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2.2.1 Integrals 1 to 46

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 C B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

210 210 172 4972 434 3055 63250 6927 1089

N.S.

1 1.00 0.82 23.68 2.07 14.55 301.19 32.99 5.19

time (sec)

N/A 0.182 0.685 0.399 0.343 3.748 175.912 0.677 5.644

Problem 2

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

160 160 129 2410 310 1509 24932 3415 588

N.S.

1 1.00 0.81 15.06 1.94 9.43 155.82 21.34 3.68

time (sec)

N/A 0.111 0.322 0.379 0.337 2.331 88.119 1.351 5.231

Problem 3

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

108 108 84 891 186 550 7686 1290 271

N.S.

1 1.00 0.78 8.25 1.72 5.09 71.17 11.94 2.51

time (sec)

N/A 0.056 0.137 0.081 0.322 2.002 39.423 0.802 4.958

Problem 4

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

66 66 49 262 85 176 1499 327 91

N.S.

1 1.00 0.74 3.97 1.29 2.67 22.71 4.95 1.38

time (sec)

N/A 0.027 0.062 0.057 0.310 1.209 13.538 2.278 4.830

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

120 120 115 0 0 0 666 0 -1

N.S.

1 1.00 0.96 0.00 0.00 0.00 5.55 0.00 -0.01

time (sec)

N/A 0.077 0.175 0.065 0.000 0.000 5.669 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

177 177 195 0 0 0 4129 0 -1

N.S.

1 1.00 1.10 0.00 0.00 0.00 23.33 0.00 -0.01

time (sec)

N/A 0.161 0.255 0.066 0.000 0.000 31.570 0.000 0.000

Problem 7

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

228 227 1153 0 0 0 0 0 -1

N.S.

1 1.00 5.06 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.190 0.568 0.068 0.000 0.000 0.000 0.000 0.000

Problem 8

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

318 318 273 11389 702 6617 0 15358 1882

N.S.

1 1.00 0.86 35.81 2.21 20.81 0.00 48.30 5.92

time (sec)

N/A 0.277 1.340 0.499 0.378 1.171 0.000 1.723 6.348

Problem 9

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

237 237 199 5908 506 3497 71580 8103 1119

N.S.

1 1.00 0.84 24.93 2.14 14.76 302.03 34.19 4.72

time (sec)

N/A 0.204 0.599 0.428 0.355 2.392 189.292 1.976 5.591

Problem 10

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

160 160 129 2410 310 1411 24932 3415 588

N.S.

1 1.00 0.81 15.06 1.94 8.82 155.82 21.34 3.68

time (sec)

N/A 0.116 0.337 0.379 0.375 1.806 88.963 0.901 5.196

Problem 11

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

102 102 78 732 145 515 5794 1023 265

N.S.

1 1.00 0.76 7.18 1.42 5.05 56.80 10.03 2.60

time (sec)

N/A 0.052 0.111 0.356 0.321 3.532 35.264 1.448 5.113

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

185 185 156 0 0 0 1085 0 -1

N.S.

1 1.00 0.84 0.00 0.00 0.00 5.86 0.00 -0.01

time (sec)

N/A 0.152 0.315 0.079 0.000 0.000 11.794 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

268 268 227 0 0 0 0 0 -1

N.S.

1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.445 0.874 0.081 0.000 0.000 0.000 0.000 0.000

Problem 14

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

322 322 1924 0 0 0 0 0 -1

N.S.

1 1.00 5.98 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.357 1.055 0.079 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 C B B F(-1) B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

410 410 358 20937 970 11604 0 27792 2500

N.S.

1 1.00 0.87 51.07 2.37 28.30 0.00 67.79 6.10

time (sec)

N/A 0.414 1.531 0.587 0.458 1.452 0.000 1.925 7.495

Problem 16

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

310 310 265 11389 702 6536 0 15358 1882

N.S.

1 1.00 0.85 36.74 2.26 21.08 0.00 49.54 6.07

time (sec)

N/A 0.281 1.360 0.505 0.430 1.843 0.000 1.810 6.414

Problem 17

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C B B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

210 210 172 4972 434 2815 63250 6927 1089

N.S.

1 1.00 0.82 23.68 2.07 13.40 301.19 32.99 5.19

time (sec)

N/A 0.172 0.612 0.415 0.356 1.332 180.149 0.989 5.653

Problem 18

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

A A A C A B B B B

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

137 137 106 1609 205 1089 16521 2278 563

N.S.

1 1.00 0.77 11.74 1.50 7.95 120.59 16.63 4.11

time (sec)

N/A 0.078 0.147 0.356 0.351 1.004 76.544 1.886 5.307

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

270 270 212 0 0 0 1503 0 -1

N.S.

1 1.00 0.79 0.00 0.00 0.00 5.57 0.00 -0.00

time (sec)

N/A 0.258 0.587 0.102 0.000 0.000 23.381 0.000 0.000

Problem 20

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

394 389 345 0 0 0 0 0 -1

N.S.

1 0.99 0.88 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.657 2.184 0.079 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 C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

380 380 290 0 0 0 1921 0 -1

N.S.

1 1.00 0.76 0.00 0.00 0.00 5.06 0.00 -0.00

time (sec)

N/A 0.415 1.104 0.082 0.000 0.000 44.642 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

272 272 213 0 0 0 1503 0 -1

N.S.

1 1.00 0.78 0.00 0.00 0.00 5.53 0.00 -0.00

time (sec)

N/A 0.268 0.624 0.075 0.000 0.000 23.443 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

187 187 156 0 0 0 1085 0 -1

N.S.

1 1.00 0.83 0.00 0.00 0.00 5.80 0.00 -0.01

time (sec)

N/A 0.172 0.334 0.079 0.000 0.000 12.162 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

122 122 115 0 0 0 666 0 -1

N.S.

1 1.00 0.94 0.00 0.00 0.00 5.46 0.00 -0.01

time (sec)

N/A 0.087 0.182 0.068 0.000 0.000 6.245 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

78 78 59 0 0 0 284 0 -1

N.S.

1 1.00 0.76 0.00 0.00 0.00 3.64 0.00 -0.01

time (sec)

N/A 0.027 0.086 0.094 0.000 0.000 1.998 0.000 0.000

Problem 26

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

127 127 102 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 0.092 0.190 0.122 0.000 0.000 0.000 0.000 0.000

Problem 27

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

212 212 177 0 0 0 0 0 -1

N.S.

1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.354 0.361 0.112 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(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

407 407 402 0 0 0 0 0 -1

N.S.

1 1.00 0.99 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.812 1.215 0.115 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(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

386 381 365 0 0 0 0 0 -1

N.S.

1 0.99 0.95 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.737 1.956 0.085 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

267 267 249 0 0 0 0 0 -1

N.S.

1 1.00 0.93 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.448 0.823 0.079 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 C F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

178 178 193 0 0 0 4129 0 -1

N.S.

1 1.00 1.08 0.00 0.00 0.00 23.20 0.00 -0.01

time (sec)

N/A 0.169 0.289 0.061 0.000 0.000 31.125 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

107 107 84 0 0 0 1897 0 -1

N.S.

1 1.00 0.79 0.00 0.00 0.00 17.73 0.00 -0.01

time (sec)

N/A 0.038 0.136 0.061 0.000 0.000 9.761 0.000 0.000

Problem 33

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

211 211 177 0 0 0 0 0 -1

N.S.

1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.349 0.357 0.117 0.000 0.000 0.000 0.000 0.000

Problem 34

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

315 315 242 0 0 0 0 0 -1

N.S.

1 1.00 0.77 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.717 0.736 0.146 0.000 0.000 0.000 0.000 0.000

Problem 35

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

567 567 2176 0 0 0 0 0 -1

N.S.

1 1.00 3.84 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.561 1.875 0.113 0.000 0.000 0.000 0.000 0.000

Problem 36

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

322 322 1924 0 0 0 0 0 -1

N.S.

1 1.00 5.98 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.367 1.138 0.080 0.000 0.000 0.000 0.000 0.000

Problem 37

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

228 227 1153 0 0 0 0 0 -1

N.S.

1 1.00 5.06 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.189 0.591 0.069 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(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

112 112 127 0 0 0 0 0 -1

N.S.

1 1.00 1.13 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.036 0.178 0.063 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 F(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

366 366 357 0 0 0 0 0 -1

N.S.

1 1.00 0.98 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.801 1.245 0.111 0.000 0.000 0.000 0.000 0.000

Problem 40

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

482 482 2178 0 0 0 0 0 -1

N.S.

1 1.00 4.52 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 1.356 1.850 0.115 0.000 0.000 0.000 0.000 0.000

Problem 41

Optimal Rubi MMA Maple Maxima Fricas Sympy Giac Mupad

grade

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

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

211 211 162 0 0 0 0 0 -1

N.S.

1 1.00 0.77 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.163 0.312 0.329 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

271 255 164 0 0 0 0 0 -1

N.S.

1 0.94 0.61 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.414 0.397 0.089 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(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

164 164 138 0 0 0 0 0 -1

N.S.

1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.117 0.196 0.147 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(-2) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

304 304 138 0 0 0 0 0 -1

N.S.

1 1.00 0.45 0.00 0.00 0.00 0.00 0.00 -0.00

time (sec)

N/A 0.353 0.269 0.136 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

139 139 124 0 0 0 0 0 -1

N.S.

1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.073 0.328 0.157 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 F(-1) F F

verified

N/A Yes Yes TBD TBD TBD TBD TBD TBD

size

139 167 124 0 0 0 0 0 -1

N.S.

1 1.20 0.89 0.00 0.00 0.00 0.00 0.00 -0.01

time (sec)

N/A 0.078 0.070 0.147 0.000 0.000 0.000 0.000 0.000

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