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2.2.1 Integrals 1 to 99

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

34 32 29 31 27 27 36 45 27

N.S.

1 0.94 0.85 0.91 0.79 0.79 1.06 1.32 0.79

time (sec)

N/A 0.258 0.064 1.050 0.292 0.259 0.249 0.268 0.109

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 93 82 58 67 72 209 135 0

N.S.

1 1.02 0.90 0.64 0.74 0.79 2.30 1.48 0.00

time (sec)

N/A 0.299 0.167 1.082 0.286 0.245 0.989 0.275 0.000

Problem 3

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

15 15 15 14 13 13 19 13 13

N.S.

1 1.00 1.00 0.93 0.87 0.87 1.27 0.87 0.87

time (sec)

N/A 0.193 0.005 0.621 0.242 0.267 0.091 0.289 0.060

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 57 44 48 61 61 95 51

N.S.

1 1.00 0.81 0.63 0.69 0.87 0.87 1.36 0.73

time (sec)

N/A 0.233 0.102 0.236 0.308 0.246 0.202 0.274 13.703

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 24 22 43 21 0 21 0

N.S.

1 1.00 0.96 0.88 1.72 0.84 0.00 0.84 0.00

time (sec)

N/A 0.229 0.060 0.289 0.354 0.261 0.000 0.274 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

80 86 81 57 73 70 0 0 0

N.S.

1 1.08 1.01 0.71 0.91 0.88 0.00 0.00 0.00

time (sec)

N/A 0.284 0.196 0.301 0.402 0.239 0.000 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

42 40 42 39 48 40 0 87 0

N.S.

1 0.95 1.00 0.93 1.14 0.95 0.00 2.07 0.00

time (sec)

N/A 0.408 0.083 0.333 0.366 0.249 0.000 0.315 0.000

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

51 55 40 42 42 45 78 76 41

N.S.

1 1.08 0.78 0.82 0.82 0.88 1.53 1.49 0.80

time (sec)

N/A 0.242 0.139 0.524 0.262 0.257 0.304 0.282 0.153

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

91 91 87 63 90 84 201 118 0

N.S.

1 1.00 0.96 0.69 0.99 0.92 2.21 1.30 0.00

time (sec)

N/A 0.262 0.181 0.452 0.330 0.249 1.313 0.313 0.000

Problem 10

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

31 35 27 23 23 28 60 26 22

N.S.

1 1.13 0.87 0.74 0.74 0.90 1.94 0.84 0.71

time (sec)

N/A 0.214 0.044 0.459 0.277 0.265 0.122 0.338 0.068

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

70 70 67 45 70 59 56 82 0

N.S.

1 1.00 0.96 0.64 1.00 0.84 0.80 1.17 0.00

time (sec)

N/A 0.202 0.063 0.404 0.354 0.257 0.403 0.287 0.000

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

37 37 34 68 51 31 0 35 0

N.S.

1 1.00 0.92 1.84 1.38 0.84 0.00 0.95 0.00

time (sec)

N/A 0.217 0.113 0.616 0.370 0.254 0.000 0.306 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

76 84 76 62 83 66 0 0 0

N.S.

1 1.11 1.00 0.82 1.09 0.87 0.00 0.00 0.00

time (sec)

N/A 0.379 0.175 0.398 0.631 0.274 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

57 57 50 98 61 48 0 107 0

N.S.

1 1.00 0.88 1.72 1.07 0.84 0.00 1.88 0.00

time (sec)

N/A 0.271 0.134 0.635 0.365 0.246 0.000 0.305 0.000

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

79 82 55 66 58 58 92 92 66

N.S.

1 1.04 0.70 0.84 0.73 0.73 1.16 1.16 0.84

time (sec)

N/A 0.392 0.163 0.527 0.308 0.261 0.420 0.294 13.928

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

188 188 160 130 143 148 439 259 0

N.S.

1 1.00 0.85 0.69 0.76 0.79 2.34 1.38 0.00

time (sec)

N/A 0.396 0.467 0.457 0.373 0.259 2.176 0.302 0.000

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

33 25 33 26 27 25 44 26 28

N.S.

1 0.76 1.00 0.79 0.82 0.76 1.33 0.79 0.85

time (sec)

N/A 0.226 0.019 1.250 0.266 0.277 0.162 0.292 13.870

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

153 153 116 101 112 121 129 185 0

N.S.

1 1.00 0.76 0.66 0.73 0.79 0.84 1.21 0.00

time (sec)

N/A 0.294 0.254 0.434 0.387 0.265 0.517 0.339 0.000

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

55 55 50 125 89 47 0 47 0

N.S.

1 1.00 0.91 2.27 1.62 0.85 0.00 0.85 0.00

time (sec)

N/A 0.247 0.156 1.072 0.400 0.259 0.000 0.279 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

168 172 166 128 152 136 0 0 0

N.S.

1 1.02 0.99 0.76 0.90 0.81 0.00 0.00 0.00

time (sec)

N/A 0.355 0.716 0.661 0.662 0.261 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

91 91 90 185 98 80 0 185 0

N.S.

1 1.00 0.99 2.03 1.08 0.88 0.00 2.03 0.00

time (sec)

N/A 0.368 0.190 0.972 0.376 0.258 0.000 0.313 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A A A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

67 37 54 50 55 51 94 52 55

N.S.

1 0.55 0.81 0.75 0.82 0.76 1.40 0.78 0.82

time (sec)

N/A 0.239 0.093 1.441 0.255 0.277 0.696 0.305 14.405

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 113 113 229 0 64 0 0 0

N.S.

1 1.02 1.02 2.06 0.00 0.58 0.00 0.00 0.00

time (sec)

N/A 0.301 0.210 0.572 0.000 0.089 0.000 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

111 113 111 290 0 62 0 0 0

N.S.

1 1.02 1.00 2.61 0.00 0.56 0.00 0.00 0.00

time (sec)

N/A 0.303 0.168 0.439 0.000 0.087 0.000 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 81 89 290 0 48 0 0 0

N.S.

1 1.00 1.10 3.58 0.00 0.59 0.00 0.00 0.00

time (sec)

N/A 0.242 0.106 0.429 0.000 0.086 0.000 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

81 81 89 338 0 48 0 0 0

N.S.

1 1.00 1.10 4.17 0.00 0.59 0.00 0.00 0.00

time (sec)

N/A 0.242 0.079 0.390 0.000 0.091 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

98 104 114 338 0 66 0 0 0

N.S.

1 1.06 1.16 3.45 0.00 0.67 0.00 0.00 0.00

time (sec)

N/A 0.289 0.205 0.426 0.000 0.094 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

104 108 117 358 0 75 0 0 0

N.S.

1 1.04 1.12 3.44 0.00 0.72 0.00 0.00 0.00

time (sec)

N/A 0.292 0.180 0.456 0.000 0.090 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

132 135 142 0 0 92 0 0 0

N.S.

1 1.02 1.08 0.00 0.00 0.70 0.00 0.00 0.00

time (sec)

N/A 0.340 0.738 0.000 0.000 0.107 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

132 135 142 0 0 91 0 0 0

N.S.

1 1.02 1.08 0.00 0.00 0.69 0.00 0.00 0.00

time (sec)

N/A 0.304 0.659 0.000 0.000 0.100 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

100 102 99 0 0 68 0 0 0

N.S.

1 1.02 0.99 0.00 0.00 0.68 0.00 0.00 0.00

time (sec)

N/A 0.304 0.566 0.000 0.000 0.096 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

96 102 99 0 0 62 0 0 0

N.S.

1 1.06 1.03 0.00 0.00 0.65 0.00 0.00 0.00

time (sec)

N/A 0.247 0.464 0.000 0.000 0.107 0.000 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

117 128 137 0 0 79 0 0 0

N.S.

1 1.09 1.17 0.00 0.00 0.68 0.00 0.00 0.00

time (sec)

N/A 0.329 0.563 0.000 0.000 0.109 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

116 122 137 0 0 85 0 0 0

N.S.

1 1.05 1.18 0.00 0.00 0.73 0.00 0.00 0.00

time (sec)

N/A 0.389 0.573 0.000 0.000 0.093 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

31 32 31 39 57 33 0 132 0

N.S.

1 1.03 1.00 1.26 1.84 1.06 0.00 4.26 0.00

time (sec)

N/A 0.405 0.038 0.640 0.296 0.254 0.000 0.433 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 21 43 20 15 41 0

N.S.

1 1.00 1.00 1.05 2.15 1.00 0.75 2.05 0.00

time (sec)

N/A 0.235 0.054 0.776 0.298 0.251 0.422 0.377 0.000

Problem 37

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 13 13 14 13 15 15 15 13

N.S.

1 1.00 1.00 1.08 1.00 1.15 1.15 1.15 1.00

time (sec)

N/A 0.196 0.006 0.293 0.292 0.239 0.282 0.345 13.872

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

30 30 29 35 51 33 31 49 30

N.S.

1 1.00 0.97 1.17 1.70 1.10 1.03 1.63 1.00

time (sec)

N/A 0.264 0.056 0.935 0.330 0.262 0.386 0.385 13.486

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A A B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

46 51 46 47 50 43 46 107 47

N.S.

1 1.11 1.00 1.02 1.09 0.93 1.00 2.33 1.02

time (sec)

N/A 0.352 0.007 0.810 0.320 0.244 0.540 0.412 13.366

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 87 80 57 127 73 0 0 0

N.S.

1 1.10 1.01 0.72 1.61 0.92 0.00 0.00 0.00

time (sec)

N/A 0.329 0.151 0.477 0.379 0.282 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

25 25 24 22 43 21 0 0 0

N.S.

1 1.00 0.96 0.88 1.72 0.84 0.00 0.00 0.00

time (sec)

N/A 0.229 0.049 0.496 0.313 0.254 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

74 74 62 48 98 65 0 0 55

N.S.

1 1.00 0.84 0.65 1.32 0.88 0.00 0.00 0.74

time (sec)

N/A 0.273 0.121 0.571 0.357 0.265 0.000 0.000 13.343

Problem 43

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

15 15 15 14 13 17 22 17 13

N.S.

1 1.00 1.00 0.93 0.87 1.13 1.47 1.13 0.87

time (sec)

N/A 0.200 0.005 0.332 0.244 0.284 0.510 0.379 13.978

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

97 99 88 64 74 84 0 0 0

N.S.

1 1.02 0.91 0.66 0.76 0.87 0.00 0.00 0.00

time (sec)

N/A 0.334 0.180 0.532 0.308 0.275 0.000 0.000 0.000

Problem 45

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

19 28 18 14 12 13 39 12 12

N.S.

1 1.47 0.95 0.74 0.63 0.68 2.05 0.63 0.63

time (sec)

N/A 0.194 0.036 0.295 0.253 0.256 0.117 0.361 13.923

Problem 46

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

8 8 8 7 6 6 7 6 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.88 0.75 0.75

time (sec)

N/A 0.184 0.004 0.148 0.243 0.282 0.108 0.338 0.036

Problem 47

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

22 21 22 17 16 16 20 16 16

N.S.

1 0.95 1.00 0.77 0.73 0.73 0.91 0.73 0.73

time (sec)

N/A 0.235 0.025 0.271 0.275 0.252 0.098 0.340 13.769

Problem 48

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

36 41 31 34 23 24 51 23 23

N.S.

1 1.14 0.86 0.94 0.64 0.67 1.42 0.64 0.64

time (sec)

N/A 0.207 0.035 0.273 0.251 0.275 0.101 0.409 13.709

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

235 267 165 196 136 145 0 241 0

N.S.

1 1.14 0.70 0.83 0.58 0.62 0.00 1.03 0.00

time (sec)

N/A 1.389 0.640 0.516 0.460 0.297 0.000 0.396 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

169 186 141 131 112 118 0 193 0

N.S.

1 1.10 0.83 0.78 0.66 0.70 0.00 1.14 0.00

time (sec)

N/A 0.947 0.388 0.466 0.287 0.267 0.000 0.437 0.000

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 102 94 64 73 78 0 143 0

N.S.

1 1.03 0.95 0.65 0.74 0.79 0.00 1.44 0.00

time (sec)

N/A 0.528 0.177 0.428 0.268 0.271 0.000 0.601 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

110 122 110 78 74 96 0 0 0

N.S.

1 1.11 1.00 0.71 0.67 0.87 0.00 0.00 0.00

time (sec)

N/A 0.638 0.274 0.465 0.409 0.275 0.000 0.000 0.000

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

184 196 180 129 76 134 0 0 0

N.S.

1 1.07 0.98 0.70 0.41 0.73 0.00 0.00 0.00

time (sec)

N/A 0.981 0.263 0.468 0.440 0.260 0.000 0.000 0.000

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

250 272 238 180 76 164 0 0 0

N.S.

1 1.09 0.95 0.72 0.30 0.66 0.00 0.00 0.00

time (sec)

N/A 1.476 0.364 0.459 0.432 0.260 0.000 0.000 0.000

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

310 328 174 219 161 184 0 224 0

N.S.

1 1.06 0.56 0.71 0.52 0.59 0.00 0.72 0.00

time (sec)

N/A 0.848 0.727 0.579 0.423 0.291 0.000 0.377 0.000

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

218 226 148 145 137 144 0 176 0

N.S.

1 1.04 0.68 0.67 0.63 0.66 0.00 0.81 0.00

time (sec)

N/A 0.599 0.487 0.612 0.368 0.272 0.000 0.360 0.000

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

102 109 103 67 96 90 0 124 0

N.S.

1 1.07 1.01 0.66 0.94 0.88 0.00 1.22 0.00

time (sec)

N/A 0.359 0.212 0.525 0.386 0.298 0.000 0.316 0.000

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

116 151 116 87 88 100 0 0 0

N.S.

1 1.30 1.00 0.75 0.76 0.86 0.00 0.00 0.00

time (sec)

N/A 0.447 0.272 0.587 0.447 0.262 0.000 0.000 0.000

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

228 234 185 146 90 154 0 0 0

N.S.

1 1.03 0.81 0.64 0.39 0.68 0.00 0.00 0.00

time (sec)

N/A 0.984 0.296 0.656 0.452 0.293 0.000 0.000 0.000

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

328 364 249 207 90 192 0 0 0

N.S.

1 1.11 0.76 0.63 0.27 0.59 0.00 0.00 0.00

time (sec)

N/A 0.966 0.428 0.577 0.447 0.284 0.000 0.000 0.000

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 No Yes Yes TBD TBD TBD TBD TBD

size

86 100 66 58 47 48 513 47 62

N.S.

1 1.16 0.77 0.67 0.55 0.56 5.97 0.55 0.72

time (sec)

N/A 0.485 0.105 1.300 0.243 0.255 0.988 0.296 13.557

Problem 62

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

8 8 8 7 6 6 7 6 6

N.S.

1 1.00 1.00 0.88 0.75 0.75 0.88 0.75 0.75

time (sec)

N/A 0.183 0.005 0.140 0.405 0.254 6.713 0.263 13.585

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

18 18 20 18 20 20 17 20 20

N.S.

1 1.00 1.11 1.00 1.11 1.11 0.94 1.11 1.11

time (sec)

N/A 0.175 1.532 0.328 1.220 0.274 8.542 0.944 13.233

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

20 20 22 20 22 22 19 22 22

N.S.

1 1.00 1.10 1.00 1.10 1.10 0.95 1.10 1.10

time (sec)

N/A 0.178 1.667 0.240 1.610 0.270 27.056 5.770 13.098

Problem 65

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

93 93 89 0 0 0 0 0 0

N.S.

1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.325 0.204 0.000 0.000 0.000 0.000 0.000 0.000

Problem 66

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

22 22 24 22 24 24 20 24 24

N.S.

1 1.00 1.09 1.00 1.09 1.09 0.91 1.09 1.09

time (sec)

N/A 0.246 1.750 0.403 1.421 0.274 8.259 0.940 13.325

Problem 67

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

131 131 149 0 0 0 0 0 0

N.S.

1 1.00 1.14 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.416 0.817 0.000 0.000 0.000 0.000 0.000 0.000

Problem 68

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

24 24 26 24 26 26 22 26 26

N.S.

1 1.00 1.08 1.00 1.08 1.08 0.92 1.08 1.08

time (sec)

N/A 0.252 1.853 0.371 1.683 0.263 25.848 5.988 14.403

Problem 69

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 24 25 90 24 0 0 0

N.S.

1 1.00 0.92 0.96 3.46 0.92 0.00 0.00 0.00

time (sec)

N/A 0.248 0.074 1.141 0.401 0.254 0.000 0.000 0.000

Problem 70

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

43 43 37 40 99 35 0 0 0

N.S.

1 1.00 0.86 0.93 2.30 0.81 0.00 0.00 0.00

time (sec)

N/A 0.226 0.153 1.111 0.411 0.279 0.000 0.000 0.000

Problem 71

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

67 67 53 52 180 51 0 0 0

N.S.

1 1.00 0.79 0.78 2.69 0.76 0.00 0.00 0.00

time (sec)

N/A 0.270 0.179 1.610 0.509 0.260 0.000 0.000 0.000

Problem 72

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

79 79 66 66 189 62 0 0 0

N.S.

1 1.00 0.84 0.84 2.39 0.78 0.00 0.00 0.00

time (sec)

N/A 0.283 0.196 2.831 0.514 0.261 0.000 0.000 0.000

Problem 73

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

83 83 92 75 0 0 0 0 0

N.S.

1 1.00 1.11 0.90 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.218 0.087 0.517 0.000 0.000 0.000 0.000 0.000

Problem 74

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

102 102 94 0 0 0 0 0 0

N.S.

1 1.00 0.92 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.255 0.267 0.000 0.000 0.000 0.000 0.000 0.000

Problem 75

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

179 179 173 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 0.297 0.266 0.000 0.000 0.000 0.000 0.000 0.000

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

105 105 115 111 0 0 0 0 0

N.S.

1 1.00 1.10 1.06 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.278 0.219 0.784 0.000 0.000 0.000 0.000 0.000

Problem 77

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

141 141 129 0 0 0 0 0 0

N.S.

1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.349 0.567 0.000 0.000 0.000 0.000 0.000 0.000

Problem 78

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

229 229 221 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 0.426 0.603 0.000 0.000 0.000 0.000 0.000 0.000

Problem 79

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 42 45 45 0 45 0 0 0

N.S.

1 0.89 0.96 0.96 0.00 0.96 0.00 0.00 0.00

time (sec)

N/A 0.422 0.099 1.365 0.000 0.250 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

69 69 53 65 0 53 0 0 0

N.S.

1 1.00 0.77 0.94 0.00 0.77 0.00 0.00 0.00

time (sec)

N/A 0.299 0.205 2.574 0.000 0.262 0.000 0.000 0.000

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

113 113 95 101 0 85 0 0 0

N.S.

1 1.00 0.84 0.89 0.00 0.75 0.00 0.00 0.00

time (sec)

N/A 0.405 0.245 10.355 0.000 0.256 0.000 0.000 0.000

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

78 65 70 65 0 70 0 0 0

N.S.

1 0.83 0.90 0.83 0.00 0.90 0.00 0.00 0.00

time (sec)

N/A 0.540 0.139 1.545 0.000 0.291 0.000 0.000 0.000

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

95 95 82 89 0 87 0 0 0

N.S.

1 1.00 0.86 0.94 0.00 0.92 0.00 0.00 0.00

time (sec)

N/A 0.347 0.236 2.741 0.000 0.266 0.000 0.000 0.000

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 165 141 144 0 127 0 0 0

N.S.

1 1.00 0.85 0.87 0.00 0.77 0.00 0.00 0.00

time (sec)

N/A 0.489 0.377 10.520 0.000 0.260 0.000 0.000 0.000

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

99 91 76 131 258 112 0 159 80

N.S.

1 0.92 0.77 1.32 2.61 1.13 0.00 1.61 0.81

time (sec)

N/A 0.241 0.288 1.816 0.635 0.276 0.000 0.287 0.172

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 45 42 63 199 63 0 119 39

N.S.

1 0.96 0.89 1.34 4.23 1.34 0.00 2.53 0.83

time (sec)

N/A 0.200 0.175 1.182 0.555 0.253 0.000 0.391 13.295

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A C A F C B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

29 29 29 36 84 40 0 55 32

N.S.

1 1.00 1.00 1.24 2.90 1.38 0.00 1.90 1.10

time (sec)

N/A 0.164 0.023 0.246 0.347 0.256 0.000 0.347 13.023

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

12 12 14 12 14 23 20 14 14

N.S.

1 1.00 1.17 1.00 1.17 1.92 1.67 1.17 1.17

time (sec)

N/A 0.159 2.301 0.153 0.418 0.246 0.993 0.308 13.149

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A N/A N/A N/A N/A N/A N/A N/A N/A

verified

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

size

12 12 14 12 14 23 22 14 14

N.S.

1 1.00 1.17 1.00 1.17 1.92 1.83 1.17 1.17

time (sec)

N/A 0.164 3.929 0.158 0.416 0.253 0.949 0.318 13.085

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

346 348 224 825 672 103 269 480 0

N.S.

1 1.01 0.65 2.38 1.94 0.30 0.78 1.39 0.00

time (sec)

N/A 0.477 0.930 1.511 0.290 0.255 0.379 0.284 0.000

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

167 171 71 297 263 67 151 166 0

N.S.

1 1.02 0.43 1.78 1.57 0.40 0.90 0.99 0.00

time (sec)

N/A 0.305 0.372 1.590 0.248 0.250 0.231 0.281 0.000

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

54 51 48 61 60 42 65 42 42

N.S.

1 0.94 0.89 1.13 1.11 0.78 1.20 0.78 0.78

time (sec)

N/A 0.278 0.103 0.990 0.296 0.268 0.205 0.268 13.131

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

126 150 145 271 0 149 0 0 0

N.S.

1 1.19 1.15 2.15 0.00 1.18 0.00 0.00 0.00

time (sec)

N/A 0.405 1.275 1.083 0.000 0.273 0.000 0.000 0.000

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

184 194 240 714 0 210 0 0 0

N.S.

1 1.05 1.30 3.88 0.00 1.14 0.00 0.00 0.00

time (sec)

N/A 0.539 1.382 1.339 0.000 0.325 0.000 0.000 0.000

Problem 95

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

537 540 382 1809 1349 182 0 1104 0

N.S.

1 1.01 0.71 3.37 2.51 0.34 0.00 2.06 0.00

time (sec)

N/A 0.661 1.212 1.619 0.401 0.254 0.000 0.284 0.000

Problem 96

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

261 265 117 655 523 110 0 370 0

N.S.

1 1.02 0.45 2.51 2.00 0.42 0.00 1.42 0.00

time (sec)

N/A 0.401 0.529 2.100 0.244 0.263 0.000 0.278 0.000

Problem 97

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

85 85 65 131 118 57 94 81 68

N.S.

1 1.00 0.76 1.54 1.39 0.67 1.11 0.95 0.80

time (sec)

N/A 0.364 0.157 0.913 0.269 0.305 0.293 0.271 14.020

Problem 98

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

234 262 243 279 0 287 0 0 0

N.S.

1 1.12 1.04 1.19 0.00 1.23 0.00 0.00 0.00

time (sec)

N/A 0.630 11.083 1.105 0.000 0.278 0.000 0.000 0.000

Problem 99

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

332 334 138 931 0 406 0 0 0

N.S.

1 1.01 0.42 2.80 0.00 1.22 0.00 0.00 0.00

time (sec)

N/A 0.768 0.768 1.332 0.000 0.311 0.000 0.000 0.000

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