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2.2.1 Integrals 1 to 64

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 C F A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

233 215 148 160 179 465 0 248 828

N.S.

1 0.92 0.64 0.69 0.77 2.00 0.00 1.06 3.55

time (sec)

N/A 0.663 0.905 2.079 0.322 0.272 0.000 0.473 13.647

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 34 29 23 48 22 40 20

N.S.

1 1.00 1.70 1.45 1.15 2.40 1.10 2.00 1.00

time (sec)

N/A 0.158 0.016 0.023 0.321 0.306 0.065 0.274 13.255

Problem 3

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

47 51 71 48 63 127 68 114 45

N.S.

1 1.09 1.51 1.02 1.34 2.70 1.45 2.43 0.96

time (sec)

N/A 0.233 1.259 0.054 0.299 0.271 0.096 0.320 0.121

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

78 79 111 77 112 253 126 229 76

N.S.

1 1.01 1.42 0.99 1.44 3.24 1.62 2.94 0.97

time (sec)

N/A 0.251 2.954 0.091 0.305 0.265 0.134 0.378 12.915

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

49 49 49 56 48 252 238 65 41

N.S.

1 1.00 1.00 1.14 0.98 5.14 4.86 1.33 0.84

time (sec)

N/A 0.324 0.070 0.076 0.323 0.284 0.740 0.305 0.118

Problem 6

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

97 117 90 99 115 534 2125 123 119

N.S.

1 1.21 0.93 1.02 1.19 5.51 21.91 1.27 1.23

time (sec)

N/A 0.270 1.021 0.118 0.324 0.305 9.066 0.316 12.401

Problem 7

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

150 184 138 148 228 1068 8964 206 4866

N.S.

1 1.23 0.92 0.99 1.52 7.12 59.76 1.37 32.44

time (sec)

N/A 0.334 0.352 0.210 0.324 0.328 48.202 0.398 16.089

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

22 24 51 19 300 91 0 32 18

N.S.

1 1.09 2.32 0.86 13.64 4.14 0.00 1.45 0.82

time (sec)

N/A 0.226 0.134 0.098 0.373 0.270 0.000 0.265 13.184

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

5 5 28 6 35 53 0 10 5

N.S.

1 1.00 5.60 1.20 7.00 10.60 0.00 2.00 1.00

time (sec)

N/A 0.209 0.033 0.033 0.360 0.293 0.000 0.273 12.971

Problem 10

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

12 14 12 13 10 21 14 28 12

N.S.

1 1.17 1.00 1.08 0.83 1.75 1.17 2.33 1.00

time (sec)

N/A 0.226 0.030 0.018 0.314 0.260 0.187 0.280 13.109

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B C F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 39 48 32 284 73 0 34 31

N.S.

1 1.11 1.37 0.91 8.11 2.09 0.00 0.97 0.89

time (sec)

N/A 0.246 0.115 0.039 0.390 0.271 0.000 0.268 13.017

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A C F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 16 30 15 17 19 0 11 14

N.S.

1 1.14 2.14 1.07 1.21 1.36 0.00 0.79 1.00

time (sec)

N/A 0.228 0.039 0.042 0.338 0.276 0.000 0.280 12.874

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A C F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

14 16 14 15 12 14 0 28 13

N.S.

1 1.14 1.00 1.07 0.86 1.00 0.00 2.00 0.93

time (sec)

N/A 0.222 0.030 0.032 0.315 0.255 0.000 0.265 13.203

Problem 14

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

28 36 19 29 24 27 0 25 17

N.S.

1 1.29 0.68 1.04 0.86 0.96 0.00 0.89 0.61

time (sec)

N/A 0.340 0.030 0.079 0.237 0.263 0.000 0.278 13.096

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 22 32 38 27 77 0 49 0

N.S.

1 0.71 1.03 1.23 0.87 2.48 0.00 1.58 0.00

time (sec)

N/A 0.352 0.152 0.044 0.373 0.276 0.000 0.291 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 10 10 11 8 27 12 11 10

N.S.

1 1.00 1.00 1.10 0.80 2.70 1.20 1.10 1.00

time (sec)

N/A 0.276 0.032 0.037 0.232 0.274 0.541 0.264 12.978

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 45 19 39 52 78 0 12 20

N.S.

1 1.25 0.53 1.08 1.44 2.17 0.00 0.33 0.56

time (sec)

N/A 0.330 0.027 0.419 0.346 0.278 0.000 0.272 13.185

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

29 23 19 24 18 35 0 25 34

N.S.

1 0.79 0.66 0.83 0.62 1.21 0.00 0.86 1.17

time (sec)

N/A 0.360 0.141 0.242 0.319 0.271 0.000 0.266 13.354

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 72 65 84 0 330 0 0 66

N.S.

1 1.09 0.98 1.27 0.00 5.00 0.00 0.00 1.00

time (sec)

N/A 0.296 0.203 0.163 0.000 0.342 0.000 0.000 15.109

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 53 48 71 0 248 0 95 53

N.S.

1 1.10 1.00 1.48 0.00 5.17 0.00 1.98 1.10

time (sec)

N/A 0.252 0.034 0.032 0.000 0.343 0.000 0.340 13.957

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 65 60 194 0 351 0 187 69

N.S.

1 1.08 1.00 3.23 0.00 5.85 0.00 3.12 1.15

time (sec)

N/A 0.274 0.034 7.154 0.000 0.287 0.000 0.325 13.781

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 93 140 174 0 768 0 0 0

N.S.

1 1.04 1.57 1.96 0.00 8.63 0.00 0.00 0.00

time (sec)

N/A 0.324 4.414 0.056 0.000 0.312 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F(-2) B F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

65 65 78 137 0 515 0 210 0

N.S.

1 1.00 1.20 2.11 0.00 7.92 0.00 3.23 0.00

time (sec)

N/A 0.239 0.173 0.046 0.000 0.284 0.000 0.498 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

51 51 44 312 0 193 0 239 0

N.S.

1 1.00 0.86 6.12 0.00 3.78 0.00 4.69 0.00

time (sec)

N/A 0.277 0.102 0.870 0.000 0.310 0.000 0.294 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

85 88 174 495 0 239 0 476 0

N.S.

1 1.04 2.05 5.82 0.00 2.81 0.00 5.60 0.00

time (sec)

N/A 0.327 1.763 1.508 0.000 0.329 0.000 0.329 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

88 95 91 150 0 486 0 0 120

N.S.

1 1.08 1.03 1.70 0.00 5.52 0.00 0.00 1.36

time (sec)

N/A 0.283 0.607 0.038 0.000 0.353 0.000 0.000 24.407

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

127 136 253 286 0 1134 0 0 0

N.S.

1 1.07 1.99 2.25 0.00 8.93 0.00 0.00 0.00

time (sec)

N/A 0.401 1.316 0.031 0.000 0.335 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 77 63 136 0 330 0 0 70

N.S.

1 1.12 0.91 1.97 0.00 4.78 0.00 0.00 1.01

time (sec)

N/A 0.262 0.188 0.024 0.000 0.333 0.000 0.000 16.991

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

75 80 75 341 0 565 0 0 506

N.S.

1 1.07 1.00 4.55 0.00 7.53 0.00 0.00 6.75

time (sec)

N/A 0.301 0.087 1.279 0.000 0.790 0.000 0.000 0.260

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

80 80 222 642 0 543 0 625 0

N.S.

1 1.00 2.78 8.02 0.00 6.79 0.00 7.81 0.00

time (sec)

N/A 0.313 0.815 0.821 0.000 0.761 0.000 18.701 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

171 171 169 462 0 1520 0 0 0

N.S.

1 1.00 0.99 2.70 0.00 8.89 0.00 0.00 0.00

time (sec)

N/A 0.359 0.885 0.185 0.000 0.323 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F B F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 124 143 298 0 1071 0 0 0

N.S.

1 0.98 1.13 2.37 0.00 8.50 0.00 0.00 0.00

time (sec)

N/A 0.290 0.499 0.035 0.000 0.321 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F(-2) B F F(-2) F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

87 84 107 170 0 703 0 0 0

N.S.

1 0.97 1.23 1.95 0.00 8.08 0.00 0.00 0.00

time (sec)

N/A 0.238 0.077 0.048 0.000 0.302 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 47 111 68 0 239 0 97 41

N.S.

1 1.00 2.36 1.45 0.00 5.09 0.00 2.06 0.87

time (sec)

N/A 0.212 0.482 0.111 0.000 0.315 0.000 1.323 13.726

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F(-2) B F B F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

85 84 231 102 0 526 0 300 0

N.S.

1 0.99 2.72 1.20 0.00 6.19 0.00 3.53 0.00

time (sec)

N/A 0.245 3.719 0.046 0.000 0.336 0.000 0.846 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F(-2) B F B F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

135 145 367 162 0 898 0 1160 0

N.S.

1 1.07 2.72 1.20 0.00 6.65 0.00 8.59 0.00

time (sec)

N/A 0.297 8.138 0.039 0.000 0.354 0.000 1.136 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F(-2) B F B F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

190 214 2553 253 0 1452 0 3249 0

N.S.

1 1.13 13.44 1.33 0.00 7.64 0.00 17.10 0.00

time (sec)

N/A 0.375 15.969 0.042 0.000 0.420 0.000 2.089 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 57 123 51 0 110 0 257 104

N.S.

1 1.06 2.28 0.94 0.00 2.04 0.00 4.76 1.93

time (sec)

N/A 0.225 0.505 0.090 0.000 0.310 0.000 0.330 14.224

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C B F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 62 34 507 68 0 170 88

N.S.

1 1.00 1.94 1.06 15.84 2.12 0.00 5.31 2.75

time (sec)

N/A 0.203 0.104 0.078 0.848 0.276 0.000 0.285 14.192

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F C B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

28 28 26 31 90 56 0 34 85

N.S.

1 1.00 0.93 1.11 3.21 2.00 0.00 1.21 3.04

time (sec)

N/A 0.194 0.056 0.081 0.481 0.306 0.000 0.270 13.177

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 64 121 48 0 170 0 179 0

N.S.

1 1.05 1.98 0.79 0.00 2.79 0.00 2.93 0.00

time (sec)

N/A 0.229 0.255 0.041 0.000 0.282 0.000 0.520 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 42 60 35 941 123 0 0 34

N.S.

1 1.00 1.43 0.83 22.40 2.93 0.00 0.00 0.81

time (sec)

N/A 0.209 0.090 0.030 0.692 0.294 0.000 0.000 13.918

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

26 26 48 21 143 60 0 45 20

N.S.

1 1.00 1.85 0.81 5.50 2.31 0.00 1.73 0.77

time (sec)

N/A 0.185 0.073 0.063 0.530 0.301 0.000 0.301 13.907

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

52 56 52 44 0 284 0 96 44

N.S.

1 1.08 1.00 0.85 0.00 5.46 0.00 1.85 0.85

time (sec)

N/A 0.266 0.191 0.037 0.000 0.352 0.000 0.364 14.609

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

64 64 158 80 0 588 0 229 0

N.S.

1 1.00 2.47 1.25 0.00 9.19 0.00 3.58 0.00

time (sec)

N/A 0.274 0.353 0.035 0.000 0.318 0.000 0.544 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

33 33 33 29 0 127 0 61 27

N.S.

1 1.00 1.00 0.88 0.00 3.85 0.00 1.85 0.82

time (sec)

N/A 0.242 0.027 0.078 0.000 0.285 0.000 0.328 13.513

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 65 60 149 0 419 0 203 93

N.S.

1 1.08 1.00 2.48 0.00 6.98 0.00 3.38 1.55

time (sec)

N/A 0.282 0.056 0.802 0.000 0.321 0.000 0.372 13.099

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

54 54 134 283 0 229 0 216 0

N.S.

1 1.00 2.48 5.24 0.00 4.24 0.00 4.00 0.00

time (sec)

N/A 0.269 0.852 0.914 0.000 0.330 0.000 0.337 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 64 59 68 0 385 0 109 52

N.S.

1 1.08 1.00 1.15 0.00 6.53 0.00 1.85 0.88

time (sec)

N/A 0.282 0.259 0.057 0.000 0.310 0.000 0.320 14.397

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A F(-2) B F B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

59 59 137 99 0 388 0 159 0

N.S.

1 1.00 2.32 1.68 0.00 6.58 0.00 2.69 0.00

time (sec)

N/A 0.282 0.806 0.058 0.000 0.368 0.000 0.339 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

55 60 44 56 0 344 88 105 47

N.S.

1 1.09 0.80 1.02 0.00 6.25 1.60 1.91 0.85

time (sec)

N/A 0.264 0.052 0.038 0.000 0.309 4.816 0.305 14.409

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C B F B F B B

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

84 109 75 517 0 863 0 295 1451

N.S.

1 1.30 0.89 6.15 0.00 10.27 0.00 3.51 17.27

time (sec)

N/A 0.314 0.065 1.522 0.000 0.369 0.000 0.354 0.479

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

92 101 674 631 0 393 0 359 0

N.S.

1 1.10 7.33 6.86 0.00 4.27 0.00 3.90 0.00

time (sec)

N/A 0.336 6.947 2.931 0.000 0.354 0.000 0.328 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 96 69 88 0 698 0 219 88

N.S.

1 1.17 0.84 1.07 0.00 8.51 0.00 2.67 1.07

time (sec)

N/A 0.315 0.110 0.062 0.000 0.309 0.000 0.294 16.211

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F(-2) B F B F(-1)

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

94 105 197 161 0 720 0 281 0

N.S.

1 1.12 2.10 1.71 0.00 7.66 0.00 2.99 0.00

time (sec)

N/A 0.311 6.340 0.060 0.000 0.386 0.000 0.340 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 93 47 75 0 627 110 215 82

N.S.

1 1.19 0.60 0.96 0.00 8.04 1.41 2.76 1.05

time (sec)

N/A 0.281 0.056 0.046 0.000 0.337 7.393 0.320 17.273

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C F F B F B B

verified

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

size

118 159 78 0 0 1531 0 483 2817

N.S.

1 1.35 0.66 0.00 0.00 12.97 0.00 4.09 23.87

time (sec)

N/A 0.372 0.074 0.000 0.000 0.488 0.000 0.383 13.682

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

141 161 1450 934 0 647 0 537 0

N.S.

1 1.14 10.28 6.62 0.00 4.59 0.00 3.81 0.00

time (sec)

N/A 0.426 8.162 1.563 0.000 0.343 0.000 0.355 0.000

Problem 59

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

37 43 57 31 33 24 34 34 37

N.S.

1 1.16 1.54 0.84 0.89 0.65 0.92 0.92 1.00

time (sec)

N/A 0.310 0.047 0.135 0.294 0.289 0.124 0.264 13.795

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

90 86 86 139 0 1063 0 204 0

N.S.

1 0.96 0.96 1.54 0.00 11.81 0.00 2.27 0.00

time (sec)

N/A 0.323 0.187 0.242 0.000 0.451 0.000 0.303 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 130 167 245 0 1486 0 445 0

N.S.

1 1.03 1.33 1.94 0.00 11.79 0.00 3.53 0.00

time (sec)

N/A 0.398 4.810 0.071 0.000 0.483 0.000 0.539 0.000

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

41 41 41 65 0 264 0 58 0

N.S.

1 1.00 1.00 1.59 0.00 6.44 0.00 1.41 0.00

time (sec)

N/A 0.257 0.022 0.202 0.000 0.385 0.000 0.320 0.000

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 73 73 248 0 670 0 111 0

N.S.

1 0.99 0.99 3.35 0.00 9.05 0.00 1.50 0.00

time (sec)

N/A 0.294 0.332 1.025 0.000 0.451 0.000 0.290 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 130 114 586 0 1365 0 276 0

N.S.

1 1.11 0.97 5.01 0.00 11.67 0.00 2.36 0.00

time (sec)

N/A 0.360 0.831 0.135 0.000 0.517 0.000 0.313 0.000

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