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2 detailed summary tables of results

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

2.1 Detailed conclusion table per each integral for all CAS systems

Detailed conclusion table per each integral is given by table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given just an F.

In this table,the column normalized size is defined as \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 18 14 22 65 19 46 14
normalized size 1 1. 1.5 1.17 1.83 5.42 1.58 3.83 1.17
time (sec) N/A 0.017 0.005 0. 1.49 0.221 0.052 0.21 0.502
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 13 13 13 12 20 26 14 20 12
normalized size 1 1. 1. 0.92 1.54 2. 1.08 1.54 0.92
time (sec) N/A 0.017 0.006 0.007 1.484 0.21 0.117 0.202 2.248
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 19 19 14 11 15 19 15 15 15
normalized size 1 1. 0.74 0.58 0.79 1. 0.79 0.79 0.79
time (sec) N/A 0.008 0.004 0.003 1.331 0.211 0.272 0.198 1.025
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 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 0.005 0.002 0.001 1.372 0.208 0.03 0.2 0.023
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 9 9 9 7 8 8 5 8 5
normalized size 1 1. 1. 0.78 0.89 0.89 0.56 0.89 0.56
time (sec) N/A 0.01 0.002 0. 1.37 0.205 0.06 0.2 1.036
Problem 6 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 0.017 0.003 0.009 1.326 0.224 0.051 0.198 0.
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 13 13 13 10 12 93 22 12 8
normalized size 1 1. 1. 0.77 0.92 7.15 1.69 0.92 0.62
time (sec) N/A 0.005 0.003 0.003 1.34 0.234 0.216 0.204 0.763
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 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 0.003 1.353 0.226 0.358 0.2 1.193
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 8 8 8 7 8 19 8 8 8
normalized size 1 1. 1. 0.88 1. 2.38 1. 1. 1.
time (sec) N/A 0.021 0.004 0.018 1.357 0.22 0.051 0.201 1.111
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A F F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 4 4 4 4 20 0 0 4 3
normalized size 1 1. 1. 1. 5. 0. 0. 1. 0.75
time (sec) N/A 0.019 0.009 0.004 1.52 0. 0. 0.202 1.36
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 2 2 2 3 18 0 2 3 2
normalized size 1 1. 1. 1.5 9. 0. 1. 1.5 1.
time (sec) N/A 0.018 0.008 0.001 1.487 0. 0.829 0.199 0.697
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 8 9 9 5 9 5
normalized size 1 1. 1. 1. 1.12 1.12 0.62 1.12 0.62
time (sec) N/A 0.008 0.005 0.001 1.355 0.236 0.059 0.198 0.476
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 7 7 7 7 8 8 5 8 5
normalized size 1 1. 1. 1. 1.14 1.14 0.71 1.14 0.71
time (sec) N/A 0.032 0.004 0.003 1.349 0.202 0.069 0.209 1.617
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 26 22 26 26 20 26 0
normalized size 1 1. 0.93 0.79 0.93 0.93 0.71 0.93 0.
time (sec) N/A 0.037 0.009 0.003 1.377 0.203 0.094 0.214 0.
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 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 0.011 0.004 0.004 1.392 0.214 0.083 0.211 0.637
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 7 8 8 5 8 0
normalized size 1 1. 1. 0.88 1. 1. 0.62 1. 0.
time (sec) N/A 0.012 0.002 0. 1.344 0.226 0.034 0.215 0.
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 9 9 9 7 8 8 5 8 5
normalized size 1 1. 1. 0.78 0.89 0.89 0.56 0.89 0.56
time (sec) N/A 0.012 0.001 0. 1.352 0.212 0.059 0.224 1.061
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 13 13 13 10 12 93 22 12 8
normalized size 1 1. 1. 0.77 0.92 7.15 1.69 0.92 0.62
time (sec) N/A 0.005 0.001 0. 1.333 0.244 0.23 0.222 0.759
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 6 6 6 6 7 7 5 7 5
normalized size 1 1. 1. 1. 1.17 1.17 0.83 1.17 0.83
time (sec) N/A 0.026 0.002 0.003 1.328 0.198 0.058 0.212 2.742
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 9 9 9 6 7 7 7 7 7
normalized size 1 1. 1. 0.67 0.78 0.78 0.78 0.78 0.78
time (sec) N/A 0.003 0.001 0.003 1.335 0.203 0.028 0.201 0.454
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 10 10 10 9 11 11 7 11 7
normalized size 1 1. 1. 0.9 1.1 1.1 0.7 1.1 0.7
time (sec) N/A 0.007 0.003 0.007 1.366 0.215 0.122 0.198 0.515
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 8 9 9 7 9 7
normalized size 1 1. 1. 1. 1.12 1.12 0.88 1.12 0.88
time (sec) N/A 0.007 0.001 0.003 1.347 0.234 0.072 0.2 0.839
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 19 8 9 9 8 9 8
normalized size 1 1. 1.9 0.8 0.9 0.9 0.8 0.9 0.8
time (sec) N/A 0.039 0.017 0.007 1.372 0.231 2.943 0.198 6.09
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 16 13 20 20 34 20 19
normalized size 1 1. 0.7 0.57 0.87 0.87 1.48 0.87 0.83
time (sec) N/A 0.012 0.005 0.004 1.34 0.205 1.449 0.198 0.968
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 13 13 25 10 23 23 17 26 10
normalized size 1 1. 1.92 0.77 1.77 1.77 1.31 2. 0.77
time (sec) N/A 0.008 0.005 0.001 1.528 0.205 0.162 0.199 0.62
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 18 18 18 14 18 18 15 18 17
normalized size 1 1. 1. 0.78 1. 1. 0.83 1. 0.94
time (sec) N/A 0.036 0.013 0.005 1.55 0.207 0.113 0.207 3.154
Problem 27 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 31 31 31 20 0 1 22 26 27
normalized size 1 1. 1. 0.65 0. 0.03 0.71 0.84 0.87
time (sec) N/A 0.059 0.012 0.01 0. 0.215 0.171 0.203 4.474
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 8 8 8 9 11 15 7 11 7
normalized size 1 1. 1. 1.12 1.38 1.88 0.88 1.38 0.88
time (sec) N/A 0.049 0.002 0.003 1.355 0.222 0.08 0.2 2.739
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 13 16 16 8 16 8
normalized size 1 1. 1. 1.08 1.33 1.33 0.67 1.33 0.67
time (sec) N/A 0.011 0.005 0.02 1.345 0.222 0.074 0.199 0.487
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 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 0.027 0.005 0. 1.335 0.229 0.776 0.198 1.413
Problem 31 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 49 49 260 41 54 63 46 54 42
normalized size 1 1. 5.31 0.84 1.1 1.29 0.94 1.1 0.86
time (sec) N/A 0.076 0.198 0.001 1.535 0.21 0.258 0.208 3.955
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 142 41 0 0 0 0 87
normalized size 1 1. 1.23 0.36 0. 0. 0. 0. 0.76
time (sec) N/A 0.099 0.457 0.149 0. 0. 0. 0. 5.274
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 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 0.01 0.012 1.339 0.24 0.405 0.2 2.596
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 16 13 20 20 34 20 19
normalized size 1 1. 0.7 0.57 0.87 0.87 1.48 0.87 0.83
time (sec) N/A 0.011 0.005 0. 1.34 0.209 1.445 0.199 0.981
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 32 92 32 32 0 32 0
normalized size 1 1. 1. 2.88 1. 1. 0. 1. 0.
time (sec) N/A 0.027 0.013 0.001 1.352 0.207 0. 0.206 0.
Problem 36 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 44 44 66 75 108 82 0 82 48
normalized size 1 1. 1.5 1.7 2.45 1.86 0. 1.86 1.09
time (sec) N/A 0.033 0.063 0.014 1.519 0.21 0. 0.215 1.928
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 35 35 26 30 59 182 105 39 26
normalized size 1 1. 0.74 0.86 1.69 5.2 3. 1.11 0.74
time (sec) N/A 0.028 0.045 0.009 1.5 0.392 3.934 0.207 2.5
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 75 75 41 70 153 266 190 111 66
normalized size 1 1. 0.55 0.93 2.04 3.55 2.53 1.48 0.88
time (sec) N/A 0.037 0.04 0.006 1.348 0.214 39.165 0.29 2.669
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 35 35 26 30 59 182 105 39 26
normalized size 1 1. 0.74 0.86 1.69 5.2 3. 1.11 0.74
time (sec) N/A 0.028 0.011 0. 1.493 0.214 4.139 0.207 2.478
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 134 262 0 174 0 0 46
normalized size 1 1. 2.63 5.14 0. 3.41 0. 0. 0.9
time (sec) N/A 0.077 0.032 0.035 0. 0.25 0. 0. 12.011
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 11 14 14 10 14 10
normalized size 1 1. 1. 0.79 1. 1. 0.71 1. 0.71
time (sec) N/A 0.01 0.003 0. 1.339 0.221 0.036 0.236 0.488
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B C F(-2) A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 57 99 149 0 378 0 0 54
normalized size 1 1.16 2.02 3.04 0. 7.71 0. 0. 1.1
time (sec) N/A 0.159 0.132 0.156 0. 0.33 0. 0. 15.247
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 9 9 6 5 12 12 3 41 7
normalized size 1 1. 0.67 0.56 1.33 1.33 0.33 4.56 0.78
time (sec) N/A 0.015 0.006 0. 1.425 0.211 0.212 0.206 0.483
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 7 7 8 8 5 8 7
normalized size 1 1. 0.64 0.64 0.73 0.73 0.45 0.73 0.64
time (sec) N/A 0.011 0.002 0. 1.4 0.228 0.058 0.226 1.018
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 9 11 11 5 0 5
normalized size 1 1. 1. 1. 1.22 1.22 0.56 0. 0.56
time (sec) N/A 0.038 0.005 0.005 1.349 0.202 0.076 0. 2.003
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 7 7 7 7 8 8 5 8 5
normalized size 1 1. 1. 1. 1.14 1.14 0.71 1.14 0.71
time (sec) N/A 0.047 0.004 0.003 1.358 0.199 0.068 0.209 2.778
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 11 11 11 8 12 9 8 12 8
normalized size 1 1. 1. 0.73 1.09 0.82 0.73 1.09 0.73
time (sec) N/A 0.005 0.002 0.002 1.36 0.219 0.301 0.215 0.495
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 2 2 2 8 3 3 2 3 2
normalized size 1 1. 1. 4. 1.5 1.5 1. 1.5 1.
time (sec) N/A 0.014 0.002 0.003 1.421 0.212 1.271 0.226 1.32
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 41 41 40 35 46 55 41 47 37
normalized size 1 1. 0.98 0.85 1.12 1.34 1. 1.15 0.9
time (sec) N/A 0.044 0.013 0. 1.486 0.208 0.173 0.224 3.185
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 47 73 75 66 88 101 83 90 68
normalized size 1 1.55 1.6 1.4 1.87 2.15 1.77 1.91 1.45
time (sec) N/A 0.189 0.021 0. 1.527 0.203 0.358 0.225 16.996
Problem 51 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 21 21 21 44 53 36 70 55 12
normalized size 1 1. 1. 2.1 2.52 1.71 3.33 2.62 0.57
time (sec) N/A 0.02 0.006 0.009 1.349 0.198 0.4 0.209 1.311
Problem 52 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 0.002 12.108 0.202 0.07 0.233 0.
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 40 40 29 34 45 32 32 51 27
normalized size 1 1. 0.72 0.85 1.12 0.8 0.8 1.27 0.68
time (sec) N/A 0.049 0.02 0. 1.498 0.221 0.461 0.212 3.12
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 7 7 7 8 9 9 5 9 15
normalized size 1 1. 1. 1.14 1.29 1.29 0.71 1.29 2.14
time (sec) N/A 0.005 0.001 0.001 1.327 0.208 0.062 0.227 0.561
Problem 55 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 9 11 11 5 11 0
normalized size 1 1. 1. 1.12 1.38 1.38 0.62 1.38 0.
time (sec) N/A 0.063 0.005 0.051 1.451 0.217 0.077 0.227 0.
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 3 3 3 4 4 4 15 4 3
normalized size 1 1. 1. 1.33 1.33 1.33 5. 1.33 1.
time (sec) N/A 0.028 0.006 0.005 1.509 0.221 0.142 0.232 3.264
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A F F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 2 2 2 9 4 0 0 4 2
normalized size 1 1. 1. 4.5 2. 0. 0. 2. 1.
time (sec) N/A 0.004 0.003 0. 1.415 0. 0. 0.214 0.026
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 15 19 19 15 19 0
normalized size 1 1. 1. 1.07 1.36 1.36 1.07 1.36 0.
time (sec) N/A 0.032 0.008 0.016 1.358 0.209 0.191 0.222 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 13 16 15 19 8 15 0
normalized size 1 1. 0.76 0.94 0.88 1.12 0.47 0.88 0.
time (sec) N/A 0.05 0.01 0.003 1.352 0.22 0.07 0.229 0.
Problem 60 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 38 38 29 29 32 32 26 32 0
normalized size 1 1. 0.76 0.76 0.84 0.84 0.68 0.84 0.
time (sec) N/A 0.049 0.016 0.002 1.357 0.213 0.084 0.214 0.
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 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 0.015 0.004 0. 1.341 0.219 0.181 0.206 0.767
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 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 0.017 0.01 0. 1.345 0.23 0.401 0.229 2.612
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 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 0.003 0. 1.313 0.233 0.181 0.226 0.784
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 28 23 23 30 22 30 0
normalized size 1 1. 1. 0.82 0.82 1.07 0.79 1.07 0.
time (sec) N/A 0.016 0.002 0. 1.346 0.225 0.093 0.21 0.
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 11 11 11 10 12 20 8 12 8
normalized size 1 1. 1. 0.91 1.09 1.82 0.73 1.09 0.73
time (sec) N/A 0.019 0.005 0.023 1.344 0.238 0.816 0.207 1.17
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 3 3 3 4 4 4 15 4 3
normalized size 1 1. 1. 1.33 1.33 1.33 5. 1.33 1.
time (sec) N/A 0.029 0.005 0.002 1.497 0.223 0.141 0.206 3.182
Problem 67 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 3 3 3 4 0 4 3 4 3
normalized size 1 1. 1. 1.33 0. 1.33 1. 1.33 1.
time (sec) N/A 0.075 0.007 0.009 0. 0.23 0.714 0.212 4.847
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 16 16 16 21 72 20 12 28 12
normalized size 1 1. 1. 1.31 4.5 1.25 0.75 1.75 0.75
time (sec) N/A 0.058 0.011 0.036 1.502 0.226 0.157 0.232 4.644
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 127 262 0 173 0 0 48
normalized size 1 1. 2.4 4.94 0. 3.26 0. 0. 0.91
time (sec) N/A 0.129 0.086 0.016 0. 0.243 0. 0. 14.425
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 35 127 93 90 0 112 17
normalized size 1 1. 2.19 7.94 5.81 5.62 0. 7. 1.06
time (sec) N/A 0.136 0.09 0.056 1.509 0.271 0. 0.257 14.036
Problem 71 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 16 16 35 121 92 35 422 111 0
normalized size 1 1. 2.19 7.56 5.75 2.19 26.38 6.94 0.
time (sec) N/A 0.199 0.028 0.012 1.506 0.214 2.324 0.222 0.
Problem 72 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 16 16 35 121 88 35 422 107 14
normalized size 1 1. 2.19 7.56 5.5 2.19 26.38 6.69 0.88
time (sec) N/A 0.041 0.02 0.01 1.505 0.216 2.275 0.209 9.155
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 35 35 26 30 59 182 105 39 26
normalized size 1 1. 0.74 0.86 1.69 5.2 3. 1.11 0.74
time (sec) N/A 0.029 0.044 0. 1.479 0.212 4.076 0.207 2.561
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 18 13 16 35 19 16 19
normalized size 1 1. 1.29 0.93 1.14 2.5 1.36 1.14 1.36
time (sec) N/A 0.014 0.01 0.011 1.503 0.229 0.047 0.207 2.583
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 13 13 13 12 15 15 8 15 8
normalized size 1 1. 1. 0.92 1.15 1.15 0.62 1.15 0.62
time (sec) N/A 0.015 0.006 0.002 1.496 0.199 0.075 0.203 1.564
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 7 7 7 7 8 8 5 8 5
normalized size 1 1. 1. 1. 1.14 1.14 0.71 1.14 0.71
time (sec) N/A 0.046 0.004 0. 1.332 0.209 0.068 0.205 2.783
Problem 77 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 24 24 19 24 31 31 20 41 0
normalized size 1 1. 0.79 1. 1.29 1.29 0.83 1.71 0.
time (sec) N/A 0.493 0.021 0.007 1.631 0.236 0.116 0.204 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 9 11 11 7 11 7
normalized size 1 1. 1. 1. 1.22 1.22 0.78 1.22 0.78
time (sec) N/A 0.006 0.002 0.001 1.339 0.231 0.053 0.203 0.522
Problem 79 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 32 26 19 26 0
normalized size 1 1. 1. 0.8 1.28 1.04 0.76 1.04 0.
time (sec) N/A 0.048 0.002 0.006 1.33 0.212 0.081 0.205 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 7 8 8 5 8 5
normalized size 1 1. 1. 0.88 1. 1. 0.62 1. 0.62
time (sec) N/A 0.009 0.005 0.003 1.54 0.204 0.088 0.205 1.064
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 13 16 16 10 16 10
normalized size 1 1. 1. 0.81 1. 1. 0.62 1. 0.62
time (sec) N/A 0.018 0.005 0.003 1.529 0.197 0.09 0.203 2.225
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 14 14 14 17 22 27 36 22 10
normalized size 1 1. 1. 1.21 1.57 1.93 2.57 1.57 0.71
time (sec) N/A 0.019 0.004 0.011 1.48 0.217 0.725 0.209 0.564
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 35 35 26 30 59 182 105 39 26
normalized size 1 1. 0.74 0.86 1.69 5.2 3. 1.11 0.74
time (sec) N/A 0.03 0.012 0. 1.49 0.224 4.099 0.209 2.543
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 17 17 17 16 20 86 34 28 12
normalized size 1 1. 1. 0.94 1.18 5.06 2. 1.65 0.71
time (sec) N/A 0.017 0.024 0.007 1.485 0.243 0.97 0.209 1.668
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 14 14 15 18 15 15 15
normalized size 1 1. 0.74 0.74 0.79 0.95 0.79 0.79 0.79
time (sec) N/A 0.014 0.016 0. 1.341 0.257 0.365 0.203 1.207
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 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. 1.332 0.227 0.025 0.201 0.022
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 73 31 346 96 0 45 0
normalized size 1 1. 1.62 0.69 7.69 2.13 0. 1. 0.
time (sec) N/A 0.198 0.254 0.194 1.695 0.272 0. 0.22 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi 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 22 10
normalized size 1 1. 1. 0.79 1. 1. 0.71 1.57 0.71
time (sec) N/A 0.011 0.003 0. 1.359 0.247 0.044 0.209 0.493
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 14 11 15 14 14 15 14
normalized size 1 1. 0.82 0.65 0.88 0.82 0.82 0.88 0.82
time (sec) N/A 0.007 0.004 0.006 1.324 0.232 0.27 0.203 0.977
Problem 90 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 23 23 23 20 26 107 0 36 31
normalized size 1 1. 1. 0.87 1.13 4.65 0. 1.57 1.35
time (sec) N/A 0.023 0.013 0.008 1.496 0.233 0. 0.213 1.722
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 8 8 8 7 8 14 5 8 5
normalized size 1 1. 1. 0.88 1. 1.75 0.62 1. 0.62
time (sec) N/A 0.019 0.002 0.003 1.339 0.273 0.039 0.201 1.093
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 6 6 6 6 7 7 5 7 5
normalized size 1 1. 1. 1. 1.17 1.17 0.83 1.17 0.83
time (sec) N/A 0.026 0.002 0. 1.363 0.22 0.06 0.204 2.757
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 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 0.036 0.005 0.001 1.369 0.234 0.076 0.204 3.397
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 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 0.008 0.003 1.33 0.223 0.656 0.212 0.511
Problem 95 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. 1.373 0.256 0.052 0.202 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 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 0.001 1.339 0.232 0.069 0.201 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 8 8 8 7 8 8 5 8 0
normalized size 1 1. 1. 0.88 1. 1. 0.62 1. 0.
time (sec) N/A 0.012 0.002 0. 1.337 0.221 0.033 0.201 0.
Problem 98 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 45 21 30 43 0 27 15
normalized size 1 1. 1.88 0.88 1.25 1.79 0. 1.12 0.62
time (sec) N/A 0.024 0.027 0.008 1.503 0.248 0. 0.212 1.901
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 20 20 20 14 18 26 15 18 17
normalized size 1 1. 1. 0.7 0.9 1.3 0.75 0.9 0.85
time (sec) N/A 0.038 0.014 0.003 1.485 0.219 0.115 0.21 3.228
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 26 30 59 182 105 39 26
normalized size 1 1. 0.74 0.86 1.69 5.2 3. 1.11 0.74
time (sec) N/A 0.029 0.041 0. 1.495 0.246 4.03 0.209 2.551
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 20 20 20 15 19 19 24 19 14
normalized size 1 1. 1. 0.75 0.95 0.95 1.2 0.95 0.7
time (sec) N/A 0.04 0.009 0.006 1.484 0.222 0.12 0.201 4.071
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 33 27 35 54 31 35 31
normalized size 1 1. 1. 0.82 1.06 1.64 0.94 1.06 0.94
time (sec) N/A 0.024 0.019 0. 1.486 0.222 0.14 0.206 1.897
Problem 103 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 21 20 26 26 15 26 0
normalized size 1 1. 1. 0.95 1.24 1.24 0.71 1.24 0.
time (sec) N/A 0.03 0. 0.002 1.344 0.227 0.034 0.203 0.
Problem 104 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 25 32 32 19 31 0
normalized size 1 1. 1. 0.96 1.23 1.23 0.73 1.19 0.
time (sec) N/A 0.036 0. 0.001 1.343 0.202 0.037 0.201 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 26 34 34 22 34 0
normalized size 1 1. 1. 0.96 1.26 1.26 0.81 1.26 0.
time (sec) N/A 0.04 0. 0.001 1.337 0.226 0.037 0.211 0.
Problem 106 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 32 31 41 41 26 39 0
normalized size 1 1. 1. 0.97 1.28 1.28 0.81 1.22 0.
time (sec) N/A 0.047 0. 0.001 1.348 0.201 0.04 0.2 0.
Problem 107 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 24 24 25 24 31 31 20 31 0
normalized size 1 1. 1.04 1. 1.29 1.29 0.83 1.29 0.
time (sec) N/A 0.052 0. 0.002 1.368 0.203 0.037 0.206 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 30 29 38 38 24 36 0
normalized size 1 1. 1.03 1. 1.31 1.31 0.83 1.24 0.
time (sec) N/A 0.059 0. 0.002 1.364 0.203 0.04 0.208 0.
Problem 109 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 18 23 23 15 23 0
normalized size 1 1. 1. 0.95 1.21 1.21 0.79 1.21 0.
time (sec) N/A 0.019 0. 0.002 1.439 0.199 0.033 0.203 0.
Problem 110 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 24 24 24 23 30 30 19 28 0
normalized size 1 1. 1. 0.96 1.25 1.25 0.79 1.17 0.
time (sec) N/A 0.023 0. 0.002 1.345 0.207 0.036 0.203 0.
Problem 111 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 31 22 31 0
normalized size 1 1. 1. 0.96 1.24 1.24 0.88 1.24 0.
time (sec) N/A 0.025 0. 0.001 1.361 0.206 0.036 0.207 0.
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 30 30 30 29 38 38 26 36 0
normalized size 1 1. 1. 0.97 1.27 1.27 0.87 1.2 0.
time (sec) N/A 0.03 0. 0.002 1.351 0.202 0.04 0.207 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 28 27 35 35 24 34 0
normalized size 1 1. 1.04 1. 1.3 1.3 0.89 1.26 0.
time (sec) N/A 0.018 0. 0.001 1.422 0.198 0.039 0.208 0.

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 [50] had the largest ratio of [ 0.8571 ]

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 3 2 1. 4 0.5
2 A 3 2 1. 11 0.182
3 A 2 1 1. 11 0.091
4 A 1 1 1. 2 0.5
5 A 1 1 1. 7 0.143
6 A 2 2 1. 7 0.286
7 A 1 1 1. 11 0.091
8 A 1 1 1. 6 0.167
9 A 2 2 1. 7 0.286
10 A 2 2 1. 4 0.5
11 A 1 1 1. 6 0.167
12 A 3 2 1. 6 0.333
13 A 4 2 1. 16 0.125
14 A 5 3 1. 7 0.429
15 A 3 1 1. 14 0.071
16 A 2 2 1. 5 0.4
17 A 1 1 1. 7 0.143
18 A 1 1 1. 11 0.091
19 A 2 2 1. 11 0.182
20 A 1 1 1. 5 0.2
21 A 1 1 1. 6 0.167
22 A 2 2 1. 9 0.222
23 A 3 3 1. 14 0.214
24 A 2 1 1. 9 0.111
25 A 3 3 1. 7 0.429
26 A 2 2 1. 15 0.133
27 A 2 2 1. 17 0.118
28 A 3 3 1. 13 0.231
29 A 1 1 1. 5 0.2
30 A 3 3 1. 8 0.375
31 A 7 7 1. 11 0.636
32 A 3 2 1. 12 0.167
33 A 3 3 1. 6 0.5
34 A 2 1 1. 9 0.111
35 A 4 3 1. 13 0.231
36 A 4 4 1. 15 0.267
37 A 3 2 1. 15 0.133
38 A 6 3 1. 13 0.231
39 A 3 2 1. 15 0.133
40 A 5 5 1. 29 0.172
41 A 2 2 1. 4 0.5
42 A 6 6 1.16 19 0.316
43 A 1 1 1. 6 0.167
44 A 2 2 1. 5 0.4
45 A 1 1 1. 10 0.1
46 A 5 3 1. 13 0.231
47 A 1 1 1. 5 0.2
48 A 1 1 1. 7 0.143
49 A 6 6 1. 9 0.667
50 A 10 6 1.55 7 0.857
51 A 1 1 1. 27 0.037
52 A 1 1 1. 4 0.25
53 A 4 3 1. 6 0.5
54 A 2 2 1. 10 0.2
55 A 7 4 1. 9 0.444
56 A 2 1 1. 12 0.083
57 A 1 1 1. 4 0.25
58 A 6 4 1. 7 0.571
59 A 4 3 1. 11 0.273
60 A 6 3 1. 9 0.333
61 A 2 2 1. 4 0.5
62 A 3 3 1. 6 0.5
63 A 2 2 1. 4 0.5
64 A 2 2 1. 6 0.333
65 A 2 1 1. 9 0.111
66 A 2 1 1. 12 0.083
67 A 2 2 1. 20 0.1
68 A 2 2 1. 10 0.2
69 A 6 6 1. 30 0.2
70 A 5 5 1. 39 0.128
71 A 6 5 1. 45 0.111
72 A 4 4 1. 31 0.129
73 A 3 2 1. 15 0.133
74 A 3 2 1. 4 0.5
75 A 3 2 1. 11 0.182
76 A 5 3 1. 13 0.231
77 A 10 6 1. 33 0.182
78 A 1 1 1. 7 0.143
79 A 5 5 1. 8 0.625
80 A 2 2 1. 9 0.222
81 A 3 3 1. 11 0.273
82 A 3 3 1. 8 0.375
83 A 3 2 1. 15 0.133
84 A 2 2 1. 16 0.125
85 A 1 1 1. 6 0.167
86 A 1 1 1. 3 0.333
87 A 4 2 1. 17 0.118
88 A 2 2 1. 4 0.5
89 A 2 1 1. 11 0.091
90 A 3 3 1. 14 0.214
91 A 2 2 1. 7 0.286
92 A 2 2 1. 11 0.182
93 A 3 2 1. 13 0.154
94 A 1 1 1. 8 0.125
95 A 2 2 1. 7 0.286
96 A 1 1 1. 4 0.25
97 A 2 2 1. 5 0.4
98 A 3 3 1. 17 0.176
99 A 3 3 1. 16 0.188
100 A 3 2 1. 15 0.133
101 A 3 3 1. 15 0.2
102 A 3 3 1. 8 0.375
103 A 1 1 1. 20 0.05
104 A 1 1 1. 25 0.04
105 A 1 1 1. 26 0.038
106 A 1 1 1. 31 0.032
107 A 1 1 1. 24 0.042
108 A 1 1 1. 29 0.034
109 A 1 1 1. 18 0.056
110 A 1 1 1. 23 0.043
111 A 1 1 1. 24 0.042
112 A 1 1 1. 29 0.034
113 A 1 1 1. 27 0.037

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