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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 B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

151 151 134 199 116 123 184 293 259

N.S.

1 1.00 0.89 1.32 0.77 0.81 1.22 1.94 1.72

time (sec)

N/A 0.048 0.458 0.163 0.275 2.705 2.337 5.998 5.133

Problem 2

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

118 118 106 159 94 101 148 247 204

N.S.

1 1.00 0.90 1.35 0.80 0.86 1.25 2.09 1.73

time (sec)

N/A 0.044 0.440 0.105 0.275 2.501 1.149 3.508 5.693

Problem 3

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

87 87 82 123 72 79 112 201 151

N.S.

1 1.00 0.94 1.41 0.83 0.91 1.29 2.31 1.74

time (sec)

N/A 0.036 0.314 0.119 0.280 4.539 0.522 1.813 5.734

Problem 4

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

57 57 55 83 50 57 76 155 96

N.S.

1 1.00 0.96 1.46 0.88 1.00 1.33 2.72 1.68

time (sec)

N/A 0.028 0.121 0.082 0.270 3.612 0.217 0.808 1.993

Problem 5

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

25 25 25 20 26 34 37 106 40

N.S.

1 1.00 1.00 0.80 1.04 1.36 1.48 4.24 1.60

time (sec)

N/A 0.014 0.024 0.037 0.284 3.810 0.085 0.493 1.172

Problem 6

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

16 16 29 26 14 16 0 58 34

N.S.

1 1.00 1.81 1.62 0.88 1.00 0.00 3.62 2.12

time (sec)

N/A 0.015 0.026 0.064 0.272 3.071 0.000 0.433 1.239

Problem 7

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

57 57 114 48 42 69 0 103 46

N.S.

1 1.00 2.00 0.84 0.74 1.21 0.00 1.81 0.81

time (sec)

N/A 0.032 0.790 0.118 0.294 2.361 0.000 0.479 1.275

Problem 8

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

95 95 127 73 86 150 0 149 88

N.S.

1 1.00 1.34 0.77 0.91 1.58 0.00 1.57 0.93

time (sec)

N/A 0.045 0.554 0.128 0.284 3.033 0.000 0.504 1.178

Problem 9

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

133 133 165 96 126 241 0 197 118

N.S.

1 1.00 1.24 0.72 0.95 1.81 0.00 1.48 0.89

time (sec)

N/A 0.061 0.406 0.128 0.275 3.009 0.000 0.543 1.227

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

129 129 115 180 164 156 0 174 242

N.S.

1 1.00 0.89 1.40 1.27 1.21 0.00 1.35 1.88

time (sec)

N/A 0.091 1.825 0.112 0.497 2.897 0.000 4.940 2.469

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

102 102 95 143 134 134 0 146 188

N.S.

1 1.00 0.93 1.40 1.31 1.31 0.00 1.43 1.84

time (sec)

N/A 0.068 1.297 0.099 0.483 2.840 0.000 2.355 2.383

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

73 73 75 104 102 112 0 118 134

N.S.

1 1.00 1.03 1.42 1.40 1.53 0.00 1.62 1.84

time (sec)

N/A 0.045 0.438 0.099 0.488 3.205 0.000 1.064 1.852

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 60 67 65 87 0 88 80

N.S.

1 1.00 1.33 1.49 1.44 1.93 0.00 1.96 1.78

time (sec)

N/A 0.024 0.035 0.071 0.495 2.651 0.000 0.624 1.139

Problem 14

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

26 26 43 35 31 33 0 26 19

N.S.

1 1.00 1.65 1.35 1.19 1.27 0.00 1.00 0.73

time (sec)

N/A 0.017 0.033 0.069 0.513 2.385 0.000 0.465 1.073

Problem 15

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

55 55 62 86 59 72 0 56 53

N.S.

1 1.00 1.13 1.56 1.07 1.31 0.00 1.02 0.96

time (sec)

N/A 0.035 0.042 0.100 0.479 2.913 0.000 0.494 1.200

Problem 16

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

84 84 79 129 79 139 0 83 156

N.S.

1 1.00 0.94 1.54 0.94 1.65 0.00 0.99 1.86

time (sec)

N/A 0.058 0.064 0.094 0.502 2.688 0.000 0.494 1.449

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C A A B F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

111 111 92 162 100 210 0 113 204

N.S.

1 1.00 0.83 1.46 0.90 1.89 0.00 1.02 1.84

time (sec)

N/A 0.085 0.056 0.124 0.470 2.560 0.000 0.507 1.983

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

140 140 111 205 119 279 0 140 252

N.S.

1 1.00 0.79 1.46 0.85 1.99 0.00 1.00 1.80

time (sec)

N/A 0.111 0.072 0.161 0.494 3.354 0.000 0.539 3.175

Problem 19

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

192 192 140 225 149 156 314 342 308

N.S.

1 1.00 0.73 1.17 0.78 0.81 1.64 1.78 1.60

time (sec)

N/A 0.068 0.499 0.175 0.278 4.484 3.240 6.402 5.142

Problem 20

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

132 132 110 185 110 117 252 292 249

N.S.

1 1.00 0.83 1.40 0.83 0.89 1.91 2.21 1.89

time (sec)

N/A 0.056 0.292 0.128 0.273 3.216 1.734 3.663 4.819

Problem 21

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

120 120 125 149 97 104 189 242 192

N.S.

1 1.00 1.04 1.24 0.81 0.87 1.58 2.02 1.60

time (sec)

N/A 0.052 0.391 0.109 0.263 3.049 0.790 1.930 5.052

Problem 22

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 83 109 58 65 126 192 133

N.S.

1 1.00 1.28 1.68 0.89 1.00 1.94 2.95 2.05

time (sec)

N/A 0.040 0.183 0.091 0.278 2.771 0.345 0.902 3.870

Problem 23

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

48 48 51 34 43 52 60 142 76

N.S.

1 1.00 1.06 0.71 0.90 1.08 1.25 2.96 1.58

time (sec)

N/A 0.025 0.104 0.056 0.268 3.288 0.147 0.535 1.214

Problem 24

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

35 35 29 28 31 35 0 64 36

N.S.

1 1.00 0.83 0.80 0.89 1.00 0.00 1.83 1.03

time (sec)

N/A 0.027 0.041 0.096 0.274 4.268 0.000 0.485 1.255

Problem 25

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

40 40 56 39 34 48 0 111 50

N.S.

1 1.00 1.40 0.98 0.85 1.20 0.00 2.78 1.25

time (sec)

N/A 0.035 0.070 0.096 0.272 4.553 0.000 0.489 1.229

Problem 26

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

85 85 86 63 72 122 0 138 62

N.S.

1 1.00 1.01 0.74 0.85 1.44 0.00 1.62 0.73

time (sec)

N/A 0.049 0.287 0.112 0.274 3.732 0.000 0.548 1.260

Problem 27

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

127 127 114 86 109 191 0 186 113

N.S.

1 1.00 0.90 0.68 0.86 1.50 0.00 1.46 0.89

time (sec)

N/A 0.063 0.246 0.125 0.263 3.056 0.000 0.572 1.269

Problem 28

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

169 169 146 111 165 322 0 238 149

N.S.

1 1.00 0.86 0.66 0.98 1.91 0.00 1.41 0.88

time (sec)

N/A 0.081 0.351 0.149 0.280 3.547 0.000 0.608 1.589

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

161 161 337 169 151 165 0 180 234

N.S.

1 1.00 2.09 1.05 0.94 1.02 0.00 1.12 1.45

time (sec)

N/A 0.136 1.474 0.119 0.473 2.910 0.000 2.659 2.648

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 558 130 119 139 0 148 174

N.S.

1 1.00 4.69 1.09 1.00 1.17 0.00 1.24 1.46

time (sec)

N/A 0.100 5.687 0.092 0.488 2.855 0.000 1.240 1.953

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 773 93 83 111 0 99 101

N.S.

1 1.00 10.74 1.29 1.15 1.54 0.00 1.38 1.40

time (sec)

N/A 0.081 6.333 0.092 0.473 2.374 0.000 0.735 1.208

Problem 32

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

35 35 46 50 48 42 0 31 24

N.S.

1 1.00 1.31 1.43 1.37 1.20 0.00 0.89 0.69

time (sec)

N/A 0.053 0.043 0.082 0.475 2.159 0.000 0.459 1.078

Problem 33

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

69 69 112 112 77 81 0 50 39

N.S.

1 1.00 1.62 1.62 1.12 1.17 0.00 0.72 0.57

time (sec)

N/A 0.081 0.276 0.082 0.480 2.523 0.000 0.481 1.096

Problem 34

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

107 107 194 155 97 118 0 80 78

N.S.

1 1.00 1.81 1.45 0.91 1.10 0.00 0.75 0.73

time (sec)

N/A 0.091 0.835 0.092 0.478 3.593 0.000 0.510 1.259

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 312 188 117 173 0 112 182

N.S.

1 1.00 2.24 1.35 0.84 1.24 0.00 0.81 1.31

time (sec)

N/A 0.105 1.133 0.116 0.482 3.702 0.000 0.540 1.755

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

179 179 428 231 137 274 0 145 230

N.S.

1 1.00 2.39 1.29 0.77 1.53 0.00 0.81 1.28

time (sec)

N/A 0.121 1.927 0.135 0.477 2.917 0.000 0.582 2.778

Problem 37

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

210 210 214 386 162 169 439 367 337

N.S.

1 1.00 1.02 1.84 0.77 0.80 2.09 1.75 1.60

time (sec)

N/A 0.072 0.699 0.197 0.263 3.580 4.609 6.189 5.263

Problem 38

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

137 137 110 318 110 117 350 317 278

N.S.

1 1.00 0.80 2.32 0.80 0.85 2.55 2.31 2.03

time (sec)

N/A 0.056 0.381 0.148 0.265 3.273 2.402 3.968 5.169

Problem 39

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

138 138 140 254 110 117 255 267 221

N.S.

1 1.00 1.01 1.84 0.80 0.85 1.85 1.93 1.60

time (sec)

N/A 0.055 0.407 0.122 0.284 2.224 1.214 2.133 5.483

Problem 40

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

99 99 92 186 84 91 165 217 162

N.S.

1 1.00 0.93 1.88 0.85 0.92 1.67 2.19 1.64

time (sec)

N/A 0.046 0.294 0.101 0.267 2.930 0.533 1.064 5.546

Problem 41

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

66 66 64 44 58 65 76 167 105

N.S.

1 1.00 0.97 0.67 0.88 0.98 1.15 2.53 1.59

time (sec)

N/A 0.028 0.168 0.070 0.274 3.266 0.215 0.588 1.940

Problem 42

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

48 48 36 36 43 61 0 145 86

N.S.

1 1.00 0.75 0.75 0.90 1.27 0.00 3.02 1.79

time (sec)

N/A 0.033 0.092 0.101 0.267 3.326 0.000 0.506 1.201

Problem 43

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

40 40 46 39 34 50 0 109 48

N.S.

1 1.00 1.15 0.98 0.85 1.25 0.00 2.72 1.20

time (sec)

N/A 0.036 0.142 0.111 0.264 2.369 0.000 0.515 1.234

Problem 44

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

61 61 72 52 59 82 0 138 78

N.S.

1 1.00 1.18 0.85 0.97 1.34 0.00 2.26 1.28

time (sec)

N/A 0.043 0.188 0.122 0.266 2.473 0.000 0.546 1.220

Problem 45

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

107 107 102 74 96 178 0 165 94

N.S.

1 1.00 0.95 0.69 0.90 1.66 0.00 1.54 0.88

time (sec)

N/A 0.055 0.692 0.130 0.270 2.192 0.000 0.567 1.291

Problem 46

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

149 149 130 99 142 272 0 213 130

N.S.

1 1.00 0.87 0.66 0.95 1.83 0.00 1.43 0.87

time (sec)

N/A 0.071 0.367 0.148 0.268 3.012 0.000 0.615 1.204

Problem 47

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

237 237 363 290 262 178 0 196 263

N.S.

1 1.00 1.53 1.22 1.11 0.75 0.00 0.83 1.11

time (sec)

N/A 0.229 2.125 0.135 0.497 2.610 0.000 2.682 2.429

Problem 48

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

169 169 303 223 210 152 0 164 203

N.S.

1 1.00 1.79 1.32 1.24 0.90 0.00 0.97 1.20

time (sec)

N/A 0.170 1.173 0.110 0.499 3.079 0.000 1.367 2.439

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

98 98 230 157 147 113 0 132 146

N.S.

1 1.00 2.35 1.60 1.50 1.15 0.00 1.35 1.49

time (sec)

N/A 0.119 0.877 0.086 0.488 3.118 0.000 0.817 1.909

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 109 79 85 84 0 66 35

N.S.

1 1.00 2.22 1.61 1.73 1.71 0.00 1.35 0.71

time (sec)

N/A 0.072 0.249 0.082 0.491 3.158 0.000 0.519 1.200

Problem 51

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

69 69 112 125 90 82 0 50 39

N.S.

1 1.00 1.62 1.81 1.30 1.19 0.00 0.72 0.57

time (sec)

N/A 0.098 0.253 0.098 0.483 2.695 0.000 0.534 1.198

Problem 52

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

107 107 112 232 122 118 0 66 62

N.S.

1 1.00 1.05 2.17 1.14 1.10 0.00 0.62 0.58

time (sec)

N/A 0.117 0.699 0.110 0.483 3.452 0.000 0.526 1.446

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

141 141 252 293 152 160 0 96 91

N.S.

1 1.00 1.79 2.08 1.08 1.13 0.00 0.68 0.65

time (sec)

N/A 0.133 0.994 0.112 0.497 3.140 0.000 0.568 1.700

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

179 179 370 364 182 235 0 128 206

N.S.

1 1.00 2.07 2.03 1.02 1.31 0.00 0.72 1.15

time (sec)

N/A 0.153 1.359 0.132 0.504 2.977 0.000 0.605 1.944

Problem 55

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

213 213 268 425 212 314 0 161 254

N.S.

1 1.00 1.26 2.00 1.00 1.47 0.00 0.76 1.19

time (sec)

N/A 0.171 6.194 0.174 0.490 3.108 0.000 0.660 3.032

Problem 56

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

135 135 137 82 90 95 0 245 208

N.S.

1 1.00 1.01 0.61 0.67 0.70 0.00 1.81 1.54

time (sec)

N/A 0.057 0.525 0.154 0.290 4.925 0.000 5.548 5.142

Problem 57

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

97 97 103 65 70 75 0 201 153

N.S.

1 1.00 1.06 0.67 0.72 0.77 0.00 2.07 1.58

time (sec)

N/A 0.051 0.257 0.113 0.273 3.764 0.000 3.358 6.021

Problem 58

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

66 66 65 44 50 55 0 157 99

N.S.

1 1.00 0.98 0.67 0.76 0.83 0.00 2.38 1.50

time (sec)

N/A 0.042 0.191 0.100 0.268 3.789 0.000 1.643 2.193

Problem 59

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

28 28 21 25 28 33 0 111 44

N.S.

1 1.00 0.75 0.89 1.00 1.18 0.00 3.96 1.57

time (sec)

N/A 0.034 0.067 0.065 0.266 2.912 0.000 0.739 1.224

Problem 60

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

17 17 19 27 17 19 41 31 21

N.S.

1 1.00 1.12 1.59 1.00 1.12 2.41 1.82 1.24

time (sec)

N/A 0.019 0.020 0.033 0.264 2.723 2.136 0.457 1.211

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

61 61 67 43 47 60 0 86 49

N.S.

1 1.00 1.10 0.70 0.77 0.98 0.00 1.41 0.80

time (sec)

N/A 0.040 0.123 0.106 0.275 2.598 0.000 0.443 1.252

Problem 62

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

103 103 107 67 91 139 0 157 76

N.S.

1 1.00 1.04 0.65 0.88 1.35 0.00 1.52 0.74

time (sec)

N/A 0.058 0.605 0.125 0.266 2.536 0.000 0.476 1.343

Problem 63

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

145 145 135 91 130 217 0 211 132

N.S.

1 1.00 0.93 0.63 0.90 1.50 0.00 1.46 0.91

time (sec)

N/A 0.071 0.552 0.137 0.276 3.102 0.000 0.517 1.313

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

105 105 301 230 329 127 0 149 193

N.S.

1 1.00 2.87 2.19 3.13 1.21 0.00 1.42 1.84

time (sec)

N/A 0.102 0.870 0.129 0.484 3.948 0.000 4.411 2.524

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 893 170 247 107 0 123 139

N.S.

1 1.00 11.45 2.18 3.17 1.37 0.00 1.58 1.78

time (sec)

N/A 0.078 6.469 0.111 0.476 5.207 0.000 2.086 1.997

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

49 49 241 110 163 86 0 96 83

N.S.

1 1.00 4.92 2.24 3.33 1.76 0.00 1.96 1.69

time (sec)

N/A 0.056 0.951 0.091 0.483 3.633 0.000 1.005 1.287

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

21 21 60 50 78 35 0 50 25

N.S.

1 1.00 2.86 2.38 3.71 1.67 0.00 2.38 1.19

time (sec)

N/A 0.036 0.102 0.067 0.492 3.674 0.000 0.595 1.108

Problem 68

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

61 61 100 59 93 64 0 66 65

N.S.

1 1.00 1.64 0.97 1.52 1.05 0.00 1.08 1.07

time (sec)

N/A 0.070 0.875 0.091 0.482 3.095 0.000 0.498 1.293

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

88 88 254 85 137 134 0 98 158

N.S.

1 1.00 2.89 0.97 1.56 1.52 0.00 1.11 1.80

time (sec)

N/A 0.094 0.862 0.115 0.482 2.202 0.000 0.478 1.434

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

117 117 359 111 177 198 0 127 206

N.S.

1 1.00 3.07 0.95 1.51 1.69 0.00 1.09 1.76

time (sec)

N/A 0.122 1.139 0.113 0.470 3.463 0.000 0.518 2.036

Problem 71

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

120 120 125 74 80 85 0 223 193

N.S.

1 1.00 1.04 0.62 0.67 0.71 0.00 1.86 1.61

time (sec)

N/A 0.054 0.517 0.148 0.267 2.635 0.000 5.850 5.181

Problem 72

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

65 65 83 45 50 55 0 180 135

N.S.

1 1.00 1.28 0.69 0.77 0.85 0.00 2.77 2.08

time (sec)

N/A 0.042 0.199 0.111 0.263 4.514 0.000 3.688 3.869

Problem 73

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

48 48 51 34 40 45 0 136 77

N.S.

1 1.00 1.06 0.71 0.83 0.94 0.00 2.83 1.60

time (sec)

N/A 0.037 0.118 0.087 0.281 3.821 0.000 1.816 1.350

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

33 33 30 28 31 31 0 33 22

N.S.

1 1.00 0.91 0.85 0.94 0.94 0.00 1.00 0.67

time (sec)

N/A 0.034 0.068 0.092 0.267 3.096 0.000 0.766 1.388

Problem 75

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

36 36 56 37 35 43 177 57 35

N.S.

1 1.00 1.56 1.03 0.97 1.19 4.92 1.58 0.97

time (sec)

N/A 0.028 0.141 0.042 0.267 2.892 11.710 0.513 1.130

Problem 76

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

81 81 83 55 74 106 0 117 62

N.S.

1 1.00 1.02 0.68 0.91 1.31 0.00 1.44 0.77

time (sec)

N/A 0.046 0.188 0.118 0.277 2.561 0.000 0.454 1.263

Problem 77

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

123 123 121 79 110 162 0 186 89

N.S.

1 1.00 0.98 0.64 0.89 1.32 0.00 1.51 0.72

time (sec)

N/A 0.062 0.371 0.132 0.265 2.383 0.000 0.536 1.366

Problem 78

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

165 165 154 103 167 283 0 236 151

N.S.

1 1.00 0.93 0.62 1.01 1.72 0.00 1.43 0.92

time (sec)

N/A 0.081 0.825 0.138 0.274 2.277 0.000 0.557 1.245

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 495 200 301 117 0 136 179

N.S.

1 1.00 4.16 1.68 2.53 0.98 0.00 1.14 1.50

time (sec)

N/A 0.143 5.880 0.126 0.484 3.025 0.000 4.825 2.258

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 767 140 196 97 0 99 111

N.S.

1 1.00 10.65 1.94 2.72 1.35 0.00 1.38 1.54

time (sec)

N/A 0.113 6.330 0.107 0.475 3.193 0.000 2.320 1.389

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B B B A F B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

34 34 177 80 123 66 0 79 61

N.S.

1 1.00 5.21 2.35 3.62 1.94 0.00 2.32 1.79

time (sec)

N/A 0.051 0.562 0.086 0.491 3.830 0.000 1.134 1.192

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

33 35 42 31 49 42 0 29 22

N.S.

1 1.06 1.27 0.94 1.48 1.27 0.00 0.88 0.67

time (sec)

N/A 0.085 0.022 0.096 0.471 2.993 0.000 0.634 1.096

Problem 83

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

107 107 149 72 113 106 0 84 78

N.S.

1 1.00 1.39 0.67 1.06 0.99 0.00 0.79 0.73

time (sec)

N/A 0.130 1.396 0.111 0.485 2.699 0.000 0.490 1.395

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 314 98 157 154 0 114 182

N.S.

1 1.00 2.26 0.71 1.13 1.11 0.00 0.82 1.31

time (sec)

N/A 0.148 1.017 0.119 0.477 3.050 0.000 0.525 1.645

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

179 179 802 124 197 250 0 144 230

N.S.

1 1.00 4.48 0.69 1.10 1.40 0.00 0.80 1.28

time (sec)

N/A 0.158 6.602 0.129 0.490 2.451 0.000 0.532 2.507

Problem 86

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

137 137 140 85 90 95 0 246 225

N.S.

1 1.00 1.02 0.62 0.66 0.69 0.00 1.80 1.64

time (sec)

N/A 0.058 0.311 0.171 0.274 2.607 0.000 18.012 5.287

Problem 87

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

99 99 93 62 70 75 0 202 167

N.S.

1 1.00 0.94 0.63 0.71 0.76 0.00 2.04 1.69

time (sec)

N/A 0.048 0.357 0.125 0.266 2.527 0.000 5.886 5.916

Problem 88

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

65 65 64 45 50 55 0 158 109

N.S.

1 1.00 0.98 0.69 0.77 0.85 0.00 2.43 1.68

time (sec)

N/A 0.040 0.184 0.105 0.268 3.667 0.000 3.721 2.033

Problem 89

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

46 46 36 33 45 53 0 112 72

N.S.

1 1.00 0.78 0.72 0.98 1.15 0.00 2.43 1.57

time (sec)

N/A 0.039 0.117 0.092 0.264 3.735 0.000 1.809 1.269

Problem 90

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

35 35 33 40 36 42 457 56 36

N.S.

1 1.00 0.94 1.14 1.03 1.20 13.06 1.60 1.03

time (sec)

N/A 0.039 0.068 0.106 0.270 3.011 11.445 0.896 1.171

Problem 91

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

56 56 77 49 60 76 411 87 48

N.S.

1 1.00 1.38 0.88 1.07 1.36 7.34 1.55 0.86

time (sec)

N/A 0.031 0.189 0.054 0.276 2.632 11.129 0.580 1.154

Problem 92

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

101 101 97 67 98 151 0 143 75

N.S.

1 1.00 0.96 0.66 0.97 1.50 0.00 1.42 0.74

time (sec)

N/A 0.051 0.331 0.135 0.264 2.412 0.000 0.538 1.245

Problem 93

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

143 143 140 91 146 240 0 212 102

N.S.

1 1.00 0.98 0.64 1.02 1.68 0.00 1.48 0.71

time (sec)

N/A 0.070 0.635 0.145 0.273 3.225 0.000 0.569 1.399

Problem 94

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

185 185 169 115 188 317 0 261 170

N.S.

1 1.00 0.91 0.62 1.02 1.71 0.00 1.41 0.92

time (sec)

N/A 0.089 1.184 0.151 0.268 2.570 0.000 0.647 1.328

Problem 95

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

237 237 362 290 429 147 0 175 265

N.S.

1 1.00 1.53 1.22 1.81 0.62 0.00 0.74 1.12

time (sec)

N/A 0.274 1.332 0.181 0.487 3.374 0.000 20.478 2.564

Problem 96

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

169 169 303 230 343 127 0 149 208

N.S.

1 1.00 1.79 1.36 2.03 0.75 0.00 0.88 1.23

time (sec)

N/A 0.202 0.868 0.145 0.503 3.001 0.000 12.017 2.355

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

99 99 230 170 257 97 0 123 148

N.S.

1 1.00 2.32 1.72 2.60 0.98 0.00 1.24 1.49

time (sec)

N/A 0.147 0.806 0.117 0.482 3.635 0.000 4.902 1.934

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 241 110 171 87 0 97 92

N.S.

1 1.00 3.65 1.67 2.59 1.32 0.00 1.47 1.39

time (sec)

N/A 0.066 0.997 0.101 0.497 3.935 0.000 2.462 1.309

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 48 117 61 98 83 0 63 37

N.S.

1 1.04 2.54 1.33 2.13 1.80 0.00 1.37 0.80

time (sec)

N/A 0.104 0.279 0.095 0.490 3.390 0.000 1.174 1.161

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A A A F A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 71 125 45 72 80 0 50 35

N.S.

1 1.18 2.08 0.75 1.20 1.33 0.00 0.83 0.58

time (sec)

N/A 0.129 0.401 0.095 0.498 2.947 0.000 0.722 1.161

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