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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 A A B A A B F

verified

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

size

305 305 334 329 282 3224 165 288 1331 0

N.S.

1 1.00 1.10 1.08 0.92 10.57 0.54 0.94 4.36 0.00

time (sec)

N/A 0.249 0.100 0.115 1.494 1.625 3.111 0.429 1.542 0.000

Problem 2

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

grade

A A A A A B A A B F

verified

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

size

323 323 337 386 313 3178 168 308 1293 0

N.S.

1 1.00 1.04 1.20 0.97 9.84 0.52 0.95 4.00 0.00

time (sec)

N/A 0.189 0.116 0.110 1.341 1.943 3.123 0.379 2.973 0.001

Problem 3

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

grade

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

verified

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

size

754 754 534 34 0 3406 0 601 2510 0

N.S.

1 1.00 0.71 0.05 0.00 4.52 0.00 0.80 3.33 0.00

time (sec)

N/A 1.247 0.628 0.018 0.000 2.406 0.000 0.737 2.780 0.001

Problem 4

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

grade

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

verified

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

size

329 329 425 39 0 3385 0 633 2438 0

N.S.

1 1.00 1.29 0.12 0.00 10.29 0.00 1.92 7.41 0.00

time (sec)

N/A 0.209 0.134 0.013 0.000 2.843 0.000 0.753 2.719 0.001

Problem 5

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

grade

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

verified

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

size

791 791 67 53 0 3059 136 0 10409 0

N.S.

1 1.00 0.08 0.07 0.00 3.87 0.17 0.00 13.16 0.00

time (sec)

N/A 0.863 0.045 0.049 0.000 1.858 8.503 0.000 3.825 0.001

Problem 6

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

grade

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

verified

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

size

791 791 67 53 0 3059 136 0 10411 0

N.S.

1 1.00 0.08 0.07 0.00 3.87 0.17 0.00 13.16 0.00

time (sec)

N/A 0.805 0.035 0.049 0.000 1.798 7.139 0.000 4.030 0.001

Problem 7

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

grade

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

verified

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

size

349 349 69 55 0 3048 136 0 10337 0

N.S.

1 1.00 0.20 0.16 0.00 8.73 0.39 0.00 29.62 0.00

time (sec)

N/A 0.422 0.045 0.033 0.000 1.706 8.251 0.000 4.035 0.001

Problem 8

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

grade

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

verified

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

size

751 751 69 55 0 3051 136 0 10343 0

N.S.

1 1.00 0.09 0.07 0.00 4.06 0.18 0.00 13.77 0.00

time (sec)

N/A 0.925 0.039 0.034 0.000 1.615 7.255 0.000 4.204 0.001

Problem 9

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

grade

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

verified

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

size

411 411 55 42 0 1443 75 0 5341 0

N.S.

1 1.00 0.13 0.10 0.00 3.51 0.18 0.00 13.00 0.00

time (sec)

N/A 0.292 0.026 0.056 0.000 1.408 3.669 0.000 3.683 0.000

Problem 10

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

grade

A A C C F B A A B F

verified

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

size

451 451 55 42 0 951 24 239 459 0

N.S.

1 1.00 0.12 0.09 0.00 2.11 0.05 0.53 1.02 0.00

time (sec)

N/A 0.407 0.015 0.010 0.000 1.243 1.475 0.931 0.176 0.001

Problem 11

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

grade

A A A A A A A A B F

verified

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

size

85 85 64 58 72 95 73 72 33 0

N.S.

1 1.00 0.75 0.68 0.85 1.12 0.86 0.85 0.39 0.00

time (sec)

N/A 0.045 0.020 0.003 1.587 1.010 0.154 0.388 1.562 0.000

Problem 12

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

grade

A A C A F A C A B F

verified

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

size

140 140 135 109 0 211 190 108 95 0

N.S.

1 1.00 0.96 0.78 0.00 1.51 1.36 0.77 0.68 0.00

time (sec)

N/A 0.095 0.174 0.018 0.000 1.461 0.702 0.420 0.144 0.000

Problem 13

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

grade

A A A C F B A A B F

verified

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

size

347 347 258 27 0 991 19 247 311 0

N.S.

1 1.00 0.74 0.08 0.00 2.86 0.05 0.71 0.90 0.00

time (sec)

N/A 0.247 0.188 0.008 0.000 1.342 2.784 0.875 2.284 0.000

Problem 14

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

grade

A A C C F A A A B F

verified

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

size

331 331 55 42 0 377 20 245 145 0

N.S.

1 1.00 0.17 0.13 0.00 1.14 0.06 0.74 0.44 0.00

time (sec)

N/A 0.235 0.016 0.013 0.000 1.321 3.100 0.498 0.225 0.001

Problem 15

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

grade

A A A A A B A A B F

verified

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

size

27 27 31 42 27 43 26 29 21 0

N.S.

1 1.00 1.15 1.56 1.00 1.59 0.96 1.07 0.78 0.00

time (sec)

N/A 0.008 0.013 0.012 1.326 1.490 0.147 0.518 0.047 0.000

Problem 16

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

grade

A A A A F B A A B F

verified

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

size

131 131 131 96 0 247 49 147 269 0

N.S.

1 1.00 1.00 0.73 0.00 1.89 0.37 1.12 2.05 0.00

time (sec)

N/A 0.086 0.077 0.040 0.000 1.570 1.189 0.960 0.200 0.000

Problem 17

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

grade

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

verified

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

size

157 157 53 40 0 331 24 0 399 0

N.S.

1 1.00 0.34 0.25 0.00 2.11 0.15 0.00 2.54 0.00

time (sec)

N/A 0.087 0.013 0.013 0.000 1.260 0.192 0.000 1.721 0.000

Problem 18

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

grade

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

verified

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

size

171 171 55 42 0 574 24 0 483 0

N.S.

1 1.00 0.32 0.25 0.00 3.36 0.14 0.00 2.82 0.00

time (sec)

N/A 0.151 0.013 0.013 0.000 1.651 0.195 0.000 1.758 0.000

Problem 19

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

grade

A A A A F B A A B F

verified

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

size

117 117 111 78 0 181 49 123 233 0

N.S.

1 1.00 0.95 0.67 0.00 1.55 0.42 1.05 1.99 0.00

time (sec)

N/A 0.057 0.054 0.062 0.000 1.233 1.157 0.907 0.190 0.000

Problem 20

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

grade

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

verified

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

size

511 511 57 44 0 1443 76 0 5341 0

N.S.

1 1.00 0.11 0.09 0.00 2.82 0.15 0.00 10.45 0.00

time (sec)

N/A 0.359 0.025 0.003 0.000 1.354 3.632 0.000 3.743 0.001

Problem 21

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

grade

A A C C F B A A B F

verified

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

size

411 411 57 44 0 894 26 223 447 0

N.S.

1 1.00 0.14 0.11 0.00 2.18 0.06 0.54 1.09 0.00

time (sec)

N/A 0.321 0.015 0.012 0.000 1.583 1.455 0.685 1.677 0.000

Problem 22

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

grade

A A A A A A A A B F

verified

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

size

97 97 90 68 82 126 82 82 44 0

N.S.

1 1.00 0.93 0.70 0.85 1.30 0.85 0.85 0.45 0.00

time (sec)

N/A 0.052 0.065 0.007 1.557 1.230 0.176 0.300 1.616 0.000

Problem 23

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

grade

A A C A F A C A B F

verified

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

size

140 140 129 109 0 137 148 108 109 0

N.S.

1 1.00 0.92 0.78 0.00 0.98 1.06 0.77 0.78 0.00

time (sec)

N/A 0.099 0.173 0.013 0.000 1.161 0.621 0.371 0.185 0.000

Problem 24

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

grade

A A A C F B A A B F

verified

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

size

347 347 257 29 0 991 20 247 312 0

N.S.

1 1.00 0.74 0.08 0.00 2.86 0.06 0.71 0.90 0.00

time (sec)

N/A 0.270 0.164 0.008 0.000 1.556 2.746 0.719 1.956 0.001

Problem 25

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

grade

A A C C F B A A B F

verified

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

size

355 355 57 44 0 715 26 253 208 0

N.S.

1 1.00 0.16 0.12 0.00 2.01 0.07 0.71 0.59 0.00

time (sec)

N/A 0.277 0.016 0.009 0.000 1.627 3.103 0.462 1.666 0.001

Problem 26

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

grade

A A A A A A B B B F

verified

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

size

13 13 25 10 17 17 17 19 9 0

N.S.

1 1.00 1.92 0.77 1.31 1.31 1.31 1.46 0.69 0.00

time (sec)

N/A 0.005 0.005 0.001 1.596 1.420 0.130 0.449 0.025 0.000

Problem 27

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

grade

A A A A F B A A B F

verified

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

size

129 129 129 110 0 255 51 147 269 0

N.S.

1 1.00 1.00 0.85 0.00 1.98 0.40 1.14 2.09 0.00

time (sec)

N/A 0.118 0.077 0.026 0.000 1.442 1.172 0.746 1.709 0.001

Problem 28

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

grade

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

verified

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

size

165 165 55 42 0 302 26 0 399 0

N.S.

1 1.00 0.33 0.25 0.00 1.83 0.16 0.00 2.42 0.00

time (sec)

N/A 0.104 0.013 0.010 0.000 1.579 0.198 0.000 0.181 0.001

Problem 29

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

grade

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

verified

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

size

169 169 57 44 0 546 26 0 483 0

N.S.

1 1.00 0.34 0.26 0.00 3.23 0.15 0.00 2.86 0.00

time (sec)

N/A 0.142 0.014 0.012 0.000 1.809 0.194 0.000 1.787 0.000

Problem 30

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

grade

A A A A F B A A B F

verified

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

size

125 125 114 90 0 199 51 135 245 0

N.S.

1 1.00 0.91 0.72 0.00 1.59 0.41 1.08 1.96 0.00

time (sec)

N/A 0.067 0.054 0.031 0.000 1.403 1.165 0.633 0.199 0.001

Problem 31

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

grade

A A C C F A A A B F

verified

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

size

135 135 71 47 0 104 163 107 133 0

N.S.

1 1.00 0.53 0.35 0.00 0.77 1.21 0.79 0.99 0.00

time (sec)

N/A 0.124 0.034 0.056 0.000 0.774 0.904 0.494 2.235 0.001

Problem 32

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

grade

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

verified

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

size

164 164 72 62 0 111 0 123 1 0

N.S.

1 1.00 0.44 0.38 0.00 0.68 0.00 0.75 0.01 0.00

time (sec)

N/A 0.095 0.038 0.045 0.000 1.229 0.000 0.432 2.190 0.001

Problem 33

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

grade

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

verified

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

size

180 180 89 62 0 141 0 131 1 0

N.S.

1 1.00 0.49 0.34 0.00 0.78 0.00 0.73 0.01 0.00

time (sec)

N/A 0.122 0.046 0.014 0.000 1.552 0.000 0.448 2.230 0.001

Problem 34

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

grade

A A A A A A B A B F

verified

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

size

49 49 49 43 42 108 112 43 39 0

N.S.

1 1.00 1.00 0.88 0.86 2.20 2.29 0.88 0.80 0.00

time (sec)

N/A 0.030 0.024 0.006 1.619 0.749 0.283 0.268 1.594 0.001

Problem 35

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

grade

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

verified

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

size

86 86 86 161 0 291 423 85 127 0

N.S.

1 1.00 1.00 1.87 0.00 3.38 4.92 0.99 1.48 0.00

time (sec)

N/A 0.081 0.090 0.003 0.000 1.200 1.372 0.324 1.772 0.002

Problem 36

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

grade

A A A A A B A A B F

verified

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

size

253 253 293 266 240 754 109 247 555 0

N.S.

1 1.00 1.16 1.05 0.95 2.98 0.43 0.98 2.19 0.00

time (sec)

N/A 0.211 0.096 0.006 1.298 1.356 0.704 0.352 0.313 0.001

Problem 37

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

grade

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

verified

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

size

208 208 251 560 0 2540 0 3183 6366 0

N.S.

1 1.00 1.21 2.69 0.00 12.21 0.00 15.30 30.61 0.00

time (sec)

N/A 0.543 0.173 0.027 0.000 1.672 0.000 3.756 2.854 0.002

Problem 38

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

grade

A A A A A B A A B F

verified

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

size

311 311 346 334 295 3169 167 295 1308 0

N.S.

1 1.00 1.11 1.07 0.95 10.19 0.54 0.95 4.21 0.00

time (sec)

N/A 0.290 0.112 0.084 1.525 2.134 2.981 0.534 3.100 0.001

Problem 39

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

grade

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

verified

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

size

716 716 88 67 0 0 0 0 11453 0

N.S.

1 1.00 0.12 0.09 0.00 0.00 0.00 0.00 16.00 0.00

time (sec)

N/A 1.634 0.054 0.016 0.000 0.000 0.000 0.000 29.420 0.001

Problem 40

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

grade

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

verified

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

size

753 753 551 45 0 3378 0 647 2520 0

N.S.

1 1.00 0.73 0.06 0.00 4.49 0.00 0.86 3.35 0.00

time (sec)

N/A 1.436 0.903 0.004 0.000 2.072 0.000 0.808 1.220 0.001

Problem 41

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

grade

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

verified

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

size

433 433 88 67 0 0 0 0 50213 0

N.S.

1 1.00 0.20 0.15 0.00 0.00 0.00 0.00 115.97 0.00

time (sec)

N/A 0.989 0.075 0.007 0.000 0.000 0.000 0.000 9.242 0.001

Problem 42

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

grade

A A A A A B A B B F

verified

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

size

62 62 57 66 82 137 656 207 59 0

N.S.

1 1.00 0.92 1.06 1.32 2.21 10.58 3.34 0.95 0.00

time (sec)

N/A 0.039 0.152 0.013 0.550 0.938 1.320 0.351 1.662 0.068

Problem 43

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

grade

A A A A A B A B B F

verified

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

size

132 132 123 138 208 495 3128 828 131 0

N.S.

1 1.00 0.93 1.05 1.58 3.75 23.70 6.27 0.99 0.00

time (sec)

N/A 0.102 0.248 0.015 0.695 0.766 10.968 0.453 1.711 0.663

Problem 44

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

grade

A A A A A B A B B F

verified

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

size

218 218 205 226 386 1209 9190 2134 227 0

N.S.

1 1.00 0.94 1.04 1.77 5.55 42.16 9.79 1.04 0.00

time (sec)

N/A 0.201 0.426 0.020 0.882 0.876 89.545 0.779 1.850 3.400

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