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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

151 169 261 162 0 363 0 223 0

N.S.

1 1.12 1.73 1.07 0.00 2.40 0.00 1.48 0.00

time (sec)

N/A 0.965 6.057 1.342 0.000 0.303 0.000 0.450 0.000

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

227 275 360 222 0 485 0 290 0

N.S.

1 1.21 1.59 0.98 0.00 2.14 0.00 1.28 0.00

time (sec)

N/A 1.787 6.663 6.971 0.000 0.308 0.000 0.439 0.000

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 241 118 241 0 229 0 211 0

N.S.

1 1.61 0.79 1.61 0.00 1.53 0.00 1.41 0.00

time (sec)

N/A 1.229 0.786 0.787 0.000 0.317 0.000 0.530 0.000

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 109 118 134 0 200 0 156 0

N.S.

1 1.02 1.10 1.25 0.00 1.87 0.00 1.46 0.00

time (sec)

N/A 0.480 0.477 0.714 0.000 0.310 0.000 0.388 0.000

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 62 138 103 0 263 0 132 0

N.S.

1 1.00 2.23 1.66 0.00 4.24 0.00 2.13 0.00

time (sec)

N/A 0.334 0.530 0.638 0.000 0.315 0.000 0.346 0.000

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

135 253 292 144 0 369 0 185 0

N.S.

1 1.87 2.16 1.07 0.00 2.73 0.00 1.37 0.00

time (sec)

N/A 1.478 0.689 0.825 0.000 0.303 0.000 0.352 0.000

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

177 195 334 311 0 270 0 220 0

N.S.

1 1.10 1.89 1.76 0.00 1.53 0.00 1.24 0.00

time (sec)

N/A 1.679 0.651 0.760 0.000 0.311 0.000 0.407 0.000

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

134 146 128 212 0 237 0 121 0

N.S.

1 1.09 0.96 1.58 0.00 1.77 0.00 0.90 0.00

time (sec)

N/A 0.598 0.624 0.729 0.000 0.298 0.000 0.395 0.000

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 121 206 134 0 421 0 205 0

N.S.

1 1.07 1.82 1.19 0.00 3.73 0.00 1.81 0.00

time (sec)

N/A 0.619 1.807 0.803 0.000 0.326 0.000 0.444 0.000

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 262 294 144 0 383 0 168 0

N.S.

1 1.82 2.04 1.00 0.00 2.66 0.00 1.17 0.00

time (sec)

N/A 1.639 0.927 0.769 0.000 0.310 0.000 0.470 0.000

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

207 344 394 381 0 307 0 184 0

N.S.

1 1.66 1.90 1.84 0.00 1.48 0.00 0.89 0.00

time (sec)

N/A 2.075 0.824 0.979 0.000 0.322 0.000 0.635 0.000

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

167 175 284 288 0 279 0 140 0

N.S.

1 1.05 1.70 1.72 0.00 1.67 0.00 0.84 0.00

time (sec)

N/A 0.751 0.608 0.797 0.000 0.299 0.000 0.629 0.000

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

141 152 451 219 0 539 0 262 0

N.S.

1 1.08 3.20 1.55 0.00 3.82 0.00 1.86 0.00

time (sec)

N/A 0.839 0.861 0.806 0.000 0.316 0.000 0.383 0.000

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

191 376 332 182 0 564 0 240 0

N.S.

1 1.97 1.74 0.95 0.00 2.95 0.00 1.26 0.00

time (sec)

N/A 2.807 1.975 0.902 0.000 0.316 0.000 0.348 0.000

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes N/A TBD TBD TBD TBD TBD

size

982 988 232 0 0 0 0 0 0

N.S.

1 1.01 0.24 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.828 3.327 0.000 0.000 0.000 0.000 0.000 0.000

Problem 116

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

123 131 209 0 0 0 0 0 0

N.S.

1 1.07 1.70 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.579 2.368 0.000 0.000 0.000 0.000 0.000 0.000

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No No N/A TBD TBD TBD TBD TBD

size

80 136 2692 0 0 0 0 0 0

N.S.

1 1.70 33.65 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.352 35.531 0.000 0.000 0.000 0.000 0.000 0.000

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No No N/A TBD TBD TBD TBD TBD

size

80 136 2796 0 0 0 0 0 0

N.S.

1 1.70 34.95 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.374 42.172 0.000 0.000 0.000 0.000 0.000 0.000

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No Yes N/A TBD TBD TBD TBD TBD

size

551 578 128 0 0 0 0 0 0

N.S.

1 1.05 0.23 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.498 1.182 0.000 0.000 0.000 0.000 0.000 0.000

Problem 120

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

126 133 100 0 0 0 0 0 0

N.S.

1 1.06 0.79 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.597 0.655 0.000 0.000 0.000 0.000 0.000 0.000

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No N/A N/A TBD TBD TBD TBD TBD

size

80 136 0 0 0 0 0 0 0

N.S.

1 1.70 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.361 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A No N/A N/A TBD TBD TBD TBD TBD

size

80 136 0 0 0 0 0 0 0

N.S.

1 1.70 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.361 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

269 269 4715 0 0 0 0 0 0

N.S.

1 1.00 17.53 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.611 22.052 0.000 0.000 0.000 0.000 0.000 0.000

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

187 187 2054 0 0 0 0 0 0

N.S.

1 1.00 10.98 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.472 17.282 0.000 0.000 0.000 0.000 0.000 0.000

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

129 129 0 0 0 0 0 0 0

N.S.

1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.336 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

108 108 232 0 0 0 0 0 0

N.S.

1 1.00 2.15 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.399 2.276 0.000 0.000 0.000 0.000 0.000 0.000

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

138 142 626 0 0 0 0 0 0

N.S.

1 1.03 4.54 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.452 6.135 0.000 0.000 0.000 0.000 0.000 0.000

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

248 252 1276 0 0 0 0 0 0

N.S.

1 1.02 5.15 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.615 17.383 0.000 0.000 0.000 0.000 0.000 0.000

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

111 156 0 0 0 0 0 0 0

N.S.

1 1.41 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.366 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 130

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

163 167 105 0 0 0 0 0 0

N.S.

1 1.02 0.64 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.294 0.174 0.000 0.000 0.000 0.000 0.000 0.000

Problem 131

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

72 75 63 0 0 0 0 0 0

N.S.

1 1.04 0.88 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.215 0.053 0.000 0.000 0.000 0.000 0.000 0.000

Problem 132

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

43 43 43 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.213 0.045 0.000 0.000 0.000 0.000 0.000 0.000

Problem 133

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

83 81 68 0 0 0 0 0 0

N.S.

1 0.98 0.82 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.239 0.129 0.000 0.000 0.000 0.000 0.000 0.000

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

123 123 83 0 0 0 0 0 0

N.S.

1 1.00 0.67 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.269 0.191 0.000 0.000 0.000 0.000 0.000 0.000

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

311 352 0 0 0 0 0 0 0

N.S.

1 1.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.455 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No N/A TBD TBD TBD TBD TBD

size

157 161 1756 0 0 0 0 0 0

N.S.

1 1.03 11.18 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.562 22.768 0.000 0.000 0.000 0.000 0.000 0.000

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

74 74 70 0 0 0 0 0 0

N.S.

1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.239 0.118 0.000 0.000 0.000 0.000 0.000 0.000

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

89 116 0 0 0 0 0 0 0

N.S.

1 1.30 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.287 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

89 116 0 0 0 0 0 0 0

N.S.

1 1.30 0.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.275 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Problem 140

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

88 96 82 81 73 90 0 22388 176

N.S.

1 1.09 0.93 0.92 0.83 1.02 0.00 254.41 2.00

time (sec)

N/A 0.293 0.083 0.809 0.200 0.283 0.000 83.239 6.116

Problem 141

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

55 46 38 41 43 45 0 1200 74

N.S.

1 0.84 0.69 0.75 0.78 0.82 0.00 21.82 1.35

time (sec)

N/A 0.215 0.012 0.712 0.191 0.302 0.000 0.448 6.261

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

24 24 47 23 22 24 0 23 47

N.S.

1 1.00 1.96 0.96 0.92 1.00 0.00 0.96 1.96

time (sec)

N/A 0.191 0.025 0.349 0.212 0.283 0.000 0.300 6.002

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

54 48 60 67 45 69 0 60 146

N.S.

1 0.89 1.11 1.24 0.83 1.28 0.00 1.11 2.70

time (sec)

N/A 0.220 0.140 0.964 0.191 0.291 0.000 0.361 6.065

Problem 144

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

81 69 96 101 69 110 0 82 207

N.S.

1 0.85 1.19 1.25 0.85 1.36 0.00 1.01 2.56

time (sec)

N/A 0.232 0.024 1.341 0.196 0.304 0.000 0.378 6.182

Problem 145

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

72 72 81 98 65 73 0 13744 110

N.S.

1 1.00 1.12 1.36 0.90 1.01 0.00 190.89 1.53

time (sec)

N/A 0.261 0.104 1.395 0.279 0.280 0.000 294.678 9.959

Problem 146

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 47 59 39 47 0 1008 55

N.S.

1 1.00 1.24 1.55 1.03 1.24 0.00 26.53 1.45

time (sec)

N/A 0.231 0.058 1.078 0.278 0.280 0.000 1.031 6.461

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 75 49 54 84 0 108 158

N.S.

1 1.00 1.83 1.20 1.32 2.05 0.00 2.63 3.85

time (sec)

N/A 0.228 0.065 0.531 0.290 0.285 0.000 0.312 5.948

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 82 125 86 92 160 0 141 225

N.S.

1 1.00 1.52 1.05 1.12 1.95 0.00 1.72 2.74

time (sec)

N/A 0.271 0.087 0.806 0.291 0.289 0.000 0.340 6.024

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 122 164 129 125 222 0 199 288

N.S.

1 1.00 1.34 1.06 1.02 1.82 0.00 1.63 2.36

time (sec)

N/A 0.298 0.110 1.342 0.283 0.294 0.000 0.383 6.071

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 123 108 135 105 140 0 0 232

N.S.

1 1.11 0.97 1.22 0.95 1.26 0.00 0.00 2.09

time (sec)

N/A 0.339 0.303 1.891 0.189 0.324 0.000 0.000 6.061

Problem 151

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

78 70 145 69 70 74 0 6671 150

N.S.

1 0.90 1.86 0.88 0.90 0.95 0.00 85.53 1.92

time (sec)

N/A 0.253 0.058 1.046 0.199 0.302 0.000 1.339 6.005

Problem 152

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 43 46 40 40 42 0 41 117

N.S.

1 0.93 1.00 0.87 0.87 0.91 0.00 0.89 2.54

time (sec)

N/A 0.215 0.019 0.473 0.200 0.292 0.000 0.336 6.156

Problem 153

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

84 75 92 93 69 115 0 99 221

N.S.

1 0.89 1.10 1.11 0.82 1.37 0.00 1.18 2.63

time (sec)

N/A 0.248 0.035 1.349 0.193 0.302 0.000 0.381 6.133

Problem 154

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

126 111 142 157 105 177 0 138 310

N.S.

1 0.88 1.13 1.25 0.83 1.40 0.00 1.10 2.46

time (sec)

N/A 0.283 0.052 2.263 0.206 0.308 0.000 0.452 5.924

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 149 176 185 119 118 0 0 235

N.S.

1 1.00 1.18 1.24 0.80 0.79 0.00 0.00 1.58

time (sec)

N/A 0.371 0.782 3.142 0.282 0.292 0.000 0.000 9.211

Problem 156

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

94 94 77 116 83 81 0 7670 147

N.S.

1 1.00 0.82 1.23 0.88 0.86 0.00 81.60 1.56

time (sec)

N/A 0.309 0.553 2.191 0.276 0.285 0.000 5.677 8.606

Problem 157

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

78 78 116 79 79 118 0 148 277

N.S.

1 1.00 1.49 1.01 1.01 1.51 0.00 1.90 3.55

time (sec)

N/A 0.272 0.593 0.703 0.282 0.301 0.000 0.345 6.834

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 133 293 145 138 218 0 241 584

N.S.

1 1.00 2.20 1.09 1.04 1.64 0.00 1.81 4.39

time (sec)

N/A 0.358 6.478 1.684 0.289 0.301 0.000 0.413 8.124

Problem 159

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

202 202 351 216 183 306 0 337 888

N.S.

1 1.00 1.74 1.07 0.91 1.51 0.00 1.67 4.40

time (sec)

N/A 0.397 1.134 3.130 0.287 0.298 0.000 0.514 10.566

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

150 157 141 206 162 194 0 0 366

N.S.

1 1.05 0.94 1.37 1.08 1.29 0.00 0.00 2.44

time (sec)

N/A 0.406 0.180 5.456 0.190 0.288 0.000 0.000 6.136

Problem 161

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

105 104 90 110 113 116 0 47033 226

N.S.

1 0.99 0.86 1.05 1.08 1.10 0.00 447.93 2.15

time (sec)

N/A 0.329 0.133 2.590 0.195 0.293 0.000 15.439 6.517

Problem 162

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

67 61 67 56 57 66 0 58 118

N.S.

1 0.91 1.00 0.84 0.85 0.99 0.00 0.87 1.76

time (sec)

N/A 0.223 0.020 0.855 0.213 0.305 0.000 0.450 5.807

Problem 163

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

116 104 130 118 98 153 0 131 312

N.S.

1 0.90 1.12 1.02 0.84 1.32 0.00 1.13 2.69

time (sec)

N/A 0.285 0.058 2.523 0.216 0.297 0.000 0.667 6.081

Problem 164

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

165 147 195 212 142 225 0 185 424

N.S.

1 0.89 1.18 1.28 0.86 1.36 0.00 1.12 2.57

time (sec)

N/A 0.327 0.080 4.564 0.208 0.310 0.000 0.678 6.006

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

220 220 226 268 167 157 0 0 297

N.S.

1 1.00 1.03 1.22 0.76 0.71 0.00 0.00 1.35

time (sec)

N/A 0.464 0.929 8.787 0.310 0.294 0.000 0.000 8.900

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

146 146 113 169 119 116 0 0 249

N.S.

1 1.00 0.77 1.16 0.82 0.79 0.00 0.00 1.71

time (sec)

N/A 0.400 0.893 4.616 0.308 0.293 0.000 0.000 8.465

Problem 167

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

102 102 143 96 95 143 0 199 289

N.S.

1 1.00 1.40 0.94 0.93 1.40 0.00 1.95 2.83

time (sec)

N/A 0.303 1.244 1.764 0.285 0.330 0.000 0.393 6.372

Problem 168

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

194 194 355 186 187 293 0 421 405

N.S.

1 1.00 1.83 0.96 0.96 1.51 0.00 2.17 2.09

time (sec)

N/A 0.410 6.586 3.070 0.292 0.291 0.000 0.446 6.342

Problem 169

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

291 291 346 289 252 412 0 471 507

N.S.

1 1.00 1.19 0.99 0.87 1.42 0.00 1.62 1.74

time (sec)

N/A 0.492 2.260 6.131 0.297 0.328 0.000 0.552 6.489

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

204 264 184 189 288 261 0 343 498

N.S.

1 1.29 0.90 0.93 1.41 1.28 0.00 1.68 2.44

time (sec)

N/A 0.634 0.878 1.296 0.252 0.428 0.000 1.539 6.796

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

126 159 117 121 142 157 0 177 217

N.S.

1 1.26 0.93 0.96 1.13 1.25 0.00 1.40 1.72

time (sec)

N/A 0.379 0.350 0.885 0.205 0.365 0.000 0.608 6.398

Problem 172

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

74 75 65 71 65 63 0 71 91

N.S.

1 1.01 0.88 0.96 0.88 0.85 0.00 0.96 1.23

time (sec)

N/A 0.244 0.047 0.605 0.227 0.294 0.000 0.341 6.139

Problem 173

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

34 34 34 33 33 31 0 35 48

N.S.

1 1.00 1.00 0.97 0.97 0.91 0.00 1.03 1.41

time (sec)

N/A 0.201 0.016 0.539 0.204 0.308 0.000 0.305 5.942

Problem 174

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

84 78 65 76 77 118 0 114 144

N.S.

1 0.93 0.77 0.90 0.92 1.40 0.00 1.36 1.71

time (sec)

N/A 0.273 0.114 0.910 0.234 0.299 0.000 0.336 6.299

Problem 175

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

148 136 115 137 139 271 0 201 281

N.S.

1 0.92 0.78 0.93 0.94 1.83 0.00 1.36 1.90

time (sec)

N/A 0.335 0.698 1.625 0.217 0.318 0.000 0.379 6.057

Problem 176

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

177 184 195 214 0 476 0 241 372

N.S.

1 1.04 1.10 1.21 0.00 2.69 0.00 1.36 2.10

time (sec)

N/A 0.921 1.103 0.947 0.000 0.315 0.000 0.945 9.185

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 102 152 112 0 305 0 107 148

N.S.

1 1.06 1.58 1.17 0.00 3.18 0.00 1.11 1.54

time (sec)

N/A 0.473 0.285 0.640 0.000 0.308 0.000 0.471 6.341

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 93 108 109 0 314 0 129 204

N.S.

1 1.16 1.35 1.36 0.00 3.92 0.00 1.61 2.55

time (sec)

N/A 0.631 0.304 0.806 0.000 0.353 0.000 0.339 6.479

Problem 179

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F(-2) A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

154 170 350 223 0 633 0 273 654

N.S.

1 1.10 2.27 1.45 0.00 4.11 0.00 1.77 4.25

time (sec)

N/A 0.955 6.241 1.286 0.000 0.422 0.000 0.378 6.866

Problem 180

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

307 345 504 390 0 1079 0 490 1099

N.S.

1 1.12 1.64 1.27 0.00 3.51 0.00 1.60 3.58

time (sec)

N/A 2.181 1.174 2.147 0.000 0.606 0.000 0.393 6.770

Problem 181

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

242 288 204 205 505 555 0 494 755

N.S.

1 1.19 0.84 0.85 2.09 2.29 0.00 2.04 3.12

time (sec)

N/A 1.009 4.111 2.104 0.248 0.481 0.000 1.597 7.712

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 184 145 143 274 388 0 248 351

N.S.

1 1.14 0.90 0.89 1.70 2.41 0.00 1.54 2.18

time (sec)

N/A 0.550 0.502 1.275 0.207 0.352 0.000 0.658 7.041

Problem 183

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

109 127 162 98 124 195 0 156 158

N.S.

1 1.17 1.49 0.90 1.14 1.79 0.00 1.43 1.45

time (sec)

N/A 0.319 0.204 0.941 0.200 0.317 0.000 0.404 6.628

Problem 184

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 50 42 49 47 69 0 51 105

N.S.

1 0.94 0.79 0.92 0.89 1.30 0.00 0.96 1.98

time (sec)

N/A 0.232 0.061 0.798 0.209 0.297 0.000 0.377 6.202

Problem 185

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 105 96 105 116 259 0 165 235

N.S.

1 0.92 0.84 0.92 1.02 2.27 0.00 1.45 2.06

time (sec)

N/A 0.302 0.422 2.033 0.194 0.298 0.000 0.348 6.254

Problem 186

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 173 187 172 189 542 0 278 439

N.S.

1 0.92 0.99 0.91 1.01 2.88 0.00 1.48 2.34

time (sec)

N/A 0.380 6.100 4.060 0.198 0.330 0.000 0.445 6.398

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

333 333 341 248 0 815 0 406 722

N.S.

1 1.00 1.02 0.74 0.00 2.45 0.00 1.22 2.17

time (sec)

N/A 0.846 1.442 1.789 0.000 0.323 0.000 1.098 9.795

Problem 188

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

200 200 169 162 0 569 0 251 313

N.S.

1 1.00 0.84 0.81 0.00 2.84 0.00 1.26 1.56

time (sec)

N/A 0.550 0.862 1.171 0.000 0.303 0.000 0.544 8.028

Problem 189

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

115 161 139 156 0 768 0 218 1616

N.S.

1 1.40 1.21 1.36 0.00 6.68 0.00 1.90 14.05

time (sec)

N/A 0.985 0.713 1.725 0.000 0.353 0.000 0.364 8.182

Problem 190

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

238 266 403 287 0 1149 0 356 973

N.S.

1 1.12 1.69 1.21 0.00 4.83 0.00 1.50 4.09

time (sec)

N/A 1.447 6.337 2.955 0.000 0.384 0.000 0.410 6.810

Problem 191

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

424 506 361 465 0 2011 0 596 1424

N.S.

1 1.19 0.85 1.10 0.00 4.74 0.00 1.41 3.36

time (sec)

N/A 3.251 1.264 5.897 0.000 0.620 0.000 0.457 6.656

Problem 192

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

321 365 304 263 730 981 0 585 1229

N.S.

1 1.14 0.95 0.82 2.27 3.06 0.00 1.82 3.83

time (sec)

N/A 1.390 6.235 4.136 0.232 0.764 0.000 1.774 10.692

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

232 256 196 197 441 788 0 464 690

N.S.

1 1.10 0.84 0.85 1.90 3.40 0.00 2.00 2.97

time (sec)

N/A 0.777 1.507 2.188 0.223 0.500 0.000 0.813 7.440

Problem 194

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

149 163 213 134 228 462 0 257 304

N.S.

1 1.09 1.43 0.90 1.53 3.10 0.00 1.72 2.04

time (sec)

N/A 0.369 1.456 1.993 0.200 0.364 0.000 0.441 6.418

Problem 195

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 69 60 66 81 154 0 69 369

N.S.

1 0.92 0.80 0.88 1.08 2.05 0.00 0.92 4.92

time (sec)

N/A 0.242 0.195 1.467 0.197 0.312 0.000 0.347 6.368

Problem 196

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 133 121 131 156 404 0 154 334

N.S.

1 0.92 0.83 0.90 1.08 2.79 0.00 1.06 2.30

time (sec)

N/A 0.330 0.642 5.471 0.193 0.327 0.000 0.395 6.708

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

221 203 195 207 236 754 0 327 563

N.S.

1 0.92 0.88 0.94 1.07 3.41 0.00 1.48 2.55

time (sec)

N/A 0.442 4.828 10.754 0.200 0.347 0.000 0.440 6.690

Problem 198

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

474 474 351 354 0 1249 0 632 1099

N.S.

1 1.00 0.74 0.75 0.00 2.64 0.00 1.33 2.32

time (sec)

N/A 1.144 0.915 2.981 0.000 0.367 0.000 1.062 10.802

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

350 350 212 258 0 934 0 384 627

N.S.

1 1.00 0.61 0.74 0.00 2.67 0.00 1.10 1.79

time (sec)

N/A 0.804 2.450 2.027 0.000 0.331 0.000 0.572 9.613

Problem 200

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F(-2) B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

202 249 195 299 0 1394 0 339 1762

N.S.

1 1.23 0.97 1.48 0.00 6.90 0.00 1.68 8.72

time (sec)

N/A 1.506 3.757 4.013 0.000 0.633 0.000 0.411 7.377

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