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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 B F(-1)

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 67 56 58 47 74 0 646 0

N.S.

1 0.68 0.57 0.59 0.48 0.76 0.00 6.59 0.00

time (sec)

N/A 0.380 0.403 0.274 0.339 0.266 0.000 0.997 0.000

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 49 47 48 34 52 0 226 0

N.S.

1 0.80 0.77 0.79 0.56 0.85 0.00 3.70 0.00

time (sec)

N/A 0.311 0.121 0.030 0.351 0.275 0.000 0.520 0.000

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

32 32 32 37 19 38 0 23 0

N.S.

1 1.00 1.00 1.16 0.59 1.19 0.00 0.72 0.00

time (sec)

N/A 0.236 0.042 0.032 0.339 0.277 0.000 0.282 0.000

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 33 39 47 33 50 0 0 34

N.S.

1 1.06 1.26 1.52 1.06 1.61 0.00 0.00 1.10

time (sec)

N/A 0.241 0.097 0.034 0.324 0.302 0.000 0.000 10.648

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

66 54 56 64 46 69 0 169 0

N.S.

1 0.82 0.85 0.97 0.70 1.05 0.00 2.56 0.00

time (sec)

N/A 0.331 0.407 0.033 0.336 0.264 0.000 0.353 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 70 66 74 66 82 0 225 0

N.S.

1 0.72 0.68 0.76 0.68 0.85 0.00 2.32 0.00

time (sec)

N/A 0.407 0.293 0.037 0.334 0.268 0.000 0.382 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

364 232 204 266 178 332 0 291 0

N.S.

1 0.64 0.56 0.73 0.49 0.91 0.00 0.80 0.00

time (sec)

N/A 0.771 1.049 0.110 0.406 0.265 0.000 0.457 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

286 198 115 236 140 279 0 253 0

N.S.

1 0.69 0.40 0.83 0.49 0.98 0.00 0.88 0.00

time (sec)

N/A 0.568 0.740 0.035 0.354 0.276 0.000 0.362 0.000

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

255 178 162 208 133 272 0 195 0

N.S.

1 0.70 0.64 0.82 0.52 1.07 0.00 0.76 0.00

time (sec)

N/A 0.484 0.302 0.035 0.347 0.289 0.000 0.301 0.000

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

255 178 87 211 126 307 0 251 0

N.S.

1 0.70 0.34 0.83 0.49 1.20 0.00 0.98 0.00

time (sec)

N/A 0.486 0.485 0.037 0.347 0.292 0.000 0.400 0.000

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

298 200 98 236 163 320 0 279 0

N.S.

1 0.67 0.33 0.79 0.55 1.07 0.00 0.94 0.00

time (sec)

N/A 0.564 0.391 0.029 0.341 0.275 0.000 0.507 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

364 232 139 272 172 348 0 305 0

N.S.

1 0.64 0.38 0.75 0.47 0.96 0.00 0.84 0.00

time (sec)

N/A 0.747 0.709 0.032 0.350 0.277 0.000 0.767 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

182 100 86 84 79 96 0 960 0

N.S.

1 0.55 0.47 0.46 0.43 0.53 0.00 5.27 0.00

time (sec)

N/A 0.561 0.908 0.092 0.348 0.281 0.000 5.878 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 68 66 64 53 62 0 992 0

N.S.

1 0.62 0.60 0.58 0.48 0.56 0.00 9.02 0.00

time (sec)

N/A 0.381 0.911 0.031 0.335 0.268 0.000 2.413 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 37 41 42 26 37 0 229 0

N.S.

1 0.74 0.82 0.84 0.52 0.74 0.00 4.58 0.00

time (sec)

N/A 0.240 0.119 0.030 0.380 0.260 0.000 0.365 0.000

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 38 43 40 27 39 0 45 0

N.S.

1 0.75 0.84 0.78 0.53 0.76 0.00 0.88 0.00

time (sec)

N/A 0.243 0.072 0.030 0.345 0.269 0.000 0.379 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

119 71 45 63 50 62 0 114 0

N.S.

1 0.60 0.38 0.53 0.42 0.52 0.00 0.96 0.00

time (sec)

N/A 0.406 0.062 0.033 0.335 0.286 0.000 0.505 0.000

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

183 101 45 83 70 82 0 169 0

N.S.

1 0.55 0.25 0.45 0.38 0.45 0.00 0.92 0.00

time (sec)

N/A 0.564 0.043 0.042 0.353 0.290 0.000 1.046 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

71 71 63 0 0 0 0 0 0

N.S.

1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.286 0.184 0.000 0.000 0.000 0.000 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

65 65 61 0 0 0 0 0 0

N.S.

1 1.00 0.94 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.292 0.141 0.000 0.000 0.000 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

56 70 56 0 0 0 0 0 0

N.S.

1 1.25 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.275 0.131 0.000 0.000 0.000 0.000 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

62 62 60 0 0 0 0 0 0

N.S.

1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.284 0.141 0.000 0.000 0.000 0.000 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

71 71 61 0 0 0 0 0 0

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.283 0.164 0.000 0.000 0.000 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

71 71 63 0 0 0 0 0 0

N.S.

1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.290 0.156 0.000 0.000 0.000 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

59 59 59 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.284 0.137 0.000 0.000 0.000 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

59 59 51 0 0 0 0 0 0

N.S.

1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.283 0.130 0.000 0.000 0.000 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

57 57 57 0 0 0 0 0 0

N.S.

1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.283 0.133 0.000 0.000 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

59 59 55 0 0 0 0 0 0

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.280 0.122 0.000 0.000 0.000 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

32 32 32 5979 0 23 0 0 0

N.S.

1 1.00 1.00 186.84 0.00 0.72 0.00 0.00 0.00

time (sec)

N/A 0.246 0.032 1.728 0.000 0.266 0.000 0.000 0.000

Problem 30

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

70 62 104 92 62 64 0 54384 92

N.S.

1 0.89 1.49 1.31 0.89 0.91 0.00 776.91 1.31

time (sec)

N/A 0.257 0.438 1.889 0.225 0.307 0.000 17.595 10.471

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

48 43 72 72 44 46 0 71 68

N.S.

1 0.90 1.50 1.50 0.92 0.96 0.00 1.48 1.42

time (sec)

N/A 0.237 0.291 0.345 0.279 0.272 0.000 0.441 10.174

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

28 26 46 52 31 31 0 38 39

N.S.

1 0.93 1.64 1.86 1.11 1.11 0.00 1.36 1.39

time (sec)

N/A 0.218 0.199 0.151 0.248 0.280 0.000 0.411 10.281

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 23 51 34 40 56 0 58 37

N.S.

1 0.92 2.04 1.36 1.60 2.24 0.00 2.32 1.48

time (sec)

N/A 0.209 0.075 0.293 0.226 0.291 0.000 0.403 10.211

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

51 58 123 68 76 124 0 171 95

N.S.

1 1.14 2.41 1.33 1.49 2.43 0.00 3.35 1.86

time (sec)

N/A 0.234 0.315 0.323 0.260 0.285 0.000 0.433 10.244

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 94 276 102 101 178 0 239 138

N.S.

1 1.19 3.49 1.29 1.28 2.25 0.00 3.03 1.75

time (sec)

N/A 0.271 6.368 1.052 0.243 0.280 0.000 0.449 10.247

Problem 36

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

102 128 89 122 111 90 0 7296 105

N.S.

1 1.25 0.87 1.20 1.09 0.88 0.00 71.53 1.03

time (sec)

N/A 0.385 0.690 3.968 0.351 0.296 0.000 2.565 10.799

Problem 37

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

74 94 58 102 82 72 0 4018 79

N.S.

1 1.27 0.78 1.38 1.11 0.97 0.00 54.30 1.07

time (sec)

N/A 0.267 0.622 0.725 0.341 0.273 0.000 1.885 10.424

Problem 38

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

46 59 43 81 51 54 0 368 41

N.S.

1 1.28 0.93 1.76 1.11 1.17 0.00 8.00 0.89

time (sec)

N/A 0.231 0.498 0.217 0.305 0.292 0.000 0.456 10.038

Problem 39

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

19 19 28 20 23 21 20 231 21

N.S.

1 1.00 1.47 1.05 1.21 1.11 1.05 12.16 1.11

time (sec)

N/A 0.169 0.002 0.014 0.294 0.280 0.067 0.359 10.291

Problem 40

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

24 22 24 25 24 37 0 24 26

N.S.

1 0.92 1.00 1.04 1.00 1.54 0.00 1.00 1.08

time (sec)

N/A 0.220 0.086 0.124 0.244 0.276 0.000 0.412 10.618

Problem 41

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

42 37 60 54 40 66 0 49 41

N.S.

1 0.88 1.43 1.29 0.95 1.57 0.00 1.17 0.98

time (sec)

N/A 0.228 0.358 0.504 0.215 0.263 0.000 0.424 10.720

Problem 42

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

64 56 106 83 59 91 0 73 59

N.S.

1 0.88 1.66 1.30 0.92 1.42 0.00 1.14 0.92

time (sec)

N/A 0.249 0.295 1.695 0.226 0.263 0.000 0.444 10.877

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 96 97 185 104 105 0 0 183

N.S.

1 0.90 0.91 1.73 0.97 0.98 0.00 0.00 1.71

time (sec)

N/A 0.298 1.500 2.626 0.271 0.266 0.000 0.000 11.169

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 72 72 155 80 80 0 135 128

N.S.

1 0.90 0.90 1.94 1.00 1.00 0.00 1.69 1.60

time (sec)

N/A 0.286 1.047 1.122 0.301 0.272 0.000 0.718 13.799

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

54 49 48 125 71 59 0 88 126

N.S.

1 0.91 0.89 2.31 1.31 1.09 0.00 1.63 2.33

time (sec)

N/A 0.240 0.635 0.456 0.338 0.289 0.000 0.636 12.610

Problem 46

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

52 47 66 97 68 87 0 139 86

N.S.

1 0.90 1.27 1.87 1.31 1.67 0.00 2.67 1.65

time (sec)

N/A 0.248 0.674 0.181 0.314 0.287 0.000 0.614 11.343

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 78 376 85 111 168 0 236 188

N.S.

1 0.95 4.59 1.04 1.35 2.05 0.00 2.88 2.29

time (sec)

N/A 0.277 6.904 0.594 0.339 0.289 0.000 0.644 11.311

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

123 134 447 145 163 284 0 391 243

N.S.

1 1.09 3.63 1.18 1.33 2.31 0.00 3.18 1.98

time (sec)

N/A 0.354 7.510 2.206 0.318 0.304 0.000 0.693 10.295

Problem 49

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

122 137 96 199 130 120 0 12581 128

N.S.

1 1.12 0.79 1.63 1.07 0.98 0.00 103.12 1.05

time (sec)

N/A 0.355 2.274 1.646 0.374 0.290 0.000 23.408 10.110

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A B A A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 84 71 168 87 94 0 1325 114

N.S.

1 0.99 0.84 1.98 1.02 1.11 0.00 15.59 1.34

time (sec)

N/A 0.271 1.433 0.669 0.370 0.277 0.000 0.839 10.343

Problem 51

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

46 50 73 49 58 51 68 359 76

N.S.

1 1.09 1.59 1.07 1.26 1.11 1.48 7.80 1.65

time (sec)

N/A 0.227 0.613 0.028 0.385 0.274 0.106 0.469 10.281

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

46 41 44 48 41 71 0 41 67

N.S.

1 0.89 0.96 1.04 0.89 1.54 0.00 0.89 1.46

time (sec)

N/A 0.244 1.336 0.306 0.333 0.297 0.000 0.609 10.223

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

70 62 59 81 66 92 0 78 69

N.S.

1 0.89 0.84 1.16 0.94 1.31 0.00 1.11 0.99

time (sec)

N/A 0.269 1.951 1.206 0.309 0.299 0.000 0.617 10.137

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

93 82 88 136 88 137 0 119 90

N.S.

1 0.88 0.95 1.46 0.95 1.47 0.00 1.28 0.97

time (sec)

N/A 0.280 2.168 3.983 0.334 0.268 0.000 0.659 10.738

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

117 109 177 144 0 294 0 356 643

N.S.

1 0.93 1.51 1.23 0.00 2.51 0.00 3.04 5.50

time (sec)

N/A 0.351 3.781 10.415 0.000 0.300 0.000 0.516 13.622

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

84 87 149 87 0 206 0 173 382

N.S.

1 1.04 1.77 1.04 0.00 2.45 0.00 2.06 4.55

time (sec)

N/A 0.282 1.182 2.150 0.000 0.300 0.000 0.505 12.287

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 58 121 61 0 158 0 78 112

N.S.

1 0.97 2.02 1.02 0.00 2.63 0.00 1.30 1.87

time (sec)

N/A 0.239 0.528 0.359 0.000 0.303 0.000 0.489 10.921

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 58 144 70 0 184 0 108 91

N.S.

1 0.97 2.40 1.17 0.00 3.07 0.00 1.80 1.52

time (sec)

N/A 0.249 0.592 0.180 0.000 0.335 0.000 0.460 11.053

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 97 195 117 0 327 0 201 591

N.S.

1 1.09 2.19 1.31 0.00 3.67 0.00 2.26 6.64

time (sec)

N/A 0.289 1.024 0.292 0.000 0.336 0.000 0.463 11.476

Problem 60

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

130 149 326 185 0 630 0 354 740

N.S.

1 1.15 2.51 1.42 0.00 4.85 0.00 2.72 5.69

time (sec)

N/A 0.370 6.715 0.820 0.000 0.355 0.000 0.473 12.902

Problem 61

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

178 223 140 185 305 521 0 279 4910

N.S.

1 1.25 0.79 1.04 1.71 2.93 0.00 1.57 27.58

time (sec)

N/A 0.441 1.090 21.624 0.497 0.341 0.000 0.516 15.185

Problem 62

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

129 161 99 131 183 383 0 182 3588

N.S.

1 1.25 0.77 1.02 1.42 2.97 0.00 1.41 27.81

time (sec)

N/A 0.339 0.717 5.167 0.308 0.322 0.000 0.498 13.777

Problem 63

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

82 101 69 83 93 274 0 108 190

N.S.

1 1.23 0.84 1.01 1.13 3.34 0.00 1.32 2.32

time (sec)

N/A 0.287 0.598 0.907 0.321 0.310 0.000 0.490 11.419

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A B A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

50 50 49 50 48 182 240 65 948

N.S.

1 1.00 0.98 1.00 0.96 3.64 4.80 1.30 18.96

time (sec)

N/A 0.305 0.086 0.069 0.299 0.289 1.253 0.401 10.869

Problem 65

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

48 46 48 44 42 257 0 59 40

N.S.

1 0.96 1.00 0.92 0.88 5.35 0.00 1.23 0.83

time (sec)

N/A 0.244 0.550 0.191 0.318 0.296 0.000 0.471 10.330

Problem 66

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

76 71 73 67 68 373 0 92 67

N.S.

1 0.93 0.96 0.88 0.89 4.91 0.00 1.21 0.88

time (sec)

N/A 0.260 0.650 0.433 0.301 0.304 0.000 0.483 10.073

Problem 67

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

105 97 103 99 104 543 0 143 115

N.S.

1 0.92 0.98 0.94 0.99 5.17 0.00 1.36 1.10

time (sec)

N/A 0.306 1.270 1.128 0.292 0.315 0.000 0.483 10.729

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

204 213 215 197 0 593 0 530 1049

N.S.

1 1.04 1.05 0.97 0.00 2.91 0.00 2.60 5.14

time (sec)

N/A 0.523 4.480 30.600 0.000 0.390 0.000 0.681 14.669

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

133 134 182 152 0 456 0 354 737

N.S.

1 1.01 1.37 1.14 0.00 3.43 0.00 2.66 5.54

time (sec)

N/A 0.409 4.192 7.737 0.000 0.333 0.000 0.638 13.952

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 104 146 103 0 307 0 147 436

N.S.

1 1.03 1.45 1.02 0.00 3.04 0.00 1.46 4.32

time (sec)

N/A 0.265 1.376 1.536 0.000 0.307 0.000 0.616 12.977

Problem 71

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

110 122 184 128 0 470 0 255 1140

N.S.

1 1.11 1.67 1.16 0.00 4.27 0.00 2.32 10.36

time (sec)

N/A 0.309 1.549 0.341 0.000 0.379 0.000 0.542 13.091

Problem 72

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

147 154 325 156 0 672 0 390 917

N.S.

1 1.05 2.21 1.06 0.00 4.57 0.00 2.65 6.24

time (sec)

N/A 0.355 6.937 0.613 0.000 0.379 0.000 0.567 11.391

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

210 226 392 232 0 1052 0 516 1113

N.S.

1 1.08 1.87 1.10 0.00 5.01 0.00 2.46 5.30

time (sec)

N/A 0.460 7.029 1.229 0.000 0.376 0.000 0.587 11.141

Problem 74

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

196 230 136 159 312 705 0 256 4616

N.S.

1 1.17 0.69 0.81 1.59 3.60 0.00 1.31 23.55

time (sec)

N/A 0.413 2.203 15.249 0.316 0.382 0.000 0.640 15.287

Problem 75

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

138 161 111 120 185 568 0 186 3301

N.S.

1 1.17 0.80 0.87 1.34 4.12 0.00 1.35 23.92

time (sec)

N/A 0.342 2.231 3.549 0.296 0.354 0.000 0.630 13.807

Problem 76

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

97 116 88 93 114 390 2125 122 2489

N.S.

1 1.20 0.91 0.96 1.18 4.02 21.91 1.26 25.66

time (sec)

N/A 0.257 1.208 0.118 0.309 0.296 14.422 0.429 12.399

Problem 77

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

82 81 83 69 73 373 0 88 70

N.S.

1 0.99 1.01 0.84 0.89 4.55 0.00 1.07 0.85

time (sec)

N/A 0.256 1.254 0.403 0.331 0.320 0.000 0.558 10.639

Problem 78

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

116 118 112 100 115 587 0 134 108

N.S.

1 1.02 0.97 0.86 0.99 5.06 0.00 1.16 0.93

time (sec)

N/A 0.363 1.499 0.769 0.306 0.320 0.000 0.589 10.624

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

182 187 151 144 161 855 0 200 178

N.S.

1 1.03 0.83 0.79 0.88 4.70 0.00 1.10 0.98

time (sec)

N/A 0.435 2.302 1.565 0.334 0.339 0.000 0.626 11.690

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

264 273 278 282 0 1018 0 834 1536

N.S.

1 1.03 1.05 1.07 0.00 3.86 0.00 3.16 5.82

time (sec)

N/A 0.643 6.417 73.243 0.000 0.401 0.000 1.039 15.625

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

180 182 230 196 0 775 0 541 1154

N.S.

1 1.01 1.28 1.09 0.00 4.31 0.00 3.01 6.41

time (sec)

N/A 0.481 6.712 23.299 0.000 0.396 0.000 1.005 14.778

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

138 150 170 132 0 556 0 215 780

N.S.

1 1.09 1.23 0.96 0.00 4.03 0.00 1.56 5.65

time (sec)

N/A 0.291 2.297 5.465 0.000 0.360 0.000 0.991 14.012

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

166 192 247 183 0 1050 0 503 1844

N.S.

1 1.16 1.49 1.10 0.00 6.33 0.00 3.03 11.11

time (sec)

N/A 0.417 5.255 0.653 0.000 0.491 0.000 0.832 15.572

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

205 233 414 206 0 1419 0 583 1652

N.S.

1 1.14 2.02 1.00 0.00 6.92 0.00 2.84 8.06

time (sec)

N/A 0.438 7.649 1.672 0.000 0.478 0.000 0.859 12.697

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

259 275 468 265 0 1693 0 861 1357

N.S.

1 1.06 1.81 1.02 0.00 6.54 0.00 3.32 5.24

time (sec)

N/A 0.534 7.273 3.182 0.000 0.459 0.000 0.909 11.940

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

250 289 194 209 460 1191 0 381 5965

N.S.

1 1.16 0.78 0.84 1.84 4.76 0.00 1.52 23.86

time (sec)

N/A 0.496 1.608 42.121 0.322 0.432 0.000 1.001 15.652

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

193 233 164 172 346 1076 0 272 4997

N.S.

1 1.21 0.85 0.89 1.79 5.58 0.00 1.41 25.89

time (sec)

N/A 0.415 3.557 11.627 0.300 0.389 0.000 0.985 15.106

Problem 88

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

150 183 138 142 227 742 8964 205 3901

N.S.

1 1.22 0.92 0.95 1.51 4.95 59.76 1.37 26.01

time (sec)

N/A 0.338 2.054 0.200 0.326 0.328 71.341 0.496 14.164

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 116 144 83 105 555 0 103 102

N.S.

1 1.04 1.29 0.74 0.94 4.96 0.00 0.92 0.91

time (sec)

N/A 0.280 1.705 1.019 0.324 0.356 0.000 0.828 10.480

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

154 156 146 123 158 857 0 165 147

N.S.

1 1.01 0.95 0.80 1.03 5.56 0.00 1.07 0.95

time (sec)

N/A 0.445 2.411 1.984 0.315 0.361 0.000 0.874 11.757

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

231 236 346 175 212 1199 0 248 199

N.S.

1 1.02 1.50 0.76 0.92 5.19 0.00 1.07 0.86

time (sec)

N/A 0.545 2.400 4.258 0.326 0.374 0.000 0.904 12.410

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

161 173 208 1242 203 378 0 2554 0

N.S.

1 1.07 1.29 7.71 1.26 2.35 0.00 15.86 0.00

time (sec)

N/A 0.353 3.925 2.161 0.333 0.409 0.000 1.033 0.000

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 108 170 643 132 277 0 1182 0

N.S.

1 0.96 1.50 5.69 1.17 2.45 0.00 10.46 0.00

time (sec)

N/A 0.293 1.471 0.499 0.331 0.404 0.000 0.791 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

72 70 140 454 97 203 0 389 0

N.S.

1 0.97 1.94 6.31 1.35 2.82 0.00 5.40 0.00

time (sec)

N/A 0.242 0.835 0.595 0.322 0.398 0.000 0.702 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

84 82 170 428 0 514 0 0 0

N.S.

1 0.98 2.02 5.10 0.00 6.12 0.00 0.00 0.00

time (sec)

N/A 0.289 2.685 0.519 0.000 0.383 0.000 0.000 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

127 134 586 1345 0 849 0 0 0

N.S.

1 1.06 4.61 10.59 0.00 6.69 0.00 0.00 0.00

time (sec)

N/A 0.336 5.746 0.611 0.000 0.795 0.000 0.000 0.000

Problem 97

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes No No TBD TBD TBD TBD TBD

size

187 207 1049 2048 0 1273 0 0 0

N.S.

1 1.11 5.61 10.95 0.00 6.81 0.00 0.00 0.00

time (sec)

N/A 0.429 7.082 1.401 0.000 1.081 0.000 0.000 0.000

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

189 213 330 851 0 2068 0 0 0

N.S.

1 1.13 1.75 4.50 0.00 10.94 0.00 0.00 0.00

time (sec)

N/A 0.416 4.182 8.073 0.000 7.789 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

128 132 273 370 0 1847 0 0 0

N.S.

1 1.03 2.13 2.89 0.00 14.43 0.00 0.00 0.00

time (sec)

N/A 0.310 4.361 5.081 0.000 0.850 0.000 0.000 0.000

Problem 100

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

85 83 108 169 0 410 0 0 0

N.S.

1 0.98 1.27 1.99 0.00 4.82 0.00 0.00 0.00

time (sec)

N/A 0.245 0.528 0.065 0.000 0.366 0.000 0.000 0.000

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