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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 A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 16 17 22 29 17 18 22

N.S.

1 1.00 0.64 0.68 0.88 1.16 0.68 0.72 0.88

time (sec)

N/A 0.009 0.011 0.180 0.206 0.227 0.040 0.284 0.205

Problem 102

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

36 36 36 33 32 39 31 45 32

N.S.

1 1.00 1.00 0.92 0.89 1.08 0.86 1.25 0.89

time (sec)

N/A 0.012 0.016 0.171 0.204 0.252 0.030 0.278 0.038

Problem 103

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

41 41 37 25 30 45 31 27 30

N.S.

1 1.00 0.90 0.61 0.73 1.10 0.76 0.66 0.73

time (sec)

N/A 0.034 0.022 0.042 0.216 0.244 0.064 0.266 0.066

Problem 104

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 27 28 29 45 26 37 29

N.S.

1 1.00 1.00 1.04 1.07 1.67 0.96 1.37 1.07

time (sec)

N/A 0.028 0.018 0.193 0.206 0.271 0.052 0.294 0.269

Problem 105

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

39 39 47 31 29 45 32 35 31

N.S.

1 1.00 1.21 0.79 0.74 1.15 0.82 0.90 0.79

time (sec)

N/A 0.028 0.019 0.211 0.220 0.252 0.063 0.282 0.054

Problem 106

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

46 46 40 35 40 65 37 40 40

N.S.

1 1.00 0.87 0.76 0.87 1.41 0.80 0.87 0.87

time (sec)

N/A 0.017 0.018 0.049 0.206 0.239 0.068 0.290 0.245

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

29 29 29 24 23 23 22 24 29

N.S.

1 1.00 1.00 0.83 0.79 0.79 0.76 0.83 1.00

time (sec)

N/A 0.025 0.008 0.072 0.313 0.237 0.055 0.268 0.052

Problem 108

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 27 22 21 21 22 23 27

N.S.

1 1.00 1.00 0.81 0.78 0.78 0.81 0.85 1.00

time (sec)

N/A 0.020 0.009 0.233 0.326 0.242 0.080 0.292 0.051

Problem 109

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

24 24 32 26 25 25 29 27 17

N.S.

1 1.00 1.33 1.08 1.04 1.04 1.21 1.12 0.71

time (sec)

N/A 0.008 0.012 0.049 0.309 0.242 0.061 0.279 0.065

Problem 110

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

41 41 41 33 32 44 39 33 49

N.S.

1 1.00 1.00 0.80 0.78 1.07 0.95 0.80 1.20

time (sec)

N/A 0.068 0.025 0.053 0.312 0.238 0.063 0.291 0.336

Problem 111

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

46 46 40 35 36 57 37 62 38

N.S.

1 1.00 0.87 0.76 0.78 1.24 0.80 1.35 0.83

time (sec)

N/A 0.187 0.021 0.276 0.330 0.241 0.089 0.288 0.223

Problem 112

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

47 47 37 31 36 59 36 32 42

N.S.

1 1.00 0.79 0.66 0.77 1.26 0.77 0.68 0.89

time (sec)

N/A 0.030 0.028 0.253 0.295 0.245 0.076 0.279 0.050

Problem 113

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 73 54 53 53 70 53 47

N.S.

1 1.00 1.09 0.81 0.79 0.79 1.04 0.79 0.70

time (sec)

N/A 0.028 0.064 0.030 0.295 0.241 0.086 0.294 0.116

Problem 114

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 67 46 54 58 306 64 73

N.S.

1 1.00 1.40 0.96 1.12 1.21 6.38 1.33 1.52

time (sec)

N/A 0.039 0.020 0.244 0.298 0.239 0.286 0.297 0.181

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

58 58 46 38 43 66 46 39 44

N.S.

1 1.00 0.79 0.66 0.74 1.14 0.79 0.67 0.76

time (sec)

N/A 0.054 0.027 0.369 0.285 0.239 0.078 0.284 0.229

Problem 116

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

51 51 47 36 35 35 44 35 35

N.S.

1 1.00 0.92 0.71 0.69 0.69 0.86 0.69 0.69

time (sec)

N/A 0.232 0.029 0.316 0.291 0.243 0.205 0.271 0.301

Problem 117

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

41 41 41 34 33 33 32 33 33

N.S.

1 1.00 1.00 0.83 0.80 0.80 0.78 0.80 0.80

time (sec)

N/A 0.264 0.010 0.243 0.198 0.245 0.076 0.277 0.062

Problem 118

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 52 51 49 45 73 50 64

N.S.

1 1.00 0.93 0.91 0.88 0.80 1.30 0.89 1.14

time (sec)

N/A 0.032 0.016 0.226 0.280 0.240 0.058 0.308 0.463

Problem 119

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 50 43 49 43 71 50 68

N.S.

1 1.00 0.89 0.77 0.88 0.77 1.27 0.89 1.21

time (sec)

N/A 0.025 0.010 0.207 0.287 0.238 0.050 0.280 0.123

Problem 120

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

12 12 12 11 10 10 8 11 10

N.S.

1 1.00 1.00 0.92 0.83 0.83 0.67 0.92 0.83

time (sec)

N/A 0.002 0.003 0.193 0.193 0.236 0.038 0.287 0.032

Problem 121

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

22 22 22 21 23 18 19 22 18

N.S.

1 1.00 1.00 0.95 1.05 0.82 0.86 1.00 0.82

time (sec)

N/A 0.007 0.006 0.200 0.201 0.230 0.096 0.325 0.291

Problem 122

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 63 60 60 57 53 83 58 88

N.S.

1 1.00 0.95 0.95 0.90 0.84 1.32 0.92 1.40

time (sec)

N/A 0.031 0.019 0.230 0.276 0.238 0.071 0.296 0.319

Problem 123

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 65 68 60 57 62 80 58 86

N.S.

1 1.00 1.05 0.92 0.88 0.95 1.23 0.89 1.32

time (sec)

N/A 0.034 0.021 0.234 0.285 0.241 0.091 0.299 0.301

Problem 124

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

33 33 33 34 31 33 29 40 29

N.S.

1 1.00 1.00 1.03 0.94 1.00 0.88 1.21 0.88

time (sec)

N/A 0.023 0.007 0.207 0.198 0.235 0.125 0.271 0.086

Problem 125

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 74 66 66 68 90 67 99

N.S.

1 1.00 1.01 0.90 0.90 0.93 1.23 0.92 1.36

time (sec)

N/A 0.042 0.017 0.227 0.284 0.242 0.098 0.273 0.112

Problem 126

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

46 46 45 0 0 0 92 0 0

N.S.

1 1.00 0.98 0.00 0.00 0.00 2.00 0.00 0.00

time (sec)

N/A 0.009 0.142 0.000 0.000 0.000 1.229 0.000 0.000

Problem 127

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 38 33 32 26 37 34 18

N.S.

1 1.00 1.41 1.22 1.19 0.96 1.37 1.26 0.67

time (sec)

N/A 0.006 0.012 0.249 0.288 0.244 0.065 0.277 0.093

Problem 128

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

15 15 15 27 29 26 24 30 13

N.S.

1 1.00 1.00 1.80 1.93 1.73 1.60 2.00 0.87

time (sec)

N/A 0.008 0.005 0.205 0.191 0.239 0.063 0.287 0.054

Problem 129

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

24 24 24 23 25 20 19 26 20

N.S.

1 1.00 1.00 0.96 1.04 0.83 0.79 1.08 0.83

time (sec)

N/A 0.011 0.008 0.203 0.196 0.231 0.120 0.284 0.338

Problem 130

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 35 46 41 40 36 44 42 31

N.S.

1 1.00 1.31 1.17 1.14 1.03 1.26 1.20 0.89

time (sec)

N/A 0.010 0.012 0.256 0.285 0.243 0.089 0.285 0.270

Problem 131

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

26 26 50 42 37 41 34 38 22

N.S.

1 1.00 1.92 1.62 1.42 1.58 1.31 1.46 0.85

time (sec)

N/A 0.013 0.009 0.216 0.210 0.236 0.098 0.275 0.260

Problem 132

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 48 41 40 45 48 42 31

N.S.

1 1.00 1.30 1.11 1.08 1.22 1.30 1.14 0.84

time (sec)

N/A 0.011 0.015 0.254 0.292 0.242 0.104 0.281 0.081

Problem 133

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

45 45 44 0 0 0 95 0 0

N.S.

1 1.00 0.98 0.00 0.00 0.00 2.11 0.00 0.00

time (sec)

N/A 0.008 0.234 0.000 0.000 0.000 0.497 0.000 0.000

Problem 134

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 15 14 13 13 29 13 13

N.S.

1 1.00 1.00 0.93 0.87 0.87 1.93 0.87 0.87

time (sec)

N/A 0.007 0.005 0.237 0.278 0.245 0.068 0.322 0.262

Problem 135

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 109 79 24 98 96 19 114 33

N.S.

1 1.00 0.72 0.22 0.90 0.88 0.17 1.05 0.30

time (sec)

N/A 0.056 0.034 0.232 0.295 0.243 0.059 0.301 0.112

Problem 136

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

201 201 204 55 180 11094 39 177 174

N.S.

1 1.00 1.01 0.27 0.90 55.19 0.19 0.88 0.87

time (sec)

N/A 0.301 0.183 0.230 0.293 0.962 0.058 0.290 0.714

Problem 137

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

201 201 204 60 160 18781 41 177 182

N.S.

1 1.00 1.01 0.30 0.80 93.44 0.20 0.88 0.91

time (sec)

N/A 0.264 0.067 0.211 0.285 0.985 0.054 0.304 0.690

Problem 138

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

201 201 204 58 160 12656 41 177 202

N.S.

1 1.00 1.01 0.29 0.80 62.97 0.20 0.88 1.00

time (sec)

N/A 0.289 0.072 0.210 0.298 0.964 0.062 0.316 0.954

Problem 139

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

201 201 204 73 180 17865 39 177 202

N.S.

1 1.00 1.01 0.36 0.90 88.88 0.19 0.88 1.00

time (sec)

N/A 0.290 0.041 0.213 0.285 0.972 0.062 0.288 0.427

Problem 140

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

12 12 12 11 10 10 8 11 10

N.S.

1 1.00 1.00 0.92 0.83 0.83 0.67 0.92 0.83

time (sec)

N/A 0.003 0.003 0.204 0.196 0.227 0.042 0.298 0.257

Problem 141

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

22 22 22 21 23 18 19 22 18

N.S.

1 1.00 1.00 0.95 1.05 0.82 0.86 1.00 0.82

time (sec)

N/A 0.007 0.007 0.205 0.201 0.229 0.119 0.291 0.342

Problem 142

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

209 209 172 76 192 15275 48 185 210

N.S.

1 1.00 0.82 0.36 0.92 73.09 0.23 0.89 1.00

time (sec)

N/A 0.312 0.180 0.233 0.290 0.977 0.080 0.317 0.415

Problem 143

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

211 211 174 78 173 15499 51 185 210

N.S.

1 1.00 0.82 0.37 0.82 73.45 0.24 0.88 1.00

time (sec)

N/A 0.305 0.171 0.227 0.290 1.018 0.097 0.303 0.818

Problem 144

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

211 211 175 81 172 15501 51 185 214

N.S.

1 1.00 0.83 0.38 0.82 73.46 0.24 0.88 1.01

time (sec)

N/A 0.253 0.129 0.226 0.283 0.973 0.091 0.320 0.763

Problem 145

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

46 46 45 0 0 0 92 0 0

N.S.

1 1.00 0.98 0.00 0.00 0.00 2.00 0.00 0.00

time (sec)

N/A 0.010 0.263 0.000 0.000 0.000 8.408 0.000 0.000

Problem 146

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

35 35 21 10 27 9 8 27 9

N.S.

1 1.00 0.60 0.29 0.77 0.26 0.23 0.77 0.26

time (sec)

N/A 0.367 0.008 0.240 0.282 0.239 0.051 0.269 0.034

Problem 147

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

60 60 51 44 54 71 63 44 45

N.S.

1 1.00 0.85 0.73 0.90 1.18 1.05 0.73 0.75

time (sec)

N/A 0.018 0.031 0.812 0.274 0.251 0.072 0.285 0.081

Problem 148

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

43 43 30 28 38 52 36 28 27

N.S.

1 1.00 0.70 0.65 0.88 1.21 0.84 0.65 0.63

time (sec)

N/A 0.012 0.014 0.234 0.274 0.253 0.059 0.287 0.227

Problem 149

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

90 90 88 103 0 448 323 92 159

N.S.

1 1.00 0.98 1.14 0.00 4.98 3.59 1.02 1.77

time (sec)

N/A 0.061 0.085 0.536 0.000 0.267 0.541 0.282 0.336

Problem 150

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 38 35 33 50 31 33 41

N.S.

1 1.00 1.00 0.92 0.87 1.32 0.82 0.87 1.08

time (sec)

N/A 0.025 0.015 0.322 0.278 0.241 0.050 0.289 0.218

Problem 151

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

57 57 49 41 42 58 53 43 60

N.S.

1 1.00 0.86 0.72 0.74 1.02 0.93 0.75 1.05

time (sec)

N/A 0.025 0.024 0.205 0.280 0.238 0.063 0.277 0.090

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

36 36 33 29 31 40 32 28 29

N.S.

1 1.00 0.92 0.81 0.86 1.11 0.89 0.78 0.81

time (sec)

N/A 0.024 0.017 0.234 0.268 0.226 0.063 0.278 0.217

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

49 49 78 39 40 40 46 40 52

N.S.

1 1.00 1.59 0.80 0.82 0.82 0.94 0.82 1.06

time (sec)

N/A 0.029 0.017 0.221 0.282 0.246 0.056 0.293 0.101

Problem 154

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

13 20 13 14 14 13 14 0 14

N.S.

1 1.54 1.00 1.08 1.08 1.00 1.08 0.00 1.08

time (sec)

N/A 0.035 0.028 0.290 0.204 0.246 0.784 0.000 0.370

Problem 155

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

41 41 38 35 34 34 42 34 34

N.S.

1 1.00 0.93 0.85 0.83 0.83 1.02 0.83 0.83

time (sec)

N/A 0.035 0.013 0.053 0.280 0.245 0.048 0.429 0.228

Problem 156

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

32 32 32 25 24 24 24 25 22

N.S.

1 1.00 1.00 0.78 0.75 0.75 0.75 0.78 0.69

time (sec)

N/A 0.020 0.007 0.051 0.189 0.249 0.049 0.311 0.087

Problem 157

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

25 25 25 18 17 17 15 19 16

N.S.

1 1.00 1.00 0.72 0.68 0.68 0.60 0.76 0.64

time (sec)

N/A 0.015 0.006 0.048 0.191 0.242 0.040 0.303 0.614

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

36 36 24 22 32 46 29 23 22

N.S.

1 1.00 0.67 0.61 0.89 1.28 0.81 0.64 0.61

time (sec)

N/A 0.017 0.015 0.197 0.188 0.240 0.043 0.303 0.042

Problem 159

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 24 22 72 72 70 22 29

N.S.

1 1.00 0.53 0.49 1.60 1.60 1.56 0.49 0.64

time (sec)

N/A 0.012 0.008 0.198 0.192 0.232 0.061 0.284 0.100

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

55 55 41 34 48 67 42 55 43

N.S.

1 1.00 0.75 0.62 0.87 1.22 0.76 1.00 0.78

time (sec)

N/A 0.033 0.014 0.191 0.188 0.238 0.051 0.274 0.053

Problem 161

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

36 36 38 35 38 59 41 43 31

N.S.

1 1.00 1.06 0.97 1.06 1.64 1.14 1.19 0.86

time (sec)

N/A 0.014 0.024 0.207 0.197 0.240 0.056 0.287 0.043

Problem 162

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

35 35 31 28 31 48 29 40 34

N.S.

1 1.00 0.89 0.80 0.89 1.37 0.83 1.14 0.97

time (sec)

N/A 0.012 0.019 0.237 0.188 0.250 0.053 0.312 0.257

Problem 163

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

61 61 46 40 50 85 51 42 45

N.S.

1 1.00 0.75 0.66 0.82 1.39 0.84 0.69 0.74

time (sec)

N/A 0.013 0.025 0.243 0.205 0.246 0.069 0.284 0.137

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

51 51 36 36 44 62 42 34 39

N.S.

1 1.00 0.71 0.71 0.86 1.22 0.82 0.67 0.76

time (sec)

N/A 0.012 0.018 0.546 0.282 0.240 0.071 0.277 0.254

Problem 165

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

54 54 54 45 60 105 58 47 55

N.S.

1 1.00 1.00 0.83 1.11 1.94 1.07 0.87 1.02

time (sec)

N/A 0.019 0.018 0.196 0.191 0.235 0.069 0.279 0.060

Problem 166

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

36 42 53 32 40 53 49 48 33

N.S.

1 1.17 1.47 0.89 1.11 1.47 1.36 1.33 0.92

time (sec)

N/A 0.015 0.040 0.226 0.275 0.244 0.036 0.301 0.273

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

58 58 40 31 41 59 39 31 40

N.S.

1 1.00 0.69 0.53 0.71 1.02 0.67 0.53 0.69

time (sec)

N/A 0.011 0.021 0.237 0.291 0.241 0.051 0.281 0.077

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

43 43 43 34 36 45 42 36 36

N.S.

1 1.00 1.00 0.79 0.84 1.05 0.98 0.84 0.84

time (sec)

N/A 0.021 0.037 0.856 0.289 0.244 0.061 0.279 0.222

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

43 43 62 37 47 68 58 51 34

N.S.

1 1.00 1.44 0.86 1.09 1.58 1.35 1.19 0.79

time (sec)

N/A 0.020 0.041 0.313 0.291 0.232 0.061 0.289 0.262

Problem 170

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

37 37 25 27 30 38 24 40 32

N.S.

1 1.00 0.68 0.73 0.81 1.03 0.65 1.08 0.86

time (sec)

N/A 0.010 0.013 0.247 0.284 0.239 0.059 0.309 0.039

Problem 171

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

32 39 26 29 28 38 26 32 28

N.S.

1 1.22 0.81 0.91 0.88 1.19 0.81 1.00 0.88

time (sec)

N/A 0.020 0.017 0.183 0.205 0.230 0.047 0.485 0.223

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

13 13 13 12 11 19 20 11 11

N.S.

1 1.00 1.00 0.92 0.85 1.46 1.54 0.85 0.85

time (sec)

N/A 0.003 0.005 0.217 0.205 0.230 0.115 0.275 0.229

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

54 54 46 45 57 81 51 56 52

N.S.

1 1.00 0.85 0.83 1.06 1.50 0.94 1.04 0.96

time (sec)

N/A 0.026 0.027 0.221 0.195 0.245 0.219 0.310 0.115

Problem 174

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 157 134 75 147 227 66 150 76

N.S.

1 1.00 0.85 0.48 0.94 1.45 0.42 0.96 0.48

time (sec)

N/A 0.087 0.112 0.273 0.275 0.239 0.205 0.294 0.148

Problem 175

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A C A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 75 53 60 78 78 50 53

N.S.

1 1.00 1.17 0.83 0.94 1.22 1.22 0.78 0.83

time (sec)

N/A 0.027 0.051 0.279 0.288 0.236 0.226 0.294 0.263

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

39 39 33 29 34 45 27 30 29

N.S.

1 1.00 0.85 0.74 0.87 1.15 0.69 0.77 0.74

time (sec)

N/A 0.024 0.016 0.215 0.190 0.225 0.058 0.320 0.051

Problem 177

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A C A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

319 319 293 47 335 1751 37 250 285

N.S.

1 1.00 0.92 0.15 1.05 5.49 0.12 0.78 0.89

time (sec)

N/A 0.509 0.351 0.247 0.280 2.695 0.113 0.590 1.704

Problem 178

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 59 65 39 56 73 58 55 41

N.S.

1 1.00 1.10 0.66 0.95 1.24 0.98 0.93 0.69

time (sec)

N/A 0.016 0.074 0.222 0.301 0.232 0.070 0.292 0.275

Problem 179

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

36 36 33 29 31 40 32 28 29

N.S.

1 1.00 0.92 0.81 0.86 1.11 0.89 0.78 0.81

time (sec)

N/A 0.020 0.016 0.228 0.292 0.237 0.059 0.301 0.004

Problem 180

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

38 38 32 31 38 65 36 35 33

N.S.

1 1.00 0.84 0.82 1.00 1.71 0.95 0.92 0.87

time (sec)

N/A 0.050 0.025 0.050 0.221 0.226 0.057 0.288 0.070

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

64 64 65 50 50 73 60 60 63

N.S.

1 1.00 1.02 0.78 0.78 1.14 0.94 0.94 0.98

time (sec)

N/A 0.062 0.032 0.225 0.301 0.238 0.098 0.307 0.111

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

63 63 63 54 59 97 68 72 73

N.S.

1 1.00 1.00 0.86 0.94 1.54 1.08 1.14 1.16

time (sec)

N/A 0.106 0.039 0.471 0.279 0.248 0.083 0.303 0.284

Problem 183

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

43 43 46 32 36 55 34 33 25

N.S.

1 1.00 1.07 0.74 0.84 1.28 0.79 0.77 0.58

time (sec)

N/A 0.014 0.020 0.226 0.198 0.234 0.068 0.290 0.059

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

27 27 20 18 43 43 39 18 18

N.S.

1 1.00 0.74 0.67 1.59 1.59 1.44 0.67 0.67

time (sec)

N/A 0.016 0.011 0.210 0.202 0.229 0.067 0.302 0.119

Problem 185

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

46 46 44 34 39 55 36 40 34

N.S.

1 1.00 0.96 0.74 0.85 1.20 0.78 0.87 0.74

time (sec)

N/A 0.022 0.018 0.200 0.185 0.225 0.045 0.306 0.220

Problem 186

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

44 50 39 35 37 56 34 43 33

N.S.

1 1.14 0.89 0.80 0.84 1.27 0.77 0.98 0.75

time (sec)

N/A 0.012 0.024 0.200 0.189 0.230 0.061 0.288 0.050

Problem 187

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

54 54 54 45 60 105 58 47 55

N.S.

1 1.00 1.00 0.83 1.11 1.94 1.07 0.87 1.02

time (sec)

N/A 0.012 0.009 0.187 0.186 0.233 0.069 0.278 0.002

Problem 188

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

36 36 36 33 32 39 31 45 32

N.S.

1 1.00 1.00 0.92 0.89 1.08 0.86 1.25 0.89

time (sec)

N/A 0.011 0.015 0.182 0.182 0.237 0.025 0.299 0.002

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

44 44 41 38 38 38 39 39 37

N.S.

1 1.00 0.93 0.86 0.86 0.86 0.89 0.89 0.84

time (sec)

N/A 0.029 0.013 0.074 0.182 0.241 0.021 0.299 0.049

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

96 96 91 89 91 91 100 98 88

N.S.

1 1.00 0.95 0.93 0.95 0.95 1.04 1.02 0.92

time (sec)

N/A 0.091 0.030 0.362 0.194 0.234 0.022 0.277 0.218

Problem 191

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

167 167 167 165 171 171 189 188 164

N.S.

1 1.00 1.00 0.99 1.02 1.02 1.13 1.13 0.98

time (sec)

N/A 0.148 0.032 0.342 0.180 0.223 0.030 0.288 0.242

Problem 192

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

263 263 263 264 273 273 313 307 263

N.S.

1 1.00 1.00 1.00 1.04 1.04 1.19 1.17 1.00

time (sec)

N/A 0.268 0.061 0.350 0.189 0.246 0.036 0.282 0.294

Problem 193

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

159 159 267 0 0 0 0 0 0

N.S.

1 1.00 1.68 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.076 0.673 0.000 0.000 0.000 0.000 0.000 0.000

Problem 194

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

65 65 66 63 0 203 246 60 155

N.S.

1 1.00 1.02 0.97 0.00 3.12 3.78 0.92 2.38

time (sec)

N/A 0.035 0.046 0.463 0.000 0.248 0.401 0.293 0.308

Problem 195

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

89 89 88 103 0 447 323 92 159

N.S.

1 1.00 0.99 1.16 0.00 5.02 3.63 1.03 1.79

time (sec)

N/A 0.051 0.073 0.464 0.000 0.259 0.522 0.292 0.304

Problem 196

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

130 130 127 155 0 1104 622 194 360

N.S.

1 1.00 0.98 1.19 0.00 8.49 4.78 1.49 2.77

time (sec)

N/A 0.061 0.127 0.457 0.000 0.269 0.996 0.289 0.528

Problem 197

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

173 173 168 206 0 1950 1027 363 640

N.S.

1 1.00 0.97 1.19 0.00 11.27 5.94 2.10 3.70

time (sec)

N/A 0.095 0.190 0.478 0.000 0.298 1.528 0.306 0.728

Problem 198

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

169 169 264 0 0 0 0 0 0

N.S.

1 1.00 1.56 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.065 0.791 0.000 0.000 0.000 0.000 0.000 0.000

Problem 199

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

49 49 44 31 41 52 46 46 36

N.S.

1 1.00 0.90 0.63 0.84 1.06 0.94 0.94 0.73

time (sec)

N/A 0.014 0.026 0.263 0.262 0.232 0.041 0.294 0.176

Problem 200

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

61 61 70 56 67 97 76 61 53

N.S.

1 1.00 1.15 0.92 1.10 1.59 1.25 1.00 0.87

time (sec)

N/A 0.018 0.051 0.261 0.278 0.239 0.066 0.290 0.249

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