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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 A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

147 171 151 128 180 258 699 130 151

N.S.

1 1.16 1.03 0.87 1.22 1.76 4.76 0.88 1.03

time (sec)

N/A 0.268 1.219 3.678 0.212 0.276 0.801 0.280 9.864

Problem 2

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

121 136 117 69 130 69 269 140 100

N.S.

1 1.12 0.97 0.57 1.07 0.57 2.22 1.16 0.83

time (sec)

N/A 0.232 0.202 2.131 0.265 0.298 1.244 0.292 0.293

Problem 3

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

95 105 86 58 103 59 162 130 80

N.S.

1 1.11 0.91 0.61 1.08 0.62 1.71 1.37 0.84

time (sec)

N/A 0.210 0.156 2.121 0.275 0.298 0.749 0.277 9.359

Problem 4

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

69 74 83 47 76 49 92 120 60

N.S.

1 1.07 1.20 0.68 1.10 0.71 1.33 1.74 0.87

time (sec)

N/A 0.180 0.126 2.051 0.270 0.281 0.519 0.276 0.162

Problem 5

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

43 43 62 31 49 39 32 110 39

N.S.

1 1.00 1.44 0.72 1.14 0.91 0.74 2.56 0.91

time (sec)

N/A 0.156 0.084 2.129 0.270 0.420 0.286 0.269 0.085

Problem 6

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

101 118 102 63 117 68 211 57 81

N.S.

1 1.17 1.01 0.62 1.16 0.67 2.09 0.56 0.80

time (sec)

N/A 0.236 0.170 2.429 0.275 0.384 0.711 0.270 9.299

Problem 7

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

79 91 92 53 90 58 129 47 63

N.S.

1 1.15 1.16 0.67 1.14 0.73 1.63 0.59 0.80

time (sec)

N/A 0.209 0.126 2.051 0.271 0.354 0.527 0.281 9.276

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

57 64 82 43 63 48 68 37 45

N.S.

1 1.12 1.44 0.75 1.11 0.84 1.19 0.65 0.79

time (sec)

N/A 0.181 0.113 2.426 0.284 0.408 0.403 0.279 0.086

Problem 9

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 37 55 28 36 38 29 27 26

N.S.

1 1.06 1.57 0.80 1.03 1.09 0.83 0.77 0.74

time (sec)

N/A 0.164 0.076 1.989 0.281 0.795 0.240 0.263 9.078

Problem 10

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 37 47 27 36 35 26 25 26

N.S.

1 1.06 1.34 0.77 1.03 1.00 0.74 0.71 0.74

time (sec)

N/A 0.158 0.074 2.206 0.278 0.274 0.233 0.267 0.048

Problem 11

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 37 55 28 36 38 29 27 26

N.S.

1 1.06 1.57 0.80 1.03 1.09 0.83 0.77 0.74

time (sec)

N/A 0.162 0.082 2.267 0.270 0.268 0.238 0.270 9.101

Problem 12

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 56 67 39 55 43 56 35 39

N.S.

1 1.10 1.31 0.76 1.08 0.84 1.10 0.69 0.76

time (sec)

N/A 0.178 0.181 2.149 0.288 0.267 0.342 0.275 9.121

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

35 35 46 32 41 32 34 33 29

N.S.

1 1.00 1.31 0.91 1.17 0.91 0.97 0.94 0.83

time (sec)

N/A 0.154 0.070 1.895 0.201 0.265 0.213 0.261 0.110

Problem 14

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 46 32 43 32 34 33 29

N.S.

1 1.00 1.24 0.86 1.16 0.86 0.92 0.89 0.78

time (sec)

N/A 0.160 0.074 1.863 0.187 0.267 0.217 0.272 9.139

Problem 15

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 50 33 43 36 32 37 29

N.S.

1 1.00 1.28 0.85 1.10 0.92 0.82 0.95 0.74

time (sec)

N/A 0.161 0.108 1.864 0.199 0.273 0.198 0.266 0.080

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

83 89 70 75 111 105 0 74 96

N.S.

1 1.07 0.84 0.90 1.34 1.27 0.00 0.89 1.16

time (sec)

N/A 0.193 0.200 1.921 0.192 0.276 0.000 0.278 9.223

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 51 10 21 19 8 110 19

N.S.

1 1.00 3.19 0.62 1.31 1.19 0.50 6.88 1.19

time (sec)

N/A 0.142 0.050 1.861 0.271 0.271 0.294 0.273 9.247

Problem 18

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

26 26 24 19 28 39 0 64 20

N.S.

1 1.00 0.92 0.73 1.08 1.50 0.00 2.46 0.77

time (sec)

N/A 0.135 0.078 1.801 0.190 0.267 0.000 0.287 0.045

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

53 53 36 39 55 63 0 74 31

N.S.

1 1.00 0.68 0.74 1.04 1.19 0.00 1.40 0.58

time (sec)

N/A 0.155 0.110 1.854 0.187 0.274 0.000 0.306 9.112

Problem 20

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

79 84 48 50 82 83 0 84 40

N.S.

1 1.06 0.61 0.63 1.04 1.05 0.00 1.06 0.51

time (sec)

N/A 0.182 0.146 1.904 0.188 0.283 0.000 0.289 9.231

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 14 46 9 8 19 8 27 8

N.S.

1 1.17 3.83 0.75 0.67 1.58 0.67 2.25 0.67

time (sec)

N/A 0.137 0.051 1.899 0.291 0.276 0.256 0.271 8.972

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

22 22 21 19 28 29 0 29 18

N.S.

1 1.00 0.95 0.86 1.27 1.32 0.00 1.32 0.82

time (sec)

N/A 0.138 0.079 1.803 0.216 0.266 0.000 0.269 0.043

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

45 45 31 31 55 46 0 39 28

N.S.

1 1.00 0.69 0.69 1.22 1.02 0.00 0.87 0.62

time (sec)

N/A 0.158 0.106 1.824 0.189 0.256 0.000 0.276 9.005

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

67 72 41 41 82 61 0 49 73

N.S.

1 1.07 0.61 0.61 1.22 0.91 0.00 0.73 1.09

time (sec)

N/A 0.180 0.129 1.829 0.189 0.398 0.000 0.276 9.082

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B B A B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 18 57 25 21 27 54 41 42

N.S.

1 1.50 4.75 2.08 1.75 2.25 4.50 3.42 3.50

time (sec)

N/A 0.142 0.070 2.184 0.291 0.378 0.258 0.281 9.098

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

24 24 58 37 29 27 51 59 36

N.S.

1 1.00 2.42 1.54 1.21 1.12 2.12 2.46 1.50

time (sec)

N/A 0.142 0.092 2.089 0.218 0.434 0.247 0.284 9.074

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 12 40 7 8 18 5 25 6

N.S.

1 1.20 4.00 0.70 0.80 1.80 0.50 2.50 0.60

time (sec)

N/A 0.134 0.049 2.281 0.301 0.775 0.231 0.290 9.067

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 39 9 17 17 17 33 11

N.S.

1 1.00 2.44 0.56 1.06 1.06 1.06 2.06 0.69

time (sec)

N/A 0.135 0.039 1.899 0.204 0.257 0.238 0.280 9.374

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 16 39 14 17 17 17 33 11

N.S.

1 1.00 2.44 0.88 1.06 1.06 1.06 2.06 0.69

time (sec)

N/A 0.137 0.045 1.928 0.196 0.280 0.216 0.283 9.631

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

N/A No Yes N/A TBD TBD TBD TBD TBD

size

448 350 48 0 0 0 0 0 36

N.S.

1 0.78 0.11 0.00 0.00 0.00 0.00 0.00 0.08

time (sec)

N/A 0.353 10.021 0.000 0.000 0.000 0.000 0.000 9.248

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

N/A No Yes N/A TBD TBD TBD TBD TBD

size

387 313 45 0 0 0 0 0 36

N.S.

1 0.81 0.12 0.00 0.00 0.00 0.00 0.00 0.09

time (sec)

N/A 0.321 10.014 0.000 0.000 0.000 0.000 0.000 9.077

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

N/A No Yes N/A TBD TBD TBD TBD TBD

size

322 278 43 0 0 0 0 0 36

N.S.

1 0.86 0.13 0.00 0.00 0.00 0.00 0.00 0.11

time (sec)

N/A 0.292 10.016 0.000 0.000 0.000 0.000 0.000 9.044

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

N/A No Yes N/A TBD TBD TBD TBD TBD

size

384 308 47 0 0 0 0 0 36

N.S.

1 0.80 0.12 0.00 0.00 0.00 0.00 0.00 0.09

time (sec)

N/A 0.327 10.020 0.000 0.000 0.000 0.000 0.000 9.068

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

N/A No Yes N/A TBD TBD TBD TBD TBD

size

448 343 50 0 0 0 0 0 36

N.S.

1 0.77 0.11 0.00 0.00 0.00 0.00 0.00 0.08

time (sec)

N/A 0.353 10.019 0.000 0.000 0.000 0.000 0.000 9.063

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

N/A No Yes N/A TBD TBD TBD TBD TBD

size

842 727 48 0 0 0 0 0 36

N.S.

1 0.86 0.06 0.00 0.00 0.00 0.00 0.00 0.04

time (sec)

N/A 0.545 10.020 0.000 0.000 0.000 0.000 0.000 9.088

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

N/A No Yes N/A TBD TBD TBD TBD TBD

size

781 690 45 0 0 0 0 0 36

N.S.

1 0.88 0.06 0.00 0.00 0.00 0.00 0.00 0.05

time (sec)

N/A 0.478 10.015 0.000 0.000 0.000 0.000 0.000 9.058

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

N/A No Yes N/A TBD TBD TBD TBD TBD

size

715 657 45 0 0 0 0 0 36

N.S.

1 0.92 0.06 0.00 0.00 0.00 0.00 0.00 0.05

time (sec)

N/A 0.438 10.015 0.000 0.000 0.000 0.000 0.000 9.089

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

N/A No Yes N/A TBD TBD TBD TBD TBD

size

773 684 45 0 0 0 0 0 36

N.S.

1 0.88 0.06 0.00 0.00 0.00 0.00 0.00 0.05

time (sec)

N/A 0.478 10.017 0.000 0.000 0.000 0.000 0.000 9.072

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

N/A No Yes N/A TBD TBD TBD TBD TBD

size

838 719 50 0 0 0 0 0 36

N.S.

1 0.86 0.06 0.00 0.00 0.00 0.00 0.00 0.04

time (sec)

N/A 0.527 10.019 0.000 0.000 0.000 0.000 0.000 9.053

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

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

size

119 139 48 0 0 0 0 0 36

N.S.

1 1.17 0.40 0.00 0.00 0.00 0.00 0.00 0.30

time (sec)

N/A 0.261 10.021 0.000 0.000 0.000 0.000 0.000 9.065

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

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

size

90 102 45 0 0 0 0 0 36

N.S.

1 1.13 0.50 0.00 0.00 0.00 0.00 0.00 0.40

time (sec)

N/A 0.224 10.018 0.000 0.000 0.000 0.000 0.000 9.028

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

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

size

90 102 45 0 0 0 0 0 36

N.S.

1 1.13 0.50 0.00 0.00 0.00 0.00 0.00 0.40

time (sec)

N/A 0.220 10.014 0.000 0.000 0.000 0.000 0.000 8.998

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

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

size

58 71 45 0 0 0 0 0 36

N.S.

1 1.22 0.78 0.00 0.00 0.00 0.00 0.00 0.62

time (sec)

N/A 0.196 10.016 0.000 0.000 0.000 0.000 0.000 9.018

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

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

size

59 71 43 0 0 0 0 0 36

N.S.

1 1.20 0.73 0.00 0.00 0.00 0.00 0.00 0.61

time (sec)

N/A 0.195 10.015 0.000 0.000 0.000 0.000 0.000 9.040

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

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

size

83 95 45 0 0 0 0 0 36

N.S.

1 1.14 0.54 0.00 0.00 0.00 0.00 0.00 0.43

time (sec)

N/A 0.218 10.019 0.000 0.000 0.000 0.000 0.000 9.091

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

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

size

115 130 50 0 0 0 0 0 36

N.S.

1 1.13 0.43 0.00 0.00 0.00 0.00 0.00 0.31

time (sec)

N/A 0.251 10.023 0.000 0.000 0.000 0.000 0.000 9.249

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F F F F B

verified

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

size

146 165 50 0 0 0 0 0 36

N.S.

1 1.13 0.34 0.00 0.00 0.00 0.00 0.00 0.25

time (sec)

N/A 0.286 10.019 0.000 0.000 0.000 0.000 0.000 9.225

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A F F F F F B

verified

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

size

55 55 45 0 0 0 0 0 48

N.S.

1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 0.87

time (sec)

N/A 0.166 0.038 0.000 0.000 0.000 0.000 0.000 9.355

Problem 49

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 51 44 43 43 49 43 43

N.S.

1 1.00 1.00 0.86 0.84 0.84 0.96 0.84 0.84

time (sec)

N/A 0.184 0.004 2.128 0.194 0.256 0.019 0.313 0.025

Problem 50

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 35 32 31 31 32 31 31

N.S.

1 1.00 1.00 0.91 0.89 0.89 0.91 0.89 0.89

time (sec)

N/A 0.167 0.003 2.136 0.195 0.267 0.023 0.314 0.039

Problem 51

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 22 21 21 22 21 21

N.S.

1 1.00 1.00 0.88 0.84 0.84 0.88 0.84 0.84

time (sec)

N/A 0.158 0.002 2.173 0.189 0.289 0.016 0.296 0.030

Problem 52

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 10 10

N.S.

1 1.00 1.00 0.92 0.83 0.83 0.67 0.83 0.83

time (sec)

N/A 0.141 0.000 0.024 0.193 0.266 0.017 0.262 0.017

Problem 53

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

24 24 24 16 15 67 53 15 16

N.S.

1 1.00 1.00 0.67 0.62 2.79 2.21 0.62 0.67

time (sec)

N/A 0.138 0.005 2.069 0.277 0.300 0.063 0.278 0.055

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

45 45 45 36 35 120 78 35 33

N.S.

1 1.00 1.00 0.80 0.78 2.67 1.73 0.78 0.73

time (sec)

N/A 0.153 0.032 2.140 0.278 0.554 0.101 0.309 9.204

Problem 55

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

62 70 55 57 58 188 105 45 55

N.S.

1 1.13 0.89 0.92 0.94 3.03 1.69 0.73 0.89

time (sec)

N/A 0.166 0.050 2.121 0.277 0.469 0.166 0.285 9.121

Problem 56

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

84 90 71 59 58 146 97 63 37

N.S.

1 1.07 0.85 0.70 0.69 1.74 1.15 0.75 0.44

time (sec)

N/A 0.182 0.134 2.149 0.221 0.456 2.653 0.270 9.090

Problem 57

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

65 68 60 48 43 124 70 49 37

N.S.

1 1.05 0.92 0.74 0.66 1.91 1.08 0.75 0.57

time (sec)

N/A 0.177 0.093 2.109 0.205 0.756 1.583 0.292 8.969

Problem 58

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 48 36 28 94 41 37 35

N.S.

1 1.00 1.04 0.78 0.61 2.04 0.89 0.80 0.76

time (sec)

N/A 0.158 0.054 2.205 0.185 0.281 0.959 0.274 0.126

Problem 59

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 21 13 59 17 37 20

N.S.

1 1.00 1.00 0.84 0.52 2.36 0.68 1.48 0.80

time (sec)

N/A 0.146 0.008 2.371 0.199 0.272 0.509 0.273 9.004

Problem 60

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

16 16 16 15 14 23 17 14 14

N.S.

1 1.00 1.00 0.94 0.88 1.44 1.06 0.88 0.88

time (sec)

N/A 0.135 0.046 2.438 0.191 0.270 0.343 0.278 0.034

Problem 61

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

39 39 29 26 31 47 95 27 28

N.S.

1 1.00 0.74 0.67 0.79 1.21 2.44 0.69 0.72

time (sec)

N/A 0.149 0.079 2.098 0.186 0.271 0.495 0.282 8.981

Problem 62

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

58 66 40 37 46 69 413 41 44

N.S.

1 1.14 0.69 0.64 0.79 1.19 7.12 0.71 0.76

time (sec)

N/A 0.162 0.097 1.978 0.185 0.290 0.804 0.298 9.041

Problem 63

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

77 93 51 48 61 91 1265 55 61

N.S.

1 1.21 0.66 0.62 0.79 1.18 16.43 0.71 0.79

time (sec)

N/A 0.176 0.115 2.123 0.192 0.282 1.230 0.280 9.085

Problem 64

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

23 25 20 17 30 19 80 45 19

N.S.

1 1.09 0.87 0.74 1.30 0.83 3.48 1.96 0.83

time (sec)

N/A 0.141 0.012 2.072 0.288 0.394 0.462 0.272 0.050

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A A A B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

23 23 25 16 30 9 19 26 19

N.S.

1 1.00 1.09 0.70 1.30 0.39 0.83 1.13 0.83

time (sec)

N/A 0.145 0.006 2.067 0.270 0.451 0.294 0.280 9.027

Problem 66

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 26 9 6 8 22 25 14

N.S.

1 1.00 0.90 0.31 0.21 0.28 0.76 0.86 0.48

time (sec)

N/A 0.144 0.007 2.253 0.279 0.443 0.315 0.273 9.091

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

25 25 20 16 9 14 0 17 21

N.S.

1 1.00 0.80 0.64 0.36 0.56 0.00 0.68 0.84

time (sec)

N/A 0.146 0.006 2.147 0.280 0.667 0.000 0.268 9.005

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C A A A A B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

23 23 25 16 30 9 19 26 13

N.S.

1 1.00 1.09 0.70 1.30 0.39 0.83 1.13 0.57

time (sec)

N/A 0.144 0.014 0.172 0.272 0.257 0.422 0.277 0.114

Problem 69

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 26 23 6 8 22 15 14

N.S.

1 1.00 0.90 0.79 0.21 0.28 0.76 0.52 0.48

time (sec)

N/A 0.146 0.011 1.909 0.286 0.254 0.414 0.281 9.148

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 27 27 30 9 19 26 18

N.S.

1 1.00 1.17 1.17 1.30 0.39 0.83 1.13 0.78

time (sec)

N/A 0.143 0.008 1.970 0.269 0.268 0.432 0.272 9.115

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 28 10 6 6 24 23 15

N.S.

1 1.00 0.97 0.34 0.21 0.21 0.83 0.79 0.52

time (sec)

N/A 0.148 0.007 2.091 0.273 0.278 0.417 0.271 9.080

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

23 23 27 27 30 9 20 26 18

N.S.

1 1.00 1.17 1.17 1.30 0.39 0.87 1.13 0.78

time (sec)

N/A 0.147 0.007 2.093 0.296 0.258 0.458 0.264 0.062

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C C C A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 28 10 6 6 24 23 15

N.S.

1 1.00 0.97 0.34 0.21 0.21 0.83 0.79 0.52

time (sec)

N/A 0.152 0.004 2.223 0.286 0.262 0.414 0.265 9.119

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 113 206 273 234 233 253 334 184

N.S.

1 1.04 1.89 2.50 2.15 2.14 2.32 3.06 1.69

time (sec)

N/A 0.335 0.033 2.276 0.192 0.263 0.086 0.269 9.160

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 113 206 273 234 235 250 334 184

N.S.

1 1.04 1.89 2.50 2.15 2.16 2.29 3.06 1.69

time (sec)

N/A 0.323 0.047 2.232 0.194 0.450 0.089 0.269 9.165

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 113 198 273 234 227 253 334 176

N.S.

1 1.04 1.82 2.50 2.15 2.08 2.32 3.06 1.61

time (sec)

N/A 0.335 0.038 2.256 0.201 0.433 0.078 0.263 9.202

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

109 113 206 273 234 235 248 334 184

N.S.

1 1.04 1.89 2.50 2.15 2.16 2.28 3.06 1.69

time (sec)

N/A 0.332 0.044 2.272 0.191 0.379 0.079 0.276 9.226

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

18 21 18 17 16 16 22 16 16

N.S.

1 1.17 1.00 0.94 0.89 0.89 1.22 0.89 0.89

time (sec)

N/A 0.144 0.006 4.031 0.282 0.739 0.049 0.269 0.031

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

12 16 12 9 8 10 7 8 8

N.S.

1 1.33 1.00 0.75 0.67 0.83 0.58 0.67 0.67

time (sec)

N/A 0.148 0.018 3.558 0.284 0.264 0.081 0.258 9.296

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 45 34 17 27 39 39 31 15

N.S.

1 2.37 1.79 0.89 1.42 2.05 2.05 1.63 0.79

time (sec)

N/A 0.196 0.026 2.151 0.276 0.259 0.053 0.256 0.236

Problem 81

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 21 13 12 13 13 10 15 8

N.S.

1 1.62 1.00 0.92 1.00 1.00 0.77 1.15 0.62

time (sec)

N/A 0.159 0.005 2.104 0.184 0.259 0.044 0.277 0.084

Problem 82

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

21 23 21 14 15 15 14 17 8

N.S.

1 1.10 1.00 0.67 0.71 0.71 0.67 0.81 0.38

time (sec)

N/A 0.162 0.004 2.180 0.180 0.273 0.054 0.253 0.096

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B B B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

6 17 17 14 13 13 12 15 6

N.S.

1 2.83 2.83 2.33 2.17 2.17 2.00 2.50 1.00

time (sec)

N/A 0.158 0.005 2.043 0.199 0.265 0.050 0.264 0.079

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 27 24 38 50 76 40 23

N.S.

1 1.00 1.00 0.89 1.41 1.85 2.81 1.48 0.85

time (sec)

N/A 0.163 0.012 1.982 0.196 0.266 0.127 0.263 9.566

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 29 26 39 51 76 45 23

N.S.

1 1.00 1.07 0.96 1.44 1.89 2.81 1.67 0.85

time (sec)

N/A 0.160 0.013 2.080 0.183 0.334 0.130 0.264 9.219

Problem 86

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

31 31 31 28 27 41 87 27 23

N.S.

1 1.00 1.00 0.90 0.87 1.32 2.81 0.87 0.74

time (sec)

N/A 0.160 0.012 3.004 0.193 0.448 0.091 0.261 9.187

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

27 27 29 26 39 51 76 45 23

N.S.

1 1.00 1.07 0.96 1.44 1.89 2.81 1.67 0.85

time (sec)

N/A 0.159 0.015 1.988 0.202 0.401 0.126 0.271 9.236

Problem 88

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

38 38 38 35 0 113 124 34 46

N.S.

1 1.00 1.00 0.92 0.00 2.97 3.26 0.89 1.21

time (sec)

N/A 0.169 0.014 2.115 0.000 0.421 0.103 0.270 8.994

Problem 89

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

35 41 34 35 0 124 100 30 33

N.S.

1 1.17 0.97 1.00 0.00 3.54 2.86 0.86 0.94

time (sec)

N/A 0.168 0.011 2.313 0.000 0.306 0.122 0.257 9.062

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 37 41 32 49 67 102 55 28

N.S.

1 1.16 1.28 1.00 1.53 2.09 3.19 1.72 0.88

time (sec)

N/A 0.165 0.012 2.106 0.286 0.260 0.131 0.263 9.066

Problem 91

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 46 43 34 36 45 39 36 33

N.S.

1 1.07 1.00 0.79 0.84 1.05 0.91 0.84 0.77

time (sec)

N/A 0.170 0.027 2.199 0.285 0.259 0.066 0.261 0.038

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

43 69 62 37 47 68 58 51 34

N.S.

1 1.60 1.44 0.86 1.09 1.58 1.35 1.19 0.79

time (sec)

N/A 0.201 0.029 2.053 0.292 0.288 0.074 0.266 9.009

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

34 41 33 32 34 53 31 36 34

N.S.

1 1.21 0.97 0.94 1.00 1.56 0.91 1.06 1.00

time (sec)

N/A 0.177 0.013 1.978 0.189 0.332 0.061 0.267 0.090

Problem 94

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

42 45 42 32 34 53 32 36 34

N.S.

1 1.07 1.00 0.76 0.81 1.26 0.76 0.86 0.81

time (sec)

N/A 0.184 0.017 2.084 0.186 0.246 0.071 0.259 0.081

Problem 95

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

71 71 70 68 0 334 265 67 119

N.S.

1 1.00 0.99 0.96 0.00 4.70 3.73 0.94 1.68

time (sec)

N/A 0.206 0.064 2.220 0.000 0.307 0.309 0.263 0.160

Problem 96

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

72 78 72 86 0 317 230 75 107

N.S.

1 1.08 1.00 1.19 0.00 4.40 3.19 1.04 1.49

time (sec)

N/A 0.208 0.053 2.242 0.000 0.288 0.311 0.259 9.153

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 74 78 83 97 171 218 90 100

N.S.

1 1.07 1.13 1.20 1.41 2.48 3.16 1.30 1.45

time (sec)

N/A 0.201 0.071 2.603 0.289 0.283 0.292 0.266 9.118

Problem 98

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

62 76 62 111 0 89 212 100 110

N.S.

1 1.23 1.00 1.79 0.00 1.44 3.42 1.61 1.77

time (sec)

N/A 0.246 0.134 3.144 0.000 0.454 0.486 0.283 0.153

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 63 120 31 55 63 56 56 38

N.S.

1 1.91 3.64 0.94 1.67 1.91 1.70 1.70 1.15

time (sec)

N/A 0.227 0.118 2.302 0.191 0.426 0.140 0.274 0.154

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B B A A B B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 63 120 31 51 59 56 54 38

N.S.

1 2.03 3.87 1.00 1.65 1.90 1.81 1.74 1.23

time (sec)

N/A 0.219 0.099 2.200 0.192 0.517 0.146 0.269 0.127

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