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2.2.1 Integrals 1 to 51

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.

Problem 1

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

189 189 151 1229 353 912 5992 1708 469

N.S.

1 1.00 0.80 6.50 1.87 4.83 31.70 9.04 2.48

time (sec)

N/A 0.125 0.470 0.112 0.332 1.626 0.973 1.236 1.438

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

144 144 113 711 253 533 3271 1009 305

N.S.

1 1.00 0.78 4.94 1.76 3.70 22.72 7.01 2.12

time (sec)

N/A 0.081 0.139 0.113 0.295 1.851 0.691 1.178 1.197

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

97 97 73 96 153 236 1460 478 185

N.S.

1 1.00 0.75 0.99 1.58 2.43 15.05 4.93 1.91

time (sec)

N/A 0.040 0.077 0.028 0.297 1.910 0.439 0.989 1.028

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

60 60 43 59 73 95 439 167 97

N.S.

1 1.00 0.72 0.98 1.22 1.58 7.32 2.78 1.62

time (sec)

N/A 0.021 0.052 0.021 0.277 2.450 0.253 1.412 0.956

Problem 5

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

118 118 93 0 0 0 428 0 -1

N.S.

1 1.00 0.79 0.00 0.00 0.00 3.63 0.00 -0.01

time (sec)

N/A 0.064 0.135 0.033 0.000 0.000 4.137 0.000 0.000

Problem 6

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 113 0 0 0 2076 0 -1

N.S.

1 1.00 0.66 0.00 0.00 0.00 12.14 0.00 -0.01

time (sec)

N/A 0.155 0.284 0.029 0.000 0.000 31.659 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

209 209 133 0 0 0 6368 0 -1

N.S.

1 1.00 0.64 0.00 0.00 0.00 30.47 0.00 -0.00

time (sec)

N/A 0.202 0.511 0.042 0.000 0.000 99.641 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

292 292 247 2443 573 1712 11914 3283 694

N.S.

1 1.00 0.85 8.37 1.96 5.86 40.80 11.24 2.38

time (sec)

N/A 0.184 0.747 0.116 0.320 4.700 1.541 1.219 1.741

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

216 216 178 1471 413 1044 6836 2010 499

N.S.

1 1.00 0.82 6.81 1.91 4.83 31.65 9.31 2.31

time (sec)

N/A 0.133 0.296 0.109 0.319 10.117 1.242 0.850 1.388

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

144 144 113 711 253 496 3271 1009 305

N.S.

1 1.00 0.78 4.94 1.76 3.44 22.72 7.01 2.12

time (sec)

N/A 0.081 0.157 0.102 0.342 5.192 0.677 1.317 1.182

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

91 91 67 90 121 218 1096 380 179

N.S.

1 1.00 0.74 0.99 1.33 2.40 12.04 4.18 1.97

time (sec)

N/A 0.039 0.069 0.100 0.295 8.367 0.444 1.320 1.048

Problem 12

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

178 178 146 0 0 0 666 0 -1

N.S.

1 1.00 0.82 0.00 0.00 0.00 3.74 0.00 -0.01

time (sec)

N/A 0.114 0.260 0.043 0.000 0.000 6.794 0.000 0.000

Problem 13

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

247 247 163 0 0 0 0 0 -1

N.S.

1 1.00 0.66 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.287 0.749 0.043 0.000 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

292 292 326 0 0 0 0 0 -1

N.S.

1 1.00 1.12 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.274 0.955 0.052 0.000 0.000 0.000 0.000 0.000

Problem 15

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

379 379 327 3953 793 2658 20086 5234 933

N.S.

1 1.00 0.86 10.43 2.09 7.01 53.00 13.81 2.46

time (sec)

N/A 0.259 1.028 0.122 0.340 5.225 2.322 1.040 2.099

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

284 284 239 2443 573 1691 11914 3283 694

N.S.

1 1.00 0.84 8.60 2.02 5.95 41.95 11.56 2.44

time (sec)

N/A 0.189 0.634 0.121 0.321 2.806 1.593 1.282 1.745

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

189 189 151 1229 353 838 5992 1708 469

N.S.

1 1.00 0.80 6.50 1.87 4.43 31.70 9.04 2.48

time (sec)

N/A 0.117 0.441 0.109 0.308 1.108 1.015 1.832 1.432

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A B A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

121 121 90 475 169 382 2152 673 280

N.S.

1 1.00 0.74 3.93 1.40 3.16 17.79 5.56 2.31

time (sec)

N/A 0.052 0.108 0.104 0.305 1.295 0.599 1.106 1.133

Problem 19

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

258 258 217 0 0 0 911 0 -1

N.S.

1 1.00 0.84 0.00 0.00 0.00 3.53 0.00 -0.00

time (sec)

N/A 0.208 0.607 0.023 0.000 0.000 10.546 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

347 347 241 0 0 0 0 0 -1

N.S.

1 1.00 0.69 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.429 1.182 0.024 0.000 0.000 0.000 0.000 0.000

Problem 21

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

480 480 579 0 0 0 0 0 -1

N.S.

1 1.00 1.21 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.755 1.029 0.022 0.000 0.000 0.000 0.000 0.000

Problem 22

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

363 363 315 0 0 0 1132 0 -1

N.S.

1 1.00 0.87 0.00 0.00 0.00 3.12 0.00 -0.00

time (sec)

N/A 0.252 0.741 0.023 0.000 0.000 15.698 0.000 0.000

Problem 23

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

260 260 219 0 0 0 911 0 -1

N.S.

1 1.00 0.84 0.00 0.00 0.00 3.50 0.00 -0.00

time (sec)

N/A 0.173 0.598 0.025 0.000 0.000 10.322 0.000 0.000

Problem 24

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

180 180 147 0 0 0 666 0 -1

N.S.

1 1.00 0.82 0.00 0.00 0.00 3.70 0.00 -0.01

time (sec)

N/A 0.121 0.269 0.044 0.000 0.000 6.989 0.000 0.000

Problem 25

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

120 120 93 0 0 0 428 0 -1

N.S.

1 1.00 0.78 0.00 0.00 0.00 3.57 0.00 -0.01

time (sec)

N/A 0.065 0.130 0.027 0.000 0.000 4.250 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

77 77 56 0 0 0 204 0 -1

N.S.

1 1.00 0.73 0.00 0.00 0.00 2.65 0.00 -0.01

time (sec)

N/A 0.027 0.067 0.024 0.000 0.000 1.991 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

125 125 100 0 0 0 0 0 -1

N.S.

1 1.00 0.80 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.084 0.170 0.045 0.000 0.000 0.000 0.000 0.000

Problem 28

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

206 206 149 0 0 0 0 0 -1

N.S.

1 1.00 0.72 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.256 0.383 0.058 0.000 0.000 0.000 0.000 0.000

Problem 29

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

342 342 195 0 0 0 0 0 -1

N.S.

1 1.00 0.57 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.545 0.936 0.026 0.000 0.000 0.000 0.000 0.000

Problem 30

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

340 340 239 0 0 0 0 0 -1

N.S.

1 1.00 0.70 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.492 1.203 0.023 0.000 0.000 0.000 0.000 0.000

Problem 31

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

246 246 165 0 0 0 0 0 -1

N.S.

1 1.00 0.67 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.272 0.812 0.042 0.000 0.000 0.000 0.000 0.000

Problem 32

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

171 171 113 0 0 0 2076 0 -1

N.S.

1 1.00 0.66 0.00 0.00 0.00 12.14 0.00 -0.01

time (sec)

N/A 0.150 0.278 0.032 0.000 0.000 30.697 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 81 0 0 0 954 0 -1

N.S.

1 1.00 0.79 0.00 0.00 0.00 9.26 0.00 -0.01

time (sec)

N/A 0.032 0.093 0.027 0.000 0.000 15.396 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

205 205 147 0 0 0 0 0 -1

N.S.

1 1.00 0.72 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.264 0.373 0.062 0.000 0.000 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

304 304 207 0 0 0 0 0 -1

N.S.

1 1.00 0.68 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.541 1.167 0.023 0.000 0.000 0.000 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

491 491 268 0 0 0 0 0 -1

N.S.

1 1.00 0.55 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.979 1.624 0.027 0.000 0.000 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

433 433 581 0 0 0 0 0 -1

N.S.

1 1.00 1.34 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.761 1.046 0.023 0.000 0.000 0.000 0.000 0.000

Problem 38

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F F F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

292 292 327 0 0 0 0 0 -1

N.S.

1 1.00 1.12 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.280 0.962 0.050 0.000 0.000 0.000 0.000 0.000

Problem 39

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

208 208 133 0 0 0 6368 0 -1

N.S.

1 1.00 0.64 0.00 0.00 0.00 30.62 0.00 -0.00

time (sec)

N/A 0.205 0.521 0.042 0.000 0.000 96.354 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

103 103 81 0 0 0 3172 0 -1

N.S.

1 1.00 0.79 0.00 0.00 0.00 30.80 0.00 -0.01

time (sec)

N/A 0.032 0.108 0.041 0.000 0.000 53.643 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

333 333 197 0 0 0 0 0 -1

N.S.

1 1.00 0.59 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.507 0.907 0.025 0.000 0.000 0.000 0.000 0.000

Problem 42

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

452 452 267 0 0 0 0 0 -1

N.S.

1 1.00 0.59 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.894 1.641 0.027 0.000 0.000 0.000 0.000 0.000

Problem 43

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

665 665 327 0 0 0 0 0 -1

N.S.

1 1.00 0.49 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.504 2.243 0.024 0.000 0.000 0.000 0.000 0.000

Problem 44

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

1059 1047 248 0 0 0 0 0 -1

N.S.

1 0.99 0.23 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.587 0.414 0.029 0.000 0.000 0.000 0.000 0.000

Problem 45

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

495 464 198 0 0 0 0 0 -1

N.S.

1 0.94 0.40 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.500 0.251 0.030 0.000 0.000 0.000 0.000 0.000

Problem 46

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A F F F C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

253 238 147 0 0 0 241 0 -1

N.S.

1 0.94 0.58 0.00 0.00 0.00 0.95 0.00 -0.00

time (sec)

N/A 0.166 0.151 0.019 0.000 0.000 204.443 0.000 0.000

Problem 47

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

162 162 118 0 0 0 0 0 -1

N.S.

1 1.00 0.73 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.108 0.185 0.027 0.000 0.000 0.000 0.000 0.000

Problem 48

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

295 295 128 0 0 0 0 0 -1

N.S.

1 1.00 0.43 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.285 0.197 0.031 0.000 0.000 0.000 0.000 0.000

Problem 49

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

483 483 128 0 0 0 0 0 -1

N.S.

1 1.00 0.27 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.707 0.351 0.029 0.000 0.000 0.000 0.000 0.000

Problem 50

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 84 91 111 100 231 97 113 101

N.S.

1 1.00 1.08 1.32 1.19 2.75 1.15 1.35 1.20

time (sec)

N/A 0.049 0.119 0.119 0.284 8.902 22.140 0.762 1.510

Problem 51

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A A A A A A B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

84 84 91 111 100 217 97 113 101

N.S.

1 1.00 1.08 1.32 1.19 2.58 1.15 1.35 1.20

time (sec)

N/A 0.052 0.128 0.116 0.276 4.052 22.010 1.348 1.483

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