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2.2.1 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 F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 90 56 73 95 99 0 110 130

N.S.

1 1.06 0.66 0.86 1.12 1.16 0.00 1.29 1.53

time (sec)

N/A 0.469 0.202 0.836 0.227 0.293 0.000 0.315 16.106

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 64 60 60 70 88 0 96 102

N.S.

1 1.02 0.95 0.95 1.11 1.40 0.00 1.52 1.62

time (sec)

N/A 0.390 0.144 0.607 0.233 0.271 0.000 0.314 14.515

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 48 47 47 58 74 0 80 75

N.S.

1 1.02 1.00 1.00 1.23 1.57 0.00 1.70 1.60

time (sec)

N/A 0.363 0.011 0.482 0.247 0.273 0.000 0.313 13.215

Problem 4

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

24 24 24 30 29 60 37 63 47

N.S.

1 1.00 1.00 1.25 1.21 2.50 1.54 2.62 1.96

time (sec)

N/A 0.277 0.008 0.362 0.226 0.257 2.380 0.310 13.484

Problem 5

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

16 16 16 24 23 36 41 49 20

N.S.

1 1.00 1.00 1.50 1.44 2.25 2.56 3.06 1.25

time (sec)

N/A 0.147 0.001 0.142 0.246 0.285 0.872 0.268 13.393

Problem 6

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

15 15 26 16 20 17 17 39 15

N.S.

1 1.00 1.73 1.07 1.33 1.13 1.13 2.60 1.00

time (sec)

N/A 0.225 0.008 0.436 0.242 0.245 0.783 0.284 13.223

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 39 32 29 34 29 0 56 50

N.S.

1 1.03 0.84 0.76 0.89 0.76 0.00 1.47 1.32

time (sec)

N/A 0.277 0.053 0.429 0.237 0.272 0.000 0.286 13.764

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 55 57 40 46 42 0 72 55

N.S.

1 1.02 1.06 0.74 0.85 0.78 0.00 1.33 1.02

time (sec)

N/A 0.305 0.066 0.517 0.313 0.242 0.000 0.286 13.255

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 81 73 53 57 53 0 86 79

N.S.

1 1.07 0.96 0.70 0.75 0.70 0.00 1.13 1.04

time (sec)

N/A 0.386 0.105 0.557 0.250 0.271 0.000 0.281 16.835

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 121 68 111 133 124 0 138 170

N.S.

1 0.99 0.56 0.91 1.09 1.02 0.00 1.13 1.39

time (sec)

N/A 0.704 0.631 0.985 0.251 0.271 0.000 0.320 17.891

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 95 58 112 145 111 0 122 141

N.S.

1 0.99 0.60 1.17 1.51 1.16 0.00 1.27 1.47

time (sec)

N/A 0.548 0.428 0.681 0.257 0.277 0.000 0.302 17.006

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 80 74 75 85 96 0 106 112

N.S.

1 1.08 1.00 1.01 1.15 1.30 0.00 1.43 1.51

time (sec)

N/A 0.540 0.285 0.685 0.245 0.268 0.000 0.306 15.224

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 54 54 70 81 83 0 90 83

N.S.

1 1.00 1.00 1.30 1.50 1.54 0.00 1.67 1.54

time (sec)

N/A 0.398 0.175 0.535 0.260 0.259 0.000 0.316 13.887

Problem 14

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

34 34 34 42 41 76 0 79 56

N.S.

1 1.00 1.00 1.24 1.21 2.24 0.00 2.32 1.65

time (sec)

N/A 0.283 0.165 0.351 0.249 0.282 0.000 0.294 13.361

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

34 34 47 44 52 53 0 79 33

N.S.

1 1.00 1.38 1.29 1.53 1.56 0.00 2.32 0.97

time (sec)

N/A 0.332 0.009 0.440 0.249 0.265 0.000 0.316 13.427

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 45 34 31 48 36 0 64 57

N.S.

1 1.00 0.76 0.69 1.07 0.80 0.00 1.42 1.27

time (sec)

N/A 0.353 0.069 0.420 0.274 0.262 0.000 0.315 13.756

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 63 41 42 61 49 0 80 61

N.S.

1 1.11 0.72 0.74 1.07 0.86 0.00 1.40 1.07

time (sec)

N/A 0.438 0.092 0.468 0.279 0.248 0.000 0.297 13.361

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 86 53 55 83 63 0 96 89

N.S.

1 0.99 0.61 0.63 0.95 0.72 0.00 1.10 1.02

time (sec)

N/A 0.447 0.139 0.540 0.238 0.264 0.000 0.319 16.487

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 94 61 64 95 76 0 112 105

N.S.

1 0.91 0.59 0.62 0.92 0.74 0.00 1.09 1.02

time (sec)

N/A 0.577 0.137 0.668 0.265 0.259 0.000 0.320 16.654

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

114 114 122 145 179 124 0 138 170

N.S.

1 1.00 1.07 1.27 1.57 1.09 0.00 1.21 1.49

time (sec)

N/A 0.344 0.765 1.103 0.271 0.280 0.000 0.347 17.772

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

93 93 99 123 156 111 0 122 141

N.S.

1 1.00 1.06 1.32 1.68 1.19 0.00 1.31 1.52

time (sec)

N/A 0.318 0.482 0.678 0.245 0.259 0.000 0.322 16.314

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 72 72 94 104 98 0 106 112

N.S.

1 1.00 1.00 1.31 1.44 1.36 0.00 1.47 1.56

time (sec)

N/A 0.273 0.301 0.657 0.246 0.284 0.000 0.327 14.480

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 69 59 80 91 98 0 100 88

N.S.

1 1.05 0.89 1.21 1.38 1.48 0.00 1.52 1.33

time (sec)

N/A 0.408 0.245 0.442 0.253 0.271 0.000 0.304 13.470

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 48 33 55 64 91 0 80 57

N.S.

1 1.00 0.69 1.15 1.33 1.90 0.00 1.67 1.19

time (sec)

N/A 0.254 0.196 0.539 0.210 0.287 0.000 0.338 13.233

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 81 59 74 65 0 100 88

N.S.

1 1.00 1.37 1.00 1.25 1.10 0.00 1.69 1.49

time (sec)

N/A 0.259 0.292 0.458 0.213 0.275 0.000 0.332 13.280

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

63 63 44 42 71 50 0 80 63

N.S.

1 1.00 0.70 0.67 1.13 0.79 0.00 1.27 1.00

time (sec)

N/A 0.271 0.090 0.487 0.225 0.264 0.000 0.322 13.386

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 85 51 53 94 63 0 96 89

N.S.

1 1.00 0.60 0.62 1.11 0.74 0.00 1.13 1.05

time (sec)

N/A 0.300 0.111 0.543 0.212 0.280 0.000 0.327 16.719

Problem 28

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

105 105 63 66 117 76 0 112 105

N.S.

1 1.00 0.60 0.63 1.11 0.72 0.00 1.07 1.00

time (sec)

N/A 0.315 0.150 0.674 0.219 0.266 0.000 0.333 17.127

Problem 29

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

129 129 73 75 143 89 0 128 121

N.S.

1 1.00 0.57 0.58 1.11 0.69 0.00 0.99 0.94

time (sec)

N/A 0.340 0.186 0.766 0.213 0.257 0.000 0.328 15.429

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 136 146 171 270 137 0 154 199

N.S.

1 1.00 1.07 1.26 1.99 1.01 0.00 1.13 1.46

time (sec)

N/A 0.374 5.047 1.482 0.222 0.271 0.000 0.351 17.061

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 111 125 152 190 124 0 138 170

N.S.

1 1.00 1.13 1.37 1.71 1.12 0.00 1.24 1.53

time (sec)

N/A 0.344 2.553 0.917 0.227 0.284 0.000 0.341 17.799

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

96 96 96 133 175 111 0 122 141

N.S.

1 1.00 1.00 1.39 1.82 1.16 0.00 1.27 1.47

time (sec)

N/A 0.306 2.181 0.821 0.216 0.279 0.000 0.337 16.528

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 98 73 89 116 110 0 116 117

N.S.

1 1.08 0.80 0.98 1.27 1.21 0.00 1.27 1.29

time (sec)

N/A 0.571 2.121 0.658 0.211 0.278 0.000 0.291 13.514

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 272 91 110 111 0 129 115

N.S.

1 1.00 3.73 1.25 1.51 1.52 0.00 1.77 1.58

time (sec)

N/A 0.284 5.277 0.635 0.208 0.329 0.000 0.340 13.418

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 241 82 85 105 0 129 117

N.S.

1 1.00 3.30 1.12 1.16 1.44 0.00 1.77 1.60

time (sec)

N/A 0.281 4.816 0.529 0.216 0.300 0.000 0.323 13.430

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

73 73 91 70 97 80 0 116 93

N.S.

1 1.00 1.25 0.96 1.33 1.10 0.00 1.59 1.27

time (sec)

N/A 0.291 0.556 0.542 0.206 0.282 0.000 0.320 12.834

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 87 56 55 104 63 0 96 89

N.S.

1 1.00 0.64 0.63 1.20 0.72 0.00 1.10 1.02

time (sec)

N/A 0.307 0.144 0.618 0.220 0.272 0.000 0.326 16.639

Problem 38

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

102 102 63 66 128 76 0 112 105

N.S.

1 1.00 0.62 0.65 1.25 0.75 0.00 1.10 1.03

time (sec)

N/A 0.330 0.137 0.727 0.221 0.261 0.000 0.321 16.863

Problem 39

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

127 127 73 75 165 89 0 128 121

N.S.

1 1.00 0.57 0.59 1.30 0.70 0.00 1.01 0.95

time (sec)

N/A 0.355 0.198 0.771 0.208 0.256 0.000 0.316 15.798

Problem 40

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

147 147 83 88 187 102 0 144 137

N.S.

1 1.00 0.56 0.60 1.27 0.69 0.00 0.98 0.93

time (sec)

N/A 0.404 0.252 0.817 0.292 0.261 0.000 0.350 15.888

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

156 156 170 189 314 150 0 170 228

N.S.

1 1.00 1.09 1.21 2.01 0.96 0.00 1.09 1.46

time (sec)

N/A 0.414 5.067 1.456 0.320 0.282 0.000 0.378 17.089

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 102 83 134 205 124 0 114 96

N.S.

1 0.99 0.81 1.30 1.99 1.20 0.00 1.11 0.93

time (sec)

N/A 0.590 0.498 0.423 0.303 0.256 0.000 0.308 12.773

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 87 72 105 162 112 0 101 95

N.S.

1 1.02 0.85 1.24 1.91 1.32 0.00 1.19 1.12

time (sec)

N/A 0.550 0.305 0.378 0.298 0.263 0.000 0.308 13.158

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 51 42 74 119 97 0 84 67

N.S.

1 1.00 0.82 1.45 2.33 1.90 0.00 1.65 1.31

time (sec)

N/A 0.446 0.268 0.337 0.297 0.291 0.000 0.298 13.282

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 38 27 46 75 65 0 54 31

N.S.

1 1.00 0.71 1.21 1.97 1.71 0.00 1.42 0.82

time (sec)

N/A 0.342 0.144 0.271 0.290 0.312 0.000 0.293 13.361

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 22 17 17 23 22 0 16 16

N.S.

1 1.00 0.77 0.77 1.05 1.00 0.00 0.73 0.73

time (sec)

N/A 0.198 0.030 0.235 0.301 0.301 0.000 0.299 13.358

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 58 23 49 37 0 28 23

N.S.

1 1.00 2.00 0.79 1.69 1.28 0.00 0.97 0.79

time (sec)

N/A 0.187 0.296 0.214 0.361 0.282 0.000 0.301 13.170

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 45 89 31 92 46 0 58 66

N.S.

1 1.02 2.02 0.70 2.09 1.05 0.00 1.32 1.50

time (sec)

N/A 0.351 0.818 0.384 0.338 0.288 0.000 0.301 13.188

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 75 117 43 133 57 0 73 89

N.S.

1 1.01 1.58 0.58 1.80 0.77 0.00 0.99 1.20

time (sec)

N/A 0.445 0.880 0.412 0.362 0.292 0.000 0.270 13.283

Problem 50

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

94 92 143 54 176 70 0 88 70

N.S.

1 0.98 1.52 0.57 1.87 0.74 0.00 0.94 0.74

time (sec)

N/A 0.467 0.999 0.451 0.399 0.302 0.000 0.282 12.873

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

118 118 173 67 217 79 0 101 98

N.S.

1 1.00 1.47 0.57 1.84 0.67 0.00 0.86 0.83

time (sec)

N/A 0.561 1.030 0.490 0.414 0.338 0.000 0.305 15.074

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 129 74 120 190 162 0 122 122

N.S.

1 1.05 0.60 0.98 1.54 1.32 0.00 0.99 0.99

time (sec)

N/A 0.836 0.861 0.400 0.359 0.306 0.000 0.313 13.356

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 97 104 92 145 146 0 106 92

N.S.

1 1.09 1.17 1.03 1.63 1.64 0.00 1.19 1.03

time (sec)

N/A 0.677 0.459 0.387 0.408 0.264 0.000 0.295 13.404

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 70 84 62 98 114 0 77 43

N.S.

1 1.06 1.27 0.94 1.48 1.73 0.00 1.17 0.65

time (sec)

N/A 0.510 0.211 0.287 0.264 0.284 0.000 0.309 13.151

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 54 45 31 46 49 0 31 30

N.S.

1 0.98 0.82 0.56 0.84 0.89 0.00 0.56 0.55

time (sec)

N/A 0.311 0.078 0.243 0.244 0.262 0.000 0.282 13.476

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 54 60 31 47 51 0 31 30

N.S.

1 0.98 1.09 0.56 0.85 0.93 0.00 0.56 0.55

time (sec)

N/A 0.302 0.402 0.252 0.246 0.256 0.000 0.277 13.344

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

57 61 112 36 72 80 0 50 35

N.S.

1 1.07 1.96 0.63 1.26 1.40 0.00 0.88 0.61

time (sec)

N/A 0.398 0.450 0.268 0.365 0.271 0.000 0.278 13.354

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 80 97 55 118 90 0 79 91

N.S.

1 1.11 1.35 0.76 1.64 1.25 0.00 1.10 1.26

time (sec)

N/A 0.561 0.907 0.414 0.373 0.262 0.000 0.285 13.504

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 116 177 66 164 99 0 95 113

N.S.

1 1.05 1.61 0.60 1.49 0.90 0.00 0.86 1.03

time (sec)

N/A 0.662 1.573 0.474 0.362 0.267 0.000 0.293 13.699

Problem 60

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

124 136 199 77 207 108 0 108 135

N.S.

1 1.10 1.60 0.62 1.67 0.87 0.00 0.87 1.09

time (sec)

N/A 0.716 1.647 0.509 0.357 0.267 0.000 0.312 13.863

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

162 176 111 135 211 206 0 139 141

N.S.

1 1.09 0.69 0.83 1.30 1.27 0.00 0.86 0.87

time (sec)

N/A 1.111 1.096 0.433 0.274 0.286 0.000 0.320 12.986

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 138 116 105 165 190 0 122 111

N.S.

1 1.08 0.91 0.82 1.29 1.48 0.00 0.95 0.87

time (sec)

N/A 0.938 0.668 0.361 0.281 0.281 0.000 0.339 12.659

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 115 96 75 119 158 0 94 58

N.S.

1 1.10 0.91 0.71 1.13 1.50 0.00 0.90 0.55

time (sec)

N/A 0.753 0.290 0.267 0.341 0.287 0.000 0.334 12.393

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 85 57 45 67 75 0 46 45

N.S.

1 1.02 0.69 0.54 0.81 0.90 0.00 0.55 0.54

time (sec)

N/A 0.468 0.123 0.281 0.275 0.255 0.000 0.302 12.090

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 87 44 31 47 73 0 31 30

N.S.

1 1.05 0.53 0.37 0.57 0.88 0.00 0.37 0.36

time (sec)

N/A 0.431 0.180 0.324 0.268 0.272 0.000 0.291 13.014

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 87 86 45 67 75 0 46 45

N.S.

1 1.05 1.04 0.54 0.81 0.90 0.00 0.55 0.54

time (sec)

N/A 0.414 0.577 0.242 0.284 0.264 0.000 0.303 13.157

Problem 67

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 98 162 51 92 116 0 68 81

N.S.

1 1.11 1.84 0.58 1.05 1.32 0.00 0.77 0.92

time (sec)

N/A 0.580 0.561 0.242 0.355 0.260 0.000 0.304 13.260

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

103 114 107 66 137 126 0 96 113

N.S.

1 1.11 1.04 0.64 1.33 1.22 0.00 0.93 1.10

time (sec)

N/A 0.767 1.053 0.534 0.356 0.290 0.000 0.321 13.217

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 161 181 77 184 135 0 113 137

N.S.

1 1.10 1.23 0.52 1.25 0.92 0.00 0.77 0.93

time (sec)

N/A 0.929 2.082 0.498 0.428 0.261 0.000 0.310 13.158

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 211 121 148 231 250 0 155 160

N.S.

1 1.09 0.63 0.77 1.20 1.30 0.00 0.80 0.83

time (sec)

N/A 1.417 1.719 0.477 0.284 0.295 0.000 0.334 13.460

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 183 128 118 186 234 0 139 130

N.S.

1 1.15 0.81 0.74 1.17 1.47 0.00 0.87 0.82

time (sec)

N/A 1.247 1.186 0.424 0.289 0.274 0.000 0.315 13.254

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

136 151 108 88 139 202 0 110 83

N.S.

1 1.11 0.79 0.65 1.02 1.49 0.00 0.81 0.61

time (sec)

N/A 1.004 0.497 0.311 0.287 0.270 0.000 0.305 13.360

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

120 126 69 56 87 99 0 59 58

N.S.

1 1.05 0.58 0.47 0.72 0.82 0.00 0.49 0.48

time (sec)

N/A 0.613 0.194 0.252 0.286 0.246 0.000 0.325 13.149

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 118 56 57 87 99 0 59 58

N.S.

1 1.05 0.50 0.51 0.78 0.88 0.00 0.53 0.52

time (sec)

N/A 0.591 0.326 0.282 0.293 0.247 0.000 0.317 13.870

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 120 56 58 87 99 0 59 58

N.S.

1 1.07 0.50 0.52 0.78 0.88 0.00 0.53 0.52

time (sec)

N/A 0.574 1.550 0.325 0.266 0.272 0.000 0.303 13.975

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 120 112 57 87 99 0 59 58

N.S.

1 1.07 1.00 0.51 0.78 0.88 0.00 0.53 0.52

time (sec)

N/A 0.549 2.523 0.279 0.297 0.261 0.000 0.303 13.458

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 126 224 64 112 152 0 83 102

N.S.

1 1.14 2.02 0.58 1.01 1.37 0.00 0.75 0.92

time (sec)

N/A 0.738 2.527 0.263 0.375 0.269 0.000 0.291 13.578

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 150 117 77 158 162 0 112 137

N.S.

1 1.19 0.93 0.61 1.25 1.29 0.00 0.89 1.09

time (sec)

N/A 1.004 2.765 0.541 0.425 0.264 0.000 0.302 13.711

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

176 194 289 88 204 171 0 128 159

N.S.

1 1.10 1.64 0.50 1.16 0.97 0.00 0.73 0.90

time (sec)

N/A 1.219 3.644 0.568 0.337 0.290 0.000 0.327 13.614

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

200 232 140 131 206 278 0 155 149

N.S.

1 1.16 0.70 0.66 1.03 1.39 0.00 0.78 0.74

time (sec)

N/A 1.552 1.824 0.435 0.259 0.276 0.000 0.339 13.759

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

177 205 123 101 159 246 0 126 99

N.S.

1 1.16 0.69 0.57 0.90 1.39 0.00 0.71 0.56

time (sec)

N/A 1.328 0.737 0.318 0.298 0.284 0.000 0.332 13.564

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 167 97 69 107 123 0 72 127

N.S.

1 1.05 0.61 0.43 0.67 0.77 0.00 0.45 0.80

time (sec)

N/A 0.819 0.168 0.286 0.250 0.252 0.000 0.333 13.594

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 167 64 57 87 123 0 59 58

N.S.

1 1.05 0.40 0.36 0.55 0.77 0.00 0.37 0.36

time (sec)

N/A 0.826 0.409 0.352 0.278 0.260 0.000 0.348 13.625

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

139 147 64 45 67 123 0 46 45

N.S.

1 1.06 0.46 0.32 0.48 0.88 0.00 0.33 0.32

time (sec)

N/A 0.754 4.113 0.335 0.316 0.269 0.000 0.343 13.384

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 153 66 57 87 123 0 59 58

N.S.

1 1.07 0.46 0.40 0.61 0.86 0.00 0.41 0.41

time (sec)

N/A 0.718 4.926 0.327 0.270 0.270 0.000 0.342 13.264

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

143 153 138 71 107 123 0 72 127

N.S.

1 1.07 0.97 0.50 0.75 0.86 0.00 0.50 0.89

time (sec)

N/A 0.684 5.423 0.286 0.269 0.255 0.000 0.340 13.025

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

144 172 280 77 132 188 0 100 125

N.S.

1 1.19 1.94 0.53 0.92 1.31 0.00 0.69 0.87

time (sec)

N/A 0.960 4.873 0.299 0.392 0.266 0.000 0.297 13.439

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

159 191 127 88 178 198 0 129 159

N.S.

1 1.20 0.80 0.55 1.12 1.25 0.00 0.81 1.00

time (sec)

N/A 1.261 6.164 0.554 0.348 0.274 0.000 0.344 13.610

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

215 240 345 98 224 207 0 145 181

N.S.

1 1.12 1.60 0.46 1.04 0.96 0.00 0.67 0.84

time (sec)

N/A 1.519 6.820 0.569 0.325 0.284 0.000 0.338 13.247

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

122 138 58 72 0 82 0 0 331

N.S.

1 1.13 0.48 0.59 0.00 0.67 0.00 0.00 2.71

time (sec)

N/A 0.678 0.145 0.981 0.000 0.266 0.000 0.000 17.945

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

86 97 48 59 0 72 0 0 115

N.S.

1 1.13 0.56 0.69 0.00 0.84 0.00 0.00 1.34

time (sec)

N/A 0.512 0.115 0.868 0.000 0.283 0.000 0.000 16.664

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

56 56 36 43 0 60 0 0 108

N.S.

1 1.00 0.64 0.77 0.00 1.07 0.00 0.00 1.93

time (sec)

N/A 0.335 0.105 0.865 0.000 0.274 0.000 0.000 1.384

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 29 33 0 41 0 0 41

N.S.

1 1.00 1.12 1.27 0.00 1.58 0.00 0.00 1.58

time (sec)

N/A 0.212 0.074 0.787 0.000 0.264 0.000 0.000 0.187

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

37 37 60 76 146 133 0 0 0

N.S.

1 1.00 1.62 2.05 3.95 3.59 0.00 0.00 0.00

time (sec)

N/A 0.196 0.140 0.830 0.384 0.280 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 62 79 165 791 242 0 0 0

N.S.

1 1.00 1.27 2.66 12.76 3.90 0.00 0.00 0.00

time (sec)

N/A 0.312 0.224 24.225 0.422 0.304 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 101 47 185 1059 270 0 0 0

N.S.

1 0.99 0.46 1.81 10.38 2.65 0.00 0.00 0.00

time (sec)

N/A 0.475 0.107 22.844 0.474 0.276 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 142 47 201 1921 290 0 0 0

N.S.

1 1.03 0.34 1.46 13.92 2.10 0.00 0.00 0.00

time (sec)

N/A 0.640 0.100 22.689 0.543 0.283 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

174 183 47 217 6638 310 0 0 0

N.S.

1 1.05 0.27 1.25 38.15 1.78 0.00 0.00 0.00

time (sec)

N/A 0.845 0.098 26.775 0.709 0.281 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

162 182 70 83 0 98 0 0 429

N.S.

1 1.12 0.43 0.51 0.00 0.60 0.00 0.00 2.65

time (sec)

N/A 0.883 0.511 0.868 0.000 0.271 0.000 0.000 21.192

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 131 60 73 0 87 0 0 346

N.S.

1 1.13 0.52 0.63 0.00 0.75 0.00 0.00 2.98

time (sec)

N/A 0.677 0.184 0.831 0.000 0.271 0.000 0.000 17.842

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