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2.2.1 Integrals 1 to 100

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 74 229 72 188 156 71 62

N.S.

1 1.00 0.92 2.86 0.90 2.35 1.95 0.89 0.78

time (sec)

N/A 0.029 0.035 0.373 0.487 0.427 34.420 3.512 0.221

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 59 1190 55 57 65 97 51

N.S.

1 1.00 1.00 20.17 0.93 0.97 1.10 1.64 0.86

time (sec)

N/A 0.034 0.011 0.334 0.273 0.372 0.893 4.791 0.224

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 62 217 59 152 141 59 50

N.S.

1 1.00 0.94 3.29 0.89 2.30 2.14 0.89 0.76

time (sec)

N/A 0.025 0.018 0.305 0.495 0.410 8.501 3.392 0.228

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD 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 0.008 0.478 0.266 0.426 0.314 4.784 0.226

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD 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 0.269 0.497 0.401 2.173 4.195 0.224

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

44 44 43 232 80 0 0 0 -1

N.S.

1 1.00 0.98 5.27 1.82 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.031 0.006 0.267 0.280 0.000 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

44 44 44 195 36 105 245 40 36

N.S.

1 1.00 1.00 4.43 0.82 2.39 5.57 0.91 0.82

time (sec)

N/A 0.014 0.008 0.217 0.507 0.419 7.954 4.067 0.221

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

38 45 45 173 44 43 65 58 41

N.S.

1 1.18 1.18 4.55 1.16 1.13 1.71 1.53 1.08

time (sec)

N/A 0.026 0.003 0.217 0.277 0.382 1.090 5.851 0.245

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 49 211 49 135 479 58 46

N.S.

1 1.00 0.82 3.52 0.82 2.25 7.98 0.97 0.77

time (sec)

N/A 0.018 0.003 0.315 0.487 0.411 40.551 4.615 0.252

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 56 198 54 58 83 132 56

N.S.

1 1.00 0.88 3.09 0.84 0.91 1.30 2.06 0.88

time (sec)

N/A 0.036 0.029 0.208 0.275 0.381 3.077 4.399 0.259

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

74 74 49 236 62 170 566 71 61

N.S.

1 1.00 0.66 3.19 0.84 2.30 7.65 0.96 0.82

time (sec)

N/A 0.024 0.003 0.358 0.477 0.394 169.059 3.531 0.261

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

78 78 68 206 69 71 97 191 68

N.S.

1 1.00 0.87 2.64 0.88 0.91 1.24 2.45 0.87

time (sec)

N/A 0.043 0.047 0.261 0.270 0.385 8.345 3.650 0.257

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 59 1190 55 57 65 97 51

N.S.

1 1.00 1.00 20.17 0.93 0.97 1.10 1.64 0.86

time (sec)

N/A 0.034 0.011 0.390 0.281 0.378 2.951 5.621 0.239

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

159 159 69 196 147 161 0 162 157

N.S.

1 1.00 0.43 1.23 0.92 1.01 0.00 1.02 0.99

time (sec)

N/A 0.082 0.004 0.413 0.499 0.400 0.000 2.857 2.503

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

157 157 147 194 144 144 0 160 129

N.S.

1 1.00 0.94 1.24 0.92 0.92 0.00 1.02 0.82

time (sec)

N/A 0.076 0.035 0.362 0.502 0.395 0.000 6.140 2.555

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD 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 0.007 0.471 0.286 0.383 0.828 2.810 0.232

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

147 147 53 184 131 150 178 150 121

N.S.

1 1.00 0.36 1.25 0.89 1.02 1.21 1.02 0.82

time (sec)

N/A 0.059 0.003 0.401 0.494 0.363 63.477 4.443 2.378

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD 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 0.058 0.026 0.359 0.501 0.394 27.612 3.493 0.458

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

44 44 43 180 80 0 0 0 -1

N.S.

1 1.00 0.98 4.09 1.82 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.032 0.006 0.302 0.270 0.000 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C C A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

133 133 47 184 119 126 165 137 149

N.S.

1 1.00 0.35 1.38 0.89 0.95 1.24 1.03 1.12

time (sec)

N/A 0.051 0.003 0.251 0.507 0.378 117.591 5.587 0.810

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 139 134 197 120 150 0 138 115

N.S.

1 1.00 0.96 1.42 0.86 1.08 0.00 0.99 0.83

time (sec)

N/A 0.056 0.024 0.324 0.511 0.399 0.000 3.898 2.606

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

45 45 45 173 44 43 65 58 41

N.S.

1 1.00 1.00 3.84 0.98 0.96 1.44 1.29 0.91

time (sec)

N/A 0.026 0.003 0.225 0.280 0.387 2.356 4.697 0.259

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

151 151 49 215 127 138 0 153 125

N.S.

1 1.00 0.32 1.42 0.84 0.91 0.00 1.01 0.83

time (sec)

N/A 0.063 0.003 0.301 0.499 0.363 0.000 3.736 2.361

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

151 151 49 216 128 172 0 149 156

N.S.

1 1.00 0.32 1.43 0.85 1.14 0.00 0.99 1.03

time (sec)

N/A 0.064 0.003 0.314 0.510 0.374 0.000 4.632 2.446

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

64 64 56 198 54 58 83 132 56

N.S.

1 1.00 0.88 3.09 0.84 0.91 1.30 2.06 0.88

time (sec)

N/A 0.035 0.028 0.260 0.274 0.391 9.269 5.685 0.284

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

89 89 85 0 74 89 100 308 77

N.S.

1 1.00 0.96 0.00 0.83 1.00 1.12 3.46 0.87

time (sec)

N/A 0.036 0.037 0.053 0.287 0.389 2.385 5.220 0.241

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

75 75 74 0 64 77 87 257 65

N.S.

1 1.00 0.99 0.00 0.85 1.03 1.16 3.43 0.87

time (sec)

N/A 0.028 0.024 0.043 0.282 0.369 1.348 3.927 0.214

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

61 61 62 0 51 64 73 210 53

N.S.

1 1.00 1.02 0.00 0.84 1.05 1.20 3.44 0.87

time (sec)

N/A 0.022 0.019 0.045 0.281 0.360 0.792 5.177 0.228

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

47 47 40 0 40 50 60 152 41

N.S.

1 1.00 0.85 0.00 0.85 1.06 1.28 3.23 0.87

time (sec)

N/A 0.015 0.017 0.046 0.278 0.372 0.477 4.140 0.246

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

27 27 37 30 27 33 36 96 27

N.S.

1 1.00 1.37 1.11 1.00 1.22 1.33 3.56 1.00

time (sec)

N/A 0.006 0.003 0.069 0.274 0.364 0.280 4.378 0.205

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B F F B F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

40 40 41 0 83 0 0 152 -1

N.S.

1 1.00 1.02 0.00 2.08 0.00 0.00 3.80 -0.02

time (sec)

N/A 0.026 0.003 0.053 0.264 0.000 0.000 4.627 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD 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 0.016 0.005 0.285 0.287 0.385 0.522 5.197 0.681

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

59 59 59 0 63 55 61 150 53

N.S.

1 1.00 1.00 0.00 1.07 0.93 1.03 2.54 0.90

time (sec)

N/A 0.026 0.011 0.040 0.268 0.365 0.787 4.256 0.340

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

73 73 73 0 74 66 75 234 65

N.S.

1 1.00 1.00 0.00 1.01 0.90 1.03 3.21 0.89

time (sec)

N/A 0.034 0.014 0.053 0.276 0.381 1.399 5.721 0.321

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 87 0 85 79 88 317 78

N.S.

1 1.00 1.00 0.00 0.98 0.91 1.01 3.64 0.90

time (sec)

N/A 0.040 0.017 0.050 0.287 0.355 2.009 2.166 0.388

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 49 0 59 178 148 75 56

N.S.

1 1.00 0.68 0.00 0.82 2.47 2.06 1.04 0.78

time (sec)

N/A 0.027 0.006 0.074 0.513 0.373 33.557 4.453 0.263

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

51 51 56 0 44 56 66 59 45

N.S.

1 1.00 1.10 0.00 0.86 1.10 1.29 1.16 0.88

time (sec)

N/A 0.025 0.016 0.055 0.261 0.379 1.650 6.330 0.245

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

58 58 47 0 48 141 133 63 44

N.S.

1 1.00 0.81 0.00 0.83 2.43 2.29 1.09 0.76

time (sec)

N/A 0.019 0.003 0.044 0.495 0.379 10.997 6.091 0.241

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

37 37 45 0 33 42 53 47 33

N.S.

1 1.00 1.22 0.00 0.89 1.14 1.43 1.27 0.89

time (sec)

N/A 0.011 0.003 0.049 0.276 0.373 0.682 4.503 0.209

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

41 41 43 38 33 107 95 42 33

N.S.

1 1.00 1.05 0.93 0.80 2.61 2.32 1.02 0.80

time (sec)

N/A 0.010 0.006 0.058 0.563 0.401 3.787 4.151 0.106

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

44 44 45 0 89 0 0 0 -1

N.S.

1 1.00 1.02 0.00 2.02 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.029 0.003 0.053 0.272 0.000 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 52 0 49 119 97 54 42

N.S.

1 1.00 1.04 0.00 0.98 2.38 1.94 1.08 0.84

time (sec)

N/A 0.019 0.011 0.045 0.551 0.357 8.695 4.933 0.241

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD 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 0.018 0.007 0.306 0.281 0.368 1.048 3.276 0.236

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

68 68 70 0 62 154 138 73 55

N.S.

1 1.00 1.03 0.00 0.91 2.26 2.03 1.07 0.81

time (sec)

N/A 0.025 0.017 0.038 0.515 0.416 26.330 4.350 0.254

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B A B A C B B

verified

N/A Yes Yes TBD 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 0.004 0.330 0.277 0.387 1.583 2.993 0.257

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

153 153 134 0 120 129 146 339 121

N.S.

1 1.00 0.88 0.00 0.78 0.84 0.95 2.22 0.79

time (sec)

N/A 0.078 0.094 0.057 0.289 0.489 13.632 4.643 0.334

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

123 123 112 0 98 105 119 255 97

N.S.

1 1.00 0.91 0.00 0.80 0.85 0.97 2.07 0.79

time (sec)

N/A 0.060 0.039 0.037 0.299 0.425 4.370 3.727 0.277

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 88 0 76 80 92 171 73

N.S.

1 1.00 0.95 0.00 0.82 0.86 0.99 1.84 0.78

time (sec)

N/A 0.042 0.029 0.060 0.281 0.429 1.456 3.393 0.267

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A B B

verified

N/A Yes Yes TBD 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 0.277 0.270 0.372 0.755 4.464 0.124

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

46 46 47 0 79 0 0 0 -1

N.S.

1 1.00 1.02 0.00 1.72 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.027 0.003 0.042 0.283 0.000 0.000 0.000 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

63 63 55 0 53 55 326 132 49

N.S.

1 1.00 0.87 0.00 0.84 0.87 5.17 2.10 0.78

time (sec)

N/A 0.030 0.029 0.032 0.277 0.416 10.807 5.653 0.660

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

100 100 90 0 76 84 403 232 72

N.S.

1 1.00 0.90 0.00 0.76 0.84 4.03 2.32 0.72

time (sec)

N/A 0.044 0.032 0.029 0.353 0.401 64.493 3.993 0.460

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

130 130 114 0 98 109 0 324 97

N.S.

1 1.00 0.88 0.00 0.75 0.84 0.00 2.49 0.75

time (sec)

N/A 0.060 0.048 0.039 0.319 0.405 0.000 4.524 0.563

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

32 32 33 32 31 28 133 31 33

N.S.

1 1.00 1.03 1.00 0.97 0.88 4.16 0.97 1.03

time (sec)

N/A 0.012 0.008 0.285 0.317 0.382 0.239 2.464 0.276

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

81 81 70 0 0 0 0 0 -1

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.032 0.022 0.038 0.000 0.000 0.000 0.000 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

81 81 70 0 0 0 381 0 -1

N.S.

1 1.00 0.86 0.00 0.00 0.00 4.70 0.00 -0.01

time (sec)

N/A 0.030 0.021 0.035 0.000 0.000 31.778 0.000 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 56 0 0 0 0 0 -1

N.S.

1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.021 0.020 0.040 0.000 0.000 0.000 0.000 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

67 67 56 0 0 0 218 0 -1

N.S.

1 1.00 0.84 0.00 0.00 0.00 3.25 0.00 -0.01

time (sec)

N/A 0.030 0.013 0.077 0.000 0.000 10.208 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

82 82 76 0 0 0 369 0 -1

N.S.

1 1.00 0.93 0.00 0.00 0.00 4.50 0.00 -0.01

time (sec)

N/A 0.040 0.022 0.069 0.000 0.000 32.791 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F A F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

85 85 76 0 0 0 382 0 -1

N.S.

1 1.00 0.89 0.00 0.00 0.00 4.49 0.00 -0.01

time (sec)

N/A 0.042 0.024 0.072 0.000 0.000 232.750 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

83 83 76 0 0 0 0 0 -1

N.S.

1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.035 0.027 0.072 0.000 0.000 0.000 0.000 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 77 0 0 0 0 0 -1

N.S.

1 1.00 1.10 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.031 0.029 0.069 0.000 0.000 0.000 0.000 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

87 87 77 0 0 0 0 0 -1

N.S.

1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.030 0.029 0.055 0.000 0.000 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

141 141 92 0 115 109 0 0 -1

N.S.

1 1.00 0.65 0.00 0.82 0.77 0.00 0.00 -0.01

time (sec)

N/A 0.055 0.057 0.066 0.284 0.374 0.000 0.000 0.000

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 74 0 95 90 0 0 -1

N.S.

1 1.00 0.66 0.00 0.85 0.80 0.00 0.00 -0.01

time (sec)

N/A 0.040 0.032 0.051 0.285 0.393 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

69 69 48 0 70 60 0 0 -1

N.S.

1 1.00 0.70 0.00 1.01 0.87 0.00 0.00 -0.01

time (sec)

N/A 0.028 0.026 0.061 0.288 0.478 0.000 0.000 0.000

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

50 50 46 201 0 66 0 0 -1

N.S.

1 1.00 0.92 4.02 0.00 1.32 0.00 0.00 -0.02

time (sec)

N/A 0.033 0.007 1.453 0.000 0.374 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 57 0 71 78 0 0 -1

N.S.

1 1.00 0.71 0.00 0.89 0.98 0.00 0.00 -0.01

time (sec)

N/A 0.024 0.014 0.064 0.284 0.388 0.000 0.000 0.000

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 76 0 99 103 0 0 -1

N.S.

1 1.00 0.63 0.00 0.82 0.86 0.00 0.00 -0.01

time (sec)

N/A 0.038 0.036 0.055 0.280 0.415 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 61 0 0 0 104 0 -1

N.S.

1 1.00 0.94 0.00 0.00 0.00 1.60 0.00 -0.02

time (sec)

N/A 0.021 0.025 0.046 0.000 0.000 7.902 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

65 65 61 0 0 0 104 0 -1

N.S.

1 1.00 0.94 0.00 0.00 0.00 1.60 0.00 -0.02

time (sec)

N/A 0.018 0.025 0.047 0.000 0.000 3.683 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

54 54 52 0 0 0 48 0 -1

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.89 0.00 -0.02

time (sec)

N/A 0.014 0.023 0.048 0.000 0.000 1.769 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C F A F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

44 44 43 177 0 63 0 0 -1

N.S.

1 1.00 0.98 4.02 0.00 1.43 0.00 0.00 -0.02

time (sec)

N/A 0.027 0.004 1.233 0.000 0.376 0.000 0.000 0.000

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 59 0 0 0 46 0 -1

N.S.

1 1.00 0.89 0.00 0.00 0.00 0.70 0.00 -0.02

time (sec)

N/A 0.023 0.025 0.048 0.000 0.000 4.297 0.000 0.000

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 62 0 0 0 51 0 -1

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.71 0.00 -0.01

time (sec)

N/A 0.022 0.021 0.049 0.000 0.000 8.872 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

70 70 62 0 0 0 51 0 -1

N.S.

1 1.00 0.89 0.00 0.00 0.00 0.73 0.00 -0.01

time (sec)

N/A 0.022 0.022 0.036 0.000 0.000 19.772 0.000 0.000

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

215 215 200 1436 145 189 182 370 126

N.S.

1 1.00 0.93 6.68 0.67 0.88 0.85 1.72 0.59

time (sec)

N/A 0.196 0.049 0.444 0.280 0.364 4.194 2.941 0.308

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

145 145 105 24297 120 148 139 216 100

N.S.

1 1.00 0.72 167.57 0.83 1.02 0.96 1.49 0.69

time (sec)

N/A 0.110 0.041 1.581 0.312 0.387 1.539 6.025 0.259

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

61 61 63 1034 97 96 90 96 70

N.S.

1 1.00 1.03 16.95 1.59 1.57 1.48 1.57 1.15

time (sec)

N/A 0.033 0.008 0.691 0.281 0.364 0.588 3.775 0.229

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F A F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

72 72 163 0 118 0 0 0 -1

N.S.

1 1.00 2.26 0.00 1.64 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.074 0.079 0.046 0.297 0.000 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

80 80 93 841 118 0 0 0 -1

N.S.

1 1.00 1.16 10.51 1.48 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.057 0.019 0.323 0.279 0.000 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

129 129 137 1080 142 0 0 0 -1

N.S.

1 1.00 1.06 8.37 1.10 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.154 0.057 0.300 0.288 0.000 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

193 193 205 1289 173 0 0 0 -1

N.S.

1 1.00 1.06 6.68 0.90 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.245 0.041 0.351 0.289 0.000 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

336 336 248 0 0 0 0 0 -1

N.S.

1 1.00 0.74 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.259 0.138 0.064 0.000 0.000 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

294 294 223 0 0 0 0 0 -1

N.S.

1 1.00 0.76 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.215 0.093 0.042 0.000 0.000 0.000 0.000 0.000

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

237 237 193 0 0 0 0 0 -1

N.S.

1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.175 0.058 0.052 0.000 0.000 0.000 0.000 0.000

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

190 190 173 0 0 0 0 0 -1

N.S.

1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.115 0.040 0.049 0.000 0.000 0.000 0.000 0.000

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

254 254 207 0 0 0 0 0 -1

N.S.

1 1.00 0.81 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.190 0.066 0.046 0.000 0.000 0.000 0.000 0.000

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

296 296 277 0 0 0 0 0 -1

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.217 0.192 0.032 0.000 0.000 0.000 0.000 0.000

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A C F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

338 338 334 0 0 0 0 0 -1

N.S.

1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.250 0.161 0.036 0.000 0.000 0.000 0.000 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

334 334 309 5905 239 359 289 662 187

N.S.

1 1.00 0.93 17.68 0.72 1.07 0.87 1.98 0.56

time (sec)

N/A 0.242 0.139 1.308 0.288 0.398 6.588 4.590 0.356

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

211 211 237 241142 203 275 223 385 144

N.S.

1 1.00 1.12 1142.85 0.96 1.30 1.06 1.82 0.68

time (sec)

N/A 0.142 0.062 14.816 0.308 0.392 2.628 5.233 0.305

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

93 93 87 3925 164 176 143 169 103

N.S.

1 1.00 0.94 42.20 1.76 1.89 1.54 1.82 1.11

time (sec)

N/A 0.046 0.010 1.452 0.294 0.451 0.954 4.672 0.240

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F B F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

106 106 279 0 217 0 0 0 -1

N.S.

1 1.00 2.63 0.00 2.05 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.108 0.110 0.046 0.314 0.000 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F A F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

119 119 302 0 202 0 0 0 -1

N.S.

1 1.00 2.54 0.00 1.70 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.098 0.233 0.050 0.350 0.000 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A B F A F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

219 219 478 0 270 0 0 0 -1

N.S.

1 1.00 2.18 0.00 1.23 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.259 0.273 0.048 0.346 0.000 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F A F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

352 352 571 0 338 0 0 0 -1

N.S.

1 1.00 1.62 0.00 0.96 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.435 0.304 0.046 0.353 0.000 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

380 0 909 0 0 0 0 0 -1

N.S.

1 0.00 2.39 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.519 2.511 0.060 0.000 0.000 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A A

verified

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

size

290 0 789 0 0 0 0 0 -1

N.S.

1 0.00 2.72 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.274 2.262 0.043 0.000 0.000 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

51 0 505 0 0 0 0 0 -1

N.S.

1 0.00 9.90 0.00 0.00 0.00 0.00 0.00 -0.02

time (sec)

N/A 0.029 0.585 0.044 0.000 0.000 0.000 0.000 0.000

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