.S.

1 1.00 0.71 1.23 0.82 2.01 0.00 0.66 -0.01

time (sec)

N/A 0.076 0.043 0.048 0.491 0.516 0.000 4.214 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 45 38 66 43 0 40 48

N.S.

1 1.00 0.58 0.49 0.86 0.56 0.00 0.52 0.62

time (sec)

N/A 0.045 0.013 0.026 0.292 0.369 0.000 5.577 0.179

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

156 156 108 188 125 308 0 101 -1

N.S.

1 1.00 0.69 1.21 0.80 1.97 0.00 0.65 -0.01

time (sec)

N/A 0.055 0.037 0.042 0.492 0.437 0.000 4.069 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 92 132 89 120 0 107 -1

N.S.

1 1.00 0.57 0.82 0.55 0.75 0.00 0.66 -0.01

time (sec)

N/A 0.082 0.028 0.042 0.280 0.355 0.000 4.561 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

190 190 124 206 135 340 0 116 -1

N.S.

1 1.00 0.65 1.08 0.71 1.79 0.00 0.61 -0.01

time (sec)

N/A 0.121 0.048 0.051 0.491 0.340 0.000 3.629 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F A F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

223 223 130 249 139 212 0 188 -1

N.S.

1 1.00 0.58 1.12 0.62 0.95 0.00 0.84 -0.00

time (sec)

N/A 0.122 0.048 0.054 0.283 0.368 0.000 3.530 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

400 400 160 1099 494 866 0 2213 -1

N.S.

1 1.00 0.40 2.75 1.24 2.16 0.00 5.53 -0.00

time (sec)

N/A 0.159 0.448 0.036 0.313 0.370 0.000 3.650 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

276 276 112 495 246 390 0 1013 -1

N.S.

1 1.00 0.41 1.79 0.89 1.41 0.00 3.67 -0.00

time (sec)

N/A 0.100 0.135 0.017 0.290 0.376 0.000 5.421 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

153 153 86 131 78 98 0 269 -1

N.S.

1 1.00 0.56 0.86 0.51 0.64 0.00 1.76 -0.01

time (sec)

N/A 0.048 0.060 0.015 0.287 0.386 0.000 2.787 0.000

Problem 90

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

134 134 78 0 0 0 0 0 -1

N.S.

1 1.00 0.58 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.054 0.078 0.009 0.000 0.000 0.000 0.000 0.000

Problem 91

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

154 154 101 0 0 0 0 0 -1

N.S.

1 1.00 0.66 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.076 0.118 0.006 0.000 0.000 0.000 0.000 0.000

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 25 40 86 47 155 32 59

N.S.

1 1.00 0.74 1.18 2.53 1.38 4.56 0.94 1.74

time (sec)

N/A 0.019 0.007 0.044 0.302 0.383 4.119 4.595 0.142

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

86 86 45 62 135 92 0 196 108

N.S.

1 1.00 0.52 0.72 1.57 1.07 0.00 2.28 1.26

time (sec)

N/A 0.058 0.048 0.032 0.280 0.374 0.000 3.440 0.171

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

128 128 68 99 196 140 0 331 169

N.S.

1 1.00 0.53 0.77 1.53 1.09 0.00 2.59 1.32

time (sec)

N/A 0.084 0.060 0.040 0.291 0.357 0.000 3.992 0.202

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

166 166 166 226 166 166 202 193 169

N.S.

1 1.00 1.00 1.36 1.00 1.00 1.22 1.16 1.02

time (sec)

N/A 0.252 0.035 0.080 0.274 0.349 0.023 4.390 0.076

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

166 166 166 226 166 166 204 193 169

N.S.

1 1.00 1.00 1.36 1.00 1.00 1.23 1.16 1.02

time (sec)

N/A 0.096 0.035 0.083 0.275 0.337 0.022 3.667 0.096

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

166 166 154 226 166 166 199 193 169

N.S.

1 1.00 0.93 1.36 1.00 1.00 1.20 1.16 1.02

time (sec)

N/A 0.182 0.040 0.089 0.280 0.326 0.022 3.046 0.048

Problem 98

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

161 161 161 223 163 163 199 189 165

N.S.

1 1.00 1.00 1.39 1.01 1.01 1.24 1.17 1.02

time (sec)

N/A 0.073 0.032 0.089 0.284 0.348 0.022 4.131 0.049

Problem 99

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

162 162 162 191 167 164 199 193 166

N.S.

1 1.00 1.00 1.18 1.03 1.01 1.23 1.19 1.02

time (sec)

N/A 0.138 0.040 0.020 0.286 0.346 0.125 5.277 0.103

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

156 156 156 186 162 168 185 185 163

N.S.

1 1.00 1.00 1.19 1.04 1.08 1.19 1.19 1.04

time (sec)

N/A 0.067 0.059 0.022 0.279 0.335 0.123 4.839 0.051

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