[next] [prev] [prev-tail] [tail] [up]

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 F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 164 169 224 1 187 234 0
normalized size 1 1. 1.01 1.04 1.37 0.01 1.15 1.44 0.
time (sec) N/A 0.384 0.08 0.003 0.74 0.225 0.187 0.273 0.
Problem 2 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 135 135 135 136 182 1 151 190 0
normalized size 1 1. 1. 1.01 1.35 0.01 1.12 1.41 0.
time (sec) N/A 0.256 0.071 0.001 0.738 0.237 0.164 0.27 0.
Problem 3 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 103 103 104 103 138 1 117 147 0
normalized size 1 1. 1.01 1. 1.34 0.01 1.14 1.43 0.
time (sec) N/A 0.203 0.047 0.001 0.742 0.235 0.15 0.27 0.
Problem 4 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 73 73 73 70 93 1 75 103 0
normalized size 1 1. 1. 0.96 1.27 0.01 1.03 1.41 0.
time (sec) N/A 0.132 0.037 0.001 0.743 0.233 0.121 0.268 0.
Problem 5 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 37 49 1 39 58 0
normalized size 1 1. 1. 0.88 1.17 0.02 0.93 1.38 0.
time (sec) N/A 0.061 0.015 0.001 0.744 0.228 0.087 0.266 0.
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 188 188 176 313 0 231 175 279 175
normalized size 1 1. 0.94 1.66 0. 1.23 0.93 1.48 0.93
time (sec) N/A 0.411 0.297 0.008 0. 0.29 3.723 0.285 49.891
Problem 7 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 213 213 199 345 0 385 206 306 202
normalized size 1 1. 0.93 1.62 0. 1.81 0.97 1.44 0.95
time (sec) N/A 0.449 0.492 0.014 0. 0.292 6.965 0.279 64.426
Problem 8 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 242 242 209 362 0 552 246 340 233
normalized size 1 1. 0.86 1.5 0. 2.28 1.02 1.4 0.96
time (sec) N/A 0.525 0.49 0.015 0. 0.263 22.238 0.28 66.666
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 126 260 0 1 619 177 0
normalized size 1 1. 0.95 1.97 0. 0.01 4.69 1.34 0.
time (sec) N/A 0.441 0.108 0.008 0. 0.613 46.176 0.27 0.
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 93 175 0 1 434 128 0
normalized size 1 1. 0.96 1.8 0. 0.01 4.47 1.32 0.
time (sec) N/A 0.256 0.113 0.005 0. 0.353 29.424 0.272 0.
Problem 11 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 72 72 71 99 0 1 287 95 63
normalized size 1 1. 0.99 1.38 0. 0.01 3.99 1.32 0.88
time (sec) N/A 0.168 0.086 0.004 0. 0.295 13.78 0.274 23.899
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 80 106 0 1 0 103 73
normalized size 1 1. 1.03 1.36 0. 0.01 0. 1.32 0.94
time (sec) N/A 0.27 0.056 0.01 0. 0.424 0. 0.275 36.073
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 112 112 130 191 0 1 0 173 105
normalized size 1 1. 1.16 1.71 0. 0.01 0. 1.54 0.94
time (sec) N/A 0.403 0.081 0.013 0. 0.826 0. 0.283 54.575
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 723 723 88 70 0 0 0 0 0
normalized size 1 1. 0.12 0.1 0. 0. 0. 0. 0.
time (sec) N/A 3.97 0.078 0.031 0. 0. 0. 0. 0.
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 718 718 88 67 0 0 0 0 0
normalized size 1 1. 0.12 0.09 0. 0. 0. 0. 0.
time (sec) N/A 3.448 0.082 0.007 0. 0. 0. 0. 0.
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 634 634 59 49 0 19340 0 0 0
normalized size 1 1. 0.09 0.08 0. 30.5 0. 0. 0.
time (sec) N/A 1.887 0.047 0.005 0. 4.371 0. 0. 0.
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 634 634 61 47 0 18004 0 0 661
normalized size 1 1. 0.1 0.07 0. 28.4 0. 0. 1.04
time (sec) N/A 1.65 0.048 0.004 0. 1.88 0. 0. 174.044
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 653 653 85 70 0 0 0 0 0
normalized size 1 1. 0.13 0.11 0. 0. 0. 0. 0.
time (sec) N/A 2.606 0.075 0.01 0. 0. 0. 0. 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 655 655 89 68 0 0 0 0 0
normalized size 1 1. 0.14 0.1 0. 0. 0. 0. 0.
time (sec) N/A 2.514 0.078 0.01 0. 0. 0. 0. 0.
Problem 20 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 46 46 46 38 50 59 42 50 0
normalized size 1 1. 1. 0.83 1.09 1.28 0.91 1.09 0.
time (sec) N/A 0.124 0.025 0.004 0.817 0.257 0.286 0.269 0.
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 31 31 31 25 32 38 32 32 29
normalized size 1 1. 1. 0.81 1.03 1.23 1.03 1.03 0.94
time (sec) N/A 0.083 0.012 0.004 0.817 0.272 0.269 0.271 14.248
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 39 39 39 33 43 49 37 43 34
normalized size 1 1. 1. 0.85 1.1 1.26 0.95 1.1 0.87
time (sec) N/A 0.087 0.013 0.004 0.816 0.26 0.298 0.274 13.659
Problem 23 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 41 41 44 35 51 58 41 47 41
normalized size 1 1. 1.07 0.85 1.24 1.41 1. 1.15 1.
time (sec) N/A 0.115 0.02 0.008 0.819 0.27 0.34 0.288 15.463
Problem 24 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 31 31 45 25 32 41 36 32 32
normalized size 1 1. 1.45 0.81 1.03 1.32 1.16 1.03 1.03
time (sec) N/A 0.102 0.02 0.006 0.817 0.254 0.376 0.275 14.516
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 418 418 47 46 0 886 31 867 340
normalized size 1 1. 0.11 0.11 0. 2.12 0.07 2.07 0.81
time (sec) N/A 1.124 0.019 0.009 0. 0.272 0.482 0.293 131.602
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 382 382 48 44 0 1447 32 1 340
normalized size 1 1. 0.13 0.12 0. 3.79 0.08 0. 0.89
time (sec) N/A 0.778 0.02 0.008 0. 0.282 0.492 0.286 125.338
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 378 378 46 41 0 884 24 853 337
normalized size 1 1. 0.12 0.11 0. 2.34 0.06 2.26 0.89
time (sec) N/A 0.635 0.019 0.007 0. 0.277 0.478 0.286 101.496
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 411 411 55 44 0 1415 22 1 352
normalized size 1 1. 0.13 0.11 0. 3.44 0.05 0. 0.86
time (sec) N/A 0.682 0.018 0.006 0. 0.276 0.489 0.285 105.392
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 411 411 57 44 0 873 26 860 352
normalized size 1 1. 0.14 0.11 0. 2.12 0.06 2.09 0.86
time (sec) N/A 0.693 0.017 0.007 0. 0.286 0.483 0.315 103.32
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 416 416 47 46 0 1463 31 1 338
normalized size 1 1. 0.11 0.11 0. 3.52 0.07 0. 0.81
time (sec) N/A 0.697 0.02 0.01 0. 0.282 0.549 0.295 108.539
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 418 418 47 46 0 930 32 867 342
normalized size 1 1. 0.11 0.11 0. 2.22 0.08 2.07 0.82
time (sec) N/A 0.854 0.02 0.009 0. 0.28 0.562 0.298 129.123
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 36 36 37 33 43 49 37 43 34
normalized size 1 1. 1.03 0.92 1.19 1.36 1.03 1.19 0.94
time (sec) N/A 0.091 0.014 0.003 0.827 0.259 0.285 0.279 11.439
Problem 33 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 39 39 55 35 51 58 41 47 41
normalized size 1 1. 1.41 0.9 1.31 1.49 1.05 1.21 1.05
time (sec) N/A 0.117 0.021 0.008 0.82 0.276 0.328 0.272 16.682
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 55 35 0 58 41 47 41
normalized size 1 1. 1.41 0.9 0. 1.49 1.05 1.21 1.05
time (sec) N/A 0.114 0.016 0.006 0. 0.253 0.326 0.273 18.013
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F A F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 396 396 279 1070 0 0 400 0 379
normalized size 1 1. 0.7 2.7 0. 0. 1.01 0. 0.96
time (sec) N/A 0.774 0.582 0.203 0. 0. 25.683 0. 46.905
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F A F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 356 356 249 1010 0 0 257 0 337
normalized size 1 1. 0.7 2.84 0. 0. 0.72 0. 0.95
time (sec) N/A 0.602 0.524 0.045 0. 0. 13.534 0. 39.809
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F A F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 316 316 219 956 0 0 124 0 294
normalized size 1 1. 0.69 3.03 0. 0. 0.39 0. 0.93
time (sec) N/A 0.504 0.476 0.044 0. 0. 6.816 0. 33.445
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F A F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 278 278 194 907 0 0 119 0 253
normalized size 1 1. 0.7 3.26 0. 0. 0.43 0. 0.91
time (sec) N/A 0.37 0.606 0.044 0. 0. 6.305 0. 27.432
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F A F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 289 289 197 934 0 0 119 0 262
normalized size 1 1. 0.68 3.23 0. 0. 0.41 0. 0.91
time (sec) N/A 0.402 0.456 0.06 0. 0. 59.45 0. 42.235
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 309 309 224 1005 0 0 0 0 286
normalized size 1 1. 0.72 3.25 0. 0. 0. 0. 0.93
time (sec) N/A 0.438 0.674 0.07 0. 0. 0. 0. 43.763
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 349 349 262 1095 0 0 0 0 328
normalized size 1 1. 0.75 3.14 0. 0. 0. 0. 0.94
time (sec) N/A 0.642 0.838 0.074 0. 0. 0. 0. 50.55
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 389 389 296 1182 0 0 0 0 371
normalized size 1 1. 0.76 3.04 0. 0. 0. 0. 0.95
time (sec) N/A 0.737 1.032 0.078 0. 0. 0. 0. 57.496
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 433 433 88 67 0 17662 0 0 432
normalized size 1 1. 0.2 0.15 0. 40.79 0. 0. 1.
time (sec) N/A 2.402 0.104 0.007 0. 4.467 0. 0. 169.92
Problem 44 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 72 72 71 99 0 1 287 95 63
normalized size 1 1. 0.99 1.38 0. 0.01 3.99 1.32 0.88
time (sec) N/A 0.177 0.098 0.004 0. 0.395 24.314 0.276 24.648
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 375 375 59 51 0 19648 0 0 379
normalized size 1 1. 0.16 0.14 0. 52.39 0. 0. 1.01
time (sec) N/A 0.948 0.064 0.005 0. 16.728 0. 0. 119.001
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 184 184 179 340 0 2072 0 1 189
normalized size 1 1. 0.97 1.85 0. 11.26 0. 0.01 1.03
time (sec) N/A 0.421 0.286 0.023 0. 0.398 0. 0.998 54.637
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 375 375 61 47 0 12872 0 0 379
normalized size 1 1. 0.16 0.13 0. 34.33 0. 0. 1.01
time (sec) N/A 0.804 0.066 0.009 0. 1.842 0. 0. 113.172
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 80 106 0 1 0 105 73
normalized size 1 1. 1.03 1.36 0. 0.01 0. 1.35 0.94
time (sec) N/A 0.278 0.057 0.009 0. 0.862 0. 0.282 36.743
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 392 392 85 72 0 0 0 0 391
normalized size 1 1. 0.22 0.18 0. 0. 0. 0. 1.
time (sec) N/A 1.458 0.089 0.01 0. 0. 0. 0. 160.037
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 199 199 89 365 0 3742 0 1 201
normalized size 1 1. 0.45 1.83 0. 18.8 0. 0.01 1.01
time (sec) N/A 0.697 0.074 0.025 0. 0.835 0. 0.495 84.805
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F F(-1) F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 394 394 86 68 0 0 0 0 394
normalized size 1 1. 0.22 0.17 0. 0. 0. 0. 1.
time (sec) N/A 1.386 0.099 0.009 0. 0. 0. 0. 153.716
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 278 278 46 34 0 261 170 281 530
normalized size 1 1. 0.17 0.12 0. 0.94 0.61 1.01 1.91
time (sec) N/A 0.662 0.025 0.01 0. 0.263 0.652 0.279 80.625
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 39 39 39 33 43 49 37 43 34
normalized size 1 1. 1. 0.85 1.1 1.26 0.95 1.1 0.87
time (sec) N/A 0.092 0.02 0.005 0.826 0.253 0.329 0.273 14.054
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 355 355 55 46 0 1223 27 342 481
normalized size 1 1. 0.15 0.13 0. 3.45 0.08 0.96 1.35
time (sec) N/A 0.717 0.024 0.01 0. 0.282 4.618 0.283 102.214
Problem 55 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 50 50 44 39 0 59 42 42 42
normalized size 1 1. 0.88 0.78 0. 1.18 0.84 0.84 0.84
time (sec) N/A 0.08 0.026 0.015 0. 0.248 0.289 0.286 20.258
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 355 355 57 44 0 1223 26 342 495
normalized size 1 1. 0.16 0.12 0. 3.45 0.07 0.96 1.39
time (sec) N/A 0.506 0.021 0.001 0. 0.28 4.641 0.306 78.633
Problem 57 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 41 41 44 35 51 58 41 51 41
normalized size 1 1. 1.07 0.85 1.24 1.41 1. 1.24 1.
time (sec) N/A 0.117 0.021 0.009 0.822 0.251 0.386 0.303 16.454
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 280 280 47 38 0 284 168 284 512
normalized size 1 1. 0.17 0.14 0. 1.01 0.6 1.01 1.83
time (sec) N/A 0.536 0.023 0.013 0. 0.274 0.696 0.312 84.449
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 49 70 0 188 76 348 76
normalized size 1 1. 0.55 0.79 0. 2.11 0.85 3.91 0.85
time (sec) N/A 0.189 0.024 0.007 0. 0.268 0.698 0.349 40.017
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 370 370 47 46 0 1197 32 348 318
normalized size 1 1. 0.13 0.12 0. 3.24 0.09 0.94 0.86
time (sec) N/A 0.612 0.022 0.014 0. 0.299 4.69 0.294 77.103
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 280 280 283 662 0 1 0 398 0
normalized size 1 1. 1.01 2.36 0. 0. 0. 1.42 0.
time (sec) N/A 1.207 0.405 0.018 0. 28.978 0. 0.291 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 218 218 218 512 0 1 0 302 0
normalized size 1 1. 1. 2.35 0. 0. 0. 1.39 0.
time (sec) N/A 0.794 0.308 0.012 0. 17.944 0. 0.296 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 176 176 178 388 0 1 0 250 0
normalized size 1 1. 1.01 2.2 0. 0.01 0. 1.42 0.
time (sec) N/A 0.535 0.32 0.011 0. 5.411 0. 0.314 0.
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 149 149 132 275 0 1 0 201 129
normalized size 1 1. 0.89 1.85 0. 0.01 0. 1.35 0.87
time (sec) N/A 0.399 0.211 0.009 0. 1.627 0. 0.301 80.285
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 107 169 0 1 0 171 112
normalized size 1 1. 0.86 1.36 0. 0.01 0. 1.38 0.9
time (sec) N/A 0.323 0.129 0.007 0. 0.528 0. 0.299 62.253
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 105 168 0 1 0 170 112
normalized size 1 1. 0.85 1.37 0. 0.01 0. 1.38 0.91
time (sec) N/A 0.28 0.135 0.007 0. 0.546 0. 0.297 60.69
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) F(-1) F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 158 159 152 285 0 0 0 221 136
normalized size 1 1.01 0.96 1.8 0. 0. 0. 1.4 0.86
time (sec) N/A 0.553 0.34 0.011 0. 0. 0. 0.294 99.804
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 193 193 194 412 0 0 0 284 178
normalized size 1 1. 1.01 2.13 0. 0. 0. 1.47 0.92
time (sec) N/A 0.714 0.286 0.017 0. 0. 0. 0.302 137.446
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 252 252 252 562 0 0 0 377 0
normalized size 1 1. 1. 2.23 0. 0. 0. 1.5 0.
time (sec) N/A 0.913 0.377 0.018 0. 0. 0. 0.3 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 343 343 338 943 0 1 0 763 0
normalized size 1 1. 0.99 2.75 0. 0. 0. 2.22 0.
time (sec) N/A 1.804 0.658 0.02 0. 118.759 0. 0.303 0.
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 274 274 269 765 0 1 0 643 0
normalized size 1 1. 0.98 2.79 0. 0. 0. 2.35 0.
time (sec) N/A 1.104 0.545 0.016 0. 50.476 0. 0.3 0.
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 246 246 207 580 0 1 0 556 0
normalized size 1 1. 0.84 2.36 0. 0. 0. 2.26 0.
time (sec) N/A 0.834 0.407 0.014 0. 17.632 0. 0.284 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 194 194 159 389 0 1 0 455 177
normalized size 1 1. 0.82 2.01 0. 0.01 0. 2.35 0.91
time (sec) N/A 0.559 0.406 0.013 0. 6.045 0. 0.273 146.522
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 183 183 148 328 0 1 0 441 167
normalized size 1 1. 0.81 1.79 0. 0.01 0. 2.41 0.91
time (sec) N/A 0.508 0.441 0.012 0. 5.23 0. 0.277 103.401
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 151 386 0 1 0 447 177
normalized size 1 1. 0.8 2.04 0. 0.01 0. 2.37 0.94
time (sec) N/A 0.648 0.384 0.013 0. 2.751 0. 0.29 150.937
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 248 249 246 589 0 0 0 528 0
normalized size 1 1. 0.99 2.38 0. 0. 0. 2.13 0.
time (sec) N/A 0.849 0.477 0.019 0. 0. 0. 0.297 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 291 291 287 791 0 0 0 657 0
normalized size 1 1. 0.99 2.72 0. 0. 0. 2.26 0.
time (sec) N/A 1.202 0.658 0.023 0. 0. 0. 0.284 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 372 372 370 993 0 0 0 792 0
normalized size 1 1. 0.99 2.67 0. 0. 0. 2.13 0.
time (sec) N/A 1.887 0.779 0.026 0. 0. 0. 0.29 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F(-1) F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 981 981 10904 11938 0 0 0 0 0
normalized size 1 1. 11.12 12.17 0. 0. 0. 0. 0.
time (sec) N/A 10.135 14.785 0.169 0. 0. 0. 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 778 778 7531 9182 0 0 0 0 0
normalized size 1 1. 9.68 11.8 0. 0. 0. 0. 0.
time (sec) N/A 4.665 14.221 0.074 0. 0. 0. 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 636 636 5350 6302 0 0 0 0 0
normalized size 1 1. 8.41 9.91 0. 0. 0. 0. 0.
time (sec) N/A 2.514 13.577 0.06 0. 0. 0. 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 550 550 3390 4361 0 0 0 0 0
normalized size 1 1. 6.16 7.93 0. 0. 0. 0. 0.
time (sec) N/A 1.735 13.161 0.059 0. 0. 0. 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 955 955 758 3023 0 0 0 0 0
normalized size 1 1. 0.79 3.17 0. 0. 0. 0. 0.
time (sec) N/A 7.743 13.112 0.06 0. 0. 0. 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 929 929 4893 3553 0 0 0 0 0
normalized size 1 1. 5.27 3.82 0. 0. 0. 0. 0.
time (sec) N/A 7.193 13.119 0.066 0. 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1287 1287 6206 4957 0 0 0 0 0
normalized size 1 1. 4.82 3.85 0. 0. 0. 0. 0.
time (sec) N/A 13.636 13.607 0.071 0. 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 29 0 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.053 0.245 0.647 0. 0. 0. 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 358 358 249 0 0 0 0 0 320
normalized size 1 1. 0.7 0. 0. 0. 0. 0. 0.89
time (sec) N/A 0.507 0.686 0.113 0. 0. 0. 0. 65.938
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 262 262 189 0 0 0 0 0 228
normalized size 1 1. 0.72 0. 0. 0. 0. 0. 0.87
time (sec) N/A 0.348 0.335 0.119 0. 0. 0. 0. 46.79
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 166 166 136 0 0 0 0 0 136
normalized size 1 1. 0.82 0. 0. 0. 0. 0. 0.82
time (sec) N/A 0.216 0.148 0.105 0. 0. 0. 0. 27.471
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 194 194 0 0 0 0 0 0 162
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.84
time (sec) N/A 0.504 0.096 0.131 0. 0. 0. 0. 88.172
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 302 302 0 0 0 0 0 0 258
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.85
time (sec) N/A 0.763 0.195 0.131 0. 0. 0. 0. 155.763
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 412 412 0 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.054 0.879 0.131 0. 0. 0. 0. 0.
Problem 93 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 16 201 46548 19 1 1326 1 12
normalized size 1 1. 12.56 2909.25 1.19 0.06 82.88 0.06 0.75
time (sec) N/A 0.035 0.273 0.007 0.767 0.264 0.967 0.267 3.672
Problem 94 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 18 18 233 46552 1674 1 1384 1 14
normalized size 1 1. 12.94 2586.22 93. 0.06 76.89 0.06 0.78
time (sec) N/A 0.066 0.287 0.004 0.793 0.277 0.916 0.275 4.946
Problem 95 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 18 18 233 46552 1674 1 1394 1 14
normalized size 1 1. 12.94 2586.22 93. 0.06 77.44 0.06 0.78
time (sec) N/A 0.07 0.287 0.004 0.78 0.266 0.924 0.277 4.991
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 260 2042 0 1751 0 1 17
normalized size 1 1. 11.3 88.78 0. 76.13 0. 0.04 0.74
time (sec) N/A 0.069 0.727 0.099 0. 0.334 0. 0.326 14.23
Problem 97 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 18 18 201 47685 22 1 1326 1 12
normalized size 1 1. 11.17 2649.17 1.22 0.06 73.67 0.06 0.67
time (sec) N/A 0.035 0.302 0.007 0.77 0.259 0.956 0.269 4.022
Problem 98 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 20 20 233 47688 1677 1 1384 1 14
normalized size 1 1. 11.65 2384.4 83.85 0.05 69.2 0.05 0.7
time (sec) N/A 0.066 0.304 0.004 0.787 0.259 0.947 0.275 5.445
Problem 99 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 20 20 233 47688 1677 1 1394 1 14
normalized size 1 1. 11.65 2384.4 83.85 0.05 69.7 0.05 0.7
time (sec) N/A 0.07 0.315 0.004 0.791 0.259 0.948 0.274 5.487
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 260 2046 0 1754 0 1 17
normalized size 1 1. 10.4 81.84 0. 70.16 0. 0.04 0.68
time (sec) N/A 0.072 0.661 0.097 0. 0.329 0. 0.327 15.756
Problem 101 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 15 15 172 155 18 1 175 208 10
normalized size 1 1. 11.47 10.33 1.2 0.07 11.67 13.87 0.67
time (sec) N/A 0.013 0.009 0.004 0.771 0.255 0.267 0.262 3.189
Problem 102 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 17 17 182 157 211 1 182 211 12
normalized size 1 1. 10.71 9.24 12.41 0.06 10.71 12.41 0.71
time (sec) N/A 0.02 0.009 0.004 0.765 0.253 0.278 0.263 13.301
Problem 103 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 17 17 186 157 211 1 185 211 12
normalized size 1 1. 10.94 9.24 12.41 0.06 10.88 12.41 0.71
time (sec) N/A 0.021 0.01 0.004 0.771 0.269 0.283 0.269 12.684
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 21 230 0 255 0 255 15
normalized size 1 1. 1. 10.95 0. 12.14 0. 12.14 0.71
time (sec) N/A 0.062 0.054 0.057 0. 0.316 0. 0.27 12.011
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 11 11 10 12 15 15 10 15 10
normalized size 1 1. 0.91 1.09 1.36 1.36 0.91 1.36 0.91
time (sec) N/A 0.008 0.005 0.002 0.773 0.279 1.164 0.265 3.699
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 16 20 20 14 20 14
normalized size 1 1. 1. 0.94 1.18 1.18 0.82 1.18 0.82
time (sec) N/A 0.011 0.01 0.002 0.768 0.271 1.593 0.291 4.943
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 16 20 20 14 20 14
normalized size 1 1. 1. 0.94 1.18 1.18 0.82 1.18 0.82
time (sec) N/A 0.011 0.011 0.002 0.772 0.282 1.989 0.266 4.995
Problem 108 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 19 19 26 24 31 26 0 26 15
normalized size 1 1. 1.37 1.26 1.63 1.37 0. 1.37 0.79
time (sec) N/A 0.067 0.049 0.033 0.826 0.297 0. 0.266 12.138
Problem 109 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 16 16 15 15 19 473 0 19 15
normalized size 1 1. 0.94 0.94 1.19 29.56 0. 1.19 0.94
time (sec) N/A 0.009 0.018 0.001 0.763 0.328 0. 0.275 3.666
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 17 475 475 0 0 17
normalized size 1 1. 1. 0.94 26.39 26.39 0. 0. 0.94
time (sec) N/A 0.012 0.02 0.002 0.858 0.372 0. 0. 4.957
Problem 111 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 17 475 475 0 22 17
normalized size 1 1. 1. 0.94 26.39 26.39 0. 1.22 0.94
time (sec) N/A 0.013 0.021 0.001 0.877 0.363 0. 0.359 5.006
Problem 112 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 23 23 23 22 562 532 0 28 20
normalized size 1 1. 1. 0.96 24.43 23.13 0. 1.22 0.87
time (sec) N/A 0.072 0.082 0.095 1.214 0.363 0. 0.282 12.267
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi 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 12 14 18 18 10 18 10
normalized size 1 1. 0.92 1.08 1.38 1.38 0.77 1.38 0.77
time (sec) N/A 0.009 0.008 0.002 0.751 0.274 1.185 0.265 4.012
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi 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 14 23 14
normalized size 1 1. 1. 0.95 1.21 1.21 0.74 1.21 0.74
time (sec) N/A 0.01 0.01 0.001 0.744 0.254 1.597 0.291 5.4
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 19 18 23 23 14 23 14
normalized size 1 1. 1. 0.95 1.21 1.21 0.74 1.21 0.74
time (sec) N/A 0.01 0.011 0.002 0.759 0.256 1.938 0.267 5.427
Problem 116 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 21 21 29 26 34 28 0 28 15
normalized size 1 1. 1.38 1.24 1.62 1.33 0. 1.33 0.71
time (sec) N/A 0.073 0.048 0.033 0.853 0.312 0. 0.267 12.904
Problem 117 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 16 17 22 478 0 22 15
normalized size 1 1. 0.89 0.94 1.22 26.56 0. 1.22 0.83
time (sec) N/A 0.011 0.021 0.001 0.757 0.322 0. 0.275 4.02
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 19 481 481 0 0 15
normalized size 1 1. 1. 0.95 24.05 24.05 0. 0. 0.75
time (sec) N/A 0.012 0.027 0.001 0.84 0.334 0. 0. 5.426
Problem 119 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 20 20 20 19 481 481 0 24 15
normalized size 1 1. 1. 0.95 24.05 24.05 0. 1.2 0.75
time (sec) N/A 0.014 0.028 0.001 0.875 0.335 0. 0.363 5.482
Problem 120 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 25 25 25 24 566 536 0 31 19
normalized size 1 1. 1. 0.96 22.64 21.44 0. 1.24 0.76
time (sec) N/A 0.076 0.091 0.096 1.228 0.348 0. 0.281 13.299
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 9 9 14 14 8 15 8
normalized size 1 1. 0.9 0.9 1.4 1.4 0.8 1.5 0.8
time (sec) N/A 0.008 0.006 0.002 0.741 0.256 1.071 0.263 3.172
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 16 16 15 14 23 18 12 20 15
normalized size 1 1. 0.94 0.88 1.44 1.12 0.75 1.25 0.94
time (sec) N/A 0.009 0.01 0.007 0.751 0.282 1.234 0.264 11.581
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 15 14 23 18 12 20 15
normalized size 1 1. 0.94 0.88 1.44 1.12 0.75 1.25 0.94
time (sec) N/A 0.01 0.011 0.007 0.746 0.259 1.296 0.265 10.867
Problem 124 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 18 63 23 0 23 36
normalized size 1 1. 1. 1.2 4.2 1.53 0. 1.53 2.4
time (sec) N/A 0.071 0.018 0.03 0.766 0.295 0. 0.265 13.224
Problem 125 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 14 177 18 109 87 18 14
normalized size 1 1. 0.93 11.8 1.2 7.27 5.8 1.2 0.93
time (sec) N/A 0.008 0.034 0.028 0.745 0.259 17.628 0.267 3.184
Problem 126 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 17 17 16 197 109 109 0 20 15
normalized size 1 1. 0.94 11.59 6.41 6.41 0. 1.18 0.88
time (sec) N/A 0.011 0.049 0.028 0.764 0.279 0. 0.268 13.029
Problem 127 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 17 17 16 197 109 109 0 20 15
normalized size 1 1. 0.94 11.59 6.41 6.41 0. 1.18 0.88
time (sec) N/A 0.011 0.059 0.021 0.767 0.274 0. 0.269 13.166
Problem 128 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 21 21 127 203 826 142 0 27 19
normalized size 1 1. 6.05 9.67 39.33 6.76 0. 1.29 0.9
time (sec) N/A 0.063 0.079 0.086 0.798 0.354 0. 0.272 11.025
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 19 21 0 38 0 80 15
normalized size 1 1. 0.95 1.05 0. 1.9 0. 4. 0.75
time (sec) N/A 0.013 0.03 0.004 0. 0.3 0. 0.269 3.991
Problem 130 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 25 25 24 24 45 45 0 92 19
normalized size 1 1. 0.96 0.96 1.8 1.8 0. 3.68 0.76
time (sec) N/A 0.014 0.034 0.005 0.856 0.278 0. 0.272 5.556
Problem 131 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 25 25 24 24 45 45 0 92 19
normalized size 1 1. 0.96 0.96 1.8 1.8 0. 3.68 0.76
time (sec) N/A 0.014 0.033 0.008 0.849 0.276 0. 0.281 5.63
Problem 132 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 27 27 26 40 53 51 0 36 20
normalized size 1 1. 0.96 1.48 1.96 1.89 0. 1.33 0.74
time (sec) N/A 0.069 0.087 0.089 1.035 0.285 0. 0.288 12.312
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 21 23 0 43 0 89 15
normalized size 1 1. 0.95 1.05 0. 1.95 0. 4.05 0.68
time (sec) N/A 0.011 0.031 0.004 0. 0.281 0. 0.266 4.385
Problem 134 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 27 27 26 26 50 50 0 101 19
normalized size 1 1. 0.96 0.96 1.85 1.85 0. 3.74 0.7
time (sec) N/A 0.013 0.038 0.005 0.831 0.287 0. 0.273 6.069
Problem 135 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 27 27 26 26 50 50 0 101 19
normalized size 1 1. 0.96 0.96 1.85 1.85 0. 3.74 0.7
time (sec) N/A 0.014 0.038 0.007 0.844 0.279 0. 0.275 6.138
Problem 136 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 29 29 28 45 58 57 0 39 20
normalized size 1 1. 0.97 1.55 2. 1.97 0. 1.34 0.69
time (sec) N/A 0.069 0.088 0.094 1.05 0.307 0. 0.287 13.298
Problem 137 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 19 19 17 24 0 35 46 55 14
normalized size 1 1. 0.89 1.26 0. 1.84 2.42 2.89 0.74
time (sec) N/A 0.01 0.032 0.006 0. 0.299 1.723 0.264 3.517
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 24 24 24 31 47 42 85 65 17
normalized size 1 1. 1. 1.29 1.96 1.75 3.54 2.71 0.71
time (sec) N/A 0.012 0.044 0.005 0.906 0.28 61.081 0.268 4.972
Problem 139 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 24 24 24 31 47 42 0 65 17
normalized size 1 1. 1. 1.29 1.96 1.75 0. 2.71 0.71
time (sec) N/A 0.013 0.045 0.005 0.923 0.281 0. 0.271 5.019
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 24 155 54 49 0 35 19
normalized size 1 1. 0.92 5.96 2.08 1.88 0. 1.35 0.73
time (sec) N/A 0.126 0.084 0.14 1.107 0.288 0. 0.281 15.945
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 196 196 318 0 0 0 0 0 182
normalized size 1 1. 1.62 0. 0. 0. 0. 0. 0.93
time (sec) N/A 0.549 1.538 0.047 0. 0. 0. 0. 50.056
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 374 374 5363 0 0 0 0 0 0
normalized size 1 1. 14.34 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.73 6.592 0.06 0. 0. 0. 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 816 816 20515 0 0 0 0 0 0
normalized size 1 1. 25.14 0. 0. 0. 0. 0. 0.
time (sec) N/A 9.342 7.917 0.082 0. 0. 0. 0. 0.
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 47 47 47 36 46 46 0 46 48
normalized size 1 1. 1. 0.77 0.98 0.98 0. 0.98 1.02
time (sec) N/A 0.102 0.04 0.005 0.768 0.274 0. 0.297 30.678
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 245 245 0 0 0 0 0 0 199
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.81
time (sec) N/A 1.15 0.112 0.11 0. 0. 0. 0. 110.144
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 210 210 0 0 0 0 0 0 173
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.82
time (sec) N/A 1.151 0.151 0.077 0. 0. 0. 0. 91.364
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 206 206 0 0 0 0 0 0 167
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.81
time (sec) N/A 0.862 0.137 0.076 0. 0. 0. 0. 78.156
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 194 194 0 0 0 0 0 0 167
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.86
time (sec) N/A 0.62 0.067 0.075 0. 0. 0. 0. 100.184
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 262 262 0 0 0 0 0 0 243
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.93
time (sec) N/A 1.436 0.086 0.108 0. 0. 0. 0. 121.827
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 212 212 0 0 0 0 0 0 168
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.79
time (sec) N/A 1.071 0.092 0.077 0. 0. 0. 0. 91.44
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 210 210 0 0 0 0 0 0 168
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.8
time (sec) N/A 1.053 0.091 0.076 0. 0. 0. 0. 91.395
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F(-1) F(-2) A
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 498 498 1615 0 0 0 0 0 442
normalized size 1 1. 3.24 0. 0. 0. 0. 0. 0.89
time (sec) N/A 1.387 17.638 0.09 0. 0. 0. 0. 140.812
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 323 323 922 0 0 0 0 0 279
normalized size 1 1. 2.85 0. 0. 0. 0. 0. 0.86
time (sec) N/A 0.825 2.487 0.079 0. 0. 0. 0. 86.806
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 158 158 534 0 0 0 0 0 129
normalized size 1 1. 3.38 0. 0. 0. 0. 0. 0.82
time (sec) N/A 0.328 0.92 0.079 0. 0. 0. 0. 34.908
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 34 0 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.072 0.126 0.108 0. 0. 0. 0. 0.
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 34 0 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.07 0.264 0.122 0. 0. 0. 0. 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 [83] had the largest ratio of [ 0.4231 ]

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 2 1 1. 22 0.045
2 A 2 1 1. 22 0.045
3 A 2 1 1. 22 0.045
4 A 2 1 1. 22 0.045
5 A 2 1 1. 20 0.05
6 A 8 8 1. 22 0.364
7 A 8 8 1. 22 0.364
8 A 8 8 1. 22 0.364
9 A 7 6 1. 25 0.24
10 A 6 6 1. 25 0.24
11 A 5 5 1. 25 0.2
12 A 7 6 1. 25 0.24
13 A 7 6 1. 25 0.24
14 A 14 8 1. 25 0.32
15 A 14 8 1. 25 0.32
16 A 13 7 1. 23 0.304
17 A 13 7 1. 22 0.318
18 A 14 8 1. 25 0.32
19 A 14 8 1. 25 0.32
20 A 7 6 1. 23 0.261
21 A 4 4 1. 23 0.174
22 A 5 5 1. 23 0.217
23 A 7 6 1. 23 0.261
24 A 5 4 1. 23 0.174
25 A 15 9 1. 23 0.391
26 A 15 9 1. 23 0.391
27 A 14 8 1. 23 0.348
28 A 13 7 1. 21 0.333
29 A 13 7 1. 20 0.35
30 A 14 8 1. 23 0.348
31 A 15 9 1. 23 0.391
32 A 5 5 1. 21 0.238
33 A 7 6 1. 21 0.286
34 A 8 7 1. 18 0.389
35 A 6 4 1. 24 0.167
36 A 5 4 1. 24 0.167
37 A 4 4 1. 24 0.167
38 A 3 3 1. 24 0.125
39 A 3 3 1. 24 0.125
40 A 3 3 1. 24 0.125
41 A 4 4 1. 24 0.167
42 A 5 4 1. 24 0.167
43 A 8 5 1. 25 0.2
44 A 5 5 1. 25 0.2
45 A 7 4 1. 25 0.16
46 A 4 3 1. 23 0.13
47 A 7 4 1. 22 0.182
48 A 7 6 1. 25 0.24
49 A 8 5 1. 25 0.2
50 A 5 4 1. 25 0.16
51 A 8 5 1. 25 0.2
52 A 20 7 1. 23 0.304
53 A 5 5 1. 23 0.217
54 A 21 7 1. 23 0.304
55 A 4 3 1. 21 0.143
56 A 19 6 1. 20 0.3
57 A 7 6 1. 23 0.261
58 A 20 7 1. 23 0.304
59 A 11 8 1. 23 0.348
60 A 21 9 1. 23 0.391
61 A 7 6 1. 25 0.24
62 A 7 6 1. 25 0.24
63 A 7 6 1. 23 0.261
64 A 7 6 1. 22 0.273
65 A 7 6 1. 25 0.24
66 A 7 7 1. 25 0.28
67 A 7 6 1.01 25 0.24
68 A 7 6 1. 25 0.24
69 A 7 6 1. 25 0.24
70 A 7 6 1. 25 0.24
71 A 7 6 1. 25 0.24
72 A 7 6 1. 23 0.261
73 A 7 6 1. 22 0.273
74 A 7 6 1. 25 0.24
75 A 8 7 1. 25 0.28
76 A 7 6 1. 25 0.24
77 A 7 6 1. 25 0.24
78 A 7 6 1. 25 0.24
79 A 11 7 1. 29 0.241
80 A 10 7 1. 29 0.241
81 A 8 7 1. 29 0.241
82 A 8 7 1. 27 0.259
83 A 16 11 1. 26 0.423
84 A 16 11 1. 29 0.379
85 A 24 12 1. 29 0.414
86 A 0 0 0. 0 0.
87 A 13 4 1. 26 0.154
88 A 10 4 1. 26 0.154
89 A 7 4 1. 24 0.167
90 A 6 3 1. 26 0.115
91 A 8 3 1. 26 0.115
92 A 10 3 1. 26 0.115
93 A 1 1 1. 19 0.053
94 A 1 1 1. 24 0.042
95 A 1 1 1. 26 0.038
96 A 2 2 1. 30 0.067
97 A 1 1 1. 21 0.048
98 A 1 1 1. 26 0.038
99 A 1 1 1. 28 0.036
100 A 2 2 1. 32 0.062
101 A 1 1 1. 18 0.056
102 A 1 1 1. 23 0.043
103 A 1 1 1. 25 0.04
104 A 3 3 1. 29 0.103
105 A 1 1 1. 19 0.053
106 A 1 1 1. 24 0.042
107 A 1 1 1. 26 0.038
108 A 2 2 1. 30 0.067
109 A 1 1 1. 19 0.053
110 A 1 1 1. 24 0.042
111 A 1 1 1. 26 0.038
112 A 2 2 1. 30 0.067
113 A 1 1 1. 21 0.048
114 A 1 1 1. 26 0.038
115 A 1 1 1. 28 0.036
116 A 2 2 1. 32 0.062
117 A 1 1 1. 21 0.048
118 A 1 1 1. 26 0.038
119 A 1 1 1. 28 0.036
120 A 2 2 1. 32 0.062
121 A 1 1 1. 18 0.056
122 A 1 1 1. 23 0.043
123 A 1 1 1. 25 0.04
124 A 4 3 1. 29 0.103
125 A 1 1 1. 18 0.056
126 A 1 1 1. 23 0.043
127 A 1 1 1. 25 0.04
128 A 3 3 1. 29 0.103
129 A 1 1 1. 19 0.053
130 A 1 1 1. 24 0.042
131 A 1 1 1. 26 0.038
132 A 2 2 1. 30 0.067
133 A 1 1 1. 21 0.048
134 A 1 1 1. 26 0.038
135 A 1 1 1. 28 0.036
136 A 2 2 1. 32 0.062
137 A 1 1 1. 18 0.056
138 A 1 1 1. 23 0.043
139 A 1 1 1. 25 0.04
140 A 2 2 1. 29 0.069
141 A 4 2 1. 29 0.069
142 A 5 3 1. 29 0.103
143 A 6 3 1. 29 0.103
144 A 3 3 1. 59 0.051
145 A 5 3 1. 31 0.097
146 A 5 3 1. 29 0.103
147 A 5 3 1. 27 0.111
148 A 5 3 1. 26 0.115
149 A 8 5 1. 29 0.172
150 A 5 3 1. 29 0.103
151 A 5 3 1. 29 0.103
152 A 10 4 1. 31 0.129
153 A 7 4 1. 29 0.138
154 A 2 2 1. 22 0.091
155 A 0 0 0. 0 0.
156 A 0 0 0. 0 0.

[next] [prev] [prev-tail] [front] [up]