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2.2 Detailed conclusion table per each integral for all CAS systems

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA and IntegrateAlgebraic to I.A.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

415 415 355 959 444 406 0 1948 3993 1590

N.S.

1 1.00 0.86 2.31 1.07 0.98 0.00 4.69 9.62 3.83

time (sec)

N/A 0.673 0.544 0.035 1.002 0.721 0.000 3.113 47.789 1.063

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

286 286 244 652 307 279 0 1327 2920 1079

N.S.

1 1.00 0.85 2.28 1.07 0.98 0.00 4.64 10.21 3.77

time (sec)

N/A 0.563 0.349 0.018 1.006 0.864 0.000 2.581 36.028 0.713

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

168 170 141 377 174 170 0 782 736 470

N.S.

1 1.01 0.84 2.24 1.04 1.01 0.00 4.65 4.38 2.80

time (sec)

N/A 0.250 0.212 0.013 1.070 0.928 0.000 1.996 12.065 0.392

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

95 95 71 185 93 95 0 336 361 242

N.S.

1 1.00 0.75 1.95 0.98 1.00 0.00 3.54 3.80 2.55

time (sec)

N/A 0.073 0.064 0.012 0.981 0.918 0.000 1.536 7.209 0.193

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

122 122 117 373 0 493 0 0 5803 177

N.S.

1 1.00 0.96 3.06 0.00 4.04 0.00 0.00 47.57 1.45

time (sec)

N/A 0.311 0.150 0.049 0.000 15.664 0.000 0.000 25.801 0.582

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

163 163 211 899 0 1025 0 0 10198 235

N.S.

1 1.00 1.29 5.52 0.00 6.29 0.00 0.00 62.56 1.44

time (sec)

N/A 0.331 0.473 0.039 0.000 72.527 0.000 0.000 52.173 1.488

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

248 248 273 1449 0 1580 0 0 9097 533

N.S.

1 1.00 1.10 5.84 0.00 6.37 0.00 0.00 36.68 2.15

time (sec)

N/A 0.355 0.416 0.050 0.000 1.238 0.000 0.000 59.182 2.349

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

340 340 241 643 355 286 0 427 2606 1135

N.S.

1 1.00 0.71 1.89 1.04 0.84 0.00 1.26 7.66 3.34

time (sec)

N/A 0.633 0.392 0.029 1.045 1.229 0.000 1.819 35.295 0.771

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

228 228 160 423 231 192 0 277 1732 708

N.S.

1 1.00 0.70 1.86 1.01 0.84 0.00 1.21 7.60 3.11

time (sec)

N/A 0.493 0.221 0.028 1.273 0.824 0.000 1.643 33.636 0.473

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A C A A C A B B

verified

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

size

130 133 88 235 131 114 617 146 492 275

N.S.

1 1.02 0.68 1.81 1.01 0.88 4.75 1.12 3.78 2.12

time (sec)

N/A 0.230 0.104 0.023 1.315 0.964 158.075 1.310 12.857 0.260

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A C A A C A B A

verified

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

size

63 63 45 117 57 67 282 76 232 117

N.S.

1 1.00 0.71 1.86 0.90 1.06 4.48 1.21 3.68 1.86

time (sec)

N/A 0.061 0.036 0.017 1.416 1.451 49.744 1.286 7.525 0.139

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

122 122 117 373 0 493 0 0 5803 177

N.S.

1 1.00 0.96 3.06 0.00 4.04 0.00 0.00 47.57 1.45

time (sec)

N/A 0.283 0.131 0.000 0.000 19.359 0.000 0.000 0.005 0.002

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

163 163 211 899 0 1025 0 0 10198 235

N.S.

1 1.00 1.29 5.52 0.00 6.29 0.00 0.00 62.56 1.44

time (sec)

N/A 0.295 0.431 0.000 0.000 76.120 0.000 0.000 0.008 0.002

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

248 248 273 1449 0 1580 0 0 9097 533

N.S.

1 1.00 1.10 5.84 0.00 6.37 0.00 0.00 36.68 2.15

time (sec)

N/A 0.329 0.384 0.000 0.000 0.848 0.000 0.000 0.007 0.002

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A C A A C A B B

verified

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

size

79 79 57 139 87 78 313 101 244 179

N.S.

1 1.00 0.72 1.76 1.10 0.99 3.96 1.28 3.09 2.27

time (sec)

N/A 0.139 0.068 0.000 1.270 1.139 82.521 1.305 7.606 0.002

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A C A A C A B A

verified

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

size

63 63 45 117 57 67 282 76 232 117

N.S.

1 1.00 0.71 1.86 0.90 1.06 4.48 1.21 3.68 1.86

time (sec)

N/A 0.061 0.034 0.000 1.281 0.975 49.685 1.324 7.411 0.001

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

48 48 48 96 57 81 245 0 122 95

N.S.

1 1.00 1.00 2.00 1.19 1.69 5.10 0.00 2.54 1.98

time (sec)

N/A 0.183 0.055 0.001 1.275 0.998 55.715 0.000 4.331 0.002

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

48 48 48 97 57 84 221 0 114 93

N.S.

1 1.00 1.00 2.02 1.19 1.75 4.60 0.00 2.38 1.94

time (sec)

N/A 0.176 0.061 0.000 1.325 1.314 50.054 0.000 4.266 0.002

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

71 71 56 108 98 65 218 0 312 112

N.S.

1 1.00 0.79 1.52 1.38 0.92 3.07 0.00 4.39 1.58

time (sec)

N/A 0.184 0.049 0.000 1.285 0.882 80.629 0.000 6.304 0.002

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A A F(-1) F(-1) F(-1) B

verified

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

size

591 584 427 1446 584 1001 0 0 -1 2590

N.S.

1 0.99 0.72 2.45 0.99 1.69 0.00 0.00 -0.00 4.38

time (sec)

N/A 1.517 1.463 0.043 1.461 0.888 0.000 0.000 0.000 2.002

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A A F(-1) F(-1) F(-1) B

verified

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

size

451 450 311 987 417 703 0 0 -1 1792

N.S.

1 1.00 0.69 2.19 0.92 1.56 0.00 0.00 -0.00 3.97

time (sec)

N/A 1.010 1.016 0.018 2.067 0.983 0.000 0.000 0.000 1.289

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A A F F(-1) B B

verified

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

size

300 297 200 588 248 441 0 0 1765 647

N.S.

1 0.99 0.67 1.96 0.83 1.47 0.00 0.00 5.88 2.16

time (sec)

N/A 0.446 0.682 0.014 2.255 1.199 0.000 0.000 30.577 0.640

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A F F(-1) B A

verified

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

size

221 221 142 287 140 265 0 0 876 326

N.S.

1 1.00 0.64 1.30 0.63 1.20 0.00 0.00 3.96 1.48

time (sec)

N/A 0.147 0.408 0.013 2.028 0.845 0.000 0.000 16.517 0.410

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

278 278 225 503 0 0 0 0 9298 205

N.S.

1 1.00 0.81 1.81 0.00 0.00 0.00 0.00 33.45 0.74

time (sec)

N/A 0.490 0.768 0.069 0.000 0.000 0.000 0.000 44.562 0.369

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

322 322 309 1200 0 0 0 0 -1 282

N.S.

1 1.00 0.96 3.73 0.00 0.00 0.00 0.00 -0.00 0.88

time (sec)

N/A 0.579 0.852 0.044 0.000 0.000 0.000 0.000 0.000 1.119

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

363 361 492 1848 0 1355 0 1658 9344 610

N.S.

1 0.99 1.36 5.09 0.00 3.73 0.00 4.57 25.74 1.68

time (sec)

N/A 0.677 1.795 0.057 0.000 163.672 0.000 7.021 86.666 1.473

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B A A F(-1) F(-1) B B

verified

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

size

501 496 727 965 471 700 0 0 4167 1909

N.S.

1 0.99 1.45 1.93 0.94 1.40 0.00 0.00 8.32 3.81

time (sec)

N/A 1.281 4.902 0.031 1.972 0.777 0.000 0.000 161.428 1.260

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A F(-1) F(-1) B B

verified

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

size

368 369 555 635 317 482 0 0 2799 1213

N.S.

1 1.00 1.51 1.73 0.86 1.31 0.00 0.00 7.61 3.30

time (sec)

N/A 0.875 2.684 0.029 2.021 1.220 0.000 0.000 81.648 0.816

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A A A A F(-1) F(-1) B A

verified

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

size

246 249 390 365 189 302 0 0 1011 356

N.S.

1 1.01 1.59 1.48 0.77 1.23 0.00 0.00 4.11 1.45

time (sec)

N/A 0.400 1.429 0.026 2.055 0.711 0.000 0.000 30.743 0.408

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

177 177 169 180 88 196 338 0 489 150

N.S.

1 1.00 0.95 1.02 0.50 1.11 1.91 0.00 2.76 0.85

time (sec)

N/A 0.124 0.437 0.020 2.501 0.772 56.834 0.000 14.952 0.232

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

278 278 225 503 0 0 0 0 9298 205

N.S.

1 1.00 0.81 1.81 0.00 0.00 0.00 0.00 33.45 0.74

time (sec)

N/A 0.464 0.711 0.000 0.000 0.000 0.000 0.000 0.008 0.003

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

322 322 309 1200 0 0 0 0 106511 282

N.S.

1 1.00 0.96 3.73 0.00 0.00 0.00 0.00 330.78 0.88

time (sec)

N/A 0.530 0.794 0.000 0.000 0.000 0.000 0.000 19.397 0.003

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

363 361 492 1848 0 0 0 1658 9344 610

N.S.

1 0.99 1.36 5.09 0.00 0.00 0.00 4.57 25.74 1.68

time (sec)

N/A 0.588 1.310 0.000 0.000 0.000 0.000 9.490 0.008 0.003

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A C A A C A B B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD NO

size

87 151 149 137 100 73 308 105 318 230

N.S.

1 1.74 1.71 1.57 1.15 0.84 3.54 1.21 3.66 2.64

time (sec)

N/A 0.146 0.358 0.000 1.020 1.286 80.462 1.457 14.762 0.002

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A B B C B A C A B B

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD NO

size

52 135 126 120 90 61 277 80 312 112

N.S.

1 2.60 2.42 2.31 1.73 1.17 5.33 1.54 6.00 2.15

time (sec)

N/A 0.071 0.222 0.000 1.107 1.080 48.757 1.386 14.587 0.001

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A B B C A A C A B A

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD NO

size

55 135 128 95 56 73 240 71 118 91

N.S.

1 2.45 2.33 1.73 1.02 1.33 4.36 1.29 2.15 1.65

time (sec)

N/A 0.185 0.421 0.000 2.343 0.627 47.371 1.366 5.391 0.001

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A B A C A A C A B A

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD NO

size

55 135 89 96 56 82 216 83 118 89

N.S.

1 2.45 1.62 1.75 1.02 1.49 3.93 1.51 2.15 1.62

time (sec)

N/A 0.180 0.182 0.001 2.348 1.027 45.808 1.517 5.151 0.002

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A C A A C B B A

verified

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

size

83 129 82 103 61 69 212 145 316 107

N.S.

1 1.55 0.99 1.24 0.73 0.83 2.55 1.75 3.81 1.29

time (sec)

N/A 0.191 0.125 0.000 2.468 1.114 75.514 1.442 12.773 0.002

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A C A A C B B A

verified

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

size

116 171 94 123 86 90 219 197 304 168

N.S.

1 1.47 0.81 1.06 0.74 0.78 1.89 1.70 2.62 1.45

time (sec)

N/A 0.217 0.124 0.000 3.046 1.073 128.739 1.403 11.819 0.002

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD NO

size

199 242 343 1095 0 1186 0 605 7235 546

N.S.

1 1.22 1.72 5.50 0.00 5.96 0.00 3.04 36.36 2.74

time (sec)

N/A 0.328 0.761 0.053 0.000 0.999 0.000 3.245 66.847 0.669

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

1348 1345 3599 6728 0 3096 0 4708 -1 9831

N.S.

1 1.00 2.67 4.99 0.00 2.30 0.00 3.49 -0.00 7.29

time (sec)

N/A 2.366 7.131 0.053 0.000 8.081 0.000 6.328 0.000 5.303

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

721 719 2722 3571 0 1620 0 2643 -1 4538

N.S.

1 1.00 3.78 4.95 0.00 2.25 0.00 3.67 -0.00 6.29

time (sec)

N/A 0.963 6.606 0.024 0.000 2.958 0.000 3.389 0.000 2.794

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

330 330 306 1431 0 840 0 1103 -1 643

N.S.

1 1.00 0.93 4.34 0.00 2.55 0.00 3.34 -0.00 1.95

time (sec)

N/A 0.298 1.716 0.020 0.000 0.974 0.000 2.334 0.000 0.977

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

450 453 1936 4227 0 0 0 0 -1 950

N.S.

1 1.01 4.30 9.39 0.00 0.00 0.00 0.00 -0.00 2.11

time (sec)

N/A 1.369 6.215 0.051 0.000 0.000 0.000 0.000 0.000 1.795

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD NO

size

521 521 2532 5051 0 0 0 1585 -1 942

N.S.

1 1.00 4.86 9.69 0.00 0.00 0.00 3.04 -0.00 1.81

time (sec)

N/A 1.696 6.375 0.048 0.000 0.000 0.000 13.122 0.000 2.758

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

N/A Yes NO TBD TBD TBD TBD TBD TBD NO

size

658 657 2150 12065 0 0 0 8347 -1 1687

N.S.

1 1.00 3.27 18.34 0.00 0.00 0.00 12.69 -0.00 2.56

time (sec)

N/A 2.680 6.443 0.072 0.000 0.000 0.000 39.569 0.000 6.129

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

1032 1032 3220 3958 0 2176 0 1505 -1 2260

N.S.

1 1.00 3.12 3.84 0.00 2.11 0.00 1.46 -0.00 2.19

time (sec)

N/A 1.788 6.702 0.046 0.000 13.801 0.000 2.759 0.000 9.373

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

540 540 478 2002 0 1114 0 736 -1 1096

N.S.

1 1.00 0.89 3.71 0.00 2.06 0.00 1.36 -0.00 2.03

time (sec)

N/A 0.713 3.539 0.030 0.000 3.758 0.000 1.819 0.000 3.390

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

246 246 225 763 0 576 0 315 1832 357

N.S.

1 1.00 0.91 3.10 0.00 2.34 0.00 1.28 7.45 1.45

time (sec)

N/A 0.230 1.070 0.024 0.000 1.485 0.000 1.348 90.550 1.123

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

290 290 465 1822 0 0 0 0 -1 1375

N.S.

1 1.00 1.60 6.28 0.00 0.00 0.00 0.00 -0.00 4.74

time (sec)

N/A 0.672 3.449 0.039 0.000 0.000 0.000 0.000 0.000 34.326

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

364 364 417 3670 0 0 0 1388 -1 5591

N.S.

1 1.00 1.15 10.08 0.00 0.00 0.00 3.81 -0.00 15.36

time (sec)

N/A 1.097 2.396 0.049 0.000 0.000 0.000 10.820 0.000 169.659

Problem 52

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

484 484 523 9100 0 0 0 8004 -1 0

N.S.

1 1.00 1.08 18.80 0.00 0.00 0.00 16.54 -0.00 0.00

time (sec)

N/A 1.563 5.675 0.095 0.000 0.000 0.000 134.872 0.000 180.012

Problem 53

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

685 685 729 15990 0 0 0 0 -1 0

N.S.

1 1.00 1.06 23.34 0.00 0.00 0.00 0.00 -0.00 0.00

time (sec)

N/A 1.778 6.336 0.159 0.000 0.000 0.000 0.000 0.000 180.006

Problem 54

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

718 715 2195 2528 0 1436 0 951 -1 2158

N.S.

1 1.00 3.06 3.52 0.00 2.00 0.00 1.32 -0.00 3.01

time (sec)

N/A 1.336 6.487 0.046 0.000 5.323 0.000 2.512 0.000 1.813

Problem 55

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B F(-2) A F A B B

verified

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

size

371 369 379 1199 0 720 0 447 2621 787

N.S.

1 0.99 1.02 3.23 0.00 1.94 0.00 1.20 7.06 2.12

time (sec)

N/A 0.509 1.963 0.033 0.000 2.266 0.000 1.968 105.189 0.900

Problem 56

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

A A A B F(-2) A F A B A

verified

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

size

164 164 173 425 0 380 0 194 833 229

N.S.

1 1.00 1.05 2.59 0.00 2.32 0.00 1.18 5.08 1.40

time (sec)

N/A 0.149 0.792 0.023 0.000 1.569 0.000 1.216 25.888 0.378

Problem 57

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

188 188 304 746 0 0 0 0 -1 227

N.S.

1 1.00 1.62 3.97 0.00 0.00 0.00 0.00 -0.01 1.21

time (sec)

N/A 0.341 0.938 0.034 0.000 0.000 0.000 0.000 0.000 0.616

Problem 58

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

254 254 325 2973 0 0 0 1356 -1 330

N.S.

1 1.00 1.28 11.70 0.00 0.00 0.00 5.34 -0.00 1.30

time (sec)

N/A 0.638 1.863 0.059 0.000 0.000 0.000 9.374 0.000 0.941

Problem 59

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

424 424 512 7119 0 0 0 0 -1 911

N.S.

1 1.00 1.21 16.79 0.00 0.00 0.00 0.00 -0.00 2.15

time (sec)

N/A 0.967 2.090 0.130 0.000 0.000 0.000 0.000 0.000 1.861

Problem 60

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad I.A.

grade

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

verified

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

size

826 826 794 18802 0 0 0 0 -1 3507

N.S.

1 1.00 0.96 22.76 0.00 0.00 0.00 0.00 -0.00 4.25

time (sec)

N/A 2.433 6.107 0.312 0.000 0.000 0.000 0.000 0.000 5.663

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