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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 F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 12 0 14 12 15 7
normalized size 1 1. 1. 1.09 0. 1.27 1.09 1.36 0.64
time (sec) N/A 0.007 0.002 0.003 0. 0.213 0.031 0.206 0.613
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 3 3 3 3 3 3 2 3 2
normalized size 1 1. 1. 1. 1. 1. 0.67 1. 0.67
time (sec) N/A 0.003 0. 0. 1.365 0.202 0.046 0.204 0.48
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 2 2 2 3 3 3 2 4 2
normalized size 1 1. 1. 1.5 1.5 1.5 1. 2. 1.
time (sec) N/A 0.002 0. 0. 1.364 0.192 0.026 0.202 0.023
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 8 8 8 9 11 11 8 11 5
normalized size 1 1. 1. 1.12 1.38 1.38 1. 1.38 0.62
time (sec) N/A 0.005 0.001 0.001 1.301 0.208 0.069 0.2 0.576
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 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 0.004 0.002 0. 1.325 0.22 0.032 0.202 0.026
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 2 2 2 3 3 3 2 3 2
normalized size 1 1. 1. 1.5 1.5 1.5 1. 1.5 1.
time (sec) N/A 0.003 0.001 0. 1.368 0.247 0.03 0.207 0.023
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 2 2 2 3 3 9 5 3 5
normalized size 1 1. 1. 1.5 1.5 4.5 2.5 1.5 2.5
time (sec) N/A 0.008 0.003 0.005 1.364 0.207 0.045 0.208 0.471
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 4 4 4 5 8 11 7 8 7
normalized size 1 1. 1. 1.25 2. 2.75 1.75 2. 1.75
time (sec) N/A 0.007 0.003 0.006 1.421 0.206 0.044 0.21 0.474
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 2 2 2 3 5 5 3 5 3
normalized size 1 1. 1. 1.5 2.5 2.5 1.5 2.5 1.5
time (sec) N/A 0.009 0.002 0.006 1.382 0.213 0.047 0.203 0.723
Problem 10 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 4 4 4 5 8 8 5 8 0
normalized size 1 1. 1. 1.25 2. 2. 1.25 2. 0.
time (sec) N/A 0.011 0.002 0.009 1.375 0.208 0.049 0.203 0.
Problem 11 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 2 2 2 3 3 3 2 15 0
normalized size 1 1. 1. 1.5 1.5 1.5 1. 7.5 0.
time (sec) N/A 0.005 0.003 0.002 1.48 0.202 0.106 0.203 0.
Problem 12 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 2 2 2 3 3 3 2 15 0
normalized size 1 1. 1. 1.5 1.5 1.5 1. 7.5 0.
time (sec) N/A 0.004 0.002 0.003 1.546 0.207 0.101 0.202 0.
Problem 13 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 5 5 5 6 4 15 5 8 5
normalized size 1 1. 1. 1.2 0.8 3. 1. 1.6 1.
time (sec) N/A 0.003 0.003 0.001 1.479 0.251 0.039 0.202 0.032
Problem 14 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 0.003 0.003 0. 1.443 0.221 0.043 0.202 0.031
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 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 0.012 0.003 0.002 1.361 0.223 0.182 0.199 0.782
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 8 8 8 9 11 11 5 11 5
normalized size 1 1. 1. 1.12 1.38 1.38 0.62 1.38 0.62
time (sec) N/A 0.003 0.001 0. 1.349 0.216 0.064 0.201 0.453
Problem 17 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 0.023 0.002 0. 1.338 0.2 0.066 0.199 1.78
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 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 0.013 0.016 0. 1.367 0.216 0.369 0.201 1.179
Problem 19 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 18 12
normalized size 1 1. 1. 0.93 1.2 1.2 0.8 1.2 0.8
time (sec) N/A 0.007 0.002 0.003 1.357 0.232 0.235 0.199 0.908
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 20 20 15 12 15 15 10 15 14
normalized size 1 1. 0.75 0.6 0.75 0.75 0.5 0.75 0.7
time (sec) N/A 0.014 0.002 0.003 1.353 0.206 0.064 0.202 1.137
Problem 21 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 7 7 7 8 9 9 7 9 7
normalized size 1 1. 1. 1.14 1.29 1.29 1. 1.29 1.
time (sec) N/A 0.014 0.004 0. 1.346 0.229 0.179 0.199 0.779
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 18 18 18 15 19 19 14 19 14
normalized size 1 1. 1. 0.83 1.06 1.06 0.78 1.06 0.78
time (sec) N/A 0.018 0.005 0.007 1.372 0.227 0.193 0.199 0.829
Problem 23 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. 1.339 0.217 0.07 0.201 0.
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 29 29 25 24 28 28 27 28 27
normalized size 1 1. 0.86 0.83 0.97 0.97 0.93 0.97 0.93
time (sec) N/A 0.039 0.028 0.008 1.373 0.228 0.398 0.201 1.538
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 29 29 25 24 28 28 24 28 24
normalized size 1 1. 0.86 0.83 0.97 0.97 0.83 0.97 0.83
time (sec) N/A 0.035 0.025 0.007 1.329 0.223 0.406 0.202 1.465
Problem 26 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. 1.46 0.217 0.082 0.2 0.562
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 16 16 16 15 19 19 12 19 12
normalized size 1 1. 1. 0.94 1.19 1.19 0.75 1.19 0.75
time (sec) N/A 0.008 0.005 0. 1.502 0.232 0.132 0.202 1.062
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 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 0.022 0.005 0.003 1.349 0.229 0.41 0.201 0.988
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 9 100 24 0 139 0
normalized size 1 1. 1. 1.12 12.5 3. 0. 17.38 0.
time (sec) N/A 0.028 0.011 0.007 1.522 0.243 0. 0.222 0.
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 17 17 17 14 18 18 12 18 12
normalized size 1 1. 1. 0.82 1.06 1.06 0.71 1.06 0.71
time (sec) N/A 0.013 0.002 0.003 1.416 0.22 0.082 0.201 1.129
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 27 27 17 17 22 22 15 22 26
normalized size 1 1. 0.63 0.63 0.81 0.81 0.56 0.81 0.96
time (sec) N/A 0.047 0.003 0.004 1.41 0.205 0.07 0.198 2.646
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 27 27 22 22 26 28 26 26 26
normalized size 1 1. 0.81 0.81 0.96 1.04 0.96 0.96 0.96
time (sec) N/A 0.021 0.029 0.009 1.403 0.218 0.373 0.201 1.447
Problem 33 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 20 22 23 28 20 23 20
normalized size 1 1. 0.74 0.81 0.85 1.04 0.74 0.85 0.74
time (sec) N/A 0.022 0.019 0.01 1.353 0.223 0.794 0.2 1.449
Problem 34 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 9 9 9 10 46 12 7 23 0
normalized size 1 1. 1. 1.11 5.11 1.33 0.78 2.56 0.
time (sec) N/A 0.019 0.005 0.003 1.356 0.211 0.178 0.198 0.
Problem 35 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 19 19 19 19 77 24 20 41 0
normalized size 1 1. 1. 1. 4.05 1.26 1.05 2.16 0.
time (sec) N/A 0.029 0.008 0.007 1.398 0.207 0.253 0.198 0.
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 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 0.017 0.002 0. 1.353 0.214 0.061 0.2 1.075
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 21 21 15 14 18 19 66 18 19
normalized size 1 1. 0.71 0.67 0.86 0.9 3.14 0.86 0.9
time (sec) N/A 0.014 0.004 0.004 1.347 0.249 3.081 0.219 1.105
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 18 18 18 15 19 19 14 19 14
normalized size 1 1. 1. 0.83 1.06 1.06 0.78 1.06 0.78
time (sec) N/A 0.019 0.005 0.007 1.349 0.222 0.188 0.232 0.85
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 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 0.032 0.004 0.003 1.359 0.243 0.069 0.218 1.953
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 18 18 18 17 22 22 12 22 12
normalized size 1 1. 1. 0.94 1.22 1.22 0.67 1.22 0.67
time (sec) N/A 0.01 0.005 0.001 1.481 0.225 0.138 0.215 1.021
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 10 140 27 0 70 0
normalized size 1 1. 1. 1.11 15.56 3. 0. 7.78 0.
time (sec) N/A 0.023 0.007 0.008 1.386 0.231 0. 0.221 0.
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 17 17 17 14 18 34 26 18 12
normalized size 1 1. 1. 0.82 1.06 2. 1.53 1.06 0.71
time (sec) N/A 0.015 0.012 0.104 1.354 0.292 0.717 0.199 1.046
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 17 17 17 9 18 19 22 18 12
normalized size 1 1. 1. 0.53 1.06 1.12 1.29 1.06 0.71
time (sec) N/A 0.015 0.01 0.014 1.331 0.237 0.777 0.201 1.015
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 11 11 11 12 15 15 10 15 10
normalized size 1 1. 1. 1.09 1.36 1.36 0.91 1.36 0.91
time (sec) N/A 0.016 0.003 0.006 1.338 0.24 1.379 0.199 1.061
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 22 22 14 12 15 15 10 15 15
normalized size 1 1. 0.64 0.55 0.68 0.68 0.45 0.68 0.68
time (sec) N/A 0.032 0.003 0.004 1.352 0.223 0.068 0.198 1.89
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 15 15 9 9 16 11 7 11 12
normalized size 1 1. 0.6 0.6 1.07 0.73 0.47 0.73 0.8
time (sec) N/A 0.015 0.003 0.002 1.349 0.219 0.064 0.202 1.357
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 19 19 14 15 19 19 14 22 15
normalized size 1 1. 0.74 0.79 1. 1. 0.74 1.16 0.79
time (sec) N/A 0.017 0.004 0.01 1.509 0.249 0.088 0.199 1.034
Problem 48 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 14 18 15 18 15
normalized size 1 1. 1. 0.82 0.82 1.06 0.88 1.06 0.88
time (sec) N/A 0.007 0.004 0.003 1.346 0.225 0.556 0.204 0.482
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 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 0.015 0.004 0.001 1.35 0.211 0.219 0.201 1.084
Problem 50 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 12 10 12 12 8 12 8
normalized size 1 1. 0.86 0.71 0.86 0.86 0.57 0.86 0.57
time (sec) N/A 0.005 0.001 0.001 1.363 0.213 0.068 0.199 0.559
Problem 51 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 16 18 15 18 15
normalized size 1 1. 1. 0.82 0.94 1.06 0.88 1.06 0.88
time (sec) N/A 0.006 0.004 0. 1.404 0.22 0.573 0.2 0.497
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 22 22 22 17 22 22 20 22 46
normalized size 1 1. 1. 0.77 1. 1. 0.91 1. 2.09
time (sec) N/A 0.018 0.009 0. 1.373 0.233 0.406 0.202 2.838
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 20 20 20 17 22 22 15 22 15
normalized size 1 1. 1. 0.85 1.1 1.1 0.75 1.1 0.75
time (sec) N/A 0.026 0.005 0.009 1.349 0.219 2.95 0.199 1.442
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 28 28 19 17 22 22 15 22 22
normalized size 1 1. 0.68 0.61 0.79 0.79 0.54 0.79 0.79
time (sec) N/A 0.05 0.004 0.004 1.452 0.214 0.081 0.204 2.874
Problem 55 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. 1.548 0.215 0.329 0.204 1.892
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 18 18 18 17 22 22 15 24 15
normalized size 1 1. 1. 0.94 1.22 1.22 0.83 1.33 0.83
time (sec) N/A 0.023 0.01 0.009 1.424 0.222 0.207 0.2 0.874
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 21 21 15 14 18 19 66 18 19
normalized size 1 1. 0.71 0.67 0.86 0.9 3.14 0.86 0.9
time (sec) N/A 0.011 0.004 0.001 1.548 0.212 3.091 0.204 1.072
Problem 58 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 14 15 14 19 14 14 14
normalized size 1 1. 0.78 0.83 0.78 1.06 0.78 0.78 0.78
time (sec) N/A 0.012 0.004 0.008 1.415 0.233 0.041 0.2 0.508
Problem 59 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 0.011 0.003 0. 1.404 0.216 0.036 0.2 0.487
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 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 0.001 1.435 0.22 0.037 0.204 0.57
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 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. 1.333 0.223 0.042 0.2 0.632
Problem 62 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 31 18 18 18 12 18 12
normalized size 1 1. 1.82 1.06 1.06 1.06 0.71 1.06 0.71
time (sec) N/A 0.036 0.016 0.01 1.325 0.221 0.053 0.202 2.33
Problem 63 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 17 17 31 30 18 30 12 18 12
normalized size 1 1. 1.82 1.76 1.06 1.76 0.71 1.06 0.71
time (sec) N/A 0.037 0.016 0.01 1.337 0.231 0.045 0.199 2.342
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 36 36 30 29 24 34 31 30 32
normalized size 1 1. 0.83 0.81 0.67 0.94 0.86 0.83 0.89
time (sec) N/A 0.07 0.013 0.01 1.35 0.259 0.041 0.205 2.659
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 24 24 14 19 14 26 14 14 20
normalized size 1 1. 0.58 0.79 0.58 1.08 0.58 0.58 0.83
time (sec) N/A 0.039 0.006 0.002 1.348 0.222 0.053 0.22 1.625
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 22 22 18 19 19 24 37 19 20
normalized size 1 1. 0.82 0.86 0.86 1.09 1.68 0.86 0.91
time (sec) N/A 0.016 0.007 0.039 1.335 0.22 0.21 0.212 0.6
Problem 67 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 20 20 20 15 19 77 37 19 0
normalized size 1 1. 1. 0.75 0.95 3.85 1.85 0.95 0.
time (sec) N/A 0.027 0.012 0.014 1.37 0.245 0.76 0.203 0.
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 25 25 25 28 26 26 19 26 19
normalized size 1 1. 1. 1.12 1.04 1.04 0.76 1.04 0.76
time (sec) N/A 0.06 0.016 0.01 1.333 0.231 0.053 0.213 3.445
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 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 0.026 0.003 0. 1.328 0.227 0.04 0.214 0.655
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 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 0.029 0.003 0.056 1.51 0.247 0.038 0.2 0.676
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 46 46 30 36 24 45 41 30 41
normalized size 1 1. 0.65 0.78 0.52 0.98 0.89 0.65 0.89
time (sec) N/A 0.058 0.021 0.019 1.332 0.235 0.046 0.2 1.898
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 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 0.001 1.326 0.223 0.047 0.205 0.724
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 46 46 22 36 22 42 31 22 46
normalized size 1 1. 0.48 0.78 0.48 0.91 0.67 0.48 1.
time (sec) N/A 0.079 0.009 0.011 1.369 0.231 0.055 0.206 2.724
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 22 39 18 23 0 18 19
normalized size 1 1. 1.05 1.86 0.86 1.1 0. 0.86 0.9
time (sec) N/A 0.036 0.034 0.091 1.363 0.237 0. 0.213 2.258
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 21 21 22 14 18 19 167 18 19
normalized size 1 1. 1.05 0.67 0.86 0.9 7.95 0.86 0.9
time (sec) N/A 0.036 0.028 0.037 1.492 0.227 103.477 0.202 2.256
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 18 14 16 18 39 16 17
normalized size 1 1. 0.95 0.74 0.84 0.95 2.05 0.84 0.89
time (sec) N/A 0.032 0.01 0.017 1.336 0.226 0.456 0.199 1.688
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 19 19 19 15 20 20 22 20 14
normalized size 1 1. 1. 0.79 1.05 1.05 1.16 1.05 0.74
time (sec) N/A 0.022 0.005 0.007 1.36 0.228 0.823 0.201 1.355
Problem 78 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 14 14 14 13 22 19 10 19 0
normalized size 1 1. 1. 0.93 1.57 1.36 0.71 1.36 0.
time (sec) N/A 0.022 0.007 0.017 1.484 0.235 0.078 0.203 0.
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 22 22 22 29 27 50 20 49 26
normalized size 1 1. 1. 1.32 1.23 2.27 0.91 2.23 1.18
time (sec) N/A 0.054 0.009 0.02 1.338 0.233 0.098 0.209 3.63
Problem 80 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 5 5 36 6 7 7 19 7 5
normalized size 1 1. 7.2 1.2 1.4 1.4 3.8 1.4 1.
time (sec) N/A 0.022 0.011 0.036 1.351 0.224 0.481 0.214 1.555
Problem 81 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 11 11 25 11 20 23 8 14 7
normalized size 1 1. 2.27 1. 1.82 2.09 0.73 1.27 0.64
time (sec) N/A 0.016 0.01 0.003 1.358 0.211 0.714 0.216 0.516
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 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. 1.6 0.218 0.044 0.205 0.047
Problem 83 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 0.015 0.005 0.003 1.526 0.224 0.052 0.2 0.49
Problem 84 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 17 13 12 22 19 12 19
normalized size 1 1. 1.55 1.18 1.09 2. 1.73 1.09 1.73
time (sec) N/A 0.012 0.004 0.043 1.342 0.206 0.045 0.209 0.524
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 19 19 27 19 20 30 31 20 31
normalized size 1 1. 1.42 1. 1.05 1.58 1.63 1.05 1.63
time (sec) N/A 0.016 0.005 0.043 1.352 0.208 0.048 0.202 0.607
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 8 8 8 11 8 27 29 8 5
normalized size 1 1. 1. 1.38 1. 3.38 3.62 1. 0.62
time (sec) N/A 0.032 0.003 0.021 1.343 0.222 0.052 0.199 1.783
Problem 87 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 27 22 18 27 29 18 0
normalized size 1 1. 1.59 1.29 1.06 1.59 1.71 1.06 0.
time (sec) N/A 0.036 0.017 0.022 1.343 0.212 0.053 0.199 0.
Problem 88 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 0.019 0.003 0.01 1.398 0.214 0.054 0.202 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 42 19 19 15 19 0
normalized size 1 1. 1. 2.47 1.12 1.12 0.88 1.12 0.
time (sec) N/A 0.036 0.017 0.02 1.349 0.214 0.107 0.202 0.
Problem 90 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 20 23 46 32 20 30 17
normalized size 1 1. 0.91 1.05 2.09 1.45 0.91 1.36 0.77
time (sec) N/A 0.018 0.005 0.004 1.346 0.224 0.121 0.205 0.517
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 22 22 30 19 24 24 31 24 17
normalized size 1 1. 1.36 0.86 1.09 1.09 1.41 1.09 0.77
time (sec) N/A 0.02 0.006 0.005 1.497 0.218 0.063 0.205 0.526
Problem 92 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 19 19 19 48 27 27 20 27 20
normalized size 1 1. 1. 2.53 1.42 1.42 1.05 1.42 1.05
time (sec) N/A 0.025 0.006 0.016 1.355 0.23 0.127 0.201 1.825
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 58 27 27 20 27 0
normalized size 1 1. 1. 2.32 1.08 1.08 0.8 1.08 0.
time (sec) N/A 0.047 0.008 0.019 1.36 0.23 0.152 0.205 0.
Problem 94 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 14 8 7 8 0
normalized size 1 1. 1. 0.88 1.75 1. 0.88 1. 0.
time (sec) N/A 0.019 0.003 0.01 1.363 0.216 0.051 0.199 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 32 49 19 15 19 0
normalized size 1 1. 1. 1.88 2.88 1.12 0.88 1.12 0.
time (sec) N/A 0.037 0.01 0.02 1.374 0.253 0.132 0.204 0.
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 14 8 7 8 0
normalized size 1 1. 1. 0.88 1.75 1. 0.88 1. 0.
time (sec) N/A 0.02 0.003 0.018 1.372 0.212 0.057 0.2 0.
Problem 97 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 42 24 36 46 27 39 14
normalized size 1 1. 2.62 1.5 2.25 2.88 1.69 2.44 0.88
time (sec) N/A 0.022 0.073 0.017 1.373 0.263 0.126 0.206 1.655
Problem 98 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 0.003 1.503 0.224 0.047 0.206 0.475
Problem 99 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 17 19 38 14 30 14
normalized size 1 1. 1. 1.21 1.36 2.71 1. 2.14 1.
time (sec) N/A 0.014 0.005 0.005 1.347 0.244 0.092 0.206 0.497
Problem 100 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 17 17 37 22 19 53 41 19 44
normalized size 1 1. 2.18 1.29 1.12 3.12 2.41 1.12 2.59
time (sec) N/A 0.04 0.02 0.019 1.458 0.235 0.058 0.213 2.84
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 17 17 17 22 19 41 14 24 22
normalized size 1 1. 1. 1.29 1.12 2.41 0.82 1.41 1.29
time (sec) N/A 0.04 0.008 0.019 1.336 0.265 0.119 0.198 3.339
Problem 102 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 5 5 17 9 11 26 15 8 5
normalized size 1 1. 3.4 1.8 2.2 5.2 3. 1.6 1.
time (sec) N/A 0.005 0.004 0.001 1.486 0.269 0.098 0.213 0.03
Problem 103 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 47 18 36 59 27 73 17
normalized size 1 1. 2.94 1.12 2.25 3.69 1.69 4.56 1.06
time (sec) N/A 0.012 0.007 0.047 1.42 0.265 0.13 0.205 0.516
Problem 104 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 8 8 19 12 23 28 19 26 7
normalized size 1 1. 2.38 1.5 2.88 3.5 2.38 3.25 0.88
time (sec) N/A 0.022 0.007 0.013 1.342 0.272 0.097 0.207 2.797
Problem 105 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 17 12 19 34 20 19 20
normalized size 1 1. 1.31 0.92 1.46 2.62 1.54 1.46 1.54
time (sec) N/A 0.012 0.004 0.045 1.347 0.22 0.043 0.201 0.537
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 17 17 17 14 18 32 26 18 12
normalized size 1 1. 1. 0.82 1.06 1.88 1.53 1.06 0.71
time (sec) N/A 0.015 0.011 0.059 1.394 0.226 0.717 0.199 1.02
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 17 17 17 14 18 18 22 18 14
normalized size 1 1. 1. 0.82 1.06 1.06 1.29 1.06 0.82
time (sec) N/A 0.015 0.009 0.046 1.363 0.229 0.728 0.2 0.996
Problem 108 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 32 26 15 10
normalized size 1 1. 1. 0.8 1. 2.13 1.73 1. 0.67
time (sec) N/A 0.015 0.01 0.078 1.408 0.222 0.717 0.204 1.042
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 17 17 17 9 18 19 24 18 12
normalized size 1 1. 1. 0.53 1.06 1.12 1.41 1.06 0.71
time (sec) N/A 0.016 0.011 0.018 1.342 0.215 0.772 0.202 1.021
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 8 8 8 7 8 8 7 8 7
normalized size 1 1. 1. 0.88 1. 1. 0.88 1. 0.88
time (sec) N/A 0.019 0.002 0.004 1.347 0.219 0.038 0.198 1.122
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 30 30 30 23 30 34 114 30 27
normalized size 1 1. 1. 0.77 1. 1.13 3.8 1. 0.9
time (sec) N/A 0.048 0.014 0.003 1.389 0.26 22.067 0.204 2.271
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 5 5 8 6 15 7 7 12 0
normalized size 1 1. 1.6 1.2 3. 1.4 1.4 2.4 0.
time (sec) N/A 0.031 0.003 0.023 1.323 0.252 0.768 0.199 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 61 20 93 47 32 39 0
normalized size 1 1. 4.07 1.33 6.2 3.13 2.13 2.6 0.
time (sec) N/A 0.073 0.015 0.063 1.654 0.232 0.876 0.222 0.
Problem 114 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 14 14 14 13 22 19 10 24 0
normalized size 1 1. 1. 0.93 1.57 1.36 0.71 1.71 0.
time (sec) N/A 0.022 0.007 0.014 1.335 0.265 0.071 0.201 0.
Problem 115 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 22 22 22 29 27 50 20 49 0
normalized size 1 1. 1. 1.32 1.23 2.27 0.91 2.23 0.
time (sec) N/A 0.054 0.009 0.02 1.356 0.232 0.099 0.206 0.
Problem 116 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 0.019 0.002 0. 1.341 0.305 0.052 0.2 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 42 19 19 15 19 0
normalized size 1 1. 1. 2.47 1.12 1.12 0.88 1.12 0.
time (sec) N/A 0.038 0.012 0. 1.354 0.214 0.109 0.201 0.
Problem 118 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 34 28 90 15 53 15
normalized size 1 1. 1. 1.36 1.12 3.6 0.6 2.12 0.6
time (sec) N/A 0.016 0.014 0.007 1.548 0.244 0.338 0.208 1.513
Problem 119 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 22 12 26 12
normalized size 1 1. 1. 0.81 1. 1.38 0.75 1.62 0.75
time (sec) N/A 0.012 0.009 0.005 1.495 0.207 1.23 0.203 1.274
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 9 9 9 8 9 41 7 9 7
normalized size 1 1. 1. 0.89 1. 4.56 0.78 1. 0.78
time (sec) N/A 0.005 0.001 0.004 1.346 0.209 0.152 0.201 0.762
Problem 121 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 46 15 24 24 19 26 12
normalized size 1 1. 2.88 0.94 1.5 1.5 1.19 1.62 0.75
time (sec) N/A 0.007 0.005 0.004 1.345 0.207 1.764 0.232 0.927
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 31 31 22 19 35 85 27 31 24
normalized size 1 1. 0.71 0.61 1.13 2.74 0.87 1. 0.77
time (sec) N/A 0.036 0.01 0.007 1.513 0.209 1.016 0.2 2.57
Problem 123 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 24 28 46 0 31 36
normalized size 1 1. 1. 0.89 1.04 1.7 0. 1.15 1.33
time (sec) N/A 0.026 0.017 0.007 1.545 0.216 0. 0.206 1.915
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 16 16 16 20 19 43 27 45 10
normalized size 1 1. 1. 1.25 1.19 2.69 1.69 2.81 0.62
time (sec) N/A 0.014 0.009 0.007 1.484 0.21 1.258 0.208 1.394
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 31 31 22 25 35 115 39 41 20
normalized size 1 1. 0.71 0.81 1.13 3.71 1.26 1.32 0.65
time (sec) N/A 0.035 0.012 0.005 1.505 0.211 0.878 0.2 2.507
Problem 126 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 17 15 23 8 15 8
normalized size 1 1. 1. 1.31 1.15 1.77 0.62 1.15 0.62
time (sec) N/A 0.006 0.002 0.004 1.357 0.211 0.151 0.2 0.888
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 15 15 15 18 15 82 24 15 10
normalized size 1 1. 1. 1.2 1. 5.47 1.6 1. 0.67
time (sec) N/A 0.006 0.003 0.004 1.336 0.201 0.231 0.2 0.898
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 25 25 25 20 26 112 19 26 19
normalized size 1 1. 1. 0.8 1.04 4.48 0.76 1.04 0.76
time (sec) N/A 0.01 0.011 0.004 1.492 0.208 0.244 0.207 0.619
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 25 25 18 15 30 82 24 26 19
normalized size 1 1. 0.72 0.6 1.2 3.28 0.96 1.04 0.76
time (sec) N/A 0.027 0.006 0.004 1.498 0.223 0.489 0.198 1.877
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 6 6 6 5 5 19 3 19 3
normalized size 1 1. 1. 0.83 0.83 3.17 0.5 3.17 0.5
time (sec) N/A 0.004 0.006 0.004 1.49 0.2 0.158 0.211 0.497
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 18 16 20 105 15 34 15
normalized size 1 1. 0.86 0.76 0.95 5. 0.71 1.62 0.71
time (sec) N/A 0.006 0.008 0.003 1.519 0.198 0.242 0.206 0.558
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 35 35 33 26 30 115 68 34 26
normalized size 1 1. 0.94 0.74 0.86 3.29 1.94 0.97 0.74
time (sec) N/A 0.034 0.021 0.01 1.501 0.204 4.004 0.208 2.166
Problem 133 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 23 23 23 28 0 115 76 65 17
normalized size 1 1. 1. 1.22 0. 5. 3.3 2.83 0.74
time (sec) N/A 0.016 0.012 0.007 0. 0.2 1.034 0.207 1.562
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 30 30 28 25 26 96 94 32 24
normalized size 1 1. 0.93 0.83 0.87 3.2 3.13 1.07 0.8
time (sec) N/A 0.039 0.013 0.01 1.498 0.207 2.246 0.205 2.579
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 25 19 27 39 31 12
normalized size 1 1. 1. 1.39 1.06 1.5 2.17 1.72 0.67
time (sec) N/A 0.014 0.01 0.007 1.499 0.202 1.279 0.209 1.41
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 34 34 34 31 32 123 49 32 24
normalized size 1 1. 1. 0.91 0.94 3.62 1.44 0.94 0.71
time (sec) N/A 0.022 0.048 0.011 1.502 0.203 2.647 0.221 2.111
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 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 0.021 0.019 0.01 1.492 0.206 0.262 0.211 1.735
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 29 18 19 70 15 50 24
normalized size 1 1. 1.26 0.78 0.83 3.04 0.65 2.17 1.04
time (sec) N/A 0.029 0.014 0.005 1.48 0.207 1.772 0.206 1.822
Problem 139 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 82 26 12 12
normalized size 1 1. 1. 0.77 0.92 6.31 2. 0.92 0.92
time (sec) N/A 0.005 0.003 0.004 1.327 0.2 4.084 0.201 0.763
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 31 31 22 29 35 117 44 43 24
normalized size 1 1. 0.71 0.94 1.13 3.77 1.42 1.39 0.77
time (sec) N/A 0.035 0.013 0.006 1.519 0.202 0.905 0.204 2.568
Problem 141 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 33 32 42 166 112 35 34
normalized size 1 1. 0.73 0.71 0.93 3.69 2.49 0.78 0.76
time (sec) N/A 0.032 0.024 0.007 1.507 0.21 4.457 0.216 2.771
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 13 13 13 10 12 93 26 12 10
normalized size 1 1. 1. 0.77 0.92 7.15 2. 0.92 0.77
time (sec) N/A 0.007 0.003 0.003 1.768 0.198 0.223 0.209 0.838
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 16 16 16 23 16 31 36 16 14
normalized size 1 1. 1. 1.44 1. 1.94 2.25 1. 0.88
time (sec) N/A 0.006 0.009 0.003 1.387 0.202 1.222 0.205 0.517
Problem 144 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 33 33 45 26 49 47 0 31 22
normalized size 1 1. 1.36 0.79 1.48 1.42 0. 0.94 0.67
time (sec) N/A 0.017 0.041 0.006 1.538 0.204 0. 0.213 0.799
Problem 145 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 8 8 8 7 8 24 0 24 19
normalized size 1 1. 1. 0.88 1. 3. 0. 3. 2.38
time (sec) N/A 0.013 0.008 0.006 1.638 0.201 0. 0.213 0.665
Problem 146 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 25 25 24 30 30 27 0 28 22
normalized size 1 1. 0.96 1.2 1.2 1.08 0. 1.12 0.88
time (sec) N/A 0.014 0.009 0.004 1.562 0.197 0. 0.208 0.702
Problem 147 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 44 44 53 37 49 47 0 34 32
normalized size 1 1. 1.2 0.84 1.11 1.07 0. 0.77 0.73
time (sec) N/A 0.045 0.027 0.005 1.699 0.204 0. 0.215 2.683
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 26 26 23 25 30 38 19 30 20
normalized size 1 1. 0.88 0.96 1.15 1.46 0.73 1.15 0.77
time (sec) N/A 0.013 0.012 0.006 1.624 0.196 0.131 0.209 0.73
Problem 149 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 43 43 31 36 80 66 0 49 36
normalized size 1 1. 0.72 0.84 1.86 1.53 0. 1.14 0.84
time (sec) N/A 0.018 0.026 0.004 1.438 0.206 0. 0.214 0.803
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 33 33 33 23 30 124 29 30 24
normalized size 1 1. 1. 0.7 0.91 3.76 0.88 0.91 0.73
time (sec) N/A 0.046 0.024 0.014 1.593 0.212 1.632 0.212 3.101
Problem 151 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 30 23 30 30 22 30 24
normalized size 1 1. 1. 0.77 1. 1. 0.73 1. 0.8
time (sec) N/A 0.033 0.013 0.009 1.537 0.212 1.361 0.209 2.093
Problem 152 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 14 14 42 13 11 22 3 22 12
normalized size 1 1. 3. 0.93 0.79 1.57 0.21 1.57 0.86
time (sec) N/A 0.007 0.004 0.004 1.431 0.217 1.701 0.209 0.705
Problem 153 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 10 20 10
normalized size 1 1. 1. 0.93 1.2 1.2 0.67 1.33 0.67
time (sec) N/A 0.013 0.006 0.007 1.473 0.199 0.091 0.207 1.676
Problem 154 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 26 26 25 21 27 27 19 28 0
normalized size 1 1. 0.96 0.81 1.04 1.04 0.73 1.08 0.
time (sec) N/A 0.031 0.007 0.003 1.358 0.192 0.059 0.211 0.
Problem 155 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 20 26 26 19 30 19
normalized size 1 1. 1. 0.8 1.04 1.04 0.76 1.2 0.76
time (sec) N/A 0.055 0.01 0.01 1.336 0.203 0.156 0.208 6.002
Problem 156 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 30 30 29 25 32 49 20 35 0
normalized size 1 1. 0.97 0.83 1.07 1.63 0.67 1.17 0.
time (sec) N/A 0.053 0.026 0.013 1.346 0.211 0.098 0.212 0.
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 23 23 23 18 23 23 17 24 17
normalized size 1 1. 1. 0.78 1. 1. 0.74 1.04 0.74
time (sec) N/A 0.05 0.007 0.009 1.523 0.212 0.149 0.213 4.332
Problem 158 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 38 32 42 54 34 42 32
normalized size 1 1. 1. 0.84 1.11 1.42 0.89 1.11 0.84
time (sec) N/A 0.059 0.017 0.009 1.514 0.233 0.12 0.206 5.675
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 93 73 104 211 88 100 0
normalized size 1 1. 0.9 0.71 1.01 2.05 0.85 0.97 0.
time (sec) N/A 0.829 0.074 0.016 1.521 0.245 0.823 0.208 0.
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 33 33 33 28 39 59 27 41 29
normalized size 1 1. 1. 0.85 1.18 1.79 0.82 1.24 0.88
time (sec) N/A 0.074 0.035 0.011 1.547 0.209 0.18 0.206 7.376
Problem 161 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 16 16 20 26 12 20 12
normalized size 1 1. 0.84 0.84 1.05 1.37 0.63 1.05 0.63
time (sec) N/A 0.007 0.007 0. 1.502 0.227 0.106 0.202 0.552
Problem 162 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 12 20 12
normalized size 1 1. 1. 0.74 0.95 0.95 0.63 1.05 0.63
time (sec) N/A 0.011 0.004 0.009 1.376 0.232 0.089 0.21 1.119
Problem 163 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 21 16 20 20 17 23 17
normalized size 1 1. 1.11 0.84 1.05 1.05 0.89 1.21 0.89
time (sec) N/A 0.014 0.005 0.009 1.348 0.2 0.091 0.205 1.529
Problem 164 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 32 27 35 50 26 58 26
normalized size 1 1. 1. 0.84 1.09 1.56 0.81 1.81 0.81
time (sec) N/A 0.059 0.024 0.013 1.377 0.211 0.146 0.217 3.796
Problem 165 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 43 43 33 34 46 72 32 42 34
normalized size 1 1. 0.77 0.79 1.07 1.67 0.74 0.98 0.79
time (sec) N/A 0.062 0.034 0.013 1.385 0.23 0.183 0.219 3.971
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 21 21 21 18 26 35 17 28 17
normalized size 1 1. 1. 0.86 1.24 1.67 0.81 1.33 0.81
time (sec) N/A 0.019 0.003 0.01 1.361 0.203 0.105 0.222 1.509
Problem 167 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 24 31 26 17 35 0
normalized size 1 1. 1. 0.96 1.24 1.04 0.68 1.4 0.
time (sec) N/A 0.047 0.009 0.01 1.325 0.2 0.094 0.218 0.
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 11 11 11 12 18 15 8 18 12
normalized size 1 1. 1. 1.09 1.64 1.36 0.73 1.64 1.09
time (sec) N/A 0.036 0.005 0.006 1.365 0.2 0.091 0.217 3.199
Problem 169 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 36 32 42 42 36 42 36
normalized size 1 1. 1. 0.89 1.17 1.17 1. 1.17 1.
time (sec) N/A 0.197 0.026 0.007 1.548 0.212 0.276 0.22 14.579
Problem 170 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 22 28 45 22 28 22
normalized size 1 1. 1. 0.76 0.97 1.55 0.76 0.97 0.76
time (sec) N/A 0.174 0.026 0.013 1.517 0.225 0.253 0.213 13.11
Problem 171 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 60 60 54 48 63 99 63 81 60
normalized size 1 1. 0.9 0.8 1.05 1.65 1.05 1.35 1.
time (sec) N/A 0.402 0.088 0.015 1.527 0.205 0.365 0.223 65.307
Problem 172 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 28 25 41 53 26 34 27
normalized size 1 1. 0.76 0.68 1.11 1.43 0.7 0.92 0.73
time (sec) N/A 0.024 0.02 0.009 1.512 0.198 0.156 0.214 2.39
Problem 173 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 97 97 78 68 101 197 88 96 83
normalized size 1 1. 0.8 0.7 1.04 2.03 0.91 0.99 0.86
time (sec) N/A 0.159 0.063 0.019 1.498 0.238 0.293 0.214 9.737
Problem 174 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 46 36 47 66 46 49 42
normalized size 1 1. 1. 0.78 1.02 1.43 1. 1.07 0.91
time (sec) N/A 0.085 0.043 0.013 1.524 0.206 0.198 0.214 9.327
Problem 175 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 48 48 48 38 50 76 48 51 44
normalized size 1 1. 1. 0.79 1.04 1.58 1. 1.06 0.92
time (sec) N/A 0.049 0.019 0.01 1.517 0.202 0.214 0.212 3.472
Problem 176 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 15 15 19 14 18 18 10 19 0
normalized size 1 1. 1.27 0.93 1.2 1.2 0.67 1.27 0.
time (sec) N/A 0.015 0.004 0.001 1.36 0.195 0.056 0.208 0.
Problem 177 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 8 9 11 11 7 12 7
normalized size 1 1. 0.8 0.9 1.1 1.1 0.7 1.2 0.7
time (sec) N/A 0.012 0.002 0.003 1.361 0.195 0.057 0.208 1.066
Problem 178 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 10 18 10
normalized size 1 1. 1. 0.92 1.15 1.15 0.77 1.38 0.77
time (sec) N/A 0.021 0.006 0.009 1.406 0.196 0.1 0.204 1.707
Problem 179 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 0.008 0.004 0.007 1.396 0.196 0.09 0.206 1.051
Problem 180 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 15 13 16 16 10 18 10
normalized size 1 1. 1.25 1.08 1.33 1.33 0.83 1.5 0.83
time (sec) N/A 0.016 0.004 0.003 1.411 0.19 0.06 0.207 1.617
Problem 181 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 19 27 35 27 80 38 15
normalized size 1 1. 0.73 1.04 1.35 1.04 3.08 1.46 0.58
time (sec) N/A 0.021 0.01 0.009 1.361 0.221 0.287 0.212 1.792
Problem 182 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 16 10 19 10
normalized size 1 1. 1. 0.93 1.14 1.14 0.71 1.36 0.71
time (sec) N/A 0.032 0.005 0.009 1.352 0.196 0.096 0.206 2.18
Problem 183 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 26 26 26 19 24 24 17 27 0
normalized size 1 1. 1. 0.73 0.92 0.92 0.65 1.04 0.
time (sec) N/A 0.025 0.008 0.009 1.428 0.203 0.09 0.213 0.
Problem 184 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 20 10
normalized size 1 1. 1. 1.07 1.36 1.64 0.71 1.43 0.71
time (sec) N/A 0.015 0.006 0.007 1.457 0.202 0.074 0.203 1.451
Problem 185 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 19 30 19
normalized size 1 1. 1. 0.87 1.13 1.13 0.83 1.3 0.83
time (sec) N/A 0.027 0.007 0.01 1.338 0.211 0.147 0.215 1.898
Problem 186 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 16 20 20 15 24 15
normalized size 1 1. 1. 0.94 1.18 1.18 0.88 1.41 0.88
time (sec) N/A 0.049 0.009 0.01 1.353 0.209 0.143 0.202 5.725
Problem 187 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 13 16 22 8 18 8
normalized size 1 1. 1. 1.08 1.33 1.83 0.67 1.5 0.67
time (sec) N/A 0.014 0.005 0.009 1.329 0.202 0.07 0.209 2.289
Problem 188 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 21 27 35 19 28 19
normalized size 1 1. 0.73 0.7 0.9 1.17 0.63 0.93 0.63
time (sec) N/A 0.024 0.012 0.01 1.364 0.204 0.118 0.204 1.781
Problem 189 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 26 21 27 36 22 35 22
normalized size 1 1. 0.93 0.75 0.96 1.29 0.79 1.25 0.79
time (sec) N/A 0.033 0.024 0.01 1.364 0.204 0.129 0.206 2.05
Problem 190 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 24 14 22 14
normalized size 1 1. 1. 1.07 1.36 1.71 1. 1.57 1.
time (sec) N/A 0.042 0.006 0.01 1.375 0.206 0.115 0.211 3.162
Problem 191 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 19 19 25 18 23 23 17 27 0
normalized size 1 1. 1.32 0.95 1.21 1.21 0.89 1.42 0.
time (sec) N/A 0.048 0.011 0.012 1.357 0.217 0.138 0.203 0.
Problem 192 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 19 12
normalized size 1 1. 1. 0.93 1.2 1.2 0.8 1.27 0.8
time (sec) N/A 0.007 0.007 0.002 1.341 0.196 0.081 0.21 1.83
Problem 193 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 36 54 20 41 19
normalized size 1 1. 1. 0.96 1.44 2.16 0.8 1.64 0.76
time (sec) N/A 0.02 0.019 0.01 1.381 0.198 0.117 0.208 1.53
Problem 194 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 20 30 42 19 24 17
normalized size 1 1. 1. 0.95 1.43 2. 0.9 1.14 0.81
time (sec) N/A 0.019 0.014 0.007 1.366 0.189 0.093 0.209 1.507
Problem 195 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 8 8 22 17 22 27 15 24 5
normalized size 1 1. 2.75 2.12 2.75 3.38 1.88 3. 0.62
time (sec) N/A 0.012 0.004 0.008 1.361 0.196 0.1 0.205 1.704
Problem 196 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 10 18 10
normalized size 1 1. 1. 0.93 1.2 1.2 0.67 1.2 0.67
time (sec) N/A 0.008 0.006 0.003 1.336 0.194 0.09 0.207 2.166
Problem 197 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 15 19 19 12 19 12
normalized size 1 1. 1. 0.83 1.06 1.06 0.67 1.06 0.67
time (sec) N/A 0.02 0.003 0.001 1.415 0.194 0.063 0.205 1.897
Problem 198 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 19 24 24 17 24 17
normalized size 1 1. 1. 0.95 1.2 1.2 0.85 1.2 0.85
time (sec) N/A 0.019 0.006 0.003 1.495 0.199 0.104 0.207 2.421
Problem 199 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 27 35 41 34 35 31
normalized size 1 1. 1. 0.87 1.13 1.32 1.1 1.13 1.
time (sec) N/A 0.031 0.012 0.002 1.516 0.195 0.099 0.205 1.964
Problem 200 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 31 22 28 28 22 28 24
normalized size 1 1. 1.15 0.81 1.04 1.04 0.81 1.04 0.89
time (sec) N/A 0.04 0.008 0.006 1.504 0.197 0.118 0.206 5.851
Problem 201 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 28 20 26 26 19 27 19
normalized size 1 1. 1.22 0.87 1.13 1.13 0.83 1.17 0.83
time (sec) N/A 0.056 0.011 0.009 1.493 0.202 0.149 0.208 3.863
Problem 202 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 24 31 43 29 32 29
normalized size 1 1. 1. 0.86 1.11 1.54 1.04 1.14 1.04
time (sec) N/A 0.049 0.013 0.009 1.511 0.205 0.153 0.204 3.157
Problem 203 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 41 33 43 53 41 45 37
normalized size 1 1. 1. 0.8 1.05 1.29 1. 1.1 0.9
time (sec) N/A 0.04 0.009 0.003 1.514 0.204 0.172 0.205 2.5
Problem 204 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 42 36 47 63 42 49 39
normalized size 1 1. 1.02 0.88 1.15 1.54 1.02 1.2 0.95
time (sec) N/A 0.05 0.013 0.009 1.487 0.202 0.175 0.207 4.227
Problem 205 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 21 27 49 20 63 20
normalized size 1 1. 0.92 0.88 1.12 2.04 0.83 2.62 0.83
time (sec) N/A 0.055 0.022 0.01 1.504 0.199 0.158 0.21 3.947
Problem 206 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 26 19 24 24 19 27 10
normalized size 1 1. 1.86 1.36 1.71 1.71 1.36 1.93 0.71
time (sec) N/A 0.015 0.007 0.006 1.49 0.203 0.17 0.21 1.445
Problem 207 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 25 32 32 29 32 29
normalized size 1 1. 1. 0.86 1.1 1.1 1. 1.1 1.
time (sec) N/A 0.191 0.024 0.007 1.478 0.204 0.263 0.213 17.249
Problem 208 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 19 23 19
normalized size 1 1. 1. 0.78 1. 1. 0.83 1. 0.83
time (sec) N/A 0.048 0.014 0.008 1.511 0.204 0.25 0.211 8.109
Problem 209 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 35 43 59 41 43 37
normalized size 1 1. 1. 0.9 1.1 1.51 1.05 1.1 0.95
time (sec) N/A 0.032 0.037 0.005 1.503 0.197 0.142 0.211 2.01
Problem 210 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 0.048 0.008 0. 1.387 0.193 0.104 0.212 3.577
Problem 211 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 11 11 26 12 15 20 12 20 12
normalized size 1 1. 2.36 1.09 1.36 1.82 1.09 1.82 1.09
time (sec) N/A 0.067 0.063 0.043 1.341 0.229 0.284 0.214 6.965
Problem 212 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 20 20 82 18 23 23 19 23 19
normalized size 1 1. 4.1 0.9 1.15 1.15 0.95 1.15 0.95
time (sec) N/A 0.08 0.227 0.02 1.495 0.259 1.046 0.21 8.512
Problem 213 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 12 20 12
normalized size 1 1. 1. 0.74 0.95 0.95 0.63 1.05 0.63
time (sec) N/A 0.01 0.004 0.008 1.365 0.199 0.089 0.208 0.708
Problem 214 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 12 15 15 10 18 10
normalized size 1 1. 1. 0.71 0.88 0.88 0.59 1.06 0.59
time (sec) N/A 0.009 0.003 0.007 1.341 0.195 0.087 0.205 1.109
Problem 215 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 17 26 17
normalized size 1 1. 1. 0.86 1.1 1.1 0.81 1.24 0.81
time (sec) N/A 0.018 0.007 0.009 1.336 0.197 0.102 0.207 2.204
Problem 216 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 49 49 44 27 50 62 46 54 56
normalized size 1 1. 0.9 0.55 1.02 1.27 0.94 1.1 1.14
time (sec) N/A 0.036 0.03 0.003 1.532 0.199 0.098 0.21 1.683
Problem 217 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 63 63 57 51 68 86 68 72 0
normalized size 1 1. 0.9 0.81 1.08 1.37 1.08 1.14 0.
time (sec) N/A 0.15 0.041 0.017 1.468 0.208 0.539 0.212 0.
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 67 54 80 155 63 80 0
normalized size 1 1. 0.78 0.63 0.93 1.8 0.73 0.93 0.
time (sec) N/A 0.174 0.073 0.02 1.477 0.223 0.278 0.211 0.
Problem 219 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 36 29 38 38 44 39 19
normalized size 1 1. 1.5 1.21 1.58 1.58 1.83 1.62 0.79
time (sec) N/A 0.018 0.011 0.013 1.327 0.204 1.176 0.209 1.401
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A F(-2) F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 200 200 180 175 367 0 0 188 0
normalized size 1 1. 0.9 0.88 1.84 0. 0. 0.94 0.
time (sec) N/A 0.669 0.236 0.053 1.542 0. 0. 0.311 0.
Problem 221 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 18 18 41 22 41 36 20 31 17
normalized size 1 1. 2.28 1.22 2.28 2. 1.11 1.72 0.94
time (sec) N/A 0.021 0.014 0.053 1.479 0.255 0.348 0.228 0.579
Problem 222 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 27 20 19 15 19 15
normalized size 1 1. 1. 1.5 1.11 1.06 0.83 1.06 0.83
time (sec) N/A 0.015 0.006 0.003 1.357 0.2 0.125 0.208 1.097
Problem 223 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 32 32 28 21 38 27 26 27 0
normalized size 1 1. 0.88 0.66 1.19 0.84 0.81 0.84 0.
time (sec) N/A 0.028 0.009 0.004 1.344 0.202 0.145 0.209 0.
Problem 224 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 16 51 16 14
normalized size 1 1. 1. 0.81 1. 1. 3.19 1. 0.88
time (sec) N/A 0.011 0.006 0.005 1.493 0.206 2.03 0.21 1.16
Problem 225 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 10 10 25 9 26 26 26 27 10
normalized size 1 1. 2.5 0.9 2.6 2.6 2.6 2.7 1.
time (sec) N/A 0.011 0.004 0.006 1.35 0.206 0.787 0.215 0.976
Problem 226 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 50 23 11 0 24 10
normalized size 1 1. 1. 3.57 1.64 0.79 0. 1.71 0.71
time (sec) N/A 0.01 0.006 0.008 1.361 0.199 0. 0.211 0.96
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 31 54 28 28 0 30 26
normalized size 1 1. 1. 1.74 0.9 0.9 0. 0.97 0.84
time (sec) N/A 0.042 0.008 0.02 1.325 0.197 0. 0.211 2.19
Problem 228 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 21 18 30 23 76 30 27
normalized size 1 1. 0.66 0.56 0.94 0.72 2.38 0.94 0.84
time (sec) N/A 0.018 0.008 0.006 1.355 0.226 1.954 0.207 1.288
Problem 229 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 25 32 32 76 32 29
normalized size 1 1. 1. 0.81 1.03 1.03 2.45 1.03 0.94
time (sec) N/A 0.026 0.014 0.009 1.498 0.205 2.088 0.21 1.629
Problem 230 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 22 20 26 19 117 26 24
normalized size 1 1. 0.76 0.69 0.9 0.66 4.03 0.9 0.83
time (sec) N/A 0.018 0.008 0.007 1.338 0.205 1.44 0.207 1.052
Problem 231 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 8 7 8 7
normalized size 1 1. 1. 0.88 1. 1. 0.88 1. 0.88
time (sec) N/A 0.01 0.004 0.006 1.525 0.206 0.971 0.209 1.236
Problem 232 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 21 21 20 16 20 20 17 22 0
normalized size 1 1. 0.95 0.76 0.95 0.95 0.81 1.05 0.
time (sec) N/A 0.028 0.007 0.005 1.361 0.202 0.163 0.208 0.
Problem 233 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 30 30 30 23 30 30 26 31 0
normalized size 1 1. 1. 0.77 1. 1. 0.87 1.03 0.
time (sec) N/A 0.044 0.012 0.006 1.366 0.2 0.194 0.214 0.
Problem 234 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 20 17 26 22 26 26 22
normalized size 1 1. 0.74 0.63 0.96 0.81 0.96 0.96 0.81
time (sec) N/A 0.028 0.007 0.006 1.339 0.575 1.456 0.206 1.805
Problem 235 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A F(-2) F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 201 201 183 242 396 0 0 189 267
normalized size 1 1. 0.91 1.2 1.97 0. 0. 0.94 1.33
time (sec) N/A 0.497 0.236 0.022 1.562 0. 0. 0.316 100.799
Problem 236 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 62 46 61 77 68 61 61
normalized size 1 1. 1. 0.74 0.98 1.24 1.1 0.98 0.98
time (sec) N/A 0.076 0.025 0.006 1.53 0.221 1.334 0.214 4.799
Problem 237 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 130 130 130 83 111 103 0 111 0
normalized size 1 1. 1. 0.64 0.85 0.79 0. 0.85 0.
time (sec) N/A 0.088 0.031 0.006 1.347 0.205 0. 0.209 0.
Problem 238 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 24 24 40 40 50 35 0 38 19
normalized size 1 1. 1.67 1.67 2.08 1.46 0. 1.58 0.79
time (sec) N/A 0.026 0.022 0.011 1.517 0.211 0. 0.217 1.465
Problem 239 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 20 12 15 18 10 16 10
normalized size 1 1. 1.82 1.09 1.36 1.64 0.91 1.45 0.91
time (sec) N/A 0.035 0.013 0.044 1.396 0.23 0.244 0.21 3.537
Problem 240 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 16 20 20 14 20 0
normalized size 1 1. 1. 0.94 1.18 1.18 0.82 1.18 0.
time (sec) N/A 0.056 0.01 0.01 1.378 0.213 0.129 0.204 0.
Problem 241 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 10 28 28 26 28 12
normalized size 1 1. 1. 0.83 2.33 2.33 2.17 2.33 1.
time (sec) N/A 0.018 0.007 0.006 1.385 0.211 0.574 0.204 1.359
Problem 242 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 36 47 47 32 50 20
normalized size 1 1. 1. 1.29 1.68 1.68 1.14 1.79 0.71
time (sec) N/A 0.031 0.016 0.008 1.362 0.211 0.659 0.205 2.033
Problem 243 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 43 43 43 22 41 36 20 31 20
normalized size 1 1. 1. 0.51 0.95 0.84 0.47 0.72 0.47
time (sec) N/A 0.034 0.009 0.023 1.336 0.231 0.283 0.216 0.914
Problem 244 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 0.02 0.025 0.001 1.586 0.225 15.109 0.239 0.567
Problem 245 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 11 11 24 16 34 23 14 23 14
normalized size 1 1. 2.18 1.45 3.09 2.09 1.27 2.09 1.27
time (sec) N/A 0.018 0.014 0.045 1.34 0.238 0.316 0.214 1.43
Problem 246 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 18 18 43 22 41 36 20 31 17
normalized size 1 1. 2.39 1.22 2.28 2. 1.11 1.72 0.94
time (sec) N/A 0.021 0.014 0.046 1.368 0.222 0.328 0.212 0.585
Problem 247 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 24 24 35 24 34 47 0 38 27
normalized size 1 1. 1.46 1. 1.42 1.96 0. 1.58 1.12
time (sec) N/A 0.079 0.023 0.046 1.391 0.233 0. 0.204 6.871
Problem 248 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 39 24 297 47 0 38 0
normalized size 1 1. 1.62 1. 12.38 1.96 0. 1.58 0.
time (sec) N/A 0.046 0.04 0.076 1.356 0.225 0. 0.202 0.
Problem 249 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 18 18 54 24 31 45 0 34 14
normalized size 1 1. 3. 1.33 1.72 2.5 0. 1.89 0.78
time (sec) N/A 0.055 0.038 0.039 1.396 0.218 0. 0.201 3.576
Problem 250 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 38 35 0 154 0 82 32
normalized size 1 1. 1.06 0.97 0. 4.28 0. 2.28 0.89
time (sec) N/A 0.041 0.056 0.071 0. 0.235 0. 0.225 2.184
Problem 251 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 0.043 0.052 0.003 1.537 0.233 0. 0.204 26.905
Problem 252 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 10 14 11 11 7 12 7
normalized size 1 1. 0.83 1.17 0.92 0.92 0.58 1. 0.58
time (sec) N/A 0.006 0.002 0.003 1.338 0.191 0.06 0.2 0.773
Problem 253 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 12 35 15 12 15 0
normalized size 1 1. 1. 0.71 2.06 0.88 0.71 0.88 0.
time (sec) N/A 0.008 0.004 0.001 1.344 0.195 0.143 0.198 0.
Problem 254 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 8 9 14 14 7 11 8
normalized size 1 1. 0.67 0.75 1.17 1.17 0.58 0.92 0.67
time (sec) N/A 0.015 0.007 0. 1.333 0.205 0.688 0.2 0.502
Problem 255 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 42 24 36 46 27 39 14
normalized size 1 1. 2.62 1.5 2.25 2.88 1.69 2.44 0.88
time (sec) N/A 0.024 0.069 0.002 1.337 0.225 0.128 0.204 1.629
Problem 256 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 42 19 19 15 19 0
normalized size 1 1. 1. 2.47 1.12 1.12 0.88 1.12 0.
time (sec) N/A 0.039 0.012 0. 1.381 0.209 0.134 0.198 0.
Problem 257 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 0.015 0.004 0.003 1.351 0.205 0.22 0.198 1.136
Problem 258 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 42 42 42 31 41 41 36 45 0
normalized size 1 1. 1. 0.74 0.98 0.98 0.86 1.07 0.
time (sec) N/A 0.054 0.011 0.012 1.368 0.202 0.163 0.201 0.
Problem 259 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 8 7 8 7
normalized size 1 1. 1. 0.88 1. 1. 0.88 1. 0.88
time (sec) N/A 0.021 0.002 0.006 1.366 0.198 0.546 0.215 1.496
Problem 260 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 15 8
normalized size 1 1. 1. 0.92 1.17 1.17 0.67 1.25 0.67
time (sec) N/A 0.014 0.004 0.002 1.45 0.192 0.059 0.2 1.441
Problem 261 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 5 5 5 4 4 4 3 4 3
normalized size 1 1. 1. 0.8 0.8 0.8 0.6 0.8 0.6
time (sec) N/A 0.01 0.003 0.003 1.33 0.205 0.597 0.207 1.976
Problem 262 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 14 19 14 26 14 14 20
normalized size 1 1. 0.58 0.79 0.58 1.08 0.58 0.58 0.83
time (sec) N/A 0.042 0.007 0. 1.359 0.215 0.056 0.198 1.611
Problem 263 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 15 8 24 8
normalized size 1 1. 1. 1.12 1.38 1.88 1. 3. 1.
time (sec) N/A 0.035 0.012 0.032 1.346 0.222 0.175 0.211 3.258
Problem 264 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 17 15 23 8 15 8
normalized size 1 1. 1. 1.31 1.15 1.77 0.62 1.15 0.62
time (sec) N/A 0.006 0.003 0. 1.351 0.204 0.274 0.198 0.885
Problem 265 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 12 18 12
normalized size 1 1. 1. 0.82 1.06 1.06 0.71 1.06 0.71
time (sec) N/A 0.012 0.002 0.001 1.342 0.207 0.08 0.199 1.102
Problem 266 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 19 24 24 109 24 19
normalized size 1 1. 1. 0.79 1. 1. 4.54 1. 0.79
time (sec) N/A 0.02 0.011 0.009 1.493 0.207 2.541 0.2 1.61
Problem 267 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 13 16 22 8 18 8
normalized size 1 1. 1. 1.08 1.33 1.83 0.67 1.5 0.67
time (sec) N/A 0.013 0.005 0.005 1.323 0.197 0.078 0.199 1.111
Problem 268 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 17 22 22 15 22 15
normalized size 1 1. 1. 1.06 1.38 1.38 0.94 1.38 0.94
time (sec) N/A 0.014 0.004 0.002 1.516 0.209 0.127 0.202 1.611
Problem 269 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 37 30 39 39 32 0 20
normalized size 1 1. 1.68 1.36 1.77 1.77 1.45 0. 0.91
time (sec) N/A 0.091 0.016 0.004 1.356 0.238 0.95 0. 5.202
Problem 270 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 27 27 60 43 26 62 54 57 20
normalized size 1 1. 2.22 1.59 0.96 2.3 2. 2.11 0.74
time (sec) N/A 0.019 0.01 0.003 1.335 0.194 1.209 0.236 2.076
Problem 271 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 22 41 19 15 19 0
normalized size 1 1. 1. 1.29 2.41 1.12 0.88 1.12 0.
time (sec) N/A 0.037 0.008 0.015 1.33 0.218 0.118 0.223 0.
Problem 272 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 15 22 15
normalized size 1 1. 1. 0.77 1. 1. 0.68 1. 0.68
time (sec) N/A 0.018 0.005 0.006 1.514 0.197 0.093 0.223 2.016
Problem 273 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 28 25 32 32 24 35 24
normalized size 1 1. 0.88 0.78 1. 1. 0.75 1.09 0.75
time (sec) N/A 0.027 0.015 0.003 1.481 0.22 0.248 0.227 2.033
Problem 274 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 32 25 47 65 68 54 20
normalized size 1 1. 1.07 0.83 1.57 2.17 2.27 1.8 0.67
time (sec) N/A 0.04 0.012 0.006 1.509 0.201 2.255 0.223 2.565
Problem 275 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 14 18 18 10 20 10
normalized size 1 1. 1. 1.08 1.38 1.38 0.77 1.54 0.77
time (sec) N/A 0.011 0.005 0.002 1.346 0.196 0.093 0.237 1.592
Problem 276 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 16 16 14 17 59 19 17 36 0
normalized size 1 1. 0.88 1.06 3.69 1.19 1.06 2.25 0.
time (sec) N/A 0.041 0.009 0.008 1.378 0.205 0.387 0.224 0.
Problem 277 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 20 14 20 20 14 24 12
normalized size 1 1. 1.18 0.82 1.18 1.18 0.82 1.41 0.71
time (sec) N/A 0.007 0.009 0.003 1.324 0.195 0.1 0.22 6.535
Problem 278 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 4 3
normalized size 1 1. 1. 1.33 1.33 1.33 1. 1.33 1.
time (sec) N/A 0.028 0.008 0.015 1.489 0.22 0.279 0.226 2.316
Problem 279 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 20 22 48
normalized size 1 1. 1. 0.77 1. 1. 0.91 1. 2.18
time (sec) N/A 0.018 0.011 0. 1.353 0.223 0.424 0.22 2.639
Problem 280 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 10 12 12 7 12 7
normalized size 1 1. 1. 1.11 1.33 1.33 0.78 1.33 0.78
time (sec) N/A 0.008 0.005 0.004 1.335 0.212 0.036 0.217 0.467
Problem 281 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 0.034 0.005 0. 1.333 0.211 0.079 0.229 3.341
Problem 282 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 22 22 26 28 26 26 26
normalized size 1 1. 0.81 0.81 0.96 1.04 0.96 0.96 0.96
time (sec) N/A 0.02 0.019 0.01 1.357 0.303 0.37 0.224 1.49
Problem 283 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 30 26 18 12
normalized size 1 1. 1. 0.82 1.06 1.76 1.53 1.06 0.71
time (sec) N/A 0.016 0.012 0.049 1.348 0.221 0.736 0.226 1.039
Problem 284 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 20 26 26 19 27 31
normalized size 1 1. 1. 0.8 1.04 1.04 0.76 1.08 1.24
time (sec) N/A 0.03 0.008 0.008 1.497 0.205 0.135 0.215 57.362
Problem 285 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 39 39 39 46 39 34 29 66 0
normalized size 1 1. 1. 1.18 1. 0.87 0.74 1.69 0.
time (sec) N/A 0.031 0.003 0.004 1.342 0.206 0.11 0.227 0.
Problem 286 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 0.046 0.005 0.003 1.348 0.208 0.079 0.223 2.518
Problem 287 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 12 14 7
normalized size 1 1. 1. 0.92 1.17 1.17 1. 1.17 0.58
time (sec) N/A 0.011 0.01 0.006 1.479 0.214 0.051 0.234 0.487
Problem 288 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 25 25 24 30 30 27 0 28 22
normalized size 1 1. 0.96 1.2 1.2 1.08 0. 1.12 0.88
time (sec) N/A 0.014 0.009 0.003 1.501 0.209 0. 0.221 0.697
Problem 289 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 22 28 28 20 28 20
normalized size 1 1. 1. 0.81 1.04 1.04 0.74 1.04 0.74
time (sec) N/A 0.032 0.003 0.004 1.346 0.218 0.496 0.227 2.624
Problem 290 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 12 15 15 15 15 15
normalized size 1 1. 1. 0.63 0.79 0.79 0.79 0.79 0.79
time (sec) N/A 0.009 0.006 0.001 1.345 0.204 0.681 0.219 1.186
Problem 291 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 6 6 23 6 26 20 15 22 7
normalized size 1 1. 3.83 1. 4.33 3.33 2.5 3.67 1.17
time (sec) N/A 0.018 0.006 0.004 1.344 0.22 0.113 0.227 3.551
Problem 292 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 0.028 0.007 0.003 1.474 0.228 0.102 0.228 2.281
Problem 293 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 9 11 11 10 43 10
normalized size 1 1. 1. 0.75 0.92 0.92 0.83 3.58 0.83
time (sec) N/A 0.009 0.005 0.003 1.5 0.208 0.606 0.228 0.896
Problem 294 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 26 24 34 31 30 31
normalized size 1 1. 0.88 0.76 0.71 1. 0.91 0.88 0.91
time (sec) N/A 0.052 0.013 0.003 1.343 0.238 0.055 0.227 1.706
Problem 295 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 12 7 11 23 0 8 22
normalized size 1 1. 1. 0.58 0.92 1.92 0. 0.67 1.83
time (sec) N/A 0.014 0.009 0.004 1.501 0.213 0. 0.23 0.673
Problem 296 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 59 19 28 17 19 12
normalized size 1 1. 1. 3.69 1.19 1.75 1.06 1.19 0.75
time (sec) N/A 0.079 0.013 0.023 1.342 0.234 1.918 0.227 3.252
Problem 297 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 7 7 20 6 7 9 12 9 5
normalized size 1 1. 2.86 0.86 1. 1.29 1.71 1.29 0.71
time (sec) N/A 0.022 0.009 0.019 1.346 0.228 2.264 0.226 1.377
Problem 298 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 6 6 23 6 20 20 15 22 5
normalized size 1 1. 3.83 1. 3.33 3.33 2.5 3.67 0.83
time (sec) N/A 0.029 0.005 0.003 1.349 0.217 0.099 0.225 2.876
Problem 299 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 43 43 43 35 43 53 41 45 37
normalized size 1 1. 1. 0.81 1. 1.23 0.95 1.05 0.86
time (sec) N/A 0.044 0.013 0.009 1.483 0.214 0.188 0.219 2.864
Problem 300 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 37 37 29 38 100 41 42 77 0
normalized size 1 1. 0.78 1.03 2.7 1.11 1.14 2.08 0.
time (sec) N/A 0.116 0.015 0.01 1.34 0.21 3.091 0.21 0.
Problem 301 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 9 9 9 8 9 16 0 9 48
normalized size 1 1. 1. 0.89 1. 1.78 0. 1. 5.33
time (sec) N/A 0.033 0.006 0.024 1.342 0.224 0. 0.205 9.289
Problem 302 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 20 20 20 17 22 1 12 22 0
normalized size 1 1. 1. 0.85 1.1 0.05 0.6 1.1 0.
time (sec) N/A 0.008 0. 0. 1.342 0.177 0.025 0.214 0.
Problem 303 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 12 12 12 8 14 15
normalized size 1 1. 1. 1. 1. 1. 0.67 1.17 1.25
time (sec) N/A 0.043 0.006 0.009 1.349 0.223 0.073 0.209 5.306
Problem 304 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 15 23 15
normalized size 1 1. 1. 0.86 1.1 1.1 0.71 1.1 0.71
time (sec) N/A 0.034 0.007 0.009 1.346 0.203 0.104 0.216 3.037
Problem 305 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 43 43 43 22 41 36 20 31 20
normalized size 1 1. 1. 0.51 0.95 0.84 0.47 0.72 0.47
time (sec) N/A 0.033 0.009 0.021 1.357 0.232 0.288 0.221 0.927
Problem 306 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 25 15 22 30 144 22 20
normalized size 1 1. 1.04 0.62 0.92 1.25 6. 0.92 0.83
time (sec) N/A 0.015 0.008 0.004 1.363 0.227 1.683 0.213 1.176
Problem 307 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 24 26 22 22 34 22 34
normalized size 1 1. 0.63 0.68 0.58 0.58 0.89 0.58 0.89
time (sec) N/A 0.033 0.006 0.003 1.374 0.231 0.438 0.214 1.95
Problem 308 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 37 93 41 51 0 41 39
normalized size 1 1. 1. 2.51 1.11 1.38 0. 1.11 1.05
time (sec) N/A 0.065 0.02 0.022 1.58 0.242 0. 0.214 2.646
Problem 309 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 16 20 28 14 23 14
normalized size 1 1. 1. 0.94 1.18 1.65 0.82 1.35 0.82
time (sec) N/A 0.033 0.006 0.011 1.374 0.247 0.107 0.209 3.494
Problem 310 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 40 40 29 35 51 35 39 35 0
normalized size 1 1. 0.72 0.88 1.27 0.88 0.98 0.88 0.
time (sec) N/A 0.101 0.038 0.012 1.344 0.237 0.434 0.215 0.
Problem 311 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 5 5 5 6 7 27 5 7 5
normalized size 1 1. 1. 1.2 1.4 5.4 1. 1.4 1.
time (sec) N/A 0.015 2.119 0.012 1.327 0.235 0.735 0.207 29.472
Problem 312 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 5 5 24 3 5 3
normalized size 1 1. 1. 0.83 0.83 4. 0.5 0.83 0.5
time (sec) N/A 0.004 0.007 0.005 1.499 0.221 0.155 0.219 0.529
Problem 313 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 24 30 84 84 61 30 32
normalized size 1 1. 0.65 0.81 2.27 2.27 1.65 0.81 0.86
time (sec) N/A 0.027 0.01 0.008 1.355 0.228 0.198 0.209 2.156
Problem 314 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 53 58 24 49 17 24 0
normalized size 1 1. 2.52 2.76 1.14 2.33 0.81 1.14 0.
time (sec) N/A 0.046 0.035 0.036 1.377 0.228 0.116 0.23 0.
Problem 315 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 30 30 30 25 32 30 41 32 0
normalized size 1 1. 1. 0.83 1.07 1. 1.37 1.07 0.
time (sec) N/A 0.053 0.063 0.014 1.449 0.22 0.236 0.212 0.
Problem 316 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 3 4 3
normalized size 1 1. 1. 1. 1. 1. 0.75 1. 0.75
time (sec) N/A 0.031 0.003 0.003 1.348 0.218 1.574 0.224 2.801
Problem 317 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 20 15 10 20 14
normalized size 1 1. 1. 0.92 1.54 1.15 0.77 1.54 1.08
time (sec) N/A 0.015 0.004 0.007 1.36 0.195 0.096 0.215 1.475
Problem 318 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 44 44 24 24 28 28 22 28 41
normalized size 1 1. 0.55 0.55 0.64 0.64 0.5 0.64 0.93
time (sec) N/A 0.059 0.006 0.005 1.33 0.201 0.073 0.208 2.823
Problem 319 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 41 28 36 34 37 36 37
normalized size 1 1. 1. 0.68 0.88 0.83 0.9 0.88 0.9
time (sec) N/A 0.033 0.014 0.004 1.493 0.215 4.81 0.213 2.712
Problem 320 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 20 26 23 114 18 0
normalized size 1 1. 1. 0.8 1.04 0.92 4.56 0.72 0.
time (sec) N/A 0.049 0.015 0.001 1.329 0.229 22.198 0.211 0.
Problem 321 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 7 14 7
normalized size 1 1. 1. 0.92 1.17 1.17 0.58 1.17 0.58
time (sec) N/A 0.005 0.002 0.003 1.329 0.237 0.07 0.213 0.465
Problem 322 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 41 41 60 41 58 43 0 41 32
normalized size 1 1. 1.46 1. 1.41 1.05 0. 1. 0.78
time (sec) N/A 0.03 0.042 0.009 1.53 0.208 0. 0.211 1.69
Problem 323 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 27 119 36 93 29 38 29
normalized size 1 1. 0.79 3.5 1.06 2.74 0.85 1.12 0.85
time (sec) N/A 0.07 0.022 0. 1.552 0.233 4.293 0.217 4.216
Problem 324 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 18 23 23 42 23 14
normalized size 1 1. 1. 0.95 1.21 1.21 2.21 1.21 0.74
time (sec) N/A 0.017 0.006 0.004 1.51 0.202 0.111 0.213 1.956
Problem 325 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 38 38 39 30 53 159 0 42 39
normalized size 1 1. 1.03 0.79 1.39 4.18 0. 1.11 1.03
time (sec) N/A 0.027 0.023 0.005 1.555 0.209 0. 0.211 0.814
Problem 326 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 9 11 11 7 11 7
normalized size 1 1. 1. 0.75 0.92 0.92 0.58 0.92 0.58
time (sec) N/A 0.014 0.005 0.002 1.525 0.229 0.142 0.214 1.236
Problem 327 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 27 35 41 36 35 32
normalized size 1 1. 1. 0.87 1.13 1.32 1.16 1.13 1.03
time (sec) N/A 0.033 0.017 0.005 1.485 0.255 0.117 0.214 2.211
Problem 328 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 10 10 37 16 163 39 0 203 8
normalized size 1 1. 3.7 1.6 16.3 3.9 0. 20.3 0.8
time (sec) N/A 0.017 0.009 0.009 1.511 0.245 0. 0.248 1.373
Problem 329 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 30 39 35 22 41 14
normalized size 1 1. 1. 2. 2.6 2.33 1.47 2.73 0.93
time (sec) N/A 0.018 0.006 0.007 1.341 0.221 0.17 0.211 1.764
Problem 330 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 19 14 0 18 63 18 17
normalized size 1 1. 0.9 0.67 0. 0.86 3. 0.86 0.81
time (sec) N/A 0.012 0.021 0.003 0. 0.251 0.702 0.214 0.637
Problem 331 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 21 18 26 23 17 24 17
normalized size 1 1. 0.91 0.78 1.13 1. 0.74 1.04 0.74
time (sec) N/A 0.03 0.015 0.01 1.348 0.226 0.134 0.212 2.504
Problem 332 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 17 22 22 17 22 17
normalized size 1 1. 1. 0.85 1.1 1.1 0.85 1.1 0.85
time (sec) N/A 0.015 0.006 0.007 1.336 0.225 0.708 0.214 1.764
Problem 333 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 16 24 26 14 27 14
normalized size 1 1. 1. 0.89 1.33 1.44 0.78 1.5 0.78
time (sec) N/A 0.018 0.004 0.01 1.349 0.216 0.127 0.21 1.505
Problem 334 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 12 12 32 20 26 34 20 27 10
normalized size 1 1. 2.67 1.67 2.17 2.83 1.67 2.25 0.83
time (sec) N/A 0.025 0.022 0.013 1.34 0.217 0.115 0.22 4.734
Problem 335 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 11 14 20 12 22 0
normalized size 1 1. 1. 1.38 1.75 2.5 1.5 2.75 0.
time (sec) N/A 0.058 0.013 0.062 1.511 0.218 2.373 0.225 0.
Problem 336 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 46 16 14
normalized size 1 1. 1. 0.72 0.89 0.89 2.56 0.89 0.78
time (sec) N/A 0.012 0.006 0.008 1.518 0.21 1.675 0.217 1.124
Problem 337 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 26 10 61 24 0 0 0
normalized size 1 1. 2.36 0.91 5.55 2.18 0. 0. 0.
time (sec) N/A 0.083 0.12 0.045 6.504 0.272 0. 0. 0.
Problem 338 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 30 23 30 41 27 30 27
normalized size 1 1. 1. 0.77 1. 1.37 0.9 1. 0.9
time (sec) N/A 0.021 0.019 0.008 1.526 0.212 0.269 0.221 1.784
Problem 339 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 0.054 0.013 0.002 1.342 0.244 0.844 0.21 2.033
Problem 340 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 50 50 38 42 66 220 0 54 54
normalized size 1 1. 0.76 0.84 1.32 4.4 0. 1.08 1.08
time (sec) N/A 0.034 0.032 0.007 1.521 0.207 0. 0.213 1.925
Problem 341 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 47 12 1 51 12 7
normalized size 1 1. 1. 4.27 1.09 0.09 4.64 1.09 0.64
time (sec) N/A 0.007 0.003 0.003 1.351 0.168 0.038 0.209 0.778
Problem 342 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 31 28 26 26 20 26 20
normalized size 1 1. 1.24 1.12 1.04 1.04 0.8 1.04 0.8
time (sec) N/A 0.047 0.017 0.016 1.369 0.227 0.051 0.205 3.105
Problem 343 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 22 22 26 28 26 26 26
normalized size 1 1. 0.81 0.81 0.96 1.04 0.96 0.96 0.96
time (sec) N/A 0.02 0.021 0.012 1.338 0.211 0.785 0.21 1.558
Problem 344 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 41 24 46 76 36 95 19
normalized size 1 1. 1.71 1. 1.92 3.17 1.5 3.96 0.79
time (sec) N/A 0.022 0.008 0.016 1.454 0.26 0.132 0.223 0.561
Problem 345 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 35 47 45 78 17 59 27
normalized size 1 1. 1.03 1.38 1.32 2.29 0.5 1.74 0.79
time (sec) N/A 0.022 0.016 0.01 1.487 0.212 0.343 0.218 1.684
Problem 346 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 32 25 47 68 75 51 24
normalized size 1 1. 1.07 0.83 1.57 2.27 2.5 1.7 0.8
time (sec) N/A 0.042 0.014 0.006 1.502 0.204 2.551 0.215 2.68
Problem 347 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 17 22 22 15 22 27
normalized size 1 1. 0.59 0.53 0.69 0.69 0.47 0.69 0.84
time (sec) N/A 0.032 0.004 0.005 1.35 0.199 0.085 0.208 2.153
Problem 348 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 31 18 23 16 26 23 20
normalized size 1 1. 1.35 0.78 1. 0.7 1.13 1. 0.87
time (sec) N/A 0.059 0.037 0.011 1.368 0.21 0.471 0.21 2.55
Problem 349 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 27 27 24 22 28 28 19 28 0
normalized size 1 1. 0.89 0.81 1.04 1.04 0.7 1.04 0.
time (sec) N/A 0.026 0.009 0.003 1.513 0.223 0.222 0.217 0.
Problem 350 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 38 38 32 31 72 38 29 43 0
normalized size 1 1. 0.84 0.82 1.89 1. 0.76 1.13 0.
time (sec) N/A 0.055 0.017 0.004 1.607 0.227 0.897 0.205 0.
Problem 351 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 5 5 11 5 5 22 0 8 0
normalized size 1 1. 2.2 1. 1. 4.4 0. 1.6 0.
time (sec) N/A 0.015 0.022 0.017 1.598 0.206 0. 0.203 0.
Problem 352 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 25 24 28 28 27 28 27
normalized size 1 1. 0.86 0.83 0.97 0.97 0.93 0.97 0.93
time (sec) N/A 0.042 0.025 0.001 1.483 0.213 0.403 0.203 1.609
Problem 353 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 36 36 33 29 49 50 0 35 44
normalized size 1 1. 0.92 0.81 1.36 1.39 0. 0.97 1.22
time (sec) N/A 0.022 0.028 0.004 1.518 0.204 0. 0.206 0.919
Problem 354 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A F(-2) A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 31 23 30 0 24 30 0
normalized size 1 1. 1.11 0.82 1.07 0. 0.86 1.07 0.
time (sec) N/A 0.046 0.014 0.01 1.485 0. 0.143 0.206 0.
Problem 355 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 26 26 58 25 57 58 46 51 29
normalized size 1 1. 2.23 0.96 2.19 2.23 1.77 1.96 1.12
time (sec) N/A 0.025 0.187 0.052 1.322 0.223 0.169 0.207 0.607
Problem 356 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 30 32 32 45 46 30 46
normalized size 1 1. 0.65 0.7 0.7 0.98 1. 0.65 1.
time (sec) N/A 0.035 0.004 0.007 1.34 0.3 0.046 0.201 0.777
Problem 357 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 15 17 22 32 17 22 17
normalized size 1 1. 0.75 0.85 1.1 1.6 0.85 1.1 0.85
time (sec) N/A 0.054 0.019 0.009 1.328 0.224 10.023 0.207 2.334
Problem 358 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 18 22 22 32 14 26 20
normalized size 1 1. 0.86 1.05 1.05 1.52 0.67 1.24 0.95
time (sec) N/A 0.044 0.012 0.017 1.337 0.23 0.088 0.2 4.164
Problem 359 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 51 31 66 78 0 68 0
normalized size 1 1. 1.38 0.84 1.78 2.11 0. 1.84 0.
time (sec) N/A 0.071 0.125 0.021 1.488 0.313 0. 0.211 0.
Problem 360 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 28 28 44 26 39 96 0 38 24
normalized size 1 1. 1.57 0.93 1.39 3.43 0. 1.36 0.86
time (sec) N/A 0.021 0.024 0.009 1.335 0.229 0. 0.203 1.496
Problem 361 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 23 17 20 24 17 20 17
normalized size 1 1. 1.21 0.89 1.05 1.26 0.89 1.05 0.89
time (sec) N/A 0.015 0.003 0.041 1.33 0.234 0.043 0.199 0.719
Problem 362 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 26 25 32 32 22 32 36
normalized size 1 1. 0.57 0.54 0.7 0.7 0.48 0.7 0.78
time (sec) N/A 0.067 0.006 0.004 1.326 0.231 0.075 0.199 4.026
Problem 363 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 42 34 45 22 34 23 14
normalized size 1 1. 2.33 1.89 2.5 1.22 1.89 1.28 0.78
time (sec) N/A 0.019 0.007 0.068 1.392 0.238 1.762 0.227 1.287
Problem 364 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 22 22 26 28 24 26 24
normalized size 1 1. 0.81 0.81 0.96 1.04 0.89 0.96 0.89
time (sec) N/A 0.018 0.026 0.008 1.357 0.23 0.381 0.212 1.419
Problem 365 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 18 18 18 17 22 20 0 22 19
normalized size 1 1. 1. 0.94 1.22 1.11 0. 1.22 1.06
time (sec) N/A 0.021 0.006 0.003 1.328 0.223 0. 0.205 4.759
Problem 366 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 22 28 28 20 28 20
normalized size 1 1. 1. 0.81 1.04 1.04 0.74 1.04 0.74
time (sec) N/A 0.032 0.003 0. 1.337 0.231 0.477 0.206 2.72
Problem 367 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 26 21 27 27 19 27 20
normalized size 1 1. 1. 0.81 1.04 1.04 0.73 1.04 0.77
time (sec) N/A 0.03 0.013 0.009 1.64 0.238 1.338 0.205 2.038
Problem 368 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 11 14 12 12 15 721 0
normalized size 1 1. 0.73 0.93 0.8 0.8 1. 48.07 0.
time (sec) N/A 0.031 0.017 0.013 1.429 0.25 3.673 0.218 0.
Problem 369 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 47 47 35 35 46 50 122 39 39
normalized size 1 1. 0.74 0.74 0.98 1.06 2.6 0.83 0.83
time (sec) N/A 0.034 0.03 0.01 1.518 0.233 4.473 0.209 2.798
Problem 370 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 36 27 12 1 27 12 7
normalized size 1 1. 3.27 2.45 1.09 0.09 2.45 1.09 0.64
time (sec) N/A 0.007 0.002 0.001 1.337 0.19 0.032 0.204 0.794
Problem 371 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 18 18 18 12 18 12
normalized size 1 1. 1. 1.06 1.06 1.06 0.71 1.06 0.71
time (sec) N/A 0.035 0.01 0.01 1.347 0.218 0.044 0.201 2.426
Problem 372 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 27 22 18 27 29 18 0
normalized size 1 1. 1.59 1.29 1.06 1.59 1.71 1.06 0.
time (sec) N/A 0.035 0.012 0.002 1.392 0.209 0.052 0.202 0.
Problem 373 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 23 36 26 19
normalized size 1 1. 0.67 0.56 0.96 0.85 1.33 0.96 0.7
time (sec) N/A 0.014 0.006 0.003 1.495 0.212 1.542 0.204 1.505
Problem 374 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 0.018 0.003 0.003 1.376 0.257 0.04 0.201 0.567
Problem 375 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 17 27 24 12 22 10
normalized size 1 1. 1. 1.42 2.25 2. 1. 1.83 0.83
time (sec) N/A 0.011 0.005 0. 1.357 0.239 0.088 0.201 0.493
Problem 376 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 25 22 46 174 53 38 31
normalized size 1 1. 0.62 0.55 1.15 4.35 1.32 0.95 0.78
time (sec) N/A 0.034 0.011 0.007 1.498 0.205 3.177 0.199 2.162

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 [19] had the largest ratio of [ 1. ]

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. 3 0.333
2 A 1 1 1. 3 0.333
3 A 1 1 1. 3 0.333
4 A 1 1 1. 3 0.333
5 A 1 1 1. 2 0.5
6 A 1 1 1. 2 0.5
7 A 2 2 1. 4 0.5
8 A 2 2 1. 4 0.5
9 A 2 2 1. 5 0.4
10 A 2 2 1. 5 0.4
11 A 1 1 1. 2 0.5
12 A 1 1 1. 2 0.5
13 A 1 1 1. 2 0.5
14 A 1 1 1. 2 0.5
15 A 2 2 1. 4 0.5
16 A 1 1 1. 2 0.5
17 A 3 2 1. 7 0.286
18 A 1 1 1. 6 0.167
19 A 2 2 1. 2 1.
20 A 2 2 1. 7 0.286
21 A 2 2 1. 4 0.5
22 A 2 2 1. 6 0.333
23 A 1 1 1. 4 0.25
24 A 3 2 1. 8 0.25
25 A 3 2 1. 8 0.25
26 A 2 2 1. 4 0.5
27 A 2 2 1. 2 1.
28 A 3 3 1. 6 0.5
29 A 2 2 1. 6 0.333
30 A 1 1 1. 6 0.167
31 A 4 2 1. 7 0.286
32 A 1 1 1. 10 0.1
33 A 1 1 1. 10 0.1
34 A 2 2 1. 4 0.5
35 A 2 2 1. 6 0.333
36 A 2 2 1. 7 0.286
37 A 1 1 1. 8 0.125
38 A 2 2 1. 6 0.333
39 A 3 2 1. 9 0.222
40 A 2 2 1. 2 1.
41 A 2 2 1. 6 0.333
42 A 1 1 1. 9 0.111
43 A 1 1 1. 9 0.111
44 A 2 2 1. 6 0.333
45 A 2 2 1. 9 0.222
46 A 2 2 1. 9 0.222
47 A 2 2 1. 5 0.4
48 A 1 1 1. 3 0.333
49 A 3 3 1. 7 0.429
50 A 1 1 1. 6 0.167
51 A 1 1 1. 3 0.333
52 A 3 3 1. 6 0.5
53 A 3 3 1. 8 0.375
54 A 3 2 1. 9 0.222
55 A 3 3 1. 4 0.75
56 A 2 2 1. 6 0.333
57 A 1 1 1. 8 0.125
58 A 2 2 1. 6 0.333
59 A 2 2 1. 4 0.5
60 A 3 2 1. 4 0.5
61 A 2 1 1. 4 0.25
62 A 3 2 1. 9 0.222
63 A 3 2 1. 9 0.222
64 A 4 3 1. 9 0.333
65 A 3 3 1. 9 0.333
66 A 1 1 1. 10 0.1
67 A 3 2 1. 11 0.182
68 A 4 3 1. 9 0.333
69 A 4 2 1. 4 0.5
70 A 4 2 1. 4 0.5
71 A 4 3 1. 13 0.231
72 A 2 1 1. 4 0.25
73 A 5 3 1. 9 0.333
74 A 3 2 1. 11 0.182
75 A 3 2 1. 11 0.182
76 A 3 3 1. 14 0.214
77 A 3 2 1. 8 0.25
78 A 3 2 1. 7 0.286
79 A 4 3 1. 9 0.333
80 A 2 2 1. 9 0.222
81 A 1 1 1. 8 0.125
82 A 2 2 1. 4 0.5
83 A 3 2 1. 4 0.5
84 A 2 1 1. 4 0.25
85 A 2 1 1. 4 0.25
86 A 2 2 1. 9 0.222
87 A 3 2 1. 9 0.222
88 A 2 2 1. 7 0.286
89 A 3 2 1. 9 0.222
90 A 3 2 1. 4 0.5
91 A 4 2 1. 4 0.5
92 A 3 2 1. 7 0.286
93 A 3 2 1. 9 0.222
94 A 2 2 1. 7 0.286
95 A 3 2 1. 9 0.222
96 A 2 2 1. 7 0.286
97 A 2 2 1. 7 0.286
98 A 2 2 1. 4 0.5
99 A 2 2 1. 4 0.5
100 A 3 2 1. 9 0.222
101 A 3 2 1. 9 0.222
102 A 1 1 1. 2 0.5
103 A 2 2 1. 4 0.5
104 A 3 3 1. 5 0.6
105 A 2 1 1. 4 0.25
106 A 1 1 1. 9 0.111
107 A 1 1 1. 7 0.143
108 A 1 1 1. 9 0.111
109 A 1 1 1. 9 0.111
110 A 2 2 1. 7 0.286
111 A 5 2 1. 11 0.182
112 A 2 2 1. 13 0.154
113 A 6 4 1. 10 0.4
114 A 3 2 1. 7 0.286
115 A 4 3 1. 9 0.333
116 A 2 2 1. 7 0.286
117 A 3 2 1. 9 0.222
118 A 2 2 1. 15 0.133
119 A 1 1 1. 13 0.077
120 A 1 1 1. 11 0.091
121 A 2 2 1. 13 0.154
122 A 3 2 1. 15 0.133
123 A 3 3 1. 16 0.188
124 A 1 1 1. 15 0.067
125 A 3 2 1. 15 0.133
126 A 1 1 1. 13 0.077
127 A 1 1 1. 13 0.077
128 A 2 2 1. 11 0.182
129 A 3 2 1. 13 0.154
130 A 1 1 1. 9 0.111
131 A 2 2 1. 9 0.222
132 A 4 4 1. 13 0.308
133 A 1 1 1. 17 0.059
134 A 4 4 1. 15 0.267
135 A 1 1 1. 15 0.067
136 A 3 3 1. 17 0.176
137 A 2 2 1. 15 0.133
138 A 3 3 1. 13 0.231
139 A 1 1 1. 11 0.091
140 A 3 2 1. 15 0.133
141 A 3 3 1. 15 0.2
142 A 2 2 1. 12 0.167
143 A 1 1 1. 11 0.091
144 A 3 3 1. 13 0.231
145 A 2 2 1. 12 0.167
146 A 2 2 1. 14 0.143
147 A 4 4 1. 17 0.235
148 A 3 3 1. 10 0.3
149 A 2 2 1. 14 0.143
150 A 3 3 1. 17 0.176
151 A 4 4 1. 11 0.364
152 A 2 2 1. 11 0.182
153 A 3 2 1. 12 0.167
154 A 3 2 1. 11 0.182
155 A 3 2 1. 25 0.08
156 A 2 1 1. 29 0.034
157 A 6 5 1. 20 0.25
158 A 6 5 1. 23 0.217
159 A 14 9 1. 32 0.281
160 A 6 5 1. 26 0.192
161 A 2 2 1. 7 0.286
162 A 3 2 1. 11 0.182
163 A 4 3 1. 14 0.214
164 A 2 1 1. 23 0.043
165 A 3 2 1. 22 0.091
166 A 3 2 1. 11 0.182
167 A 4 3 1. 26 0.115
168 A 3 2 1. 16 0.125
169 A 8 4 1. 25 0.16
170 A 6 3 1. 23 0.13
171 A 6 5 1. 26 0.192
172 A 3 2 1. 11 0.182
173 A 8 7 1. 20 0.35
174 A 7 6 1. 23 0.261
175 A 8 8 1. 11 0.727
176 A 2 1 1. 9 0.111
177 A 2 1 1. 7 0.143
178 A 2 1 1. 16 0.062
179 A 3 2 1. 11 0.182
180 A 2 1 1. 13 0.077
181 A 3 2 1. 11 0.182
182 A 3 2 1. 15 0.133
183 A 5 3 1. 20 0.15
184 A 2 1 1. 11 0.091
185 A 2 1 1. 16 0.062
186 A 3 2 1. 25 0.08
187 A 3 2 1. 12 0.167
188 A 2 1 1. 11 0.091
189 A 2 1 1. 14 0.071
190 A 3 2 1. 22 0.091
191 A 2 1 1. 24 0.042
192 A 1 1 1. 20 0.05
193 A 2 1 1. 9 0.111
194 A 2 1 1. 9 0.111
195 A 3 3 1. 11 0.273
196 A 1 1 1. 22 0.045
197 A 3 2 1. 11 0.182
198 A 4 4 1. 14 0.286
199 A 4 4 1. 10 0.4
200 A 6 5 1. 23 0.217
201 A 5 4 1. 23 0.174
202 A 6 5 1. 15 0.333
203 A 6 6 1. 7 0.857
204 A 7 7 1. 11 0.636
205 A 5 4 1. 21 0.19
206 A 4 4 1. 11 0.364
207 A 6 4 1. 30 0.133
208 A 6 5 1. 24 0.208
209 A 3 3 1. 14 0.214
210 A 3 2 1. 16 0.125
211 A 2 2 1. 21 0.095
212 A 3 3 1. 15 0.2
213 A 3 2 1. 10 0.2
214 A 4 4 1. 9 0.444
215 A 3 2 1. 18 0.111
216 A 3 2 1. 10 0.2
217 A 6 5 1. 43 0.116
218 A 7 5 1. 50 0.1
219 A 3 3 1. 11 0.273
220 A 9 9 1. 15 0.6
221 A 2 2 1. 11 0.182
222 A 3 2 1. 9 0.222
223 A 3 2 1. 9 0.222
224 A 3 3 1. 11 0.273
225 A 2 2 1. 11 0.182
226 A 2 2 1. 11 0.182
227 A 4 2 1. 13 0.154
228 A 2 1 1. 11 0.091
229 A 3 3 1. 13 0.231
230 A 3 2 1. 11 0.182
231 A 3 3 1. 13 0.231
232 A 3 2 1. 17 0.118
233 A 4 3 1. 17 0.176
234 A 3 2 1. 13 0.154
235 A 10 9 1. 21 0.429
236 A 9 9 1. 13 0.692
237 A 4 3 1. 13 0.231
238 A 5 5 1. 13 0.385
239 A 5 5 1. 12 0.417
240 A 4 3 1. 20 0.15
241 A 3 3 1. 9 0.333
242 A 4 4 1. 11 0.364
243 A 4 3 1. 8 0.375
244 A 2 2 1. 7 0.286
245 A 2 2 1. 10 0.2
246 A 2 2 1. 11 0.182
247 A 6 6 1. 7 0.857
248 A 4 2 1. 11 0.182
249 A 4 3 1. 9 0.333
250 A 2 2 1. 11 0.182
251 A 2 1 1. 19 0.053
252 A 1 1 1. 9 0.111
253 A 2 1 1. 13 0.077
254 A 1 1 1. 8 0.125
255 A 2 2 1. 7 0.286
256 A 3 2 1. 9 0.222
257 A 3 3 1. 7 0.429
258 A 3 2 1. 20 0.1
259 A 2 2 1. 10 0.2
260 A 2 1 1. 11 0.091
261 A 2 2 1. 7 0.286
262 A 3 3 1. 9 0.333
263 A 1 1 1. 15 0.067
264 A 1 1 1. 13 0.077
265 A 1 1 1. 6 0.167
266 A 3 3 1. 13 0.231
267 A 2 1 1. 7 0.143
268 A 3 3 1. 6 0.5
269 A 4 4 1. 16 0.25
270 A 3 2 1. 9 0.222
271 A 3 2 1. 9 0.222
272 A 4 4 1. 12 0.333
273 A 3 3 1. 4 0.75
274 A 4 4 1. 15 0.267
275 A 3 2 1. 12 0.167
276 A 3 2 1. 6 0.333
277 A 1 1 1. 21 0.048
278 A 2 2 1. 11 0.182
279 A 3 3 1. 6 0.5
280 A 1 1 1. 4 0.25
281 A 3 2 1. 13 0.154
282 A 1 1 1. 10 0.1
283 A 1 1 1. 9 0.111
284 A 5 4 1. 11 0.364
285 A 3 2 1. 8 0.25
286 A 2 2 1. 11 0.182
287 A 2 2 1. 6 0.333
288 A 2 2 1. 14 0.143
289 A 4 3 1. 6 0.5
290 A 2 1 1. 15 0.067
291 A 2 2 1. 13 0.154
292 A 3 3 1. 14 0.214
293 A 2 2 1. 9 0.222
294 A 4 3 1. 9 0.333
295 A 2 2 1. 14 0.143
296 A 3 2 1. 22 0.091
297 A 2 2 1. 7 0.286
298 A 2 2 1. 13 0.154
299 A 6 6 1. 7 0.857
300 A 6 2 1. 6 0.333
301 A 1 3 1. 8 0.375
302 A 1 0 1. 10 0.
303 A 3 2 1. 15 0.133
304 A 4 3 1. 16 0.188
305 A 4 3 1. 8 0.375
306 A 2 1 1. 9 0.111
307 A 4 3 1. 7 0.429
308 A 5 4 1. 12 0.333
309 A 3 2 1. 17 0.118
310 A 8 4 1. 13 0.308
311 A 2 2 1. 6 0.333
312 A 1 1 1. 11 0.091
313 A 2 1 1. 9 0.111
314 A 3 2 1. 13 0.154
315 A 6 5 1. 6 0.833
316 A 1 1 1. 12 0.083
317 A 4 4 1. 11 0.364
318 A 4 2 1. 9 0.222
319 A 7 4 1. 15 0.267
320 A 5 2 1. 11 0.182
321 A 1 1 1. 6 0.167
322 A 3 3 1. 15 0.2
323 A 5 5 1. 13 0.385
324 A 3 3 1. 13 0.231
325 A 3 3 1. 12 0.25
326 A 2 2 1. 11 0.182
327 A 4 4 1. 12 0.333
328 A 2 2 1. 6 0.333
329 A 2 2 1. 13 0.154
330 A 3 3 1. 15 0.2
331 A 4 3 1. 16 0.188
332 A 2 2 1. 12 0.167
333 A 4 4 1. 8 0.5
334 A 3 3 1. 13 0.231
335 A 4 4 1. 17 0.235
336 A 2 2 1. 13 0.154
337 A 5 4 1. 17 0.235
338 A 2 2 1. 15 0.133
339 A 4 2 1. 6 0.333
340 A 4 4 1. 14 0.286
341 A 1 1 1. 9 0.111
342 A 3 2 1. 9 0.222
343 A 1 1 1. 10 0.1
344 A 2 2 1. 8 0.25
345 A 3 3 1. 15 0.2
346 A 4 4 1. 15 0.267
347 A 3 2 1. 9 0.222
348 A 3 2 1. 13 0.154
349 A 3 3 1. 6 0.5
350 A 5 5 1. 8 0.625
351 A 2 2 1. 8 0.25
352 A 3 2 1. 8 0.25
353 A 3 3 1. 14 0.214
354 A 3 2 1. 15 0.133
355 A 3 2 1. 4 0.5
356 A 4 2 1. 6 0.333
357 A 4 4 1. 10 0.4
358 A 3 2 1. 15 0.133
359 A 4 4 1. 13 0.308
360 A 3 3 1. 13 0.231
361 A 2 1 1. 4 0.25
362 A 5 2 1. 9 0.222
363 A 3 3 1. 13 0.231
364 A 1 1 1. 10 0.1
365 A 3 3 1. 10 0.3
366 A 4 3 1. 6 0.5
367 A 4 4 1. 11 0.364
368 A 4 3 1. 9 0.333
369 A 3 3 1. 15 0.2
370 A 1 1 1. 11 0.091
371 A 3 2 1. 9 0.222
372 A 3 2 1. 9 0.222
373 A 2 1 1. 11 0.091
374 A 3 2 1. 4 0.5
375 A 2 2 1. 4 0.5
376 A 3 2 1. 13 0.154

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