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Integrals 1 to 100

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 1

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

80 80 74 71 72 188 156 71 62

N.S.

1 1.00 0.92 0.89 0.90 2.35 1.95 0.89 0.78

time (sec)

N/A 0.029 0.032 0.652 0.314 0.318 31.797 0.308 1.234

Problem 2

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 59 57 55 57 65 97 51

N.S.

1 1.00 1.00 0.97 0.93 0.97 1.10 1.64 0.86

time (sec)

N/A 0.033 0.012 0.382 0.197 0.317 0.812 0.293 1.228

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 66 62 60 59 152 141 59 50

N.S.

1 1.00 0.94 0.91 0.89 2.30 2.14 0.89 0.76

time (sec)

N/A 0.025 0.017 0.428 0.280 0.341 7.766 0.296 1.239

Problem 4

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 34 37 44 40 51 43 39

N.S.

1 1.00 0.97 1.06 1.26 1.14 1.46 1.23 1.11

time (sec)

N/A 0.018 0.007 0.452 0.205 0.311 0.293 0.275 1.295

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 45 46 45 107 100 41 37

N.S.

1 1.00 1.00 1.02 1.00 2.38 2.22 0.91 0.82

time (sec)

N/A 0.013 0.009 0.279 0.287 0.330 2.010 0.282 1.233

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 43 110 80 0 0 0 0

N.S.

1 1.00 0.98 2.50 1.82 0.00 0.00 0.00 0.00

time (sec)

N/A 0.031 0.007 0.227 0.199 0.000 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 44 37 36 105 258 40 36

N.S.

1 1.00 1.00 0.84 0.82 2.39 5.86 0.91 0.82

time (sec)

N/A 0.013 0.008 0.305 0.275 0.311 7.755 0.315 1.246

Problem 8

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 45 45 42 44 43 65 58 41

N.S.

1 1.18 1.18 1.11 1.16 1.13 1.71 1.53 1.08

time (sec)

N/A 0.025 0.004 0.246 0.191 0.303 0.900 0.297 1.245

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 60 49 52 49 135 496 58 46

N.S.

1 1.00 0.82 0.87 0.82 2.25 8.27 0.97 0.77

time (sec)

N/A 0.019 0.004 0.549 0.293 0.302 38.768 0.398 1.230

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 56 54 54 58 83 132 56

N.S.

1 1.00 0.88 0.84 0.84 0.91 1.30 2.06 0.88

time (sec)

N/A 0.034 0.028 0.416 0.205 0.304 2.630 0.305 1.240

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 49 61 62 170 583 71 61

N.S.

1 1.00 0.66 0.82 0.84 2.30 7.88 0.96 0.82

time (sec)

N/A 0.023 0.004 0.941 0.281 0.321 162.331 0.296 1.323

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 78 75 66 69 71 97 191 68

N.S.

1 1.00 0.96 0.85 0.88 0.91 1.24 2.45 0.87

time (sec)

N/A 0.039 0.021 0.769 0.200 0.298 6.674 0.285 1.267

Problem 13

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 59 57 55 57 65 97 51

N.S.

1 1.00 1.00 0.97 0.93 0.97 1.10 1.64 0.86

time (sec)

N/A 0.033 0.012 0.784 0.198 0.285 2.421 0.280 1.288

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 159 69 139 147 161 0 162 157

N.S.

1 1.00 0.43 0.87 0.92 1.01 0.00 1.02 0.99

time (sec)

N/A 0.091 0.004 0.870 0.288 0.301 0.000 0.332 3.705

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

157 157 147 136 144 144 0 160 129

N.S.

1 1.00 0.94 0.87 0.92 0.92 0.00 1.02 0.82

time (sec)

N/A 0.085 0.040 0.665 0.286 0.283 0.000 0.365 3.839

Problem 16

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 34 37 44 40 51 43 39

N.S.

1 1.00 0.97 1.06 1.26 1.14 1.46 1.23 1.11

time (sec)

N/A 0.021 0.008 0.513 0.198 0.271 0.636 0.338 1.295

Problem 17

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

147 147 53 128 131 150 178 150 121

N.S.

1 1.00 0.36 0.87 0.89 1.02 1.21 1.02 0.82

time (sec)

N/A 0.059 0.004 0.497 0.291 0.317 57.146 0.316 3.609

Problem 18

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

133 133 129 122 125 110 165 143 134

N.S.

1 1.00 0.97 0.92 0.94 0.83 1.24 1.08 1.01

time (sec)

N/A 0.054 0.027 0.388 0.279 0.331 24.860 0.297 1.675

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 43 55 80 0 0 0 0

N.S.

1 1.00 0.98 1.25 1.82 0.00 0.00 0.00 0.00

time (sec)

N/A 0.031 0.006 0.322 0.199 0.000 0.000 0.000 0.000

Problem 20

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

133 133 47 113 119 126 165 137 149

N.S.

1 1.00 0.35 0.85 0.89 0.95 1.24 1.03 1.12

time (sec)

N/A 0.049 0.004 0.437 0.284 0.354 108.289 0.295 1.911

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 139 134 113 120 150 0 138 115

N.S.

1 1.00 0.96 0.81 0.86 1.08 0.00 0.99 0.83

time (sec)

N/A 0.048 0.024 0.494 0.282 0.331 0.000 0.296 3.803

Problem 22

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 45 42 44 43 65 58 41

N.S.

1 1.00 1.00 0.93 0.98 0.96 1.44 1.29 0.91

time (sec)

N/A 0.026 0.004 0.405 0.194 0.321 1.802 0.293 1.339

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

151 151 49 128 127 138 0 153 125

N.S.

1 1.00 0.32 0.85 0.84 0.91 0.00 1.01 0.83

time (sec)

N/A 0.060 0.004 0.934 0.284 0.357 0.000 0.308 3.346

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

151 151 49 128 128 172 0 149 156

N.S.

1 1.00 0.32 0.85 0.85 1.14 0.00 0.99 1.03

time (sec)

N/A 0.060 0.004 1.310 0.283 0.342 0.000 0.319 3.663

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 56 54 54 58 83 132 56

N.S.

1 1.00 0.88 0.84 0.84 0.91 1.30 2.06 0.88

time (sec)

N/A 0.034 0.027 1.084 0.212 0.340 7.053 0.304 1.324

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 89 85 74 74 89 100 308 77

N.S.

1 1.00 0.96 0.83 0.83 1.00 1.12 3.46 0.87

time (sec)

N/A 0.035 0.037 0.398 0.192 0.295 2.513 0.322 1.277

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 75 74 63 64 77 87 257 65

N.S.

1 1.00 0.99 0.84 0.85 1.03 1.16 3.43 0.87

time (sec)

N/A 0.027 0.023 0.161 0.197 0.330 1.375 0.332 1.258

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 61 62 52 51 64 73 210 53

N.S.

1 1.00 1.02 0.85 0.84 1.05 1.20 3.44 0.87

time (sec)

N/A 0.021 0.019 0.114 0.206 0.316 0.841 0.327 1.313

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 40 41 40 50 60 152 41

N.S.

1 1.00 0.85 0.87 0.85 1.06 1.28 3.23 0.87

time (sec)

N/A 0.014 0.014 0.098 0.203 0.363 0.519 0.311 1.293

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 37 28 27 33 36 96 27

N.S.

1 1.00 1.37 1.04 1.00 1.22 1.33 3.56 1.00

time (sec)

N/A 0.006 0.003 0.072 0.204 0.360 0.290 0.337 1.287

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

40 40 41 67 83 0 0 152 0

N.S.

1 1.00 1.02 1.68 2.08 0.00 0.00 3.80 0.00

time (sec)

N/A 0.024 0.004 0.117 0.199 0.000 0.000 0.408 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 30 37 50 36 37 63 40

N.S.

1 1.00 1.00 1.23 1.67 1.20 1.23 2.10 1.33

time (sec)

N/A 0.015 0.006 0.269 0.193 0.309 0.464 0.306 1.772

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 59 63 63 55 61 150 53

N.S.

1 1.00 1.00 1.07 1.07 0.93 1.03 2.54 0.90

time (sec)

N/A 0.023 0.012 0.140 0.186 0.312 0.800 0.308 1.420

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 73 75 74 66 75 234 65

N.S.

1 1.00 1.00 1.03 1.01 0.90 1.03 3.21 0.89

time (sec)

N/A 0.033 0.016 0.185 0.189 0.340 1.033 0.320 1.475

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 87 87 85 85 79 88 317 78

N.S.

1 1.00 1.00 0.98 0.98 0.91 1.01 3.64 0.90

time (sec)

N/A 0.039 0.018 0.247 0.196 0.332 1.523 0.308 1.506

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 49 60 59 178 148 75 56

N.S.

1 1.00 0.68 0.83 0.82 2.47 2.06 1.04 0.78

time (sec)

N/A 0.026 0.006 0.670 0.274 0.309 32.991 0.306 1.366

Problem 37

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 56 46 44 56 66 59 45

N.S.

1 1.00 1.10 0.90 0.86 1.10 1.29 1.16 0.88

time (sec)

N/A 0.024 0.015 0.253 0.192 0.287 1.281 0.331 1.322

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

58 58 47 49 48 141 133 63 44

N.S.

1 1.00 0.81 0.84 0.83 2.43 2.29 1.09 0.76

time (sec)

N/A 0.018 0.003 0.265 0.273 0.301 11.200 0.299 1.335

Problem 39

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 45 34 33 42 53 47 33

N.S.

1 1.00 1.22 0.92 0.89 1.14 1.43 1.27 0.89

time (sec)

N/A 0.010 0.004 0.125 0.194 0.324 0.593 0.293 1.339

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 43 34 33 107 95 42 33

N.S.

1 1.00 1.05 0.83 0.80 2.61 2.32 1.02 0.80

time (sec)

N/A 0.010 0.007 0.128 0.277 0.345 3.582 0.299 0.097

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 44 45 126 89 0 0 0 0

N.S.

1 1.00 1.02 2.86 2.02 0.00 0.00 0.00 0.00

time (sec)

N/A 0.027 0.004 0.098 0.189 0.000 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 52 52 49 119 97 54 42

N.S.

1 1.00 1.04 1.04 0.98 2.38 1.94 1.08 0.84

time (sec)

N/A 0.019 0.011 0.196 0.282 0.306 8.310 0.304 1.439

Problem 43

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 34 37 54 41 53 57 47

N.S.

1 1.00 0.97 1.06 1.54 1.17 1.51 1.63 1.34

time (sec)

N/A 0.020 0.007 0.410 0.208 0.269 0.802 0.298 1.387

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

68 68 70 61 62 154 138 73 55

N.S.

1 1.00 1.03 0.90 0.91 2.26 2.03 1.07 0.81

time (sec)

N/A 0.024 0.017 0.434 0.281 0.353 24.503 0.371 1.338

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A C B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

8 8 34 9 35 11 8 110 8

N.S.

1 1.00 4.25 1.12 4.38 1.38 1.00 13.75 1.00

time (sec)

N/A 0.005 0.006 0.286 0.200 0.317 1.517 0.446 1.445

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 153 133 121 120 129 146 339 121

N.S.

1 1.00 0.87 0.79 0.78 0.84 0.95 2.22 0.79

time (sec)

N/A 0.081 0.084 0.519 0.195 0.324 12.254 0.301 1.382

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 123 112 99 98 105 119 255 97

N.S.

1 1.00 0.91 0.80 0.80 0.85 0.97 2.07 0.79

time (sec)

N/A 0.057 0.038 0.395 0.204 0.333 3.255 0.283 1.331

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 93 88 77 76 80 92 171 73

N.S.

1 1.00 0.95 0.83 0.82 0.86 0.99 1.84 0.78

time (sec)

N/A 0.040 0.025 0.357 0.210 0.301 1.026 0.345 1.404

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

53 53 53 52 50 51 61 97 47

N.S.

1 1.00 1.00 0.98 0.94 0.96 1.15 1.83 0.89

time (sec)

N/A 0.020 0.018 0.254 0.196 0.295 0.507 0.294 0.125

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 46 47 58 79 0 0 0 0

N.S.

1 1.00 1.02 1.26 1.72 0.00 0.00 0.00 0.00

time (sec)

N/A 0.028 0.004 0.358 0.200 0.000 0.000 0.000 0.000

Problem 51

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

63 63 55 54 53 55 352 132 49

N.S.

1 1.00 0.87 0.86 0.84 0.87 5.59 2.10 0.78

time (sec)

N/A 0.031 0.029 0.252 0.201 0.325 10.997 0.308 1.749

Problem 52

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

100 100 90 77 76 84 435 232 72

N.S.

1 1.00 0.90 0.77 0.76 0.84 4.35 2.32 0.72

time (sec)

N/A 0.040 0.032 0.230 0.201 0.343 90.875 0.305 1.571

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

130 130 114 99 98 109 0 324 97

N.S.

1 1.00 0.88 0.76 0.75 0.84 0.00 2.49 0.75

time (sec)

N/A 0.053 0.042 0.259 0.197 0.341 0.000 0.307 1.746

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 33 32 31 28 156 31 33

N.S.

1 1.00 1.03 1.00 0.97 0.88 4.88 0.97 1.03

time (sec)

N/A 0.012 0.009 0.210 0.194 0.297 0.240 0.283 1.458

Problem 55

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

81 81 70 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 0.030 0.021 0.000 0.000 0.000 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

81 81 70 0 0 0 377 0 0

N.S.

1 1.00 0.86 0.00 0.00 0.00 4.65 0.00 0.00

time (sec)

N/A 0.029 0.021 0.000 0.000 0.000 29.453 0.000 0.000

Problem 57

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

69 69 56 0 0 0 0 0 0

N.S.

1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.021 0.021 0.000 0.000 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

67 67 56 0 0 0 231 0 0

N.S.

1 1.00 0.84 0.00 0.00 0.00 3.45 0.00 0.00

time (sec)

N/A 0.028 0.014 0.000 0.000 0.000 9.209 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

82 82 76 0 0 0 366 0 0

N.S.

1 1.00 0.93 0.00 0.00 0.00 4.46 0.00 0.00

time (sec)

N/A 0.037 0.022 0.000 0.000 0.000 28.763 0.000 0.000

Problem 60

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

85 85 76 0 0 0 0 0 0

N.S.

1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.039 0.022 0.000 0.000 0.000 0.000 0.000 0.000

Problem 61

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 83 76 0 0 0 0 0 0

N.S.

1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.034 0.026 0.000 0.000 0.000 0.000 0.000 0.000

Problem 62

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

70 70 77 0 0 0 0 0 0

N.S.

1 1.00 1.10 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.030 0.028 0.000 0.000 0.000 0.000 0.000 0.000

Problem 63

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

87 87 77 0 0 0 0 0 0

N.S.

1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.029 0.027 0.000 0.000 0.000 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

141 141 92 0 115 112 0 0 0

N.S.

1 1.00 0.65 0.00 0.82 0.79 0.00 0.00 0.00

time (sec)

N/A 0.050 0.057 0.000 0.229 0.291 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

112 112 74 0 95 92 0 0 0

N.S.

1 1.00 0.66 0.00 0.85 0.82 0.00 0.00 0.00

time (sec)

N/A 0.049 0.032 0.000 0.203 0.304 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

69 69 48 0 70 57 0 0 0

N.S.

1 1.00 0.70 0.00 1.01 0.83 0.00 0.00 0.00

time (sec)

N/A 0.028 0.024 0.000 0.203 0.316 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

50 50 46 182 0 63 0 0 0

N.S.

1 1.00 0.92 3.64 0.00 1.26 0.00 0.00 0.00

time (sec)

N/A 0.032 0.007 1.278 0.000 0.311 0.000 0.000 0.000

Problem 68

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

80 80 57 0 71 75 0 0 0

N.S.

1 1.00 0.71 0.00 0.89 0.94 0.00 0.00 0.00

time (sec)

N/A 0.025 0.014 0.000 0.214 0.310 0.000 0.000 0.000

Problem 69

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

120 120 76 0 99 104 0 0 0

N.S.

1 1.00 0.63 0.00 0.82 0.87 0.00 0.00 0.00

time (sec)

N/A 0.037 0.034 0.000 0.196 0.302 0.000 0.000 0.000

Problem 70

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

65 65 61 0 0 0 128 0 0

N.S.

1 1.00 0.94 0.00 0.00 0.00 1.97 0.00 0.00

time (sec)

N/A 0.019 0.024 0.000 0.000 0.000 5.885 0.000 0.000

Problem 71

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

65 65 61 0 0 0 128 0 0

N.S.

1 1.00 0.94 0.00 0.00 0.00 1.97 0.00 0.00

time (sec)

N/A 0.019 0.024 0.000 0.000 0.000 2.884 0.000 0.000

Problem 72

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

54 54 52 0 0 0 76 0 0

N.S.

1 1.00 0.96 0.00 0.00 0.00 1.41 0.00 0.00

time (sec)

N/A 0.014 0.022 0.000 0.000 0.000 1.515 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

44 44 43 170 0 60 0 0 0

N.S.

1 1.00 0.98 3.86 0.00 1.36 0.00 0.00 0.00

time (sec)

N/A 0.028 0.001 1.089 0.000 0.342 0.000 0.000 0.000

Problem 74

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

66 66 59 0 0 0 73 0 0

N.S.

1 1.00 0.89 0.00 0.00 0.00 1.11 0.00 0.00

time (sec)

N/A 0.023 0.027 0.000 0.000 0.000 3.458 0.000 0.000

Problem 75

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

72 72 62 0 0 0 78 0 0

N.S.

1 1.00 0.86 0.00 0.00 0.00 1.08 0.00 0.00

time (sec)

N/A 0.023 0.022 0.000 0.000 0.000 6.767 0.000 0.000

Problem 76

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

70 70 62 0 0 0 78 0 0

N.S.

1 1.00 0.89 0.00 0.00 0.00 1.11 0.00 0.00

time (sec)

N/A 0.022 0.021 0.000 0.000 0.000 14.169 0.000 0.000

Problem 77

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

215 215 127 190 145 189 182 370 126

N.S.

1 1.00 0.59 0.88 0.67 0.88 0.85 1.72 0.59

time (sec)

N/A 0.195 0.067 0.910 0.213 0.312 3.223 0.296 1.406

Problem 78

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

145 145 105 151 120 148 139 216 100

N.S.

1 1.00 0.72 1.04 0.83 1.02 0.96 1.49 0.69

time (sec)

N/A 0.111 0.040 1.333 0.202 0.358 1.272 0.315 1.424

Problem 79

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 63 105 97 96 90 96 70

N.S.

1 1.00 1.03 1.72 1.59 1.57 1.48 1.57 1.15

time (sec)

N/A 0.037 0.007 0.651 0.195 0.311 0.481 0.296 1.298

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

72 72 163 0 118 0 0 0 0

N.S.

1 1.00 2.26 0.00 1.64 0.00 0.00 0.00 0.00

time (sec)

N/A 0.076 0.083 0.000 0.210 0.000 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

80 80 93 481 118 0 0 0 0

N.S.

1 1.00 1.16 6.01 1.48 0.00 0.00 0.00 0.00

time (sec)

N/A 0.054 0.019 0.383 0.202 0.000 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

129 129 141 554 142 0 0 0 0

N.S.

1 1.00 1.09 4.29 1.10 0.00 0.00 0.00 0.00

time (sec)

N/A 0.157 0.057 0.641 0.199 0.000 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

193 193 190 607 173 0 0 0 0

N.S.

1 1.00 0.98 3.15 0.90 0.00 0.00 0.00 0.00

time (sec)

N/A 0.241 0.057 1.303 0.200 0.000 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

336 336 248 612 0 0 0 0 0

N.S.

1 1.00 0.74 1.82 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.256 0.129 0.864 0.000 0.000 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

294 294 223 565 0 0 0 0 0

N.S.

1 1.00 0.76 1.92 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.212 0.087 0.591 0.000 0.000 0.000 0.000 0.000

Problem 86

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

237 237 193 0 0 0 0 0 0

N.S.

1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.169 0.062 0.000 0.000 0.000 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

190 190 173 446 0 0 0 0 0

N.S.

1 1.00 0.91 2.35 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.114 0.042 0.490 0.000 0.000 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

254 254 207 522 0 0 0 0 0

N.S.

1 1.00 0.81 2.06 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.202 0.066 0.556 0.000 0.000 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

296 296 294 568 0 0 0 0 0

N.S.

1 1.00 0.99 1.92 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.216 0.124 1.129 0.000 0.000 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

338 338 353 619 0 0 0 0 0

N.S.

1 1.00 1.04 1.83 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.252 0.150 1.924 0.000 0.000 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

334 334 178 289 239 359 289 662 187

N.S.

1 1.00 0.53 0.87 0.72 1.07 0.87 1.98 0.56

time (sec)

N/A 0.245 0.138 1.589 0.202 0.308 5.000 0.318 1.429

Problem 92

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

211 211 146 223 203 275 223 385 144

N.S.

1 1.00 0.69 1.06 0.96 1.30 1.06 1.82 0.68

time (sec)

N/A 0.143 0.083 11.034 0.201 0.325 2.075 0.292 1.449

Problem 93

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

93 93 87 151 164 176 143 169 103

N.S.

1 1.00 0.94 1.62 1.76 1.89 1.54 1.82 1.11

time (sec)

N/A 0.046 0.010 1.124 0.196 0.352 0.791 0.300 1.301

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

106 106 279 0 217 0 0 0 0

N.S.

1 1.00 2.63 0.00 2.05 0.00 0.00 0.00 0.00

time (sec)

N/A 0.104 0.106 0.000 0.212 0.000 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

119 119 302 0 202 0 0 0 0

N.S.

1 1.00 2.54 0.00 1.70 0.00 0.00 0.00 0.00

time (sec)

N/A 0.091 0.245 0.000 0.270 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

219 219 477 0 270 0 0 0 0

N.S.

1 1.00 2.18 0.00 1.23 0.00 0.00 0.00 0.00

time (sec)

N/A 0.248 0.280 0.000 0.278 0.000 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

352 352 571 0 338 0 0 0 0

N.S.

1 1.00 1.62 0.00 0.96 0.00 0.00 0.00 0.00

time (sec)

N/A 0.443 0.342 0.000 0.292 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A B N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 909 18 123 20 17 20 20

N.S.

1 1.00 50.50 1.00 6.83 1.11 0.94 1.11 1.11

time (sec)

N/A 0.532 3.127 0.039 1.121 0.297 3.881 0.379 1.275

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A B N/A N/A N/A N/A N/A N/A

verified

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

size

14 14 789 14 111 16 14 16 16

N.S.

1 1.00 56.36 1.00 7.93 1.14 1.00 1.14 1.14

time (sec)

N/A 0.281 2.667 0.035 0.850 0.324 1.871 0.353 1.305

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

18 18 505 18 0 20 17 20 20

N.S.

1 1.00 28.06 1.00 0.00 1.11 0.94 1.11 1.11

time (sec)

N/A 0.031 1.004 0.042 0.000 0.298 2.953 0.348 1.363

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