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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 B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 21 42 21 59 113 0 44 53

N.S.

1 0.91 1.83 0.91 2.57 4.91 0.00 1.91 2.30

time (sec)

N/A 0.195 0.050 0.298 0.195 0.247 0.000 0.258 0.075

Problem 102

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 28 22 33 56 31 0 45 49

N.S.

1 1.27 1.00 1.50 2.55 1.41 0.00 2.05 2.23

time (sec)

N/A 0.211 0.011 0.311 0.196 0.254 0.000 0.282 2.089

Problem 103

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

49 51 85 62 108 612 0 105 112

N.S.

1 1.04 1.73 1.27 2.20 12.49 0.00 2.14 2.29

time (sec)

N/A 0.212 0.104 0.975 0.203 0.291 0.000 0.293 0.082

Problem 104

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 42 37 51 100 89 0 71 131

N.S.

1 1.14 1.00 1.38 2.70 2.41 0.00 1.92 3.54

time (sec)

N/A 0.211 0.016 0.556 0.196 0.247 0.000 0.288 2.122

Problem 105

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 28 25 23 70 203 105 63 49

N.S.

1 1.04 0.93 0.85 2.59 7.52 3.89 2.33 1.81

time (sec)

N/A 0.210 0.017 0.499 0.185 0.253 0.826 0.273 0.078

Problem 106

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 62 31 39 66 60 0 71 50

N.S.

1 1.55 0.78 0.98 1.65 1.50 0.00 1.78 1.25

time (sec)

N/A 0.225 0.175 0.552 0.188 0.252 0.000 0.279 0.090

Problem 107

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

43 41 35 43 120 743 0 102 97

N.S.

1 0.95 0.81 1.00 2.79 17.28 0.00 2.37 2.26

time (sec)

N/A 0.229 0.036 0.772 0.196 0.264 0.000 0.302 2.100

Problem 108

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

38 33 60 31 87 357 0 69 81

N.S.

1 0.87 1.58 0.82 2.29 9.39 0.00 1.82 2.13

time (sec)

N/A 0.218 0.088 0.891 0.193 0.258 0.000 0.287 2.071

Problem 109

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 42 38 52 79 63 0 67 78

N.S.

1 1.11 1.00 1.37 2.08 1.66 0.00 1.76 2.05

time (sec)

N/A 0.225 0.015 1.293 0.192 0.249 0.000 0.288 0.106

Problem 110

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

66 63 103 81 133 1077 0 123 140

N.S.

1 0.95 1.56 1.23 2.02 16.32 0.00 1.86 2.12

time (sec)

N/A 0.244 0.126 2.700 0.189 0.282 0.000 0.318 2.119

Problem 111

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

39 41 35 33 95 457 0 85 77

N.S.

1 1.05 0.90 0.85 2.44 11.72 0.00 2.18 1.97

time (sec)

N/A 0.221 0.024 2.310 0.199 0.257 0.000 0.275 0.112

Problem 112

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

11 11 11 12 25 56 17 25 24

N.S.

1 1.00 1.00 1.09 2.27 5.09 1.55 2.27 2.18

time (sec)

N/A 0.188 0.008 0.144 0.209 0.232 0.779 0.281 0.061

Problem 113

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

15 15 15 14 13 86 22 27 13

N.S.

1 1.00 1.00 0.93 0.87 5.73 1.47 1.80 0.87

time (sec)

N/A 0.199 0.010 0.164 0.186 0.247 1.558 0.278 0.077

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 16 17 53 115 36 0 31

N.S.

1 1.00 1.00 1.06 3.31 7.19 2.25 0.00 1.94

time (sec)

N/A 0.203 0.016 0.324 0.349 0.254 2.192 0.000 2.096

Problem 115

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

15 15 15 14 13 139 0 31 31

N.S.

1 1.00 1.00 0.93 0.87 9.27 0.00 2.07 2.07

time (sec)

N/A 0.198 0.003 0.191 0.187 0.247 0.000 0.309 2.065

Problem 116

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

15 15 15 14 13 208 0 37 231

N.S.

1 1.00 1.00 0.93 0.87 13.87 0.00 2.47 15.40

time (sec)

N/A 0.200 0.004 0.214 0.197 0.245 0.000 0.318 2.086

Problem 117

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

20 20 20 21 20 70 0 39 43

N.S.

1 1.00 1.00 1.05 1.00 3.50 0.00 1.95 2.15

time (sec)

N/A 0.213 0.017 2.002 0.196 0.255 0.000 0.293 2.137

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 32 27 24 148 171 0 49 48

N.S.

1 1.19 1.00 0.89 5.48 6.33 0.00 1.81 1.78

time (sec)

N/A 0.208 0.011 0.212 0.199 0.250 0.000 0.306 2.082

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 36 31 27 214 343 0 49 252

N.S.

1 1.16 1.00 0.87 6.90 11.06 0.00 1.58 8.13

time (sec)

N/A 0.218 0.018 0.356 0.191 0.243 0.000 0.330 2.147

Problem 120

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B B F F B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

37 35 34 479 414 216 0 0 100

N.S.

1 0.95 0.92 12.95 11.19 5.84 0.00 0.00 2.70

time (sec)

N/A 0.236 0.050 0.855 0.340 0.263 0.000 0.000 2.175

Problem 121

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 42 75 45 84 387 0 84 87

N.S.

1 1.24 2.21 1.32 2.47 11.38 0.00 2.47 2.56

time (sec)

N/A 0.260 0.088 0.915 0.186 0.258 0.000 0.279 0.083

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 70 113 58 129 1109 0 106 219

N.S.

1 1.27 2.05 1.05 2.35 20.16 0.00 1.93 3.98

time (sec)

N/A 0.361 0.125 1.004 0.191 0.262 0.000 0.288 0.114

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 70 113 74 133 1114 0 110 190

N.S.

1 1.27 2.05 1.35 2.42 20.25 0.00 2.00 3.45

time (sec)

N/A 0.369 0.110 0.968 0.191 0.264 0.000 0.318 2.050

Problem 124

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 25 27 14 149 164 0 30 144

N.S.

1 1.47 1.59 0.82 8.76 9.65 0.00 1.76 8.47

time (sec)

N/A 0.208 0.035 0.476 0.191 0.248 0.000 0.263 2.074

Problem 125

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

17 17 17 22 139 222 0 29 210

N.S.

1 1.00 1.00 1.29 8.18 13.06 0.00 1.71 12.35

time (sec)

N/A 0.211 0.010 0.500 0.196 0.244 0.000 0.255 2.228

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 35 30 33 368 114 0 0 87

N.S.

1 1.35 1.15 1.27 14.15 4.38 0.00 0.00 3.35

time (sec)

N/A 0.226 0.080 34.492 0.321 0.268 0.000 0.000 2.243

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 60 95 46 98 1260 0 71 214

N.S.

1 1.58 2.50 1.21 2.58 33.16 0.00 1.87 5.63

time (sec)

N/A 0.397 0.028 1.077 0.208 0.247 0.000 0.268 2.090

Problem 128

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 35 47 20 431 430 0 48 413

N.S.

1 1.40 1.88 0.80 17.24 17.20 0.00 1.92 16.52

time (sec)

N/A 0.221 0.036 1.867 0.202 0.249 0.000 0.276 2.084

Problem 129

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 39 29 24 191 250 0 47 40

N.S.

1 1.34 1.00 0.83 6.59 8.62 0.00 1.62 1.38

time (sec)

N/A 0.203 0.014 0.279 0.199 0.254 0.000 0.285 2.094

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 45 33 26 435 442 0 54 372

N.S.

1 1.36 1.00 0.79 13.18 13.39 0.00 1.64 11.27

time (sec)

N/A 0.223 0.012 1.022 0.200 0.244 0.000 0.268 2.040

Problem 131

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 26 24 58 87 58 71 23

N.S.

1 1.00 0.96 0.89 2.15 3.22 2.15 2.63 0.85

time (sec)

N/A 0.202 0.028 0.427 0.207 0.260 0.174 0.271 0.166

Problem 132

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

27 27 27 24 59 75 61 78 23

N.S.

1 1.00 1.00 0.89 2.19 2.78 2.26 2.89 0.85

time (sec)

N/A 0.206 0.032 0.414 0.208 0.243 0.174 0.265 2.145

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 26 24 58 89 58 69 23

N.S.

1 1.00 0.96 0.89 2.15 3.30 2.15 2.56 0.85

time (sec)

N/A 0.203 0.013 0.424 0.199 0.250 0.165 0.267 2.119

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 26 24 59 77 58 74 23

N.S.

1 1.00 0.96 0.89 2.19 2.85 2.15 2.74 0.85

time (sec)

N/A 0.196 0.014 0.389 0.202 0.251 0.171 0.280 2.122

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 46 29 151 83 259 0 95 115

N.S.

1 1.24 0.78 4.08 2.24 7.00 0.00 2.57 3.11

time (sec)

N/A 0.323 0.347 0.237 0.285 0.261 0.000 0.285 2.641

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 42 30 149 87 216 0 86 121

N.S.

1 1.17 0.83 4.14 2.42 6.00 0.00 2.39 3.36

time (sec)

N/A 0.311 0.332 0.235 0.286 0.266 0.000 0.280 2.653

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 53 29 155 157 259 0 97 115

N.S.

1 1.43 0.78 4.19 4.24 7.00 0.00 2.62 3.11

time (sec)

N/A 0.317 0.324 0.247 0.216 0.253 0.000 0.281 0.524

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 50 32 153 160 216 0 90 121

N.S.

1 1.39 0.89 4.25 4.44 6.00 0.00 2.50 3.36

time (sec)

N/A 0.310 0.313 0.247 0.216 0.266 0.000 0.277 2.560

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 27 77 68 184 0 79 266

N.S.

1 1.00 0.75 2.14 1.89 5.11 0.00 2.19 7.39

time (sec)

N/A 0.243 0.150 0.431 0.284 0.251 0.000 0.288 3.044

Problem 140

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 27 75 67 156 0 70 268

N.S.

1 1.00 0.82 2.27 2.03 4.73 0.00 2.12 8.12

time (sec)

N/A 0.239 0.151 0.460 0.282 0.262 0.000 0.272 2.976

Problem 141

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 44 28 79 133 184 0 81 266

N.S.

1 1.22 0.78 2.19 3.69 5.11 0.00 2.25 7.39

time (sec)

N/A 0.250 0.157 0.203 0.204 0.256 0.000 0.285 2.332

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 41 29 77 129 156 0 74 269

N.S.

1 1.24 0.88 2.33 3.91 4.73 0.00 2.24 8.15

time (sec)

N/A 0.245 0.141 0.247 0.215 0.270 0.000 0.290 0.321

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 86 167 57 327 0 49 133

N.S.

1 1.00 2.97 5.76 1.97 11.28 0.00 1.69 4.59

time (sec)

N/A 0.260 0.041 0.343 0.286 0.249 0.000 0.267 2.288

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 102 205 105 902 0 97 173

N.S.

1 1.00 2.27 4.56 2.33 20.04 0.00 2.16 3.84

time (sec)

N/A 0.421 0.076 0.363 0.285 0.270 0.000 0.264 0.222

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 86 70 240 149 1737 0 120 0

N.S.

1 1.19 0.97 3.33 2.07 24.12 0.00 1.67 0.00

time (sec)

N/A 0.713 0.232 0.396 0.292 0.277 0.000 0.266 0.000

Problem 146

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 93 155 94 439 0 93 139

N.S.

1 1.00 3.21 5.34 3.24 15.14 0.00 3.21 4.79

time (sec)

N/A 0.258 0.042 0.327 0.210 0.247 0.000 0.260 0.158

Problem 147

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 110 197 140 1237 0 136 181

N.S.

1 1.00 2.39 4.28 3.04 26.89 0.00 2.96 3.93

time (sec)

N/A 0.418 0.076 0.330 0.212 0.267 0.000 0.261 2.281

Problem 148

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 94 70 230 186 2372 0 169 0

N.S.

1 1.29 0.96 3.15 2.55 32.49 0.00 2.32 0.00

time (sec)

N/A 0.737 0.238 0.387 0.197 0.269 0.000 0.266 0.000

Problem 149

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 26 148 49 87 0 49 65

N.S.

1 1.00 1.00 5.69 1.88 3.35 0.00 1.88 2.50

time (sec)

N/A 0.230 0.086 0.416 0.208 0.266 0.000 0.261 0.242

Problem 150

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 83 181 70 405 0 68 150

N.S.

1 1.00 2.37 5.17 2.00 11.57 0.00 1.94 4.29

time (sec)

N/A 0.289 0.068 1.136 0.291 0.258 0.000 0.265 2.245

Problem 151

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 35 42 120 246 0 51 0

N.S.

1 1.00 0.92 1.11 3.16 6.47 0.00 1.34 0.00

time (sec)

N/A 0.314 0.119 0.988 0.204 0.257 0.000 0.269 0.000

Problem 152

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A B B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 30 26 150 84 86 0 51 65

N.S.

1 1.15 1.00 5.77 3.23 3.31 0.00 1.96 2.50

time (sec)

N/A 0.233 0.080 0.186 0.206 0.272 0.000 0.268 2.243

Problem 153

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 90 172 103 617 0 104 156

N.S.

1 1.00 2.50 4.78 2.86 17.14 0.00 2.89 4.33

time (sec)

N/A 0.295 0.058 0.311 0.203 0.257 0.000 0.269 0.216

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 35 57 131 246 0 53 0

N.S.

1 1.00 0.90 1.46 3.36 6.31 0.00 1.36 0.00

time (sec)

N/A 0.320 0.126 0.554 0.199 0.242 0.000 0.274 0.000

Problem 155

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 86 167 59 327 0 53 133

N.S.

1 1.00 2.97 5.76 2.03 11.28 0.00 1.83 4.59

time (sec)

N/A 0.260 0.040 0.361 0.276 0.262 0.000 0.267 0.173

Problem 156

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 102 207 103 902 0 97 173

N.S.

1 1.00 2.27 4.60 2.29 20.04 0.00 2.16 3.84

time (sec)

N/A 0.401 0.075 0.392 0.287 0.260 0.000 0.266 0.213

Problem 157

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 86 115 238 149 1737 0 122 0

N.S.

1 1.19 1.60 3.31 2.07 24.12 0.00 1.69 0.00

time (sec)

N/A 0.714 0.230 0.444 0.303 0.274 0.000 0.270 0.000

Problem 158

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 93 155 90 439 0 91 139

N.S.

1 1.00 3.21 5.34 3.10 15.14 0.00 3.14 4.79

time (sec)

N/A 0.255 0.039 0.270 0.201 0.256 0.000 0.273 0.159

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 110 195 144 1237 0 142 183

N.S.

1 1.00 2.39 4.24 3.13 26.89 0.00 3.09 3.98

time (sec)

N/A 0.411 0.073 0.312 0.221 0.263 0.000 0.268 2.234

Problem 160

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 94 70 228 184 2372 0 167 0

N.S.

1 1.29 0.96 3.12 2.52 32.49 0.00 2.29 0.00

time (sec)

N/A 0.721 0.221 0.427 0.203 0.277 0.000 0.277 0.000

Problem 161

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 26 146 51 86 0 50 64

N.S.

1 1.00 1.00 5.62 1.96 3.31 0.00 1.92 2.46

time (sec)

N/A 0.228 0.081 0.434 0.197 0.250 0.000 0.263 0.221

Problem 162

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B C A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 83 183 70 405 0 68 148

N.S.

1 1.00 2.37 5.23 2.00 11.57 0.00 1.94 4.23

time (sec)

N/A 0.287 0.069 1.126 0.300 0.253 0.000 0.264 2.230

Problem 163

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 35 26 119 248 0 49 0

N.S.

1 1.00 0.92 0.68 3.13 6.53 0.00 1.29 0.00

time (sec)

N/A 0.313 0.124 0.954 0.202 0.249 0.000 0.264 0.000

Problem 164

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A B B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 30 26 152 80 87 0 50 66

N.S.

1 1.15 1.00 5.85 3.08 3.35 0.00 1.92 2.54

time (sec)

N/A 0.233 0.080 0.281 0.204 0.256 0.000 0.260 2.233

Problem 165

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 36 90 170 105 617 0 106 156

N.S.

1 1.00 2.50 4.72 2.92 17.14 0.00 2.94 4.33

time (sec)

N/A 0.292 0.061 0.441 0.206 0.250 0.000 0.289 2.248

Problem 166

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

39 39 35 36 132 243 0 51 0

N.S.

1 1.00 0.90 0.92 3.38 6.23 0.00 1.31 0.00

time (sec)

N/A 0.320 0.124 0.685 0.206 0.244 0.000 0.269 0.000

Problem 167

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 43 40 0 72 153 85 42

N.S.

1 1.00 1.00 0.93 0.00 1.67 3.56 1.98 0.98

time (sec)

N/A 0.223 0.156 0.442 0.000 0.245 0.323 0.288 0.169

Problem 168

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 62 69 57 0 120 405 120 76

N.S.

1 1.00 1.11 0.92 0.00 1.94 6.53 1.94 1.23

time (sec)

N/A 0.259 0.515 0.816 0.000 0.259 0.722 0.261 0.270

Problem 169

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 91 86 84 0 218 918 179 182

N.S.

1 1.00 0.95 0.92 0.00 2.40 10.09 1.97 2.00

time (sec)

N/A 0.287 0.326 1.496 0.000 0.263 1.911 0.278 0.554

Problem 170

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 88 106 89 0 192 1027 156 152

N.S.

1 1.00 1.20 1.01 0.00 2.18 11.67 1.77 1.73

time (sec)

N/A 0.276 0.501 1.815 0.000 0.265 1.557 0.294 2.695

Problem 171

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 144 158 133 0 414 2001 260 337

N.S.

1 1.00 1.10 0.92 0.00 2.88 13.90 1.81 2.34

time (sec)

N/A 0.353 1.165 4.585 0.000 0.248 5.481 0.282 2.614

Problem 172

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

195 195 177 190 0 731 3580 373 906

N.S.

1 1.00 0.91 0.97 0.00 3.75 18.36 1.91 4.65

time (sec)

N/A 0.399 1.082 10.555 0.000 0.273 16.688 0.282 2.725

Problem 173

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 43 40 0 71 153 85 42

N.S.

1 1.00 1.00 0.93 0.00 1.65 3.56 1.98 0.98

time (sec)

N/A 0.225 0.117 0.381 0.000 0.247 0.317 0.265 0.152

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 62 69 57 0 115 408 120 68

N.S.

1 1.00 1.11 0.92 0.00 1.85 6.58 1.94 1.10

time (sec)

N/A 0.246 0.484 0.808 0.000 0.255 0.703 0.265 0.247

Problem 175

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 91 85 84 0 217 921 179 180

N.S.

1 1.00 0.93 0.92 0.00 2.38 10.12 1.97 1.98

time (sec)

N/A 0.277 0.285 1.477 0.000 0.287 1.881 0.272 2.533

Problem 176

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 88 105 89 0 192 1027 156 115

N.S.

1 1.00 1.19 1.01 0.00 2.18 11.67 1.77 1.31

time (sec)

N/A 0.275 0.465 1.715 0.000 0.241 1.582 0.270 2.617

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 144 158 133 0 397 2008 260 337

N.S.

1 1.00 1.10 0.92 0.00 2.76 13.94 1.81 2.34

time (sec)

N/A 0.327 1.084 4.770 0.000 0.253 5.288 0.277 2.691

Problem 178

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

195 195 176 190 0 726 3582 373 908

N.S.

1 1.00 0.90 0.97 0.00 3.72 18.37 1.91 4.66

time (sec)

N/A 0.370 1.109 11.099 0.000 0.267 16.835 0.281 2.717

Problem 179

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 43 40 0 71 153 85 42

N.S.

1 1.00 1.00 0.93 0.00 1.65 3.56 1.98 0.98

time (sec)

N/A 0.226 0.154 0.461 0.000 0.255 0.327 0.264 0.150

Problem 180

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 62 69 57 0 119 408 120 68

N.S.

1 1.00 1.11 0.92 0.00 1.92 6.58 1.94 1.10

time (sec)

N/A 0.250 0.469 0.836 0.000 0.255 0.707 0.267 0.246

Problem 181

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 91 85 84 0 213 921 179 182

N.S.

1 1.00 0.93 0.92 0.00 2.34 10.12 1.97 2.00

time (sec)

N/A 0.284 0.314 1.619 0.000 0.263 1.956 0.274 2.565

Problem 182

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 68 74 63 0 114 408 124 76

N.S.

1 1.00 1.09 0.93 0.00 1.68 6.00 1.82 1.12

time (sec)

N/A 0.244 0.512 0.782 0.000 0.260 0.742 0.260 2.297

Problem 183

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 88 107 89 0 192 1027 156 135

N.S.

1 1.00 1.22 1.01 0.00 2.18 11.67 1.77 1.53

time (sec)

N/A 0.269 0.461 1.965 0.000 0.262 1.558 0.261 2.615

Problem 184

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 144 158 133 0 398 2001 260 337

N.S.

1 1.00 1.10 0.92 0.00 2.76 13.90 1.81 2.34

time (sec)

N/A 0.323 1.013 4.817 0.000 0.264 5.549 0.285 2.618

Problem 185

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 97 90 90 0 243 935 183 183

N.S.

1 1.00 0.93 0.93 0.00 2.51 9.64 1.89 1.89

time (sec)

N/A 0.286 0.371 1.326 0.000 0.249 1.941 0.286 0.552

Problem 186

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 138 153 127 0 443 2030 256 337

N.S.

1 1.00 1.11 0.92 0.00 3.21 14.71 1.86 2.44

time (sec)

N/A 0.335 1.126 4.009 0.000 0.262 5.342 0.278 2.645

Problem 187

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

195 195 176 190 0 729 3580 373 908

N.S.

1 1.00 0.90 0.97 0.00 3.74 18.36 1.91 4.66

time (sec)

N/A 0.405 1.044 11.361 0.000 0.268 16.865 0.300 2.795

Problem 188

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

121 121 103 0 0 0 0 0 0

N.S.

1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.331 0.717 0.000 0.000 0.000 0.000 0.000 0.000

Problem 189

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

117 117 240 0 0 0 0 0 0

N.S.

1 1.00 2.05 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.325 2.150 0.000 0.000 0.000 0.000 0.000 0.000

Problem 190

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

116 116 99 0 0 0 0 0 0

N.S.

1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.329 0.797 0.000 0.000 0.000 0.000 0.000 0.000

Problem 191

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

120 120 103 0 0 0 0 0 0

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.319 0.520 0.000 0.000 0.000 0.000 0.000 0.000

Problem 192

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

8 15 15 12 27 17 20 25 6

N.S.

1 1.88 1.88 1.50 3.38 2.12 2.50 3.12 0.75

time (sec)

N/A 0.181 0.026 0.322 0.194 0.253 0.127 0.266 0.071

Problem 193

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 17 17 14 27 22 20 27 13

N.S.

1 1.00 1.00 0.82 1.59 1.29 1.18 1.59 0.76

time (sec)

N/A 0.180 0.044 0.416 0.197 0.261 0.133 0.268 0.061

Problem 194

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

17 17 17 14 27 36 20 27 14

N.S.

1 1.00 1.00 0.82 1.59 2.12 1.18 1.59 0.82

time (sec)

N/A 0.182 0.025 0.361 0.193 0.328 0.131 0.263 0.058

Problem 195

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 25 28 0 42 78 59 26

N.S.

1 1.00 0.71 0.80 0.00 1.20 2.23 1.69 0.74

time (sec)

N/A 0.213 0.038 0.324 0.000 0.244 0.253 0.261 0.097

Problem 196

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 23 15 12 27 19 20 25 11

N.S.

1 1.53 1.00 0.80 1.80 1.27 1.33 1.67 0.73

time (sec)

N/A 0.190 0.031 0.315 0.194 0.246 0.128 0.270 2.187

Problem 197

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 25 17 14 27 33 20 26 11

N.S.

1 1.47 1.00 0.82 1.59 1.94 1.18 1.53 0.65

time (sec)

N/A 0.184 0.030 0.399 0.187 0.244 0.129 0.258 0.060

Problem 198

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A C A A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

17 25 17 14 27 38 20 27 15

N.S.

1 1.47 1.00 0.82 1.59 2.24 1.18 1.59 0.88

time (sec)

N/A 0.183 0.030 0.413 0.196 0.258 0.127 0.256 2.187

Problem 199

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 25 28 0 42 37 59 26

N.S.

1 1.00 0.71 0.80 0.00 1.20 1.06 1.69 0.74

time (sec)

N/A 0.213 0.046 0.324 0.000 0.254 0.265 0.270 2.204

Problem 200

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

19 27 19 16 53 115 0 36 47

N.S.

1 1.42 1.00 0.84 2.79 6.05 0.00 1.89 2.47

time (sec)

N/A 0.203 0.012 0.177 0.277 0.262 0.000 0.261 2.262

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