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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

44 49 22 17 26 33 32 57 35

N.S.

1 1.11 0.50 0.39 0.59 0.75 0.73 1.30 0.80

time (sec)

N/A 0.188 0.089 0.367 0.283 0.250 0.144 0.263 27.402

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

44 49 22 17 26 33 0 57 16

N.S.

1 1.11 0.50 0.39 0.59 0.75 0.00 1.30 0.36

time (sec)

N/A 0.270 0.016 0.612 0.294 0.238 0.000 0.304 27.129

Problem 3

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

48 22 22 17 16 43 246 57 35

N.S.

1 0.46 0.46 0.35 0.33 0.90 5.12 1.19 0.73

time (sec)

N/A 0.164 0.230 0.868 0.300 0.246 2.894 0.269 27.296

Problem 4

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

48 22 22 17 16 43 246 57 35

N.S.

1 0.46 0.46 0.35 0.33 0.90 5.12 1.19 0.73

time (sec)

N/A 0.179 0.838 0.781 0.284 0.251 3.026 0.277 27.497

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

48 22 22 17 16 43 246 57 35

N.S.

1 0.46 0.46 0.35 0.33 0.90 5.12 1.19 0.73

time (sec)

N/A 0.195 0.024 0.872 0.300 0.245 3.042 0.290 27.211

Problem 6

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 22 22 17 16 43 0 16 16

N.S.

1 0.46 0.46 0.35 0.33 0.90 0.00 0.33 0.33

time (sec)

N/A 0.207 0.009 1.368 0.300 0.247 0.000 0.909 26.598

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 22 22 17 16 43 0 57 16

N.S.

1 0.46 0.46 0.35 0.33 0.90 0.00 1.19 0.33

time (sec)

N/A 0.204 0.009 1.234 0.331 0.245 0.000 0.358 25.686

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

60 22 22 17 54 74 42 39 16

N.S.

1 0.37 0.37 0.28 0.90 1.23 0.70 0.65 0.27

time (sec)

N/A 0.176 0.105 0.559 0.293 0.237 0.151 0.304 25.657

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 22 22 17 54 74 0 39 16

N.S.

1 0.37 0.37 0.28 0.90 1.23 0.00 0.65 0.27

time (sec)

N/A 0.248 0.081 0.937 0.287 0.246 0.000 0.338 26.303

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

60 22 22 17 34 86 1644 39 16

N.S.

1 0.37 0.37 0.28 0.57 1.43 27.40 0.65 0.27

time (sec)

N/A 0.181 0.438 0.674 0.295 0.238 9.466 0.296 26.408

Problem 11

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

60 22 22 17 34 86 1644 39 16

N.S.

1 0.37 0.37 0.28 0.57 1.43 27.40 0.65 0.27

time (sec)

N/A 0.177 1.096 0.612 0.290 0.247 9.499 0.288 26.027

Problem 12

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

60 22 22 17 34 86 1644 39 16

N.S.

1 0.37 0.37 0.28 0.57 1.43 27.40 0.65 0.27

time (sec)

N/A 0.194 0.019 0.890 0.303 0.247 9.243 0.293 26.700

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

60 22 22 17 34 86 0 39 16

N.S.

1 0.37 0.37 0.28 0.57 1.43 0.00 0.65 0.27

time (sec)

N/A 0.204 0.009 1.248 0.294 0.244 0.000 0.936 26.664

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

60 22 22 17 34 86 0 39 16

N.S.

1 0.37 0.37 0.28 0.57 1.43 0.00 0.65 0.27

time (sec)

N/A 0.206 0.025 1.012 0.293 0.260 0.000 0.399 26.282

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

42 47 22 18 27 31 34 57 36

N.S.

1 1.12 0.52 0.43 0.64 0.74 0.81 1.36 0.86

time (sec)

N/A 0.195 0.176 0.520 0.316 0.241 0.129 0.266 26.692

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

42 47 22 18 27 31 0 57 17

N.S.

1 1.12 0.52 0.43 0.64 0.74 0.00 1.36 0.40

time (sec)

N/A 0.239 0.027 0.932 0.306 0.239 0.000 0.326 26.817

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 Yes Yes Yes TBD TBD TBD TBD TBD

size

48 22 22 18 17 43 76 57 36

N.S.

1 0.46 0.46 0.38 0.35 0.90 1.58 1.19 0.75

time (sec)

N/A 0.167 0.011 1.273 0.292 0.250 0.282 0.267 26.949

Problem 18

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

48 22 22 18 17 43 76 57 36

N.S.

1 0.46 0.46 0.38 0.35 0.90 1.58 1.19 0.75

time (sec)

N/A 0.177 0.488 1.238 0.319 0.244 0.263 0.273 27.455

Problem 19

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

48 22 22 18 17 43 76 57 36

N.S.

1 0.46 0.46 0.38 0.35 0.90 1.58 1.19 0.75

time (sec)

N/A 0.193 0.014 1.428 0.309 0.253 0.310 0.278 26.477

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

48 22 22 18 17 43 0 17 17

N.S.

1 0.46 0.46 0.38 0.35 0.90 0.00 0.35 0.35

time (sec)

N/A 0.198 0.025 1.153 0.301 0.261 0.000 0.772 26.893

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

48 22 22 18 17 43 0 57 17

N.S.

1 0.46 0.46 0.38 0.35 0.90 0.00 1.19 0.35

time (sec)

N/A 0.206 0.017 1.010 0.297 0.246 0.000 0.390 27.368

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 Yes Yes Yes TBD TBD TBD TBD TBD

size

61 22 22 18 53 74 39 39 17

N.S.

1 0.36 0.36 0.30 0.87 1.21 0.64 0.64 0.28

time (sec)

N/A 0.175 0.114 0.478 0.292 0.248 0.153 0.280 28.127

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

61 22 22 18 53 74 0 39 17

N.S.

1 0.36 0.36 0.30 0.87 1.21 0.00 0.64 0.28

time (sec)

N/A 0.239 0.017 0.912 0.285 0.249 0.000 0.327 28.620

Problem 24

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

61 22 22 18 32 85 1481 39 17

N.S.

1 0.36 0.36 0.30 0.52 1.39 24.28 0.64 0.28

time (sec)

N/A 0.177 1.214 0.607 0.297 0.245 7.832 0.295 27.985

Problem 25

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

61 22 22 18 32 85 1481 39 17

N.S.

1 0.36 0.36 0.30 0.52 1.39 24.28 0.64 0.28

time (sec)

N/A 0.177 0.563 0.597 0.294 0.253 7.951 0.284 27.786

Problem 26

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

61 22 22 18 32 85 1481 39 17

N.S.

1 0.36 0.36 0.30 0.52 1.39 24.28 0.64 0.28

time (sec)

N/A 0.196 0.024 0.865 0.303 0.243 7.917 0.297 27.873

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

61 22 22 18 32 85 0 37 17

N.S.

1 0.36 0.36 0.30 0.52 1.39 0.00 0.61 0.28

time (sec)

N/A 0.201 0.009 1.207 0.294 0.271 0.000 0.791 28.687

Problem 28

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

61 22 22 18 32 85 0 39 17

N.S.

1 0.36 0.36 0.30 0.52 1.39 0.00 0.64 0.28

time (sec)

N/A 0.205 0.020 1.079 0.294 0.239 0.000 0.419 28.103

Problem 29

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

30 30 30 25 24 22 41 24 24

N.S.

1 1.00 1.00 0.83 0.80 0.73 1.37 0.80 0.80

time (sec)

N/A 0.198 0.050 0.464 0.208 0.253 0.068 0.253 0.108

Problem 30

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

56 56 48 47 48 46 85 46 46

N.S.

1 1.00 0.86 0.84 0.86 0.82 1.52 0.82 0.82

time (sec)

N/A 0.239 0.063 1.517 0.211 0.249 0.095 0.259 28.848

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

213 213 163 233 0 187 0 0 0

N.S.

1 1.00 0.77 1.09 0.00 0.88 0.00 0.00 0.00

time (sec)

N/A 0.634 0.819 1.136 0.000 0.251 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

271 271 245 328 0 434 0 0 0

N.S.

1 1.00 0.90 1.21 0.00 1.60 0.00 0.00 0.00

time (sec)

N/A 0.905 1.650 1.671 0.000 0.257 0.000 0.000 0.000

Problem 33

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

10 10 10 9 8 8 10 8 8

N.S.

1 1.00 1.00 0.90 0.80 0.80 1.00 0.80 0.80

time (sec)

N/A 0.194 0.033 0.562 0.203 0.249 0.107 0.258 26.975

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes No TBD TBD TBD TBD TBD

size

28 28 46 72 0 0 0 0 0

N.S.

1 1.00 1.64 2.57 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.593 0.692 0.685 0.000 0.000 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A A A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

12 12 26 12 17 22 10 11 11

N.S.

1 1.00 2.17 1.00 1.42 1.83 0.83 0.92 0.92

time (sec)

N/A 0.189 0.045 0.439 0.209 0.233 0.642 0.268 28.698

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

100 108 324 142 0 104 0 630 0

N.S.

1 1.08 3.24 1.42 0.00 1.04 0.00 6.30 0.00

time (sec)

N/A 0.545 0.801 1.467 0.000 0.249 0.000 3.572 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 115 495 195 0 113 0 681 0

N.S.

1 1.07 4.63 1.82 0.00 1.06 0.00 6.36 0.00

time (sec)

N/A 0.581 3.916 1.494 0.000 0.265 0.000 25.070 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

194 180 692 295 0 212 0 1239 0

N.S.

1 0.93 3.57 1.52 0.00 1.09 0.00 6.39 0.00

time (sec)

N/A 0.482 7.776 1.733 0.000 0.285 0.000 66.416 0.000

Problem 39

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

58 57 53 0 0 0 0 0 0

N.S.

1 0.98 0.91 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.330 0.356 0.000 0.000 0.000 0.000 0.000 0.000

Problem 40

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

58 57 57 0 0 0 0 0 0

N.S.

1 0.98 0.98 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.307 0.221 0.000 0.000 0.000 0.000 0.000 0.000

Problem 41

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

26 26 26 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 0.256 0.131 0.000 0.000 0.000 0.000 0.000 0.000

Problem 42

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

34 34 36 32 35 34 48 34 35

N.S.

1 1.00 1.06 0.94 1.03 1.00 1.41 1.00 1.03

time (sec)

N/A 0.264 3.594 0.678 0.378 0.261 10.182 0.349 28.516

Problem 43

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

36 36 38 32 696 45 51 34 35

N.S.

1 1.00 1.06 0.89 19.33 1.25 1.42 0.94 0.97

time (sec)

N/A 0.295 20.517 0.678 0.456 0.244 36.783 0.362 28.717

Problem 44

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

30 30 26 25 24 23 41 24 24

N.S.

1 1.00 0.87 0.83 0.80 0.77 1.37 0.80 0.80

time (sec)

N/A 0.202 0.051 0.480 0.220 0.240 0.065 0.273 28.912

Problem 45

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

56 56 51 48 46 44 85 46 48

N.S.

1 1.00 0.91 0.86 0.82 0.79 1.52 0.82 0.86

time (sec)

N/A 0.244 0.075 1.471 0.209 0.248 0.092 0.272 0.110

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

213 213 164 231 0 189 0 0 0

N.S.

1 1.00 0.77 1.08 0.00 0.89 0.00 0.00 0.00

time (sec)

N/A 0.530 0.538 1.093 0.000 0.259 0.000 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

271 271 243 326 0 436 0 0 0

N.S.

1 1.00 0.90 1.20 0.00 1.61 0.00 0.00 0.00

time (sec)

N/A 0.831 0.669 1.740 0.000 0.273 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A B A A A A A A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

10 27 10 9 8 8 8 8 8

N.S.

1 2.70 1.00 0.90 0.80 0.80 0.80 0.80 0.80

time (sec)

N/A 0.326 0.034 0.522 0.207 0.245 0.142 0.264 25.944

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A A B A A B

verified

N/A No Yes Yes TBD TBD TBD TBD TBD

size

22 38 22 18 17 37 20 17 15

N.S.

1 1.73 1.00 0.82 0.77 1.68 0.91 0.77 0.68

time (sec)

N/A 0.380 0.054 0.572 0.298 0.235 0.203 0.262 26.192

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 No Yes Yes TBD TBD TBD TBD TBD

size

24 36 20 16 16 15 15 19 16

N.S.

1 1.50 0.83 0.67 0.67 0.62 0.62 0.79 0.67

time (sec)

N/A 0.635 0.721 4.674 0.203 0.237 1.979 0.267 26.749

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

101 108 319 142 0 105 0 633 0

N.S.

1 1.07 3.16 1.41 0.00 1.04 0.00 6.27 0.00

time (sec)

N/A 0.564 0.789 1.540 0.000 0.242 0.000 5.257 0.000

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

107 114 497 195 0 109 0 683 0

N.S.

1 1.07 4.64 1.82 0.00 1.02 0.00 6.38 0.00

time (sec)

N/A 0.582 3.567 1.655 0.000 0.247 0.000 26.794 0.000

Problem 53

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

58 57 53 0 0 0 0 0 0

N.S.

1 0.98 0.91 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.332 0.026 0.000 0.000 0.000 0.000 0.000 0.000

Problem 54

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

58 57 51 0 0 0 0 0 0

N.S.

1 0.98 0.88 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.302 0.032 0.000 0.000 0.000 0.000 0.000 0.000

Problem 55

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

26 26 26 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 0.255 0.008 0.000 0.000 0.000 0.000 0.000 0.000

Problem 56

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

34 34 36 32 35 34 48 34 35

N.S.

1 1.00 1.06 0.94 1.03 1.00 1.41 1.00 1.03

time (sec)

N/A 0.264 3.261 0.562 0.475 0.249 6.662 0.369 26.471

Problem 57

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

36 36 38 32 420 34 51 34 35

N.S.

1 1.00 1.06 0.89 11.67 0.94 1.42 0.94 0.97

time (sec)

N/A 0.296 13.936 0.688 0.430 0.252 21.289 0.347 25.939

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

9 9 9 8 7 13 10 8 19

N.S.

1 1.00 1.00 0.89 0.78 1.44 1.11 0.89 2.11

time (sec)

N/A 0.179 0.015 0.090 0.223 0.252 0.077 0.269 27.295

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

16 16 18 15 12 12 14 12 20

N.S.

1 1.00 1.12 0.94 0.75 0.75 0.88 0.75 1.25

time (sec)

N/A 0.190 0.029 0.364 0.290 0.246 0.079 0.276 26.939

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

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

size

70 90 70 0 80 0 0 0 0

N.S.

1 1.29 1.00 0.00 1.14 0.00 0.00 0.00 0.00

time (sec)

N/A 0.415 0.020 0.000 0.302 0.000 0.000 0.000 0.000

Problem 61

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

19 19 18 18 83 23 0 18 21

N.S.

1 1.00 0.95 0.95 4.37 1.21 0.00 0.95 1.11

time (sec)

N/A 0.156 1.152 0.923 0.293 0.243 0.000 4.002 28.418

Problem 62

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A A B A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

16 18 26 16 14 28 15 22 20

N.S.

1 1.12 1.62 1.00 0.88 1.75 0.94 1.38 1.25

time (sec)

N/A 0.198 0.089 0.359 0.294 0.248 0.077 0.294 28.060

Problem 63

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

92 92 85 120 0 0 0 0 0

N.S.

1 1.00 0.92 1.30 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.393 2.759 8.656 0.000 0.000 0.000 0.000 0.000

Problem 64

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 33 35 43 6257 72 0 66 29

N.S.

1 0.94 1.00 1.23 178.77 2.06 0.00 1.89 0.83

time (sec)

N/A 0.208 0.034 1.219 84.817 0.265 0.000 0.277 0.115

Problem 65

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

35 33 35 43 6257 72 0 66 29

N.S.

1 0.94 1.00 1.23 178.77 2.06 0.00 1.89 0.83

time (sec)

N/A 0.216 0.003 0.872 84.357 0.256 0.000 0.280 0.003

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

15 15 15 12 11 10 20 6 6

N.S.

1 1.00 1.00 0.80 0.73 0.67 1.33 0.40 0.40

time (sec)

N/A 0.164 0.025 0.576 0.213 0.226 0.124 0.259 0.041

Problem 67

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

17 17 17 14 13 13 20 13 13

N.S.

1 1.00 1.00 0.82 0.76 0.76 1.18 0.76 0.76

time (sec)

N/A 0.165 0.009 0.757 0.186 0.235 0.128 0.265 0.037

Problem 68

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

17 17 17 14 13 18 20 13 13

N.S.

1 1.00 1.00 0.82 0.76 1.06 1.18 0.76 0.76

time (sec)

N/A 0.164 0.024 0.852 0.192 0.242 0.123 0.264 0.041

Problem 69

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

35 35 25 28 28 26 78 29 64

N.S.

1 1.00 0.71 0.80 0.80 0.74 2.23 0.83 1.83

time (sec)

N/A 0.186 0.041 0.697 0.195 0.249 0.252 0.256 26.429

Problem 70

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 12 11 9 20 11 9

N.S.

1 1.00 1.00 0.80 0.73 0.60 1.33 0.73 0.60

time (sec)

N/A 0.162 0.024 0.603 0.190 0.236 0.126 0.260 0.027

Problem 71

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

17 17 17 14 13 13 20 13 13

N.S.

1 1.00 1.00 0.82 0.76 0.76 1.18 0.76 0.76

time (sec)

N/A 0.167 0.007 0.773 0.184 0.246 0.127 0.265 0.028

Problem 72

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

17 17 17 14 13 17 20 13 17

N.S.

1 1.00 1.00 0.82 0.76 1.00 1.18 0.76 1.00

time (sec)

N/A 0.165 0.025 0.783 0.204 0.246 0.131 0.267 0.037

Problem 73

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 24 28 28 24 37 29 55

N.S.

1 1.00 0.69 0.80 0.80 0.69 1.06 0.83 1.57

time (sec)

N/A 0.187 0.036 0.677 0.197 0.242 0.261 0.264 26.462

Problem 74

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 27 20 18 141 38 0 0 17

N.S.

1 1.35 1.00 0.90 7.05 1.90 0.00 0.00 0.85

time (sec)

N/A 0.186 0.016 0.715 0.287 0.250 0.000 0.000 25.638

Problem 75

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

47 57 21 38 0 39 0 364 26

N.S.

1 1.21 0.45 0.81 0.00 0.83 0.00 7.74 0.55

time (sec)

N/A 0.270 0.029 0.999 0.000 0.243 0.000 0.349 26.009

Problem 76

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

71 80 69 55 0 101 0 0 103

N.S.

1 1.13 0.97 0.77 0.00 1.42 0.00 0.00 1.45

time (sec)

N/A 0.274 0.062 1.206 0.000 0.251 0.000 0.000 25.838

Problem 77

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

112 112 100 236 0 136 0 0 107

N.S.

1 1.00 0.89 2.11 0.00 1.21 0.00 0.00 0.96

time (sec)

N/A 0.389 0.125 0.842 0.000 0.268 0.000 0.000 26.722

Problem 78

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F A F F B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

89 93 84 103 0 134 0 0 131

N.S.

1 1.04 0.94 1.16 0.00 1.51 0.00 0.00 1.47

time (sec)

N/A 0.355 0.108 0.793 0.000 0.275 0.000 0.000 27.666

Problem 79

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

105 105 200 0 0 0 0 0 0

N.S.

1 1.00 1.90 0.00 0.00 0.00 0.00 0.00 0.00

time (sec)

N/A 0.259 0.121 0.000 0.000 0.000 0.000 0.000 0.000

Problem 80

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

10 14 10 12 37 19 19 19 10

N.S.

1 1.40 1.00 1.20 3.70 1.90 1.90 1.90 1.00

time (sec)

N/A 0.188 0.009 0.269 0.298 0.251 0.362 0.256 25.275

Problem 81

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

20 20 20 17 127 36 0 34 16

N.S.

1 1.00 1.00 0.85 6.35 1.80 0.00 1.70 0.80

time (sec)

N/A 0.186 0.015 0.358 0.303 0.244 0.000 0.273 26.052

Problem 82

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

28 30 28 88 173 52 0 50 29

N.S.

1 1.07 1.00 3.14 6.18 1.86 0.00 1.79 1.04

time (sec)

N/A 0.249 0.026 0.384 0.292 0.253 0.000 0.263 25.320

Problem 83

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

82 82 76 55 0 127 0 111 119

N.S.

1 1.00 0.93 0.67 0.00 1.55 0.00 1.35 1.45

time (sec)

N/A 0.356 0.203 0.448 0.000 0.265 0.000 0.361 26.918

Problem 84

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

38 42 38 124 0 70 0 70 37

N.S.

1 1.11 1.00 3.26 0.00 1.84 0.00 1.84 0.97

time (sec)

N/A 0.279 0.046 0.420 0.000 0.261 0.000 0.273 28.128

Problem 85

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A B A B B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

15 15 35 13 129 33 0 49 12

N.S.

1 1.00 2.33 0.87 8.60 2.20 0.00 3.27 0.80

time (sec)

N/A 0.180 0.063 1.574 0.281 0.242 0.000 0.281 0.232

Problem 86

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

21 27 17 18 81 19 0 24 15

N.S.

1 1.29 0.81 0.86 3.86 0.90 0.00 1.14 0.71

time (sec)

N/A 0.186 0.009 1.549 0.279 0.250 0.000 0.263 27.299

Problem 87

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C C F B F B B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

71 71 4814 47 0 121 0 133 112

N.S.

1 1.00 67.80 0.66 0.00 1.70 0.00 1.87 1.58

time (sec)

N/A 0.231 52.974 1.747 0.000 0.270 0.000 0.268 27.294

Problem 88

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F A F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

62 80 57 43 0 72 0 67 47

N.S.

1 1.29 0.92 0.69 0.00 1.16 0.00 1.08 0.76

time (sec)

N/A 0.294 0.581 2.086 0.000 0.288 0.000 0.276 0.668

Problem 89

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A C A F B F B B

verified

N/A Yes No Yes TBD TBD TBD TBD TBD

size

85 85 627 80 0 153 0 182 118

N.S.

1 1.00 7.38 0.94 0.00 1.80 0.00 2.14 1.39

time (sec)

N/A 0.276 7.333 1.830 0.000 0.277 0.000 0.280 27.361

Problem 90

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

7 7 7 9 35 17 15 17 5

N.S.

1 1.00 1.00 1.29 5.00 2.43 2.14 2.43 0.71

time (sec)

N/A 0.193 0.002 0.293 0.300 0.238 0.404 0.264 26.990

Problem 91

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B A A A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

45 15 15 14 125 58 76 31 17

N.S.

1 0.33 0.33 0.31 2.78 1.29 1.69 0.69 0.38

time (sec)

N/A 0.186 0.048 0.618 0.327 0.262 0.803 0.281 28.315

Problem 92

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A B B B B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

26 26 26 28 171 50 294 48 27

N.S.

1 1.00 1.00 1.08 6.58 1.92 11.31 1.85 1.04

time (sec)

N/A 0.200 0.040 0.683 0.300 0.257 3.423 0.271 27.584

Problem 93

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A C F B F A B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

165 87 84 42 0 231 0 105 217

N.S.

1 0.53 0.51 0.25 0.00 1.40 0.00 0.64 1.32

time (sec)

N/A 0.263 0.166 0.852 0.000 0.284 0.000 0.345 27.981

Problem 94

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

N/A A A A F B F B B

verified

N/A Yes Yes Yes TBD TBD TBD TBD TBD

size

36 38 30 47 0 68 0 68 35

N.S.

1 1.06 0.83 1.31 0.00 1.89 0.00 1.89 0.97

time (sec)

N/A 0.239 0.040 0.721 0.000 0.273 0.000 0.275 28.125

Problem 95

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 16 6 7 6 8 5 6 6

N.S.

1 2.00 0.75 0.88 0.75 1.00 0.62 0.75 0.75

time (sec)

N/A 0.191 0.025 0.387 0.197 0.245 0.380 0.269 28.014

Problem 96

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 0.192 0.005 0.290 0.198 0.255 1.272 0.277 0.030

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

15 15 15 12 11 6 22 6 6

N.S.

1 1.00 1.00 0.80 0.73 0.40 1.47 0.40 0.40

time (sec)

N/A 0.166 0.007 0.390 0.200 0.241 0.127 0.266 0.029

Problem 98

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

17 17 17 14 13 13 22 13 13

N.S.

1 1.00 1.00 0.82 0.76 0.76 1.29 0.76 0.76

time (sec)

N/A 0.164 0.007 0.487 0.210 0.251 0.128 0.272 0.034

Problem 99

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

17 17 17 14 13 13 22 13 14

N.S.

1 1.00 1.00 0.82 0.76 0.76 1.29 0.76 0.82

time (sec)

N/A 0.165 0.007 0.471 0.199 0.240 0.128 0.257 0.034

Problem 100

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 26 28 27 25 44 29 57

N.S.

1 1.00 0.74 0.80 0.77 0.71 1.26 0.83 1.63

time (sec)

N/A 0.187 0.038 0.410 0.199 0.254 0.274 0.261 27.347

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