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2 detailed summary tables of results

 2.1 Detailed conclusion table per each integral for all CAS systems
 2.2 Detailed conclusion table specific for Rubi results

2.1 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 normalized size is defined as \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 10 12 12 8 12 8
normalized size 1 1. 1. 0.77 0.92 0.92 0.62 0.92 0.62
time (sec) N/A 0.005 0.003 0.264 1.325 0.209 0.031 0.231 0.518
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 18 15 26 26 39 26 22
normalized size 1 1. 0.67 0.56 0.96 0.96 1.44 0.96 0.81
time (sec) N/A 0.015 0.006 0.004 1.354 0.218 1.489 0.214 1.479
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 21 18 30 30 48 30 29
normalized size 1 1. 0.62 0.53 0.88 0.88 1.41 0.88 0.85
time (sec) N/A 0.017 0.008 0.006 1.347 0.238 2.128 0.216 1.371
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 18 15 26 19 61 26 22
normalized size 1 1. 0.67 0.56 0.96 0.7 2.26 0.96 0.81
time (sec) N/A 0.015 0.006 0.004 1.343 0.211 1.589 0.221 1.56
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 13 16 30 22 16 14
normalized size 1 1. 1. 0.93 1.14 2.14 1.57 1.14 1.
time (sec) N/A 0.006 0.007 0.172 1.343 0.219 0.132 0.222 1.235
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 15 11 15 15 8 15 8
normalized size 1 1. 1.15 0.85 1.15 1.15 0.62 1.15 0.62
time (sec) N/A 0.01 0.003 0.797 1.347 0.217 0.043 0.212 0.712
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 16 13 20 23 97 20 19
normalized size 1 1. 0.7 0.57 0.87 1. 4.22 0.87 0.83
time (sec) N/A 0.012 0.005 0.004 1.348 0.207 1.447 0.217 0.988
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 7 8 14 8 14 12
normalized size 1 1. 1. 0.88 1. 1.75 1. 1.75 1.5
time (sec) N/A 0.021 0.003 0.021 1.355 0.206 0.04 0.218 1.154
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 13 16 24 29 16 12
normalized size 1 1. 1. 0.81 1. 1.5 1.81 1. 0.75
time (sec) N/A 0.036 0.018 0.021 1.355 0.234 0.399 0.22 1.885
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 6 6 6 7 8 8 5 8 5
normalized size 1 1. 1. 1.17 1.33 1.33 0.83 1.33 0.83
time (sec) N/A 0.027 0.005 0.325 1.353 0.223 1.018 0.22 1.521
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 11 14 16 12 8 14
normalized size 1 1. 1. 0.92 1.17 1.33 1. 0.67 1.17
time (sec) N/A 0.04 0.013 0.21 1.353 0.234 1.138 0.214 2.428
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 9 11 11 10 11 10
normalized size 1 1. 1. 0.9 1.1 1.1 1. 1.1 1.
time (sec) N/A 0.027 0.005 0.015 1.371 0.218 0.434 0.213 2.317
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 10 12 12 0 12 7
normalized size 1 1. 1. 1.11 1.33 1.33 0. 1.33 0.78
time (sec) N/A 0.019 0.009 0.031 1.337 0.269 0. 0.215 1.38
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 32 15 15 10 15 10
normalized size 1 1. 1. 2.13 1. 1. 0.67 1. 0.67
time (sec) N/A 0.007 0.005 0.013 1.343 0.21 0.342 0.215 0.977
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 16 13 20 20 34 20 19
normalized size 1 1. 0.7 0.57 0.87 0.87 1.48 0.87 0.83
time (sec) N/A 0.012 0.005 0.004 1.324 0.208 1.536 0.217 1.02
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 10 12 23 8 12 8
normalized size 1 1. 1. 0.91 1.09 2.09 0.73 1.09 0.73
time (sec) N/A 0.005 0.006 0.003 1.351 0.207 1.181 0.222 0.496
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 27 15 15 27 15 10
normalized size 1 1. 1. 1.8 1. 1. 1.8 1. 0.67
time (sec) N/A 0.007 0.006 0.006 1.367 0.205 0.452 0.216 0.931
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 12 15 15 12 15 12
normalized size 1 1. 1. 0.8 1. 1. 0.8 1. 0.8
time (sec) N/A 0.043 0.029 0.017 1.347 0.223 0.482 0.229 2.863
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 37 0 18 31 0 20 26
normalized size 1 1. 1.16 0. 0.56 0.97 0. 0.62 0.81
time (sec) N/A 0.194 0.027 0.308 1.374 0.242 0. 0.223 5.816
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 14 18 18 14 18 14
normalized size 1 1. 1. 0.82 1.06 1.06 0.82 1.06 0.82
time (sec) N/A 0.191 0.014 0.007 1.36 0.24 0.479 0.217 4.909
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 13 13 9 16 15 0 15
normalized size 1 1. 0.81 0.81 0.56 1. 0.94 0. 0.94
time (sec) N/A 0.021 0.009 0.004 1.352 0.234 1.164 0. 2.341
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 9 11 11 7 11 7
normalized size 1 1. 1. 1.12 1.38 1.38 0.88 1.38 0.88
time (sec) N/A 0.015 0.003 0.093 1.364 0.242 0.181 0.214 0.754
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 15 18 20 20 17 20 17
normalized size 1 1. 0.88 1.06 1.18 1.18 1. 1.18 1.
time (sec) N/A 0.034 0.01 0.007 1.341 0.239 0.394 0.219 1.391
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 19 24 27 27 26 27 26
normalized size 1 1. 0.83 1.04 1.17 1.17 1.13 1.17 1.13
time (sec) N/A 0.053 0.012 0.01 1.335 0.24 0.87 0.216 1.922
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 20 25 28 28 26 28 26
normalized size 1 1. 0.83 1.04 1.17 1.17 1.08 1.17 1.08
time (sec) N/A 0.052 0.012 0.007 1.35 0.243 0.924 0.222 1.926
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 7 8 8 5 8 0
normalized size 1 1. 1. 0.88 1. 1. 0.62 1. 0.
time (sec) N/A 0.011 0.002 0.003 1.34 0.235 0.036 0.218 0.
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 18 18 19 23 24 19 19
normalized size 1 1. 0.78 0.78 0.83 1. 1.04 0.83 0.83
time (sec) N/A 0.02 0.004 0.004 1.396 0.226 0.413 0.214 1.04
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 11 14 14 10 14 10
normalized size 1 1. 1. 0.79 1. 1. 0.71 1. 0.71
time (sec) N/A 0.01 0.003 0.009 1.351 0.22 0.035 0.214 0.483
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 15 11 15 15 8 15 8
normalized size 1 1. 1.15 0.85 1.15 1.15 0.62 1.15 0.62
time (sec) N/A 0.011 0.003 0.001 1.361 0.212 0.039 0.227 0.633
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 22 18 22 26 24 22 24
normalized size 1 1. 0.92 0.75 0.92 1.08 1. 0.92 1.
time (sec) N/A 0.017 0.003 0.105 1.33 0.225 0.038 0.217 0.559
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 23 17 23 23 17 23 17
normalized size 1 1. 1.1 0.81 1.1 1.1 0.81 1.1 0.81
time (sec) N/A 0.013 0.003 0.053 1.481 0.216 0.046 0.223 0.744
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 30 24 32 34 36 30 36
normalized size 1 1. 0.88 0.71 0.94 1. 1.06 0.88 1.06
time (sec) N/A 0.025 0.003 0.047 1.352 0.256 0.039 0.225 0.665
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 25 26 26 36 26 0
normalized size 1 1. 1. 1. 1.04 1.04 1.44 1.04 0.
time (sec) N/A 0.023 0.005 0.007 1.348 0.237 0.41 0.23 0.
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 31 23 31 31 39 31 32
normalized size 1 1. 0.94 0.7 0.94 0.94 1.18 0.94 0.97
time (sec) N/A 0.033 0.006 0.078 1.357 0.227 0.819 0.222 1.326
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 29 37 35 39 56 35 36
normalized size 1 1. 0.71 0.9 0.85 0.95 1.37 0.85 0.88
time (sec) N/A 0.046 0.034 0.036 1.354 0.217 0.85 0.216 1.568
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 11 14 14 10 14 10
normalized size 1 1. 1. 0.79 1. 1. 0.71 1. 0.71
time (sec) N/A 0.01 0.003 0.01 1.362 0.223 0.034 0.216 0.509
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 15 11 12 14 8 12 8
normalized size 1 1. 1.36 1. 1.09 1.27 0.73 1.09 0.73
time (sec) N/A 0.011 0.003 0.04 1.355 0.206 0.04 0.235 0.671
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 22 18 22 26 24 22 24
normalized size 1 1. 0.92 0.75 0.92 1.08 1. 0.92 1.
time (sec) N/A 0.019 0.003 0.062 1.358 0.246 0.039 0.237 0.591
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 60 69 84 343 180 68 70
normalized size 1 1. 0.71 0.82 1. 4.08 2.14 0.81 0.83
time (sec) N/A 0.036 0.061 0.028 1.507 0.214 6.101 0.249 2.687
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 25 22 46 134 39 38 31
normalized size 1 1. 0.66 0.58 1.21 3.53 1.03 1. 0.82
time (sec) N/A 0.035 0.01 0.007 1.511 0.195 1.686 0.235 2.363
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F F A F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 172 172 122 168 0 0 31 0 162
normalized size 1 1. 0.71 0.98 0. 0. 0.18 0. 0.94
time (sec) N/A 0.126 0.266 0.658 0. 0. 0.9 0. 2.248
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 6 6 6 7 8 8 7 8 3
normalized size 1 1. 1. 1.17 1.33 1.33 1.17 1.33 0.5
time (sec) N/A 0.009 0.004 0.019 1.505 0.213 0.045 0.221 0.046
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 18 13 16 16 19 16 10
normalized size 1 1. 1.29 0.93 1.14 1.14 1.36 1.14 0.71
time (sec) N/A 0.016 0.005 0.004 1.499 0.243 0.05 0.233 0.473
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 12 14 27 8 24 7
normalized size 1 1. 1. 1.5 1.75 3.38 1. 3. 0.88
time (sec) N/A 0.01 0.004 0.011 1.502 0.215 0.045 0.226 0.457
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 18 14 22 65 19 46 14
normalized size 1 1. 1.5 1.17 1.83 5.42 1.58 3.83 1.17
time (sec) N/A 0.017 0.005 0.004 1.5 0.206 0.053 0.22 0.491
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 26 21 27 24 26 24 20
normalized size 1 1. 1.18 0.95 1.23 1.09 1.18 1.09 0.91
time (sec) N/A 0.021 0.008 0.019 1.325 0.215 0.212 0.218 1.16
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 10 12 93 22 12 8
normalized size 1 1. 1. 0.77 0.92 7.15 1.69 0.92 0.62
time (sec) N/A 0.005 0.004 0.005 1.355 0.203 0.215 0.22 0.739
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 11 52 12 1 58 12 7
normalized size 1 1. 0.85 4. 0.92 0.08 4.46 0.92 0.54
time (sec) N/A 0.007 0.003 0.026 1.369 0.194 0.038 0.228 0.719
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 16 20 26 26 15 19 15
normalized size 1 1. 0.89 1.11 1.44 1.44 0.83 1.06 0.83
time (sec) N/A 0.009 0.006 0.01 1.36 0.19 0.103 0.215 1.139
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 43 32 12 1 31 12 7
normalized size 1 1. 3.91 2.91 1.09 0.09 2.82 1.09 0.64
time (sec) N/A 0.007 0.002 0.003 1.413 0.21 0.033 0.219 0.761
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 140 107 143 1 131 143 36
normalized size 1 1. 2.5 1.91 2.55 0.02 2.34 2.55 0.64
time (sec) N/A 0.093 0.003 0.003 1.378 0.178 0.067 0.219 7.446
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 4 4 4 5 5 5 3 5 3
normalized size 1 1. 1. 1.25 1.25 1.25 0.75 1.25 0.75
time (sec) N/A 0.015 0.006 0.005 1.34 0.216 1.073 0.216 1.049
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 46 49 50 50 60 50 60
normalized size 1 1. 0.74 0.79 0.81 0.81 0.97 0.81 0.97
time (sec) N/A 0.07 0.028 0.007 1.386 0.215 3.389 0.218 2.242
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 9 11 11 7 11 7
normalized size 1 1. 1. 0.9 1.1 1.1 0.7 1.1 0.7
time (sec) N/A 0.013 0.004 0.003 1.353 0.25 0.36 0.225 0.994
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 49 13 16 16 15 248 15
normalized size 1 1. 3.06 0.81 1. 1. 0.94 15.5 0.94
time (sec) N/A 0.055 0.107 0.043 1.414 0.228 3.298 0.234 2.741
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 9 11 11 7 12 7
normalized size 1 1. 1. 0.9 1.1 1.1 0.7 1.2 0.7
time (sec) N/A 0.005 0.001 0. 1.445 0.204 0.031 0.215 0.51
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 16 16 20 15 20 15
normalized size 1 1. 1. 1.07 1.07 1.33 1. 1.33 1.
time (sec) N/A 0.008 0.002 0.025 1.385 0.259 0.079 0.22 0.514
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 14 18 18 12 18 0
normalized size 1 1. 1. 0.82 1.06 1.06 0.71 1.06 0.
time (sec) N/A 0.008 0.001 0.003 1.544 0.212 0.069 0.223 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 28 23 23 30 22 30 0
normalized size 1 1. 1. 0.82 0.82 1.07 0.79 1.07 0.
time (sec) N/A 0.017 0.002 0.003 1.656 0.203 0.088 0.219 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 4 4 4 5 5 5 3 7 3
normalized size 1 1. 1. 1.25 1.25 1.25 0.75 1.75 0.75
time (sec) N/A 0.003 0.001 0.002 1.624 0.191 0.026 0.216 0.462
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 3 3 3 4 4 15 3 15 3
normalized size 1 1. 1. 1.33 1.33 5. 1. 5. 1.
time (sec) N/A 0.005 0.003 0.001 1.62 0.219 0.044 0.217 0.03
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 21 36 0 43 0 0 22
normalized size 1 1. 0.75 1.29 0. 1.54 0. 0. 0.79
time (sec) N/A 0.02 0.014 0.083 0. 0.219 0. 0. 1.616
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 28 23 23 30 26 30 26
normalized size 1 1. 1. 0.82 0.82 1.07 0.93 1.07 0.93
time (sec) N/A 0.031 0.004 0.001 1.416 0.206 0.091 0.235 1.928
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 3 3 3 4 4 4 3 5 3
normalized size 1 1. 1. 1.33 1.33 1.33 1. 1.67 1.
time (sec) N/A 0.018 0.001 0. 1.43 0.218 0.079 0.238 1.118
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 11 14 14 8 14 8
normalized size 1 1. 1. 0.92 1.17 1.17 0.67 1.17 0.67
time (sec) N/A 0.026 0.003 0.002 1.448 0.207 0.08 0.24 1.463
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 16 18 23 16 20 23 24
normalized size 1 1. 0.7 0.78 1. 0.7 0.87 1. 1.04
time (sec) N/A 0.065 0.008 0.009 1.502 0.203 1.435 0.235 5.066
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 39 32 31 42 37 42 37
normalized size 1 1. 1. 0.82 0.79 1.08 0.95 1.08 0.95
time (sec) N/A 0.049 0.004 0.003 1.564 0.205 0.113 0.215 2.806
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 7 8 8 5 8 5
normalized size 1 1. 1. 0.78 0.89 0.89 0.56 0.89 0.56
time (sec) N/A 0.02 0.003 0.004 1.548 0.208 0.063 0.222 1.384
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 12 16 15 10 15 10
normalized size 1 1. 1. 0.86 1.14 1.07 0.71 1.07 0.71
time (sec) N/A 0.02 0.005 0.006 1.483 0.207 0.153 0.216 1.321
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 8 9 9 7 9 7
normalized size 1 1. 1. 0.8 0.9 0.9 0.7 0.9 0.7
time (sec) N/A 0.016 0.008 0.01 1.419 0.214 0.355 0.223 1.671
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 14 14 15 18 15 15 15
normalized size 1 1. 0.74 0.74 0.79 0.95 0.79 0.79 0.79
time (sec) N/A 0.014 0.016 0.029 1.377 0.21 0.349 0.218 1.173
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 12 14 12 18 15 12 15
normalized size 1 1. 0.63 0.74 0.63 0.95 0.79 0.63 0.79
time (sec) N/A 0.014 0.007 0.007 1.364 0.214 0.341 0.217 1.172
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 12 12 12 7 12 10
normalized size 1 1. 1. 1.2 1.2 1.2 0.7 1.2 1.
time (sec) N/A 0.013 0.003 0.008 1.349 0.218 0.056 0.219 1.188
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 7 7 8 8 5 8 7
normalized size 1 1. 0.64 0.64 0.73 0.73 0.45 0.73 0.64
time (sec) N/A 0.01 0.002 0.002 1.374 0.198 0.057 0.22 0.926
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 11 10 12 12 7 12 10
normalized size 1 1. 0.69 0.62 0.75 0.75 0.44 0.75 0.62
time (sec) N/A 0.013 0.002 0.003 1.418 0.193 0.07 0.238 1.039
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 12 12 15 15 10 15 17
normalized size 1 1. 0.63 0.63 0.79 0.79 0.53 0.79 0.89
time (sec) N/A 0.026 0.002 0.004 1.361 0.206 0.062 0.216 1.717
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 19 19 22 22 17 22 27
normalized size 1 1. 0.59 0.59 0.69 0.69 0.53 0.69 0.84
time (sec) N/A 0.03 0.004 0.003 1.416 0.208 0.079 0.237 1.892
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 16 17 15 15 20 15 20
normalized size 1 1. 0.67 0.71 0.62 0.62 0.83 0.62 0.83
time (sec) N/A 0.014 0.004 0.004 1.469 0.21 0.211 0.234 1.024
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 18 14 18 18 12 18 19
normalized size 1 1. 0.69 0.54 0.69 0.69 0.46 0.69 0.73
time (sec) N/A 0.034 0.004 0.004 1.407 0.212 0.08 0.237 1.914
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 28 40 36 42 139 49 36
normalized size 1 1. 0.68 0.98 0.88 1.02 3.39 1.2 0.88
time (sec) N/A 0.028 0.029 0.015 1.347 0.22 2.095 0.236 1.907
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 29 41 39 45 136 51 36
normalized size 1 1. 0.69 0.98 0.93 1.07 3.24 1.21 0.86
time (sec) N/A 0.026 0.029 0.006 1.385 0.224 2.135 0.236 1.884
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 14 18 18 12 20 12
normalized size 1 1. 1. 0.93 1.2 1.2 0.8 1.33 0.8
time (sec) N/A 0.007 0.002 0.004 1.387 0.224 0.234 0.218 0.843
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 64 22 47 45 0 34 15
normalized size 1 1. 3.37 1.16 2.47 2.37 0. 1.79 0.79
time (sec) N/A 0.028 0.112 0.004 1.373 0.242 0. 0.231 1.765
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 64 20 47 47 0 35 15
normalized size 1 1. 3.76 1.18 2.76 2.76 0. 2.06 0.88
time (sec) N/A 0.028 0.071 0.004 1.496 0.23 0. 0.229 1.74
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 24 31 31 22 31 22
normalized size 1 1. 1. 0.96 1.24 1.24 0.88 1.24 0.88
time (sec) N/A 0.054 0.012 0.158 1.574 0.219 0.21 0.235 2.871
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 26 21 45 53 22 51 15
normalized size 1 1. 1.18 0.95 2.05 2.41 1. 2.32 0.68
time (sec) N/A 0.035 0.008 0.013 1.529 0.238 2.239 0.237 2.698
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 15 11 31 19 12 12
normalized size 1 1. 1. 0.94 0.69 1.94 1.19 0.75 0.75
time (sec) N/A 0.007 0.005 0.005 1.572 0.2 1.632 0.239 0.883
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 14 10 15 28 0 12 22
normalized size 1 1. 1.4 1. 1.5 2.8 0. 1.2 2.2
time (sec) N/A 0.022 0.009 0.026 1.676 0.201 0. 0.223 0.689
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 11 14 14 20 14 5
normalized size 1 1. 1. 1.1 1.4 1.4 2. 1.4 0.5
time (sec) N/A 0.007 0.003 0.013 1.572 0.194 0.112 0.22 0.731
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 16 0 1 53 20 22
normalized size 1 1. 1. 0.67 0. 0.04 2.21 0.83 0.92
time (sec) N/A 0.017 0.008 0.005 0. 0.195 0.135 0.224 1.071
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 19 17 22 22 26 22 22
normalized size 1 1. 1. 0.89 1.16 1.16 1.37 1.16 1.16
time (sec) N/A 0.026 0.009 0.004 1.532 0.194 0.094 0.225 0.663
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 21 16 20 18 15 20 15
normalized size 1 1. 1. 0.76 0.95 0.86 0.71 0.95 0.71
time (sec) N/A 0.018 0.003 0.005 1.525 0.208 0.32 0.218 1.829
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 30 34 45 32 32 45 27
normalized size 1 1. 0.75 0.85 1.12 0.8 0.8 1.12 0.68
time (sec) N/A 0.048 0.014 0.019 1.523 0.22 0.495 0.212 3.055
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 26 30 46 34 29 42 29
normalized size 1 1. 0.74 0.86 1.31 0.97 0.83 1.2 0.83
time (sec) N/A 0.083 0.007 0.01 1.562 0.216 0.467 0.223 6.056
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 18 17 22 19 19 22 19
normalized size 1 1. 0.82 0.77 1. 0.86 0.86 1. 0.86
time (sec) N/A 0.013 0.011 0.003 1.54 0.217 1.135 0.215 1.368
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 7 8 8 7 8 0
normalized size 1 1. 1. 0.88 1. 1. 0.88 1. 0.
time (sec) N/A 0.055 0.004 0.006 1.376 0.231 3.551 0.218 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 20 18 23 109 15 23 15
normalized size 1 1. 0.87 0.78 1. 4.74 0.65 1. 0.65
time (sec) N/A 0.009 0.009 0.004 1.537 0.204 0.22 0.217 0.565
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 20 16 0 20 0 0 19
normalized size 1 1. 0.91 0.73 0. 0.91 0. 0. 0.86
time (sec) N/A 0.062 0.082 0.006 0. 0.222 0. 0. 3.298
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 16 0 20 0 0 17
normalized size 1 1. 1. 0.8 0. 1. 0. 0. 0.85
time (sec) N/A 0.035 0.064 0.006 0. 0.228 0. 0. 2.392
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 19 16 20 28 12 20 12
normalized size 1 1. 1. 0.84 1.05 1.47 0.63 1.05 0.63
time (sec) N/A 0.013 0.012 0.019 1.516 0.19 0.108 0.208 1.358
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 4 4 4 4 4 4 15 4 3
normalized size 1 1. 1. 1. 1. 1. 3.75 1. 0.75
time (sec) N/A 0.028 0.006 0.004 1.551 0.203 0.115 0.207 2.555
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 24 25 26 38 19 28 26
normalized size 1 1. 0.89 0.93 0.96 1.41 0.7 1.04 0.96
time (sec) N/A 0.039 0.016 0.01 1.384 0.228 22.768 0.208 2.949
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 67 62 66 51 0 49 36
normalized size 1 1. 1.6 1.48 1.57 1.21 0. 1.17 0.86
time (sec) N/A 0.034 0.082 0.027 1.501 0.209 0. 0.218 1.858
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 84 122 0 88 0 82 56
normalized size 1 1. 1.18 1.72 0. 1.24 0. 1.15 0.79
time (sec) N/A 0.052 0.185 0.02 0. 0.223 0. 0.215 1.931
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 64 28 0 35 0 30 26
normalized size 1 1. 2. 0.88 0. 1.09 0. 0.94 0.81
time (sec) N/A 0.026 0.039 0.006 0. 0.208 0. 0.242 1.191
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 14 18 18 12 20 12
normalized size 1 1. 1. 0.93 1.2 1.2 0.8 1.33 0.8
time (sec) N/A 0.015 0.006 0.007 1.378 0.198 0.114 0.222 2.017
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 19 14 18 18 14 20 14
normalized size 1 1. 1. 0.74 0.95 0.95 0.74 1.05 0.74
time (sec) N/A 0.015 0.006 0.007 1.576 0.195 0.094 0.227 2.574
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 23 20 26 26 19 28 0
normalized size 1 1. 1. 0.87 1.13 1.13 0.83 1.22 0.
time (sec) N/A 0.04 0.008 0.01 1.422 0.196 0.096 0.221 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 23 18 23 23 17 27 17
normalized size 1 1. 1. 0.78 1. 1. 0.74 1.17 0.74
time (sec) N/A 0.049 0.009 0.012 1.448 0.201 0.142 0.219 5.961
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 22 19 24 35 19 32 19
normalized size 1 1. 0.92 0.79 1. 1.46 0.79 1.33 0.79
time (sec) N/A 0.043 0.016 0.012 1.384 0.196 0.121 0.211 2.945
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 28 29 38 51 3 39 29
normalized size 1 1. 1. 1.04 1.36 1.82 0.11 1.39 1.04
time (sec) N/A 0.049 0.017 0.01 1.503 0.199 0.141 0.211 4.142
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 61 37 49 84 14 50 0
normalized size 1 1. 1.24 0.76 1. 1.71 0.29 1.02 0.
time (sec) N/A 0.136 0.051 0.014 1.577 0.204 0.196 0.21 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 24 19 54 51 0 50 22
normalized size 1 1. 1.14 0.9 2.57 2.43 0. 2.38 1.05
time (sec) N/A 0.019 0.024 0.033 1.616 0.216 14.501 0.238 0.541
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 266 19 74 17 19 12
normalized size 1 1. 1. 16.62 1.19 4.62 1.06 1.19 0.75
time (sec) N/A 0.081 0.013 0.089 1.348 0.212 2.161 0.209 3.026
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 9 9 12 12 8 15 8
normalized size 1 1. 0.82 0.82 1.09 1.09 0.73 1.36 0.73
time (sec) N/A 0.018 0.006 0.002 1.343 0.19 0.084 0.225 1.477
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 23 20 26 26 20 30 20
normalized size 1 1. 1. 0.87 1.13 1.13 0.87 1.3 0.87
time (sec) N/A 0.037 0.009 0.01 1.366 0.202 0.131 0.23 2.214
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 28 21 27 36 22 30 22
normalized size 1 1. 0.93 0.7 0.9 1.2 0.73 1. 0.73
time (sec) N/A 0.036 0.014 0.011 1.396 0.195 0.094 0.225 4.234
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 24 31 31 20 35 0
normalized size 1 1. 1. 0.89 1.15 1.15 0.74 1.3 0.
time (sec) N/A 0.047 0.009 0.012 1.431 0.201 0.13 0.232 0.
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 24 24 27 43 17 22 0
normalized size 1 1. 1.04 1.04 1.17 1.87 0.74 0.96 0.
time (sec) N/A 0.039 0.017 0.011 1.553 0.194 0.117 0.224 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 15 19 19 14 20 14
normalized size 1 1. 1. 0.94 1.19 1.19 0.88 1.25 0.88
time (sec) N/A 0.028 0.007 0.008 1.622 0.192 0.085 0.217 3.872
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 13 16 16 14 16 14
normalized size 1 1. 1. 0.72 0.89 0.89 0.78 0.89 0.78
time (sec) N/A 0.033 0.011 0.011 1.519 0.195 0.192 0.215 5.02
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 12 15 15 8 18 8
normalized size 1 1. 1. 1.09 1.36 1.36 0.73 1.64 0.73
time (sec) N/A 0.02 0.003 0.009 1.337 0.232 0.089 0.211 1.571
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 21 32 43 19 39 22
normalized size 1 1. 1. 0.88 1.33 1.79 0.79 1.62 0.92
time (sec) N/A 0.026 0.013 0.016 1.348 0.23 0.11 0.218 1.954
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 44 39 62 112 46 70 41
normalized size 1 1. 0.96 0.85 1.35 2.43 1. 1.52 0.89
time (sec) N/A 0.052 0.025 0.016 1.355 0.206 0.231 0.213 3.032
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 11 14 22 8 15 8
normalized size 1 1. 1. 1.1 1.4 2.2 0.8 1.5 0.8
time (sec) N/A 0.011 0.004 0.007 1.342 0.191 0.064 0.21 1.019
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 18 23 18 10 22 0
normalized size 1 1. 1. 1.06 1.35 1.06 0.59 1.29 0.
time (sec) N/A 0.019 0.004 0.01 1.339 0.194 0.081 0.21 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 15 19 19 17 22 17
normalized size 1 1. 1. 0.75 0.95 0.95 0.85 1.1 0.85
time (sec) N/A 0.022 0.005 0.007 1.35 0.194 0.096 0.215 2.591
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 12 13 16 22 8 18 8
normalized size 1 1. 0.75 0.81 1. 1.38 0.5 1.12 0.5
time (sec) N/A 0.016 0.005 0.01 1.363 0.194 0.071 0.212 2.189
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 15 19 23 10 19 10
normalized size 1 1. 1. 1.07 1.36 1.64 0.71 1.36 0.71
time (sec) N/A 0.024 0.012 0.009 1.487 0.197 0.141 0.221 3.553
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 21 18 23 23 20 27 20
normalized size 1 1. 1. 0.86 1.1 1.1 0.95 1.29 0.95
time (sec) N/A 0.041 0.009 0.01 1.342 0.201 0.133 0.218 4.992
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 27 28 31 46 20 34 12
normalized size 1 1. 1.29 1.33 1.48 2.19 0.95 1.62 0.57
time (sec) N/A 0.008 0.012 0.014 1.345 0.193 0.101 0.212 0.566
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 17 22 22 17 23 17
normalized size 1 1. 1. 0.77 1. 1. 0.77 1.05 0.77
time (sec) N/A 0.018 0.005 0.009 1.516 0.188 0.078 0.213 2.68
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 11 19 24 8 19 12
normalized size 1 1. 1. 1.1 1.9 2.4 0.8 1.9 1.2
time (sec) N/A 0.046 0.008 0.009 1.343 0.196 0.102 0.223 3.272
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 31 22 26 34 19 28 22
normalized size 1 1. 1. 0.71 0.84 1.1 0.61 0.9 0.71
time (sec) N/A 0.022 0.003 0.01 1.342 0.196 0.105 0.23 1.66
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 17 22 22 15 23 15
normalized size 1 1. 1. 0.94 1.22 1.22 0.83 1.28 0.83
time (sec) N/A 0.043 0.008 0.007 1.503 0.202 0.129 0.227 4.772
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 25 10 23 23 17 26 10
normalized size 1 1. 1.92 0.77 1.77 1.77 1.31 2. 0.77
time (sec) N/A 0.008 0.005 0.001 1.506 0.2 0.163 0.228 0.585
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 64 58 97 131 73 97 73
normalized size 1 1. 0.75 0.68 1.14 1.54 0.86 1.14 0.86
time (sec) N/A 0.081 0.03 0.023 1.523 0.202 0.19 0.215 5.485
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 15 16 20 35 14 20 20
normalized size 1 1. 0.65 0.7 0.87 1.52 0.61 0.87 0.87
time (sec) N/A 0.02 0.014 0.007 1.532 0.195 0.127 0.214 1.805
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 41 15 15 8 15 8
normalized size 1 1. 1. 3.73 1.36 1.36 0.73 1.36 0.73
time (sec) N/A 0.006 0.01 0.013 1.386 0.187 0.161 0.214 2.756
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 23 20 31 49 39 63 24
normalized size 1 1. 0.51 0.44 0.69 1.09 0.87 1.4 0.53
time (sec) N/A 0.084 0.035 0.053 1.607 0.221 0.835 0.216 0.802
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 31 30 0 1 110 72 34
normalized size 1 1. 0.84 0.81 0. 0.03 2.97 1.95 0.92
time (sec) N/A 0.064 0.03 0.02 0. 0.227 11.177 0.215 2.368
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 20 16 50 70 36 47 20
normalized size 1 1. 0.36 0.29 0.89 1.25 0.64 0.84 0.36
time (sec) N/A 0.038 0.013 0.013 1.484 0.222 0.537 0.249 0.58
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 20 16 26 31 32 54 20
normalized size 1 1. 0.65 0.52 0.84 1. 1.03 1.74 0.65
time (sec) N/A 0.05 0.011 0.023 1.556 0.211 0.406 0.226 0.589
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 18 15 19 51 416 65 24
normalized size 1 1. 0.5 0.42 0.53 1.42 11.56 1.81 0.67
time (sec) N/A 0.067 0.021 0.029 1.522 0.243 155.717 0.228 4.666
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 16 20 58 0 35 10
normalized size 1 1. 1. 1.07 1.33 3.87 0. 2.33 0.67
time (sec) N/A 0.042 0.053 0.083 1.502 0.239 0. 0.234 25.182
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 14 19 53 0 18 14
normalized size 1 1. 1. 0.82 1.12 3.12 0. 1.06 0.82
time (sec) N/A 0.022 0.038 0.234 1.344 0.218 0. 0.216 0.675
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 22 25 55 15 22 34 24
normalized size 1 1. 0.73 0.83 1.83 0.5 0.73 1.13 0.8
time (sec) N/A 0.045 0.011 0.066 1.489 0.231 0.419 0.225 2.118
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 29 23 30 39 24 30 24
normalized size 1 1. 1. 0.79 1.03 1.34 0.83 1.03 0.83
time (sec) N/A 0.011 0.014 0.005 1.516 0.212 0.227 0.217 0.597
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 12 15 15 8 15 8
normalized size 1 1. 1. 0.92 1.15 1.15 0.62 1.15 0.62
time (sec) N/A 0.006 0.003 0.004 1.338 0.208 0.151 0.215 0.876
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 41 30 55 54 88 63 29
normalized size 1 1. 1.11 0.81 1.49 1.46 2.38 1.7 0.78
time (sec) N/A 0.047 0.021 0.006 1.514 0.217 2.227 0.226 2.372
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 31 22 34 99 0 35 19
normalized size 1 1. 1.41 1. 1.55 4.5 0. 1.59 0.86
time (sec) N/A 0.02 0.025 0.006 1.337 0.21 0. 0.228 1.326
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 21 27 109 24 34 24
normalized size 1 1. 1. 0.78 1. 4.04 0.89 1.26 0.89
time (sec) N/A 0.01 0.013 0.004 1.504 0.21 0.271 0.225 0.557
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 21 30 104 0 36 29
normalized size 1 1. 1. 0.78 1.11 3.85 0. 1.33 1.07
time (sec) N/A 0.028 0.013 0.008 1.496 0.217 0. 0.222 1.503
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 29 12 20 23 0 24 12
normalized size 1 1. 2.07 0.86 1.43 1.64 0. 1.71 0.86
time (sec) N/A 0.008 0.011 0.004 1.345 0.198 0. 0.216 0.554
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 77 88 80 126 0 227 61
normalized size 1 1. 1.13 1.29 1.18 1.85 0. 3.34 0.9
time (sec) N/A 0.1 0.065 0.007 1.597 0.209 0. 0.233 5.768
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 13 16 0 58 0 12
normalized size 1 1. 1. 1. 1.23 0. 4.46 0. 0.92
time (sec) N/A 0.025 0.005 0.016 1.345 0. 2.177 0. 1.88
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 15 3 3 2 3 15
normalized size 1 1. 1. 1. 0.2 0.2 0.13 0.2 1.
time (sec) N/A 0.018 0.016 0.016 1.349 0.212 0.22 0.211 1.066
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 2 2 2 8 3 3 2 3 2
normalized size 1 1. 1. 4. 1.5 1.5 1. 1.5 1.
time (sec) N/A 0.017 0.002 0.004 1.414 0.2 1.241 0.228 1.278
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 4 4 4 9 5 5 3 5 3
normalized size 1 1. 1. 2.25 1.25 1.25 0.75 1.25 0.75
time (sec) N/A 0.021 0.002 0.004 1.416 0.198 1.343 0.21 1.366
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 16 7 18 7 18 7
normalized size 1 1. 1. 1.45 0.64 1.64 0.64 1.64 0.64
time (sec) N/A 0.033 0.005 0.004 1.43 0.198 1.604 0.226 1.896
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 15 18 18 10 0 10
normalized size 1 1. 1. 1.07 1.29 1.29 0.71 0. 0.71
time (sec) N/A 0.023 0.003 0.004 1.406 0.202 1.703 0. 1.363
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 17 22 19 0 19 12
normalized size 1 1. 1. 1.13 1.47 1.27 0. 1.27 0.8
time (sec) N/A 0.034 0.007 0.023 1.442 0.199 0. 0.232 2.028
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 14 18 14 0 14 8
normalized size 1 1. 1. 1.08 1.38 1.08 0. 1.08 0.62
time (sec) N/A 0.135 0.006 0.007 1.403 0.198 0. 0.225 5.998
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 19 22 22 31 0 0 12
normalized size 1 1. 1. 1.16 1.16 1.63 0. 0. 0.63
time (sec) N/A 0.04 0.011 0.008 1.439 0.201 0. 0. 2.506
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 19 24 26 0 22 14
normalized size 1 1. 1. 1.06 1.33 1.44 0. 1.22 0.78
time (sec) N/A 0.038 0.009 0.175 1.413 0.211 0. 0.211 2.456
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 11 10 12 12 7 12 10
normalized size 1 1. 0.69 0.62 0.75 0.75 0.44 0.75 0.62
time (sec) N/A 0.016 0.002 0.001 1.351 0.209 0.09 0.211 1.102
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 16 15 19 19 12 19 19
normalized size 1 1. 0.62 0.58 0.73 0.73 0.46 0.73 0.73
time (sec) N/A 0.035 0.003 0.004 1.347 0.212 0.089 0.216 1.755
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 21 20 26 26 17 26 27
normalized size 1 1. 0.58 0.56 0.72 0.72 0.47 0.72 0.75
time (sec) N/A 0.054 0.004 0.004 1.357 0.198 0.125 0.228 2.577
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 39 111 244 81 360 104 39
normalized size 1 1. 0.81 2.31 5.08 1.69 7.5 2.17 0.81
time (sec) N/A 0.069 0.111 0.119 1.529 0.233 4.261 0.246 4.609
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A F F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 2 2 2 9 4 0 0 4 2
normalized size 1 1. 1. 4.5 2. 0. 0. 2. 1.
time (sec) N/A 0.004 0.003 0.007 1.422 0. 0. 0.229 0.025
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A F F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 17 8 0 0 15 7
normalized size 1 1. 1. 1.7 0.8 0. 0. 1.5 0.7
time (sec) N/A 0.007 0.002 0.003 1.412 0. 0. 0.227 0.471
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 0 30 20 0 0 24
normalized size 1 1. 1. 0. 1.36 0.91 0. 0. 1.09
time (sec) N/A 0.029 0.033 0.135 1.501 0.226 0. 0. 0.584
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 10 12 15 12 0 12 8
normalized size 1 1. 0.83 1. 1.25 1. 0. 1. 0.67
time (sec) N/A 0.027 0.004 0.006 1.43 0.199 0. 0.224 1.598
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 23 0 27 0 27 19
normalized size 1 1. 1. 1.05 0. 1.23 0. 1.23 0.86
time (sec) N/A 0.095 0.007 0.014 0. 0.201 0. 0.226 6.847
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F A F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 103 103 88 116 0 0 27 0 95
normalized size 1 1. 0.85 1.13 0. 0. 0.26 0. 0.92
time (sec) N/A 0.04 0.069 0.096 0. 0. 0.853 0. 0.809

2.2 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac{\text{number of rules}}{\text{integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [83] had the largest ratio of [ 2. ]

Table 1: Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\)
1 A 1 1 1. 9 0.111
2 A 2 1 1. 11 0.091
3 A 2 1 1. 11 0.091
4 A 2 1 1. 11 0.091
5 A 1 1 1. 14 0.071
6 A 2 1 1. 4 0.25
7 A 2 1 1. 9 0.111
8 A 2 2 1. 7 0.286
9 A 2 2 1. 17 0.118
10 A 2 2 1. 9 0.222
11 A 3 3 1. 11 0.273
12 A 3 3 1. 16 0.188
13 A 2 2 1. 10 0.2
14 A 1 1 1. 15 0.067
15 A 2 1 1. 9 0.111
16 A 1 1 1. 9 0.111
17 A 1 1 1. 15 0.067
18 A 1 1 1. 17 0.059
19 A 3 2 1. 20 0.1
20 A 1 1 1. 26 0.038
21 A 2 2 1. 20 0.1
22 A 2 2 1. 4 0.5
23 A 3 2 1. 6 0.333
24 A 4 2 1. 6 0.333
25 A 4 2 1. 6 0.333
26 A 2 2 1. 5 0.4
27 A 3 3 1. 6 0.5
28 A 2 2 1. 4 0.5
29 A 2 1 1. 4 0.25
30 A 3 2 1. 4 0.5
31 A 2 1 1. 4 0.25
32 A 4 2 1. 4 0.5
33 A 2 2 1. 6 0.333
34 A 3 3 1. 6 0.5
35 A 4 4 1. 8 0.5
36 A 2 2 1. 4 0.5
37 A 2 1 1. 4 0.25
38 A 3 2 1. 4 0.5
39 A 5 3 1. 13 0.231
40 A 3 2 1. 13 0.154
41 A 2 2 1. 13 0.154
42 A 2 2 1. 4 0.5
43 A 3 2 1. 4 0.5
44 A 2 2 1. 4 0.5
45 A 3 2 1. 4 0.5
46 A 2 2 1. 10 0.2
47 A 1 1 1. 11 0.091
48 A 1 1 1. 9 0.111
49 A 1 1 1. 13 0.077
50 A 1 1 1. 11 0.091
51 A 2 1 1. 11 0.091
52 A 2 2 1. 8 0.25
53 A 5 3 1. 8 0.375
54 A 1 1 1. 10 0.1
55 A 3 2 1. 17 0.118
56 A 1 1 1. 7 0.143
57 A 2 2 1. 4 0.5
58 A 1 1 1. 4 0.25
59 A 2 2 1. 6 0.333
60 A 1 1 1. 5 0.2
61 A 1 1 1. 2 0.5
62 A 1 1 1. 8 0.125
63 A 2 2 1. 8 0.25
64 A 2 2 1. 8 0.25
65 A 2 2 1. 14 0.143
66 A 3 2 1. 14 0.143
67 A 3 2 1. 8 0.25
68 A 1 1 1. 9 0.111
69 A 1 1 1. 13 0.077
70 A 2 2 1. 9 0.222
71 A 1 1 1. 6 0.167
72 A 1 1 1. 6 0.167
73 A 4 4 1. 7 0.571
74 A 2 2 1. 5 0.4
75 A 2 2 1. 7 0.286
76 A 3 2 1. 7 0.286
77 A 3 2 1. 9 0.222
78 A 3 3 1. 7 0.429
79 A 2 2 1. 11 0.182
80 A 1 1 1. 10 0.1
81 A 1 1 1. 10 0.1
82 A 2 2 1. 2 1.
83 A 4 4 1. 2 2.
84 A 4 4 1. 2 2.
85 A 3 3 1. 4 0.75
86 A 4 4 1. 6 0.667
87 A 2 2 1. 13 0.154
88 A 2 2 1. 14 0.143
89 A 1 1 1. 9 0.111
90 A 1 1 1. 9 0.111
91 A 2 2 1. 10 0.2
92 A 3 3 1. 4 0.75
93 A 4 3 1. 6 0.5
94 A 5 5 1. 6 0.833
95 A 4 4 1. 6 0.667
96 A 1 3 1. 17 0.176
97 A 2 2 1. 11 0.182
98 A 1 1 1. 15 0.067
99 A 1 1 1. 14 0.071
100 A 2 2 1. 11 0.182
101 A 2 2 1. 13 0.154
102 A 6 6 1. 10 0.6
103 A 3 3 1. 15 0.2
104 A 4 4 1. 15 0.267
105 A 3 3 1. 15 0.2
106 A 3 2 1. 16 0.125
107 A 3 2 1. 16 0.125
108 A 6 4 1. 18 0.222
109 A 3 2 1. 23 0.087
110 A 2 1 1. 19 0.053
111 A 6 6 1. 18 0.333
112 A 6 5 1. 31 0.161
113 A 2 2 1. 7 0.286
114 A 3 2 1. 22 0.091
115 A 2 1 1. 16 0.062
116 A 2 1 1. 17 0.059
117 A 2 1 1. 12 0.083
118 A 3 2 1. 21 0.095
119 A 2 1 1. 20 0.05
120 A 3 3 1. 16 0.188
121 A 4 3 1. 16 0.188
122 A 3 2 1. 11 0.182
123 A 3 2 1. 11 0.182
124 A 2 1 1. 16 0.062
125 A 2 1 1. 7 0.143
126 A 5 5 1. 9 0.556
127 A 4 3 1. 12 0.25
128 A 3 2 1. 14 0.143
129 A 4 4 1. 21 0.19
130 A 3 2 1. 18 0.111
131 A 2 2 1. 7 0.286
132 A 3 3 1. 11 0.273
133 A 3 2 1. 16 0.125
134 A 3 2 1. 11 0.182
135 A 5 4 1. 18 0.222
136 A 3 3 1. 7 0.429
137 A 9 6 1. 7 0.857
138 A 3 3 1. 14 0.214
139 A 1 1 1. 16 0.062
140 A 3 3 1. 12 0.25
141 A 2 2 1. 8 0.25
142 A 2 2 1. 8 0.25
143 A 1 1 1. 10 0.1
144 A 3 3 1. 13 0.231
145 A 2 1 1. 19 0.053
146 A 1 1 1. 11 0.091
147 A 3 3 1. 11 0.273
148 A 2 2 1. 11 0.182
149 A 1 1 1. 13 0.077
150 A 4 4 1. 15 0.267
151 A 3 3 1. 13 0.231
152 A 2 2 1. 9 0.222
153 A 3 3 1. 12 0.25
154 A 2 2 1. 9 0.222
155 A 6 6 1. 18 0.333
156 A 2 2 1. 8 0.25
157 A 3 3 1. 5 0.6
158 A 1 1 1. 7 0.143
159 A 1 1 1. 9 0.111
160 A 2 2 1. 7 0.286
161 A 2 2 1. 5 0.4
162 A 1 1 1. 14 0.071
163 A 2 2 1. 14 0.143
164 A 2 2 1. 9 0.222
165 A 2 3 1. 8 0.375
166 A 2 2 1. 7 0.286
167 A 3 2 1. 9 0.222
168 A 4 2 1. 9 0.222
169 A 1 1 1. 21 0.048
170 A 1 1 1. 4 0.25
171 A 2 2 1. 4 0.5
172 A 2 2 1. 8 0.25
173 A 1 1 1. 11 0.091
174 A 4 2 1. 16 0.125
175 A 1 1 1. 9 0.111

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