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2.2.2 Integrals 101 to 183

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 A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 52 43 66 51 68 64 53

N.S.

1 1.00 1.16 0.96 1.47 1.13 1.51 1.42 1.18

time (sec)

N/A 0.268 0.411 0.083 0.179 0.247 0.165 0.281 0.094

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 54 94 70 111 0 67 0

N.S.

1 1.00 0.84 1.47 1.09 1.73 0.00 1.05 0.00

time (sec)

N/A 0.385 0.126 0.237 0.224 0.255 0.000 0.288 0.000

Problem 103

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 87 68 149 87 162 0 631 0

N.S.

1 1.00 0.78 1.71 1.00 1.86 0.00 7.25 0.00

time (sec)

N/A 0.418 0.277 0.229 0.227 0.253 0.000 0.301 0.000

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 123 90 296 98 274 0 316 0

N.S.

1 1.00 0.73 2.41 0.80 2.23 0.00 2.57 0.00

time (sec)

N/A 0.454 0.389 0.280 0.228 0.269 0.000 0.292 0.000

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

237 224 217 180 527 395 779 577 452

N.S.

1 0.95 0.92 0.76 2.22 1.67 3.29 2.43 1.91

time (sec)

N/A 0.514 0.988 0.303 0.219 0.263 0.463 0.290 3.475

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

168 168 192 123 327 227 456 329 257

N.S.

1 1.00 1.14 0.73 1.95 1.35 2.71 1.96 1.53

time (sec)

N/A 0.420 0.424 0.228 0.199 0.248 0.342 0.300 2.129

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

118 98 81 126 167 113 219 151 123

N.S.

1 0.83 0.69 1.07 1.42 0.96 1.86 1.28 1.04

time (sec)

N/A 0.311 0.635 0.078 0.195 0.247 0.245 0.280 0.149

Problem 108

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

145 139 113 191 149 228 0 135 0

N.S.

1 0.96 0.78 1.32 1.03 1.57 0.00 0.93 0.00

time (sec)

N/A 0.565 0.535 0.471 0.237 0.252 0.000 0.305 0.000

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 170 207 308 182 359 0 1134 0

N.S.

1 1.08 1.32 1.96 1.16 2.29 0.00 7.22 0.00

time (sec)

N/A 0.580 0.627 0.511 0.247 0.255 0.000 0.348 0.000

Problem 110

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

207 298 353 618 202 596 0 682 0

N.S.

1 1.44 1.71 2.99 0.98 2.88 0.00 3.29 0.00

time (sec)

N/A 0.872 1.226 0.597 0.254 0.262 0.000 0.278 0.000

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 128 178 325 228 438 0 0 0

N.S.

1 1.09 1.52 2.78 1.95 3.74 0.00 0.00 0.00

time (sec)

N/A 0.754 1.031 0.215 0.297 0.247 0.000 0.000 0.000

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 98 133 174 0 243 0 0 0

N.S.

1 1.11 1.51 1.98 0.00 2.76 0.00 0.00 0.00

time (sec)

N/A 0.580 0.666 0.152 0.000 0.252 0.000 0.000 0.000

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

49 51 70 47 71 92 76 66 53

N.S.

1 1.04 1.43 0.96 1.45 1.88 1.55 1.35 1.08

time (sec)

N/A 0.365 0.617 0.156 0.193 0.267 0.342 0.273 1.772

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 20 98 27 27 22 22

N.S.

1 1.00 1.10 1.00 4.90 1.35 1.35 1.10 1.10

time (sec)

N/A 0.243 8.189 0.062 0.297 0.249 1.103 0.269 1.800

Problem 115

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 20 154 51 58 22 22

N.S.

1 1.00 1.10 1.00 7.70 2.55 2.90 1.10 1.10

time (sec)

N/A 0.233 6.395 0.066 0.321 0.250 1.957 0.326 1.805

Problem 116

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

255 255 506 600 610 1863 0 0 0

N.S.

1 1.00 1.98 2.35 2.39 7.31 0.00 0.00 0.00

time (sec)

N/A 1.236 2.006 0.226 0.355 0.268 0.000 0.000 0.000

Problem 117

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

200 196 295 313 0 963 0 0 0

N.S.

1 0.98 1.48 1.56 0.00 4.82 0.00 0.00 0.00

time (sec)

N/A 0.903 1.051 0.211 0.000 0.255 0.000 0.000 0.000

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 119 114 82 239 385 156 192 138

N.S.

1 0.97 0.93 0.67 1.94 3.13 1.27 1.56 1.12

time (sec)

N/A 0.506 0.699 0.205 0.219 0.254 0.476 0.289 1.692

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 20 593 57 54 22 22

N.S.

1 1.00 1.10 1.00 29.65 2.85 2.70 1.10 1.10

time (sec)

N/A 0.236 21.299 0.111 0.472 0.246 1.823 0.320 1.793

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 20 710 99 105 22 22

N.S.

1 1.00 1.10 1.00 35.50 4.95 5.25 1.10 1.10

time (sec)

N/A 0.245 22.764 0.099 0.630 0.256 4.458 0.418 2.454

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 126 53 108 120 0 0 147 117

N.S.

1 1.15 0.48 0.98 1.09 0.00 0.00 1.34 1.06

time (sec)

N/A 0.618 0.229 0.103 0.284 0.000 0.000 0.300 0.229

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 99 44 86 90 0 0 107 95

N.S.

1 1.12 0.50 0.98 1.02 0.00 0.00 1.22 1.08

time (sec)

N/A 0.493 0.158 0.052 0.277 0.000 0.000 0.294 1.780

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 66 34 64 60 0 0 67 56

N.S.

1 1.25 0.64 1.21 1.13 0.00 0.00 1.26 1.06

time (sec)

N/A 0.358 0.254 0.049 0.285 0.000 0.000 0.279 1.812

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F(-2) F A F(-1)

verified

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

size

83 57 54 0 0 0 0 32 0

N.S.

1 0.69 0.65 0.00 0.00 0.00 0.00 0.39 0.00

time (sec)

N/A 0.456 0.215 0.000 0.000 0.000 0.000 0.289 0.000

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A F F F(-2) F A F(-1)

verified

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

size

110 89 75 0 0 0 0 68 0

N.S.

1 0.81 0.68 0.00 0.00 0.00 0.00 0.62 0.00

time (sec)

N/A 0.552 0.147 0.000 0.000 0.000 0.000 0.292 0.000

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A F F F(-2) F A F(-1)

verified

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

size

151 113 97 0 0 0 0 107 0

N.S.

1 0.75 0.64 0.00 0.00 0.00 0.00 0.71 0.00

time (sec)

N/A 0.658 0.183 0.000 0.000 0.000 0.000 0.290 0.000

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 69 33 62 88 0 0 0 63

N.S.

1 1.01 0.49 0.91 1.29 0.00 0.00 0.00 0.93

time (sec)

N/A 0.509 0.091 0.064 0.274 0.000 0.000 0.000 0.099

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 55 31 50 66 0 0 0 51

N.S.

1 1.04 0.58 0.94 1.25 0.00 0.00 0.00 0.96

time (sec)

N/A 0.419 0.073 0.046 0.291 0.000 0.000 0.000 0.081

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 35 22 38 44 0 0 0 39

N.S.

1 1.09 0.69 1.19 1.38 0.00 0.00 0.00 1.22

time (sec)

N/A 0.329 0.051 0.043 0.297 0.000 0.000 0.000 1.702

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F(-2) F F F(-1)

verified

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

size

23 23 23 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 0.298 0.009 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(-2) F F F(-1)

verified

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

size

42 39 33 0 0 0 0 0 0

N.S.

1 0.93 0.79 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.373 0.082 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 C A F F F(-2) F F F(-1)

verified

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

size

67 63 44 0 0 0 0 0 0

N.S.

1 0.94 0.66 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.444 0.090 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 C A F A F(-2) F A F(-1)

verified

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

size

185 170 70 0 180 0 0 192 0

N.S.

1 0.92 0.38 0.00 0.97 0.00 0.00 1.04 0.00

time (sec)

N/A 1.038 0.249 0.000 0.287 0.000 0.000 0.286 0.000

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A F A F(-2) F A F(-1)

verified

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

size

145 127 54 0 136 0 0 144 0

N.S.

1 0.88 0.37 0.00 0.94 0.00 0.00 0.99 0.00

time (sec)

N/A 0.660 0.191 0.000 0.286 0.000 0.000 0.291 0.000

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F A F(-2) F A F(-1)

verified

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

size

89 73 56 0 92 0 0 96 0

N.S.

1 0.82 0.63 0.00 1.03 0.00 0.00 1.08 0.00

time (sec)

N/A 0.418 0.088 0.000 0.266 0.000 0.000 0.279 0.000

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F(-2) F A F(-1)

verified

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

size

55 40 36 0 0 0 0 40 0

N.S.

1 0.73 0.65 0.00 0.00 0.00 0.00 0.73 0.00

time (sec)

N/A 0.366 0.017 0.000 0.000 0.000 0.000 0.312 0.000

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A F F F(-2) F A F(-1)

verified

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

size

79 64 53 0 0 0 0 112 0

N.S.

1 0.81 0.67 0.00 0.00 0.00 0.00 1.42 0.00

time (sec)

N/A 0.374 0.101 0.000 0.000 0.000 0.000 0.320 0.000

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F(-2) F B F(-1)

verified

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

size

109 91 69 0 0 0 0 170 0

N.S.

1 0.83 0.63 0.00 0.00 0.00 0.00 1.56 0.00

time (sec)

N/A 0.538 0.047 0.000 0.000 0.000 0.000 0.289 0.000

Problem 139

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

383 238 213 0 0 0 0 0 0

N.S.

1 0.62 0.56 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.866 0.251 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 F F F F F F(-1)

verified

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

size

269 170 163 0 0 0 0 0 0

N.S.

1 0.63 0.61 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.627 0.178 0.000 0.000 0.000 0.000 0.000 0.000

Problem 141

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

157 104 139 0 0 0 0 0 0

N.S.

1 0.66 0.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.416 0.352 0.000 0.000 0.000 0.000 0.000 0.000

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 16 18 30 17 18 18

N.S.

1 1.00 1.11 0.89 1.00 1.67 0.94 1.00 1.00

time (sec)

N/A 0.244 2.789 0.028 0.354 0.244 1.974 0.939 1.779

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 16 18 34 19 18 18

N.S.

1 1.00 1.11 0.89 1.00 1.89 1.06 1.00 1.00

time (sec)

N/A 0.251 1.335 0.032 0.369 0.246 3.707 1.684 1.804

Problem 144

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

402 231 234 0 0 0 0 0 0

N.S.

1 0.57 0.58 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 1.093 0.676 0.000 0.000 0.000 0.000 0.000 0.000

Problem 145

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

248 148 161 0 0 0 0 0 0

N.S.

1 0.60 0.65 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.731 0.367 0.000 0.000 0.000 0.000 0.000 0.000

Problem 146

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

140 96 110 0 0 0 0 0 0

N.S.

1 0.69 0.79 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.476 0.153 0.000 0.000 0.000 0.000 0.000 0.000

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

14 14 16 12 14 36 14 14 14

N.S.

1 1.00 1.14 0.86 1.00 2.57 1.00 1.00 1.00

time (sec)

N/A 0.247 8.835 0.026 0.351 0.241 9.085 0.547 1.839

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

14 14 16 12 14 42 15 14 14

N.S.

1 1.00 1.14 0.86 1.00 3.00 1.07 1.00 1.00

time (sec)

N/A 0.250 9.772 0.029 0.349 0.246 15.746 0.527 1.845

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

18 18 20 16 18 0 15 18 18

N.S.

1 1.00 1.11 0.89 1.00 0.00 0.83 1.00 1.00

time (sec)

N/A 0.247 2.554 0.023 0.343 0.000 1.637 0.506 1.696

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 22 20 22 22 0 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.00 1.10 1.10

time (sec)

N/A 0.225 4.879 0.042 0.332 0.259 0.000 0.722 1.793

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F A A F(-2) F F(-1)

verified

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

size

402 386 429 0 373 713 0 0 0

N.S.

1 0.96 1.07 0.00 0.93 1.77 0.00 0.00 0.00

time (sec)

N/A 0.834 1.715 0.000 0.133 0.107 0.000 0.000 0.000

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F A A F(-2) F F(-1)

verified

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

size

263 258 302 0 209 493 0 0 0

N.S.

1 0.98 1.15 0.00 0.79 1.87 0.00 0.00 0.00

time (sec)

N/A 0.639 0.723 0.000 0.090 0.094 0.000 0.000 0.000

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F A A F(-2) F F(-1)

verified

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

size

131 131 189 0 100 249 0 0 0

N.S.

1 1.00 1.44 0.00 0.76 1.90 0.00 0.00 0.00

time (sec)

N/A 0.374 0.228 0.000 0.070 0.083 0.000 0.000 0.000

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 20 22 22 17 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.85 1.10 1.10

time (sec)

N/A 0.234 3.716 0.040 0.267 0.258 1.582 0.436 1.850

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 20 22 39 29 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.95 1.45 1.10 1.10

time (sec)

N/A 0.226 7.277 0.069 0.332 0.251 10.955 0.528 1.803

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 89 123 108 237 168 264 258 187

N.S.

1 1.00 1.38 1.21 2.66 1.89 2.97 2.90 2.10

time (sec)

N/A 0.344 0.301 0.234 0.221 0.254 0.298 0.478 1.861

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 83 76 141 102 151 146 110

N.S.

1 1.00 1.24 1.13 2.10 1.52 2.25 2.18 1.64

time (sec)

N/A 0.301 0.183 0.211 0.191 0.245 0.220 0.593 1.724

Problem 158

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

45 45 46 46 66 51 68 64 49

N.S.

1 1.00 1.02 1.02 1.47 1.13 1.51 1.42 1.09

time (sec)

N/A 0.243 0.118 0.075 0.188 0.254 0.173 0.461 0.092

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 57 94 70 111 0 67 0

N.S.

1 1.00 0.89 1.47 1.09 1.73 0.00 1.05 0.00

time (sec)

N/A 0.336 0.110 0.239 0.223 0.244 0.000 0.510 0.000

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 87 71 149 87 162 0 631 0

N.S.

1 1.00 0.82 1.71 1.00 1.86 0.00 7.25 0.00

time (sec)

N/A 0.379 0.276 0.233 0.226 0.250 0.000 0.412 0.000

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 123 95 296 98 274 0 316 0

N.S.

1 1.00 0.77 2.41 0.80 2.23 0.00 2.57 0.00

time (sec)

N/A 0.424 0.421 0.307 0.259 0.252 0.000 0.456 0.000

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

250 237 232 194 523 409 779 599 481

N.S.

1 0.95 0.93 0.78 2.09 1.64 3.12 2.40 1.92

time (sec)

N/A 0.536 0.811 0.368 0.234 0.257 0.474 0.450 3.534

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

182 182 252 145 324 240 456 345 281

N.S.

1 1.00 1.38 0.80 1.78 1.32 2.51 1.90 1.54

time (sec)

N/A 0.431 0.607 0.357 0.223 0.249 0.326 0.492 2.194

Problem 164

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

116 113 96 107 165 122 219 160 135

N.S.

1 0.97 0.83 0.92 1.42 1.05 1.89 1.38 1.16

time (sec)

N/A 0.312 4.586 0.134 0.204 0.249 0.239 0.463 0.184

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 156 133 202 148 230 0 144 0

N.S.

1 1.00 0.85 1.29 0.95 1.47 0.00 0.92 0.00

time (sec)

N/A 0.528 0.217 0.340 0.260 0.258 0.000 0.447 0.000

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

183 183 233 319 181 355 0 1135 0

N.S.

1 1.00 1.27 1.74 0.99 1.94 0.00 6.20 0.00

time (sec)

N/A 0.589 0.444 0.396 0.243 0.254 0.000 0.624 0.000

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

242 242 394 626 201 586 0 678 0

N.S.

1 1.00 1.63 2.59 0.83 2.42 0.00 2.80 0.00

time (sec)

N/A 0.699 0.852 0.501 0.251 0.262 0.000 0.510 0.000

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F(-2) B F F F(-1)

verified

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

size

436 397 336 0 0 1042 0 0 0

N.S.

1 0.91 0.77 0.00 0.00 2.39 0.00 0.00 0.00

time (sec)

N/A 1.679 0.330 0.000 0.000 0.272 0.000 0.000 0.000

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F(-2) B F F F(-1)

verified

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

size

320 299 247 0 0 736 0 0 0

N.S.

1 0.93 0.77 0.00 0.00 2.30 0.00 0.00 0.00

time (sec)

N/A 1.277 0.190 0.000 0.000 0.259 0.000 0.000 0.000

Problem 170

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F(-2) B F F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

203 201 152 437 0 473 0 0 0

N.S.

1 0.99 0.75 2.15 0.00 2.33 0.00 0.00 0.00

time (sec)

N/A 0.801 0.091 0.135 0.000 0.260 0.000 0.000 0.000

Problem 171

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 20 22 27 17 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.35 0.85 1.10 1.10

time (sec)

N/A 0.234 0.885 0.049 0.338 0.239 6.383 0.474 1.827

Problem 172

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 20 22 51 19 22 22

N.S.

1 1.00 1.10 1.00 1.10 2.55 0.95 1.10 1.10

time (sec)

N/A 0.236 0.832 0.048 0.397 0.247 37.402 0.725 1.822

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B F F(-2) B F(-1) F F(-1)

verified

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

size

823 746 11178 0 0 7116 0 0 0

N.S.

1 0.91 13.58 0.00 0.00 8.65 0.00 0.00 0.00

time (sec)

N/A 4.076 13.718 0.000 0.000 0.378 0.000 0.000 0.000

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B F F(-2) B F(-1) F F(-1)

verified

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

size

593 550 2814 0 0 4105 0 0 0

N.S.

1 0.93 4.75 0.00 0.00 6.92 0.00 0.00 0.00

time (sec)

N/A 2.749 10.465 0.000 0.000 0.324 0.000 0.000 0.000

Problem 175

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F(-2) B F(-1) F F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

274 281 509 585 0 1765 0 0 0

N.S.

1 1.03 1.86 2.14 0.00 6.44 0.00 0.00 0.00

time (sec)

N/A 1.143 3.037 0.207 0.000 0.281 0.000 0.000 0.000

Problem 176

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 20 416 55 19 22 22

N.S.

1 1.00 1.10 1.00 20.80 2.75 0.95 1.10 1.10

time (sec)

N/A 0.243 27.708 0.080 0.655 0.261 173.539 0.908 1.895

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 22 20 622 96 0 22 22

N.S.

1 1.00 1.10 1.00 31.10 4.80 0.00 1.10 1.10

time (sec)

N/A 0.252 28.309 0.081 0.958 0.257 0.000 1.868 2.032

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

20 20 22 20 22 22 0 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.00 1.10 1.10

time (sec)

N/A 0.238 3.271 0.046 0.375 0.274 0.000 0.610 1.921

Problem 179

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F A A F(-2) F F(-1)

verified

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

size

543 543 447 0 375 813 0 0 0

N.S.

1 1.00 0.82 0.00 0.69 1.50 0.00 0.00 0.00

time (sec)

N/A 1.060 1.214 0.000 0.150 0.104 0.000 0.000 0.000

Problem 180

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F A A F(-2) F F(-1)

verified

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

size

282 282 254 0 208 509 0 0 0

N.S.

1 1.00 0.90 0.00 0.74 1.80 0.00 0.00 0.00

time (sec)

N/A 0.616 0.520 0.000 0.098 0.090 0.000 0.000 0.000

Problem 181

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F A A F(-2) F F(-1)

verified

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

size

131 131 119 0 100 249 0 0 0

N.S.

1 1.00 0.91 0.00 0.76 1.90 0.00 0.00 0.00

time (sec)

N/A 0.365 0.133 0.000 0.073 0.088 0.000 0.000 0.000

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 20 22 22 17 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.85 1.10 1.10

time (sec)

N/A 0.229 1.194 0.024 0.308 0.245 1.689 0.508 1.766

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 20 22 38 19 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.90 0.95 1.10 1.10

time (sec)

N/A 0.231 5.533 0.062 0.336 0.255 12.856 0.432 1.844

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