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2.2.2 Integrals 101 to 200

Detailed conclusion table per each integral is given by the 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 as F.

In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA

Problem 101

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 187 92 116 64 86 0 64 660

N.S.

1 1.31 0.64 0.81 0.45 0.60 0.00 0.45 4.62

time (sec)

N/A 0.475 0.043 0.043 0.497 0.242 0.000 0.258 5.875

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F F(-1)

verified

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

size

94 97 51 0 0 0 0 0 0

N.S.

1 1.03 0.54 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.296 0.996 0.000 0.000 0.000 0.000 0.000 0.000

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 107 114 266 81 95 0 61 867

N.S.

1 1.16 1.24 2.89 0.88 1.03 0.00 0.66 9.42

time (sec)

N/A 0.358 0.033 0.293 0.754 0.246 0.000 0.262 4.146

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 81 86 169 69 83 0 44 620

N.S.

1 1.14 1.21 2.38 0.97 1.17 0.00 0.62 8.73

time (sec)

N/A 0.302 0.055 0.159 0.749 0.246 0.000 0.274 3.924

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 52 49 54 48 61 112 37 46

N.S.

1 1.11 1.04 1.15 1.02 1.30 2.38 0.79 0.98

time (sec)

N/A 0.241 0.038 0.104 0.764 0.251 28.823 0.266 3.545

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 27 26 32 32 100 18 25

N.S.

1 1.00 0.79 0.76 0.94 0.94 2.94 0.53 0.74

time (sec)

N/A 0.190 0.112 0.088 0.752 0.251 29.242 0.263 0.087

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 15 12 24 24 12 14

N.S.

1 1.00 1.00 0.94 0.75 1.50 1.50 0.75 0.88

time (sec)

N/A 0.153 0.009 0.065 0.288 0.244 28.397 0.278 0.059

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 134 74 92 51 80 0 43 645

N.S.

1 1.38 0.76 0.95 0.53 0.82 0.00 0.44 6.65

time (sec)

N/A 0.363 0.126 0.039 0.796 0.247 0.000 0.264 6.015

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

131 181 93 117 69 109 0 60 804

N.S.

1 1.38 0.71 0.89 0.53 0.83 0.00 0.46 6.14

time (sec)

N/A 0.457 0.039 0.043 0.775 0.240 0.000 0.275 5.813

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

170 231 107 145 86 130 0 73 909

N.S.

1 1.36 0.63 0.85 0.51 0.76 0.00 0.43 5.35

time (sec)

N/A 0.578 0.036 0.042 0.760 0.263 0.000 0.285 5.720

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 125 83 154 64 64 0 150 811

N.S.

1 1.24 0.82 1.52 0.63 0.63 0.00 1.49 8.03

time (sec)

N/A 0.358 0.030 0.121 0.361 0.251 0.000 0.263 3.695

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 94 66 124 53 53 0 125 648

N.S.

1 1.18 0.82 1.55 0.66 0.66 0.00 1.56 8.10

time (sec)

N/A 0.287 0.027 0.110 0.362 0.272 0.000 0.261 3.531

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 67 49 69 42 42 0 102 485

N.S.

1 1.14 0.83 1.17 0.71 0.71 0.00 1.73 8.22

time (sec)

N/A 0.241 0.026 0.119 0.363 0.258 0.000 0.274 3.576

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 32 42 30 30 0 75 151

N.S.

1 1.00 0.84 1.11 0.79 0.79 0.00 1.97 3.97

time (sec)

N/A 0.191 0.169 0.109 0.360 0.254 0.000 0.266 4.054

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 15 12 12 26 18 95

N.S.

1 1.00 1.00 0.83 0.67 0.67 1.44 1.00 5.28

time (sec)

N/A 0.146 0.008 0.099 0.336 0.255 0.135 0.258 3.624

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 63 61 54 0 73 0 40 308

N.S.

1 1.00 0.97 0.86 0.00 1.16 0.00 0.63 4.89

time (sec)

N/A 0.244 0.116 0.097 0.000 0.253 0.000 0.259 5.025

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 65 63 0 93 0 51 341

N.S.

1 1.00 0.98 0.95 0.00 1.41 0.00 0.77 5.17

time (sec)

N/A 0.216 0.033 0.099 0.000 0.249 0.000 0.269 9.963

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

125 124 89 92 0 119 0 75 741

N.S.

1 0.99 0.71 0.74 0.00 0.95 0.00 0.60 5.93

time (sec)

N/A 0.319 0.077 0.095 0.000 0.277 0.000 0.272 9.222

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

179 196 115 185 0 145 0 93 964

N.S.

1 1.09 0.64 1.03 0.00 0.81 0.00 0.52 5.39

time (sec)

N/A 0.458 0.071 0.097 0.000 0.267 0.000 0.264 8.040

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 125 83 154 64 75 0 241 1813

N.S.

1 1.24 0.82 1.52 0.63 0.74 0.00 2.39 17.95

time (sec)

N/A 0.349 0.031 0.109 0.363 0.259 0.000 0.267 3.634

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 96 66 124 53 64 0 205 1483

N.S.

1 1.20 0.82 1.55 0.66 0.80 0.00 2.56 18.54

time (sec)

N/A 0.287 0.030 0.108 0.354 0.277 0.000 0.281 3.535

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 67 49 69 42 53 0 168 1153

N.S.

1 1.14 0.83 1.17 0.71 0.90 0.00 2.85 19.54

time (sec)

N/A 0.239 0.025 0.106 0.367 0.241 0.000 0.275 3.993

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 32 42 31 41 49 131 823

N.S.

1 1.00 0.84 1.11 0.82 1.08 1.29 3.45 21.66

time (sec)

N/A 0.185 0.193 0.107 0.369 0.246 1.673 0.259 3.612

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 15 12 28 26 84 97

N.S.

1 1.00 1.00 0.83 0.67 1.56 1.44 4.67 5.39

time (sec)

N/A 0.145 0.007 0.104 0.337 0.248 0.807 0.269 3.882

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 94 80 131 0 88 0 57 501

N.S.

1 1.03 0.88 1.44 0.00 0.97 0.00 0.63 5.51

time (sec)

N/A 0.267 0.117 0.090 0.000 0.248 0.000 0.282 8.139

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 85 79 85 0 102 0 69 459

N.S.

1 1.05 0.98 1.05 0.00 1.26 0.00 0.85 5.67

time (sec)

N/A 0.262 0.034 0.093 0.000 0.250 0.000 0.272 5.341

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 90 88 91 0 124 0 73 609

N.S.

1 0.98 0.96 0.99 0.00 1.35 0.00 0.79 6.62

time (sec)

N/A 0.262 0.052 0.102 0.000 0.263 0.000 0.283 9.239

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

146 148 117 116 0 145 0 93 1019

N.S.

1 1.01 0.80 0.79 0.00 0.99 0.00 0.64 6.98

time (sec)

N/A 0.369 0.073 0.104 0.000 0.269 0.000 0.288 8.191

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 125 83 154 64 86 0 344 2681

N.S.

1 1.24 0.82 1.52 0.63 0.85 0.00 3.41 26.54

time (sec)

N/A 0.341 0.028 0.395 0.362 0.238 0.000 0.274 4.058

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 96 66 124 53 75 94 296 2235

N.S.

1 1.20 0.82 1.55 0.66 0.94 1.18 3.70 27.94

time (sec)

N/A 0.285 0.035 0.206 0.367 0.252 76.866 0.271 3.751

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 67 49 69 42 64 71 248 1789

N.S.

1 1.14 0.83 1.17 0.71 1.08 1.20 4.20 30.32

time (sec)

N/A 0.228 0.022 0.137 0.357 0.240 40.355 0.266 3.841

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 32 42 31 52 49 197 773

N.S.

1 1.00 0.84 1.11 0.82 1.37 1.29 5.18 20.34

time (sec)

N/A 0.185 0.189 0.114 0.364 0.241 22.306 0.275 3.647

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 15 12 39 26 136 337

N.S.

1 1.00 1.00 0.83 0.67 2.17 1.44 7.56 18.72

time (sec)

N/A 0.146 0.008 0.107 0.348 0.242 11.870 0.283 3.632

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

121 125 99 222 0 114 0 73 789

N.S.

1 1.03 0.82 1.83 0.00 0.94 0.00 0.60 6.52

time (sec)

N/A 0.319 0.111 0.092 0.000 0.250 0.000 0.258 8.334

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 116 106 193 0 126 0 89 616

N.S.

1 1.05 0.96 1.75 0.00 1.15 0.00 0.81 5.60

time (sec)

N/A 0.317 0.041 0.104 0.000 0.252 0.000 0.267 8.418

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 109 108 142 0 133 0 92 614

N.S.

1 0.99 0.98 1.29 0.00 1.21 0.00 0.84 5.58

time (sec)

N/A 0.315 0.033 0.135 0.000 0.246 0.000 0.272 4.787

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 114 107 144 0 146 0 88 669

N.S.

1 1.01 0.95 1.27 0.00 1.29 0.00 0.78 5.92

time (sec)

N/A 0.300 0.052 0.236 0.000 0.260 0.000 0.270 8.342

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

167 172 134 169 0 167 0 108 1069

N.S.

1 1.03 0.80 1.01 0.00 1.00 0.00 0.65 6.40

time (sec)

N/A 0.419 0.081 0.531 0.000 0.260 0.000 0.277 8.890

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

221 244 150 262 0 189 0 123 1292

N.S.

1 1.10 0.68 1.19 0.00 0.86 0.00 0.56 5.85

time (sec)

N/A 0.565 0.087 1.227 0.000 0.258 0.000 0.273 9.725

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 119 83 153 64 53 0 61 496

N.S.

1 1.20 0.84 1.55 0.65 0.54 0.00 0.62 5.01

time (sec)

N/A 0.344 0.029 0.088 0.358 0.249 0.000 0.259 3.723

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 92 66 123 53 42 0 49 385

N.S.

1 1.21 0.87 1.62 0.70 0.55 0.00 0.64 5.07

time (sec)

N/A 0.290 0.038 0.093 0.364 0.241 0.000 0.257 3.573

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 63 49 68 42 31 0 37 211

N.S.

1 1.11 0.86 1.19 0.74 0.54 0.00 0.65 3.70

time (sec)

N/A 0.233 0.025 0.092 0.353 0.251 0.000 0.272 3.591

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 32 56 30 19 0 23 105

N.S.

1 1.00 0.89 1.56 0.83 0.53 0.00 0.64 2.92

time (sec)

N/A 0.190 0.121 0.091 0.359 0.239 0.000 0.269 3.767

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 15 12 12 24 12 52

N.S.

1 1.00 1.00 0.94 0.75 0.75 1.50 0.75 3.25

time (sec)

N/A 0.151 0.008 0.099 0.336 0.252 0.268 0.263 3.632

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 49 47 42 0 56 0 21 285

N.S.

1 1.00 0.96 0.86 0.00 1.14 0.00 0.43 5.82

time (sec)

N/A 0.182 0.107 0.104 0.000 0.270 0.000 0.276 10.015

Problem 146

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

94 100 78 95 0 93 0 47 570

N.S.

1 1.06 0.83 1.01 0.00 0.99 0.00 0.50 6.06

time (sec)

N/A 0.269 0.047 0.098 0.000 0.258 0.000 0.272 9.318

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

158 172 98 148 0 123 0 69 802

N.S.

1 1.09 0.62 0.94 0.00 0.78 0.00 0.44 5.08

time (sec)

N/A 0.402 0.062 0.095 0.000 0.252 0.000 0.268 9.106

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

212 244 117 200 0 145 0 84 1086

N.S.

1 1.15 0.55 0.94 0.00 0.68 0.00 0.40 5.12

time (sec)

N/A 0.557 0.081 0.095 0.000 0.252 0.000 0.265 8.099

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 117 83 319 64 63 0 77 1057

N.S.

1 1.23 0.87 3.36 0.67 0.66 0.00 0.81 11.13

time (sec)

N/A 0.350 0.036 0.092 0.375 0.275 0.000 0.271 4.102

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 88 66 201 52 51 0 61 660

N.S.

1 1.19 0.89 2.72 0.70 0.69 0.00 0.82 8.92

time (sec)

N/A 0.293 0.034 0.089 0.360 0.253 0.000 0.271 3.825

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 61 49 106 41 40 0 46 259

N.S.

1 1.11 0.89 1.93 0.75 0.73 0.00 0.84 4.71

time (sec)

N/A 0.238 0.029 0.087 0.381 0.248 0.000 0.268 4.236

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 29 40 30 29 46 29 152

N.S.

1 1.00 0.85 1.18 0.88 0.85 1.35 0.85 4.47

time (sec)

N/A 0.185 0.115 0.089 0.354 0.248 0.507 0.272 3.953

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 15 12 20 26 12 97

N.S.

1 1.00 1.00 0.94 0.75 1.25 1.62 0.75 6.06

time (sec)

N/A 0.151 0.008 0.094 0.344 0.246 0.471 0.268 3.865

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 78 75 68 0 110 0 37 614

N.S.

1 1.00 0.96 0.87 0.00 1.41 0.00 0.47 7.87

time (sec)

N/A 0.232 0.142 0.090 0.000 0.254 0.000 0.267 9.069

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

124 148 91 105 0 151 0 64 807

N.S.

1 1.19 0.73 0.85 0.00 1.22 0.00 0.52 6.51

time (sec)

N/A 0.349 0.056 0.098 0.000 0.256 0.000 0.269 9.850

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

191 220 115 131 0 189 0 80 1028

N.S.

1 1.15 0.60 0.69 0.00 0.99 0.00 0.42 5.38

time (sec)

N/A 0.499 0.086 0.102 0.000 0.291 0.000 0.266 9.572

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

245 292 133 186 0 211 0 95 1258

N.S.

1 1.19 0.54 0.76 0.00 0.86 0.00 0.39 5.13

time (sec)

N/A 0.670 0.085 0.103 0.000 0.265 0.000 0.265 8.559

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 117 83 295 64 74 0 75 817

N.S.

1 1.18 0.84 2.98 0.65 0.75 0.00 0.76 8.25

time (sec)

N/A 0.345 0.038 0.097 0.350 0.261 0.000 0.270 4.265

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 88 65 186 52 62 90 59 533

N.S.

1 1.16 0.86 2.45 0.68 0.82 1.18 0.78 7.01

time (sec)

N/A 0.291 0.035 0.095 0.364 0.253 2.234 0.268 4.530

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 63 48 91 42 52 71 39 259

N.S.

1 1.07 0.81 1.54 0.71 0.88 1.20 0.66 4.39

time (sec)

N/A 0.241 0.030 0.090 0.351 0.254 2.150 0.268 4.008

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 31 42 31 41 51 20 152

N.S.

1 1.00 0.82 1.11 0.82 1.08 1.34 0.53 4.00

time (sec)

N/A 0.191 0.123 0.097 0.360 0.240 2.193 0.273 4.101

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

18 18 18 15 12 31 27 12 103

N.S.

1 1.00 1.00 0.83 0.67 1.72 1.50 0.67 5.72

time (sec)

N/A 0.155 0.008 0.098 0.346 0.240 2.103 0.274 4.308

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 126 91 93 0 177 0 45 886

N.S.

1 1.17 0.84 0.86 0.00 1.64 0.00 0.42 8.20

time (sec)

N/A 0.306 0.190 0.088 0.000 0.260 0.000 0.274 9.107

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

155 196 113 130 0 221 0 65 1230

N.S.

1 1.26 0.73 0.84 0.00 1.43 0.00 0.42 7.94

time (sec)

N/A 0.441 0.096 0.108 0.000 0.266 0.000 0.271 10.730

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

224 268 133 157 0 255 0 93 1514

N.S.

1 1.20 0.59 0.70 0.00 1.14 0.00 0.42 6.76

time (sec)

N/A 0.606 0.078 0.105 0.000 0.257 0.000 0.282 10.943

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

278 340 150 211 0 277 0 115 2359

N.S.

1 1.22 0.54 0.76 0.00 1.00 0.00 0.41 8.49

time (sec)

N/A 0.774 0.137 0.099 0.000 0.252 0.000 0.275 9.611

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 23 20 19 18 26 13 57

N.S.

1 1.00 0.85 0.74 0.70 0.67 0.96 0.48 2.11

time (sec)

N/A 0.151 0.031 0.118 0.202 0.239 141.793 0.263 3.982

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 23 20 19 18 26 13 57

N.S.

1 1.00 0.85 0.74 0.70 0.67 0.96 0.48 2.11

time (sec)

N/A 0.149 0.023 0.118 0.204 0.244 12.778 0.257 3.966

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 23 20 19 18 26 13 57

N.S.

1 1.00 0.85 0.74 0.70 0.67 0.96 0.48 2.11

time (sec)

N/A 0.153 0.021 0.145 0.199 0.250 1.131 0.272 3.876

Problem 170

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 23 20 19 16 0 13 57

N.S.

1 1.00 0.85 0.74 0.70 0.59 0.00 0.48 2.11

time (sec)

N/A 0.153 0.020 0.122 0.204 0.244 0.000 0.263 3.836

Problem 171

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 23 20 19 12 0 13 56

N.S.

1 1.00 0.92 0.80 0.76 0.48 0.00 0.52 2.24

time (sec)

N/A 0.152 0.017 0.119 0.202 0.238 0.000 0.265 4.318

Problem 172

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 20 20 19 12 22 13 56

N.S.

1 1.00 0.87 0.87 0.83 0.52 0.96 0.57 2.43

time (sec)

N/A 0.152 0.021 0.107 0.207 0.252 0.278 0.268 3.985

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 21 20 19 11 27 11 52

N.S.

1 1.00 0.78 0.74 0.70 0.41 1.00 0.41 1.93

time (sec)

N/A 0.150 0.017 0.108 0.197 0.241 1.285 0.271 4.044

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 23 20 19 13 27 13 57

N.S.

1 1.00 0.85 0.74 0.70 0.48 1.00 0.48 2.11

time (sec)

N/A 0.156 0.018 0.125 0.212 0.244 13.009 0.257 4.026

Problem 175

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 51 40 38 36 29 0 24 122

N.S.

1 1.06 0.83 0.79 0.75 0.60 0.00 0.50 2.54

time (sec)

N/A 0.194 0.056 0.250 0.218 0.246 0.000 0.254 4.188

Problem 176

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 51 40 38 36 29 48 24 122

N.S.

1 1.06 0.83 0.79 0.75 0.60 1.00 0.50 2.54

time (sec)

N/A 0.193 0.035 0.253 0.217 0.244 22.477 0.280 4.075

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 51 40 38 36 29 0 24 122

N.S.

1 1.06 0.83 0.79 0.75 0.60 0.00 0.50 2.54

time (sec)

N/A 0.197 0.033 0.212 0.211 0.243 0.000 0.266 3.991

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 51 40 38 36 27 0 24 122

N.S.

1 1.06 0.83 0.79 0.75 0.56 0.00 0.50 2.54

time (sec)

N/A 0.196 0.040 0.217 0.235 0.251 0.000 0.257 4.268

Problem 179

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 47 40 47 36 24 0 24 122

N.S.

1 1.02 0.87 1.02 0.78 0.52 0.00 0.52 2.65

time (sec)

N/A 0.194 0.023 0.214 0.220 0.251 0.000 0.267 3.851

Problem 180

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 45 40 37 36 23 0 24 122

N.S.

1 1.02 0.91 0.84 0.82 0.52 0.00 0.55 2.77

time (sec)

N/A 0.194 0.034 0.221 0.259 0.242 0.000 0.265 3.881

Problem 181

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 47 40 38 36 24 48 23 122

N.S.

1 0.98 0.83 0.79 0.75 0.50 1.00 0.48 2.54

time (sec)

N/A 0.198 0.037 0.220 0.206 0.250 1.284 0.250 3.882

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 51 40 38 36 24 49 24 122

N.S.

1 1.06 0.83 0.79 0.75 0.50 1.02 0.50 2.54

time (sec)

N/A 0.192 0.034 0.229 0.219 0.251 13.306 0.266 4.042

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F(-1) A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 75 57 56 55 40 0 35 182

N.S.

1 1.09 0.83 0.81 0.80 0.58 0.00 0.51 2.64

time (sec)

N/A 0.236 0.035 0.859 0.221 0.235 0.000 0.274 4.136

Problem 184

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 75 57 56 55 40 70 35 182

N.S.

1 1.09 0.83 0.81 0.80 0.58 1.01 0.51 2.64

time (sec)

N/A 0.244 0.039 0.853 0.212 0.261 40.073 0.270 3.891

Problem 185

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 75 57 56 55 40 0 35 182

N.S.

1 1.09 0.83 0.81 0.80 0.58 0.00 0.51 2.64

time (sec)

N/A 0.240 0.026 0.783 0.228 0.257 0.000 0.263 4.300

Problem 186

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 73 57 56 55 38 0 35 182

N.S.

1 1.06 0.83 0.81 0.80 0.55 0.00 0.51 2.64

time (sec)

N/A 0.238 0.027 0.767 0.219 0.239 0.000 0.261 3.942

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 71 57 69 55 35 0 35 182

N.S.

1 1.09 0.88 1.06 0.85 0.54 0.00 0.54 2.80

time (sec)

N/A 0.240 0.024 0.803 0.223 0.250 0.000 0.258 3.979

Problem 188

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 67 57 64 55 34 0 35 182

N.S.

1 1.06 0.90 1.02 0.87 0.54 0.00 0.56 2.89

time (sec)

N/A 0.236 0.034 0.865 0.217 0.250 0.000 0.279 4.021

Problem 189

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 67 55 55 55 34 66 34 182

N.S.

1 1.03 0.85 0.85 0.85 0.52 1.02 0.52 2.80

time (sec)

N/A 0.235 0.025 0.776 0.218 0.244 1.362 0.271 3.998

Problem 190

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 71 57 56 55 35 70 34 182

N.S.

1 1.03 0.83 0.81 0.80 0.51 1.01 0.49 2.64

time (sec)

N/A 0.241 0.026 0.740 0.221 0.256 12.907 0.271 4.168

Problem 191

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 154 129 262 65 153 0 70 475

N.S.

1 1.08 0.90 1.83 0.45 1.07 0.00 0.49 3.32

time (sec)

N/A 0.391 0.054 0.161 0.279 0.252 0.000 0.265 4.402

Problem 192

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 124 108 201 54 132 0 59 415

N.S.

1 1.07 0.93 1.73 0.47 1.14 0.00 0.51 3.58

time (sec)

N/A 0.326 0.087 0.122 0.290 0.268 0.000 0.263 4.497

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 94 86 120 42 103 0 45 354

N.S.

1 1.06 0.97 1.35 0.47 1.16 0.00 0.51 3.98

time (sec)

N/A 0.267 0.072 0.108 0.295 0.261 0.000 0.271 4.690

Problem 194

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 62 66 31 85 0 31 296

N.S.

1 1.00 0.97 1.03 0.48 1.33 0.00 0.48 4.62

time (sec)

N/A 0.207 0.041 0.105 0.287 0.251 0.000 0.262 4.955

Problem 195

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 51 41 18 68 0 18 347

N.S.

1 1.00 0.96 0.77 0.34 1.28 0.00 0.34 6.55

time (sec)

N/A 0.169 0.023 0.112 0.284 0.257 0.000 0.265 6.746

Problem 196

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 76 73 76 31 93 0 31 464

N.S.

1 1.00 0.96 1.00 0.41 1.22 0.00 0.41 6.11

time (sec)

N/A 0.219 0.055 0.112 0.286 0.252 0.000 0.270 5.059

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 118 89 98 41 118 0 41 642

N.S.

1 1.17 0.88 0.97 0.41 1.17 0.00 0.41 6.36

time (sec)

N/A 0.288 0.126 0.108 0.283 0.263 0.000 0.273 5.098

Problem 198

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 160 107 120 52 144 0 52 822

N.S.

1 1.25 0.84 0.94 0.41 1.12 0.00 0.41 6.42

time (sec)

N/A 0.359 0.122 0.112 0.289 0.247 0.000 0.270 4.379

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 151 144 280 75 188 0 76 523

N.S.

1 1.12 1.07 2.07 0.56 1.39 0.00 0.56 3.87

time (sec)

N/A 0.384 0.165 0.779 0.303 0.253 0.000 0.269 4.783

Problem 200

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

108 121 119 181 64 161 0 65 463

N.S.

1 1.12 1.10 1.68 0.59 1.49 0.00 0.60 4.29

time (sec)

N/A 0.316 0.112 0.546 0.325 0.253 0.000 0.267 4.381

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