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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

87 87 79 56 92 62 105 118 90

N.S.

1 1.00 0.91 0.64 1.06 0.71 1.21 1.36 1.03

time (sec)

N/A 0.039 0.032 0.208 0.305 0.369 0.881 6.134 0.087

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

87 87 57 62 63 62 172 107 226

N.S.

1 1.00 0.66 0.71 0.72 0.71 1.98 1.23 2.60

time (sec)

N/A 0.044 0.112 0.165 0.298 0.359 0.712 7.094 8.231

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

64 64 63 46 70 51 83 88 68

N.S.

1 1.00 0.98 0.72 1.09 0.80 1.30 1.38 1.06

time (sec)

N/A 0.034 0.020 0.152 0.290 0.349 0.438 5.869 0.051

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

65 65 62 52 48 51 124 77 165

N.S.

1 1.00 0.95 0.80 0.74 0.78 1.91 1.18 2.54

time (sec)

N/A 0.034 0.058 0.116 0.306 0.376 0.260 5.328 7.991

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

45 45 44 36 48 39 60 48 46

N.S.

1 1.00 0.98 0.80 1.07 0.87 1.33 1.07 1.02

time (sec)

N/A 0.024 0.013 0.103 0.296 0.383 0.203 4.183 0.058

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

43 43 46 41 37 37 71 47 103

N.S.

1 1.00 1.07 0.95 0.86 0.86 1.65 1.09 2.40

time (sec)

N/A 0.024 0.038 0.083 0.293 0.350 0.121 4.299 6.761

Problem 7

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

22 28 39 23 20 25 34 25 20

N.S.

1 1.27 1.77 1.05 0.91 1.14 1.55 1.14 0.91

time (sec)

N/A 0.011 0.012 0.046 0.301 0.396 0.068 3.634 0.040

Problem 8

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

17 17 26 16 15 17 0 37 15

N.S.

1 1.00 1.53 0.94 0.88 1.00 0.00 2.18 0.88

time (sec)

N/A 0.013 0.013 0.068 0.303 0.360 0.000 4.060 0.047

Problem 9

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

23 23 23 24 23 40 0 19 19

N.S.

1 1.00 1.00 1.04 1.00 1.74 0.00 0.83 0.83

time (sec)

N/A 0.022 0.013 0.072 0.308 0.340 0.000 3.703 4.688

Problem 10

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

39 39 52 50 42 67 0 54 30

N.S.

1 1.00 1.33 1.28 1.08 1.72 0.00 1.38 0.77

time (sec)

N/A 0.031 0.016 0.105 0.298 0.357 0.000 5.115 0.061

Problem 11

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

44 44 41 38 35 52 0 66 63

N.S.

1 1.00 0.93 0.86 0.80 1.18 0.00 1.50 1.43

time (sec)

N/A 0.025 0.050 0.121 0.295 0.328 0.000 8.464 4.604

Problem 12

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

84 84 68 63 86 136 0 92 71

N.S.

1 1.00 0.81 0.75 1.02 1.62 0.00 1.10 0.85

time (sec)

N/A 0.045 0.060 0.151 0.304 0.374 0.000 6.166 4.501

Problem 13

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

126 126 171 129 115 85 398 123 461

N.S.

1 1.00 1.36 1.02 0.91 0.67 3.16 0.98 3.66

time (sec)

N/A 0.072 0.976 0.271 0.310 0.365 0.993 5.473 6.916

Problem 14

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 58 99 95 71 158 117 92

N.S.

1 1.00 0.87 1.48 1.42 1.06 2.36 1.75 1.37

time (sec)

N/A 0.042 0.050 0.210 0.334 0.369 0.658 4.284 4.536

Problem 15

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

102 102 151 109 89 72 287 106 349

N.S.

1 1.00 1.48 1.07 0.87 0.71 2.81 1.04 3.42

time (sec)

N/A 0.060 0.353 0.194 0.297 0.373 0.433 4.535 6.792

Problem 16

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

45 45 46 79 56 58 107 56 53

N.S.

1 1.00 1.02 1.76 1.24 1.29 2.38 1.24 1.18

time (sec)

N/A 0.031 0.060 0.176 0.293 0.352 0.262 7.269 0.064

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 131 87 65 59 180 72 237

N.S.

1 1.00 1.68 1.12 0.83 0.76 2.31 0.92 3.04

time (sec)

N/A 0.051 0.196 0.134 0.306 0.353 0.192 5.859 6.708

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 37 21 20 44 53 20 32

N.S.

1 1.00 1.68 0.95 0.91 2.00 2.41 0.91 1.45

time (sec)

N/A 0.017 0.123 0.082 0.290 0.359 0.125 3.746 4.545

Problem 19

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

34 34 29 63 30 32 0 91 26

N.S.

1 1.00 0.85 1.85 0.88 0.94 0.00 2.68 0.76

time (sec)

N/A 0.026 0.015 0.121 0.331 0.387 0.000 3.611 0.054

Problem 20

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

38 38 75 47 47 74 0 33 28

N.S.

1 1.00 1.97 1.24 1.24 1.95 0.00 0.87 0.74

time (sec)

N/A 0.053 0.041 0.112 0.524 0.355 0.000 4.844 4.561

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

20 20 32 100 18 19 0 30 18

N.S.

1 1.00 1.60 5.00 0.90 0.95 0.00 1.50 0.90

time (sec)

N/A 0.026 0.088 0.152 0.375 0.339 0.000 6.195 0.042

Problem 22

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

63 63 58 63 52 97 0 54 81

N.S.

1 1.00 0.92 1.00 0.83 1.54 0.00 0.86 1.29

time (sec)

N/A 0.048 0.007 0.168 0.304 0.351 0.000 5.874 4.558

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 56 132 71 125 0 77 58

N.S.

1 1.00 0.88 2.06 1.11 1.95 0.00 1.20 0.91

time (sec)

N/A 0.045 0.045 0.185 0.294 0.373 0.000 5.064 4.466

Problem 24

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

64 64 82 93 77 85 0 106 156

N.S.

1 1.00 1.28 1.45 1.20 1.33 0.00 1.66 2.44

time (sec)

N/A 0.039 0.008 0.216 0.307 0.343 0.000 3.976 4.634

Problem 25

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

109 109 85 160 108 203 0 119 94

N.S.

1 1.00 0.78 1.47 0.99 1.86 0.00 1.09 0.86

time (sec)

N/A 0.063 0.100 0.269 0.312 0.367 0.000 5.427 4.338

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 110 121 98 115 0 171 276

N.S.

1 1.00 1.34 1.48 1.20 1.40 0.00 2.09 3.37

time (sec)

N/A 0.040 0.017 0.214 0.313 0.338 0.000 5.552 5.066

Problem 27

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

154 154 181 163 141 98 439 157 501

N.S.

1 1.00 1.18 1.06 0.92 0.64 2.85 1.02 3.25

time (sec)

N/A 0.107 1.251 0.364 0.309 0.378 1.427 6.831 6.806

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 58 133 108 85 196 134 106

N.S.

1 1.00 0.87 1.99 1.61 1.27 2.93 2.00 1.58

time (sec)

N/A 0.043 0.063 0.323 0.289 0.357 0.957 6.184 4.539

Problem 29

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

130 130 161 143 115 85 335 123 389

N.S.

1 1.00 1.24 1.10 0.88 0.65 2.58 0.95 2.99

time (sec)

N/A 0.090 0.500 0.233 0.303 0.371 0.683 3.975 6.711

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 43 113 82 72 146 82 80

N.S.

1 1.00 0.96 2.51 1.82 1.60 3.24 1.82 1.78

time (sec)

N/A 0.029 0.097 0.209 0.318 0.357 0.426 3.719 4.472

Problem 31

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

106 106 141 121 91 72 226 89 277

N.S.

1 1.00 1.33 1.14 0.86 0.68 2.13 0.84 2.61

time (sec)

N/A 0.078 0.268 0.170 0.391 0.347 0.368 4.170 6.532

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 47 21 20 57 70 20 53

N.S.

1 1.00 2.14 0.95 0.91 2.59 3.18 0.91 2.41

time (sec)

N/A 0.016 0.273 0.114 0.287 0.355 0.170 5.672 0.056

Problem 33

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

52 52 41 88 43 45 0 128 36

N.S.

1 1.00 0.79 1.69 0.83 0.87 0.00 2.46 0.69

time (sec)

N/A 0.028 0.021 0.128 0.294 0.362 0.000 6.238 0.053

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 55 87 68 101 0 91 138

N.S.

1 1.00 1.10 1.74 1.36 2.02 0.00 1.82 2.76

time (sec)

N/A 0.087 0.025 0.135 0.537 0.369 0.000 5.608 4.776

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 59 124 33 51 0 92 35

N.S.

1 1.00 1.48 3.10 0.82 1.28 0.00 2.30 0.88

time (sec)

N/A 0.033 0.031 0.168 0.299 0.364 0.000 3.140 4.521

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

31 31 28 120 78 99 0 38 55

N.S.

1 1.00 0.90 3.87 2.52 3.19 0.00 1.23 1.77

time (sec)

N/A 0.055 0.019 0.201 0.338 0.358 0.000 4.744 4.592

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

23 23 35 154 28 30 0 63 18

N.S.

1 1.00 1.52 6.70 1.22 1.30 0.00 2.74 0.78

time (sec)

N/A 0.026 0.149 0.198 0.313 0.342 0.000 4.612 0.066

Problem 38

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

92 92 110 171 103 149 0 86 135

N.S.

1 1.00 1.20 1.86 1.12 1.62 0.00 0.93 1.47

time (sec)

N/A 0.062 0.010 0.200 0.416 0.360 0.000 7.260 4.694

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 67 202 96 185 0 90 81

N.S.

1 1.00 0.77 2.32 1.10 2.13 0.00 1.03 0.93

time (sec)

N/A 0.052 0.072 0.181 0.315 0.374 0.000 6.328 4.536

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

99 99 134 217 122 112 0 138 228

N.S.

1 1.00 1.35 2.19 1.23 1.13 0.00 1.39 2.30

time (sec)

N/A 0.060 0.009 0.186 0.308 0.384 0.000 4.502 4.865

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 58 513 173 149 558 219 134

N.S.

1 1.00 0.87 7.66 2.58 2.22 8.33 3.27 2.00

time (sec)

N/A 0.056 0.266 1.237 0.309 0.396 5.463 2.912 0.179

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

286 286 211 535 339 150 1280 208 684

N.S.

1 1.00 0.74 1.87 1.19 0.52 4.48 0.73 2.39

time (sec)

N/A 0.281 1.981 0.934 0.315 0.420 4.036 5.146 7.051

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 43 463 134 136 422 134 132

N.S.

1 1.00 0.96 10.29 2.98 3.02 9.38 2.98 2.93

time (sec)

N/A 0.032 0.658 0.688 0.316 0.391 2.837 6.633 0.117

Problem 44

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

262 262 191 480 319 137 1018 174 572

N.S.

1 1.00 0.73 1.83 1.22 0.52 3.89 0.66 2.18

time (sec)

N/A 0.253 0.908 0.493 0.318 0.404 2.124 5.697 7.258

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 97 21 20 122 148 20 118

N.S.

1 1.00 4.41 0.95 0.91 5.55 6.73 0.91 5.36

time (sec)

N/A 0.017 0.847 0.336 0.312 0.357 1.371 5.064 4.746

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 95 312 109 114 0 288 109

N.S.

1 1.00 0.59 1.93 0.67 0.70 0.00 1.78 0.67

time (sec)

N/A 0.053 0.118 0.220 0.313 0.375 0.000 4.955 4.648

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

201 201 55 389 331 231 0 231 513

N.S.

1 1.00 0.27 1.94 1.65 1.15 0.00 1.15 2.55

time (sec)

N/A 0.237 0.041 0.129 0.538 0.362 0.000 4.492 8.733

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 111 442 97 130 0 275 97

N.S.

1 1.00 0.92 3.65 0.80 1.07 0.00 2.27 0.80

time (sec)

N/A 0.062 0.176 0.206 0.293 0.381 0.000 5.321 4.623

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

179 179 59 478 311 247 0 200 437

N.S.

1 1.00 0.33 2.67 1.74 1.38 0.00 1.12 2.44

time (sec)

N/A 0.214 0.036 0.202 0.528 0.382 0.000 6.880 9.129

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

110 110 73 527 95 139 0 243 96

N.S.

1 1.00 0.66 4.79 0.86 1.26 0.00 2.21 0.87

time (sec)

N/A 0.063 0.295 0.205 0.313 0.391 0.000 6.204 4.602

Problem 51

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

73 73 141 114 258 50 1355 114 107

N.S.

1 1.00 1.93 1.56 3.53 0.68 18.56 1.56 1.47

time (sec)

N/A 0.047 0.505 0.178 0.551 0.368 15.820 6.435 8.155

Problem 52

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

47 47 46 45 47 37 530 47 54

N.S.

1 1.00 0.98 0.96 1.00 0.79 11.28 1.00 1.15

time (sec)

N/A 0.039 0.069 0.164 0.339 0.369 8.699 3.665 4.660

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 119 75 156 37 558 75 66

N.S.

1 1.00 2.43 1.53 3.18 0.76 11.39 1.53 1.35

time (sec)

N/A 0.037 0.214 0.134 0.700 0.394 4.859 4.838 6.874

Problem 54

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

32 32 24 28 25 25 158 25 22

N.S.

1 1.00 0.75 0.88 0.78 0.78 4.94 0.78 0.69

time (sec)

N/A 0.030 0.027 0.000 0.409 0.414 2.329 5.065 4.488

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

19 19 97 35 52 17 88 34 29

N.S.

1 1.00 5.11 1.84 2.74 0.89 4.63 1.79 1.53

time (sec)

N/A 0.027 0.083 0.091 0.556 0.351 1.250 4.703 4.532

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

16 16 16 19 18 16 24 19 16

N.S.

1 1.00 1.00 1.19 1.12 1.00 1.50 1.19 1.00

time (sec)

N/A 0.017 0.009 0.000 0.305 0.369 0.264 6.500 0.042

Problem 57

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

37 37 30 43 47 58 0 58 33

N.S.

1 1.00 0.81 1.16 1.27 1.57 0.00 1.57 0.89

time (sec)

N/A 0.037 0.028 0.000 0.309 0.355 0.000 5.427 0.066

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

42 42 45 70 129 49 0 67 71

N.S.

1 1.00 1.07 1.67 3.07 1.17 0.00 1.60 1.69

time (sec)

N/A 0.036 0.040 0.105 0.305 0.349 0.000 5.496 4.560

Problem 59

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 75 67 91 125 0 96 74

N.S.

1 1.00 0.97 0.87 1.18 1.62 0.00 1.25 0.96

time (sec)

N/A 0.054 0.070 0.152 0.303 0.369 0.000 3.858 4.656

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

62 62 66 130 294 75 0 119 125

N.S.

1 1.00 1.06 2.10 4.74 1.21 0.00 1.92 2.02

time (sec)

N/A 0.041 0.069 0.180 0.357 0.362 0.000 6.207 5.941

Problem 61

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

120 120 97 91 130 147 0 116 115

N.S.

1 1.00 0.81 0.76 1.08 1.22 0.00 0.97 0.96

time (sec)

N/A 0.075 0.105 0.227 0.511 0.361 0.000 6.792 0.142

Problem 62

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

104 104 151 181 393 60 2531 179 172

N.S.

1 1.00 1.45 1.74 3.78 0.58 24.34 1.72 1.65

time (sec)

N/A 0.079 0.737 0.156 0.853 0.358 78.335 6.888 8.223

Problem 63

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

47 47 46 45 47 47 1037 47 54

N.S.

1 1.00 0.98 0.96 1.00 1.00 22.06 1.00 1.15

time (sec)

N/A 0.035 0.109 0.276 0.384 0.355 45.756 4.871 4.662

Problem 64

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

80 80 131 129 267 50 1243 127 65

N.S.

1 1.00 1.64 1.61 3.34 0.62 15.54 1.59 0.81

time (sec)

N/A 0.066 0.327 0.232 0.525 0.368 29.084 5.009 4.746

Problem 65

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

23 23 39 19 35 37 394 35 32

N.S.

1 1.00 1.70 0.83 1.52 1.61 17.13 1.52 1.39

time (sec)

N/A 0.028 0.088 0.197 0.290 0.351 16.906 5.245 4.610

Problem 66

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

56 56 109 77 140 35 403 73 32

N.S.

1 1.00 1.95 1.38 2.50 0.62 7.20 1.30 0.57

time (sec)

N/A 0.055 0.116 0.201 0.503 0.349 9.436 6.030 4.653

Problem 67

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

32 32 26 28 30 27 150 54 27

N.S.

1 1.00 0.81 0.88 0.94 0.84 4.69 1.69 0.84

time (sec)

N/A 0.032 0.022 0.187 0.285 0.344 0.534 8.025 0.060

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 104 37 56 61 95 33 28

N.S.

1 1.00 3.06 1.09 1.65 1.79 2.79 0.97 0.82

time (sec)

N/A 0.026 0.113 0.198 0.530 0.370 2.671 7.748 4.641

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

21 21 31 21 20 21 32 20 18

N.S.

1 1.00 1.48 1.00 0.95 1.00 1.52 0.95 0.86

time (sec)

N/A 0.017 0.045 0.102 0.299 0.332 0.550 5.481 0.048

Problem 70

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

60 60 38 55 72 105 0 71 60

N.S.

1 1.00 0.63 0.92 1.20 1.75 0.00 1.18 1.00

time (sec)

N/A 0.039 0.065 0.214 0.304 0.366 0.000 6.296 4.519

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

71 71 53 98 204 79 0 93 156

N.S.

1 1.00 0.75 1.38 2.87 1.11 0.00 1.31 2.20

time (sec)

N/A 0.064 0.053 0.174 0.304 0.345 0.000 5.943 4.770

Problem 72

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

104 104 85 79 108 178 0 106 93

N.S.

1 1.00 0.82 0.76 1.04 1.71 0.00 1.02 0.89

time (sec)

N/A 0.058 0.078 0.236 0.299 0.353 0.000 3.665 0.103

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 78 158 396 103 0 145 276

N.S.

1 1.00 0.84 1.70 4.26 1.11 0.00 1.56 2.97

time (sec)

N/A 0.069 0.044 0.253 0.323 0.344 0.000 7.247 5.184

Problem 74

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

146 146 137 103 167 198 0 126 151

N.S.

1 1.00 0.94 0.71 1.14 1.36 0.00 0.86 1.03

time (sec)

N/A 0.081 0.213 0.340 0.305 0.422 0.000 6.554 0.186

Problem 75

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

103 103 141 142 310 60 1717 140 81

N.S.

1 1.00 1.37 1.38 3.01 0.58 16.67 1.36 0.79

time (sec)

N/A 0.079 0.671 0.149 0.537 0.403 120.347 6.943 4.721

Problem 76

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 48 19 45 45 654 45 53

N.S.

1 1.00 2.09 0.83 1.96 1.96 28.43 1.96 2.30

time (sec)

N/A 0.028 0.216 0.131 0.295 0.379 75.625 5.785 4.548

Problem 77

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

77 77 121 90 184 45 690 88 57

N.S.

1 1.00 1.57 1.17 2.39 0.58 8.96 1.14 0.74

time (sec)

N/A 0.067 0.311 0.280 0.510 0.348 48.296 5.829 4.638

Problem 78

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

50 50 38 38 41 36 564 115 36

N.S.

1 1.00 0.76 0.76 0.82 0.72 11.28 2.30 0.72

time (sec)

N/A 0.034 0.034 0.264 0.281 0.358 27.727 7.699 4.560

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A B A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 59 54 139 78 478 80 69

N.S.

1 1.00 1.20 1.10 2.84 1.59 9.76 1.63 1.41

time (sec)

N/A 0.055 0.027 0.252 0.506 0.333 16.447 6.446 4.852

Problem 80

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

39 39 58 32 37 41 299 35 36

N.S.

1 1.00 1.49 0.82 0.95 1.05 7.67 0.90 0.92

time (sec)

N/A 0.035 0.043 0.207 0.295 0.358 0.612 6.262 4.543

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 28 55 99 95 153 36 53

N.S.

1 1.00 1.04 2.04 3.67 3.52 5.67 1.33 1.96

time (sec)

N/A 0.028 0.014 0.211 0.277 0.352 5.091 5.901 4.580

Problem 82

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

22 22 33 21 20 36 51 20 18

N.S.

1 1.00 1.50 0.95 0.91 1.64 2.32 0.91 0.82

time (sec)

N/A 0.017 0.042 0.112 0.291 0.338 0.583 6.337 4.460

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 61 67 98 154 0 81 83

N.S.

1 1.00 0.74 0.82 1.20 1.88 0.00 0.99 1.01

time (sec)

N/A 0.043 0.057 0.224 0.277 0.344 0.000 5.515 4.595

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

99 99 63 130 310 106 0 119 228

N.S.

1 1.00 0.64 1.31 3.13 1.07 0.00 1.20 2.30

time (sec)

N/A 0.094 0.066 0.218 0.295 0.344 0.000 6.532 5.079

Problem 85

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

126 126 95 91 146 228 0 116 129

N.S.

1 1.00 0.75 0.72 1.16 1.81 0.00 0.92 1.02

time (sec)

N/A 0.070 0.105 0.322 0.285 0.383 0.000 8.380 0.149

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 85 190 482 130 0 171 167

N.S.

1 1.00 0.69 1.54 3.92 1.06 0.00 1.39 1.36

time (sec)

N/A 0.103 0.078 0.328 0.299 0.349 0.000 5.145 5.563

Problem 87

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

171 171 145 115 188 248 0 136 173

N.S.

1 1.00 0.85 0.67 1.10 1.45 0.00 0.80 1.01

time (sec)

N/A 0.092 0.301 0.406 0.301 0.392 0.000 4.532 4.765

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 275 110 295 244 0 99 91

N.S.

1 1.00 2.17 0.87 2.32 1.92 0.00 0.78 0.72

time (sec)

N/A 0.125 6.062 0.200 0.531 0.361 0.000 7.133 7.770

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

36 36 28 55 74 82 2006 68 64

N.S.

1 1.00 0.78 1.53 2.06 2.28 55.72 1.89 1.78

time (sec)

N/A 0.031 0.050 0.186 0.284 0.347 14.553 7.005 0.072

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 36 145 375 239 0 125 118

N.S.

1 1.00 0.62 2.50 6.47 4.12 0.00 2.16 2.03

time (sec)

N/A 0.058 0.057 0.215 0.316 0.337 0.000 7.323 6.628

Problem 91

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

65 65 58 43 93 100 1120 137 54

N.S.

1 1.00 0.89 0.66 1.43 1.54 17.23 2.11 0.83

time (sec)

N/A 0.043 0.080 0.217 0.317 0.358 14.305 6.565 4.712

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 58 175 461 291 2470 151 140

N.S.

1 1.00 0.49 1.48 3.91 2.47 20.93 1.28 1.19

time (sec)

N/A 0.120 0.054 0.250 0.328 0.376 201.182 6.195 7.148

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A B B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 43 33 96 105 493 28 28

N.S.

1 1.00 0.96 0.73 2.13 2.33 10.96 0.62 0.62

time (sec)

N/A 0.036 0.113 0.233 0.281 0.353 14.506 5.486 0.097

Problem 94

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

183 183 78 205 547 339 3405 177 162

N.S.

1 1.00 0.43 1.12 2.99 1.85 18.61 0.97 0.89

time (sec)

N/A 0.183 0.085 0.259 0.312 0.376 106.177 4.827 8.117

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

22 22 33 21 20 108 128 20 18

N.S.

1 1.00 1.50 0.95 0.91 4.91 5.82 0.91 0.82

time (sec)

N/A 0.018 0.151 0.286 0.284 0.345 14.202 6.679 4.668

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

194 194 122 127 213 374 0 131 198

N.S.

1 1.00 0.63 0.65 1.10 1.93 0.00 0.68 1.02

time (sec)

N/A 0.082 0.473 0.506 0.302 0.399 0.000 6.870 0.303

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

245 245 113 280 740 225 0 249 233

N.S.

1 1.00 0.46 1.14 3.02 0.92 0.00 1.02 0.95

time (sec)

N/A 0.285 0.218 0.249 0.351 0.359 0.000 7.840 8.035

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

238 238 175 151 248 446 0 166 231

N.S.

1 1.00 0.74 0.63 1.04 1.87 0.00 0.70 0.97

time (sec)

N/A 0.124 0.985 0.382 0.302 0.380 0.000 4.675 0.489

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

279 279 125 340 866 249 0 301 277

N.S.

1 1.00 0.45 1.22 3.10 0.89 0.00 1.08 0.99

time (sec)

N/A 0.302 0.270 0.339 0.406 0.377 0.000 4.769 9.231

Problem 100

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

284 284 195 175 305 466 0 186 290

N.S.

1 1.00 0.69 0.62 1.07 1.64 0.00 0.65 1.02

time (sec)

N/A 0.156 1.571 0.411 0.309 0.418 0.000 4.879 0.798

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