A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33 }
B grade: { }
C grade: { }
F grade: { }
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33 }
B grade: { }
C grade: { }
F grade: { }
A grade: { 1, 2, 3, 4, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 27, 30, 32, 33 }
C grade: { 11, 12, 13, 25, 26 }
A grade: { 4, 9, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 27, 30, 33 }
B grade: { 1, 2, 3, 6, 7, 8, 11, 12, 13, 28, 29, 31, 32 }
A grade: { 3, 4, 8, 9, 11, 12, 13, 14, 15, 18, 19, 22, 23, 25, 26, 27, 30, 33 }
B grade: { 1, 2, 5, 6, 7, 10, 16, 17, 20, 21, 24, 28, 29, 31, 32 }
C grade: { }
F grade: { }
A grade: { 4, 9, 14, 15, 19, 23, 27, 30, 33 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 16, 17, 18, 20, 21, 22, 24, 25, 26, 28, 29, 31, 32 }
A grade: { 1, 2, 3, 4, 6, 7, 8, 9, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 27, 28, 30, 31, 32, 33 }
B grade: { 29 }
C grade: { 11, 12, 13, 25, 26 }
A grade: { 4, 9, 14, 15, 19, 23, 27, 30, 33 }
B grade: { }
C grade: { }
F grade: { 1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 16, 17, 18, 20, 21, 22, 24, 25, 26, 28, 29, 31, 32 }
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 | Mupad |
grade | A | A | A | A | B | B | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 225 | 149 | 252 | 755 | 430 | 0 | 163 | -1 |
normalized size | 1 | 1.00 | 0.66 | 1.12 | 3.36 | 1.91 | 0.00 | 0.72 | -0.00 |
time (sec) | N/A | 0.140 | 0.303 | 0.096 | 0.667 | 0.554 | 0.000 | 0.145 | 0.000 |
Problem 2 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | B | B | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 130 | 124 | 611 | 343 | 0 | 121 | -1 |
normalized size | 1 | 1.00 | 1.17 | 1.12 | 5.50 | 3.09 | 0.00 | 1.09 | -0.01 |
time (sec) | N/A | 0.046 | 0.181 | 0.048 | 0.606 | 0.582 | 0.000 | 0.152 | 0.000 |
Problem 3 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | B | A | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 105 | 83 | 464 | 111 | 0 | 79 | -1 |
normalized size | 1 | 1.00 | 1.15 | 0.91 | 5.10 | 1.22 | 0.00 | 0.87 | -0.01 |
time (sec) | N/A | 0.032 | 0.079 | 0.043 | 0.553 | 0.446 | 0.000 | 0.124 | 0.000 |
Problem 4 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.06 |
time (sec) | N/A | 0.010 | 16.411 | 0.053 | 0.000 | 0.576 | 0.000 | 0.000 | 0.000 |
Problem 5 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | B | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 132 | 0 | 0 | 331 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.23 | 0.00 | 0.00 | 3.09 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.082 | 0.613 | 0.210 | 0.000 | 0.607 | 0.000 | 0.000 | 0.000 |
Problem 6 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | B | B | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 227 | 152 | 244 | 834 | 467 | 0 | 167 | -1 |
normalized size | 1 | 1.00 | 0.67 | 1.07 | 3.67 | 2.06 | 0.00 | 0.74 | -0.00 |
time (sec) | N/A | 0.135 | 0.305 | 0.086 | 0.669 | 0.507 | 0.000 | 0.149 | 0.000 |
Problem 7 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | B | B | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 134 | 120 | 674 | 385 | 0 | 123 | -1 |
normalized size | 1 | 1.00 | 1.20 | 1.07 | 6.02 | 3.44 | 0.00 | 1.10 | -0.01 |
time (sec) | N/A | 0.047 | 0.189 | 0.056 | 0.611 | 0.606 | 0.000 | 0.145 | 0.000 |
Problem 8 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | B | A | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 109 | 79 | 512 | 115 | 0 | 81 | -1 |
normalized size | 1 | 1.00 | 1.20 | 0.87 | 5.63 | 1.26 | 0.00 | 0.89 | -0.01 |
time (sec) | N/A | 0.032 | 0.071 | 0.041 | 0.558 | 0.474 | 0.000 | 0.150 | 0.000 |
Problem 9 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) | N/A | 0.010 | 18.488 | 0.051 | 0.000 | 0.585 | 0.000 | 0.000 | 0.000 |
Problem 10 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | B | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 136 | 0 | 0 | 371 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.26 | 0.00 | 0.00 | 3.44 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.086 | 0.682 | 0.204 | 0.000 | 0.633 | 0.000 | 0.000 | 0.000 |
Problem 11 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | C | B | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 72 | 75 | 183 | 58 | 0 | 53 | -1 |
normalized size | 1 | 1.00 | 1.09 | 1.14 | 2.77 | 0.88 | 0.00 | 0.80 | -0.02 |
time (sec) | N/A | 0.056 | 0.154 | 0.060 | 0.681 | 0.562 | 0.000 | 0.148 | 0.000 |
Problem 12 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | C | B | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 75 | 49 | 123 | 50 | 0 | 43 | -1 |
normalized size | 1 | 1.00 | 1.44 | 0.94 | 2.37 | 0.96 | 0.00 | 0.83 | -0.02 |
time (sec) | N/A | 0.024 | 0.077 | 0.046 | 0.651 | 0.682 | 0.000 | 0.124 | 0.000 |
Problem 13 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | C | B | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 24 | 25 | 94 | 16 | 0 | 21 | -1 |
normalized size | 1 | 1.00 | 0.62 | 0.64 | 2.41 | 0.41 | 0.00 | 0.54 | -0.03 |
time (sec) | N/A | 0.015 | 0.025 | 0.040 | 0.738 | 0.554 | 0.000 | 0.127 | 0.000 |
Problem 14 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.06 |
time (sec) | N/A | 0.010 | 9.405 | 0.053 | 0.000 | 0.704 | 0.000 | 0.000 | 0.000 |
Problem 15 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.039 | 11.792 | 0.062 | 0.000 | 0.630 | 0.000 | 0.000 | 0.000 |
Problem 16 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | B | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 268 | 176 | 281 | 294 | 766 | 0 | 182 | -1 |
normalized size | 1 | 1.00 | 0.66 | 1.05 | 1.10 | 2.86 | 0.00 | 0.68 | -0.00 |
time (sec) | N/A | 0.245 | 0.750 | 0.145 | 0.469 | 0.595 | 0.000 | 0.141 | 0.000 |
Problem 17 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | B | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 155 | 141 | 200 | 648 | 0 | 142 | -1 |
normalized size | 1 | 1.00 | 1.14 | 1.04 | 1.47 | 4.76 | 0.00 | 1.04 | -0.01 |
time (sec) | N/A | 0.094 | 0.390 | 0.087 | 0.437 | 0.621 | 0.000 | 0.161 | 0.000 |
Problem 18 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 140 | 94 | 96 | 128 | 0 | 94 | -1 |
normalized size | 1 | 1.00 | 1.27 | 0.85 | 0.87 | 1.16 | 0.00 | 0.85 | -0.01 |
time (sec) | N/A | 0.062 | 0.142 | 0.069 | 0.408 | 0.597 | 0.000 | 0.152 | 0.000 |
Problem 19 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) | N/A | 0.031 | 60.332 | 0.115 | 0.000 | 0.661 | 0.000 | 0.000 | 0.000 |
Problem 20 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | B | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 268 | 181 | 273 | 322 | 843 | 0 | 186 | -1 |
normalized size | 1 | 1.00 | 0.68 | 1.02 | 1.20 | 3.15 | 0.00 | 0.69 | -0.00 |
time (sec) | N/A | 0.233 | 0.761 | 0.161 | 0.469 | 0.635 | 0.000 | 0.172 | 0.000 |
Problem 21 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | B | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 159 | 137 | 216 | 730 | 0 | 144 | -1 |
normalized size | 1 | 1.00 | 1.17 | 1.01 | 1.59 | 5.37 | 0.00 | 1.06 | -0.01 |
time (sec) | N/A | 0.091 | 0.399 | 0.119 | 1.205 | 0.634 | 0.000 | 0.180 | 0.000 |
Problem 22 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 144 | 90 | 96 | 132 | 0 | 96 | -1 |
normalized size | 1 | 1.00 | 1.31 | 0.82 | 0.87 | 1.20 | 0.00 | 0.87 | -0.01 |
time (sec) | N/A | 0.062 | 0.144 | 0.084 | 0.908 | 0.583 | 0.000 | 0.133 | 0.000 |
Problem 23 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) | N/A | 0.031 | 64.393 | 0.101 | 0.000 | 0.618 | 0.000 | 0.000 | 0.000 |
Problem 24 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | C | B | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 99 | 77 | 113 | 268 | 0 | 61 | -1 |
normalized size | 1 | 1.00 | 1.46 | 1.13 | 1.66 | 3.94 | 0.00 | 0.90 | -0.01 |
time (sec) | N/A | 0.096 | 0.212 | 0.134 | 1.133 | 0.927 | 0.000 | 0.131 | 0.000 |
Problem 25 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | C | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 88 | 75 | 121 | 90 | 0 | 70 | -1 |
normalized size | 1 | 1.00 | 1.17 | 1.00 | 1.61 | 1.20 | 0.00 | 0.93 | -0.01 |
time (sec) | N/A | 0.053 | 0.208 | 0.119 | 1.178 | 0.651 | 0.000 | 0.140 | 0.000 |
Problem 26 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | C | C | A | F | C | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 48 | 49 | 45 | 40 | 0 | 42 | -1 |
normalized size | 1 | 1.00 | 0.86 | 0.88 | 0.80 | 0.71 | 0.00 | 0.75 | -0.02 |
time (sec) | N/A | 0.033 | 0.074 | 0.096 | 0.921 | 0.449 | 0.000 | 0.129 | 0.000 |
Problem 27 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.03 |
time (sec) | N/A | 0.030 | 20.676 | 0.126 | 0.000 | 0.619 | 0.000 | 0.000 | 0.000 |
Problem 28 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | B | B | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 261 | 194 | 493 | 536 | 634 | 0 | 387 | -1 |
normalized size | 1 | 1.00 | 0.74 | 1.89 | 2.05 | 2.43 | 0.00 | 1.48 | -0.00 |
time (sec) | N/A | 0.188 | 0.585 | 0.067 | 1.721 | 0.569 | 0.000 | 0.165 | 0.000 |
Problem 29 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | B | B | F | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 146 | 211 | 254 | 413 | 0 | 209 | -1 |
normalized size | 1 | 1.00 | 1.14 | 1.65 | 1.98 | 3.23 | 0.00 | 1.63 | -0.01 |
time (sec) | N/A | 0.060 | 0.269 | 0.049 | 0.858 | 0.568 | 0.000 | 0.133 | 0.000 |
Problem 30 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) | N/A | 0.015 | 7.113 | 0.103 | 0.000 | 0.585 | 0.000 | 0.000 | 0.000 |
Problem 31 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | B | B | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 311 | 240 | 558 | 601 | 1142 | 0 | 450 | -1 |
normalized size | 1 | 1.00 | 0.77 | 1.79 | 1.93 | 3.67 | 0.00 | 1.45 | -0.00 |
time (sec) | N/A | 0.379 | 1.414 | 0.116 | 1.948 | 1.473 | 0.000 | 0.159 | 0.000 |
Problem 32 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | B | B | F | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 177 | 241 | 299 | 777 | 0 | 248 | -1 |
normalized size | 1 | 1.00 | 1.11 | 1.51 | 1.87 | 4.86 | 0.00 | 1.55 | -0.01 |
time (sec) | N/A | 0.147 | 0.681 | 0.089 | 0.622 | 0.577 | 0.000 | 0.151 | 0.000 |
Problem 33 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | A | A | A | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) | N/A | 0.045 | 15.984 | 0.159 | 0.000 | 0.618 | 0.000 | 0.000 | 0.000 |
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 [11] had the largest ratio of [.5385]
# | grade |
|
|
|
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) | |||||||||||
1 | A | 12 | 7 | 1.00 | 15 | 0.467 | |||||||||||
2 | A | 6 | 5 | 1.00 | 13 | 0.385 | |||||||||||
3 | A | 5 | 4 | 1.00 | 11 | 0.364 | |||||||||||
4 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
5 | A | 7 | 5 | 1.00 | 33 | 0.152 | |||||||||||
6 | A | 12 | 7 | 1.00 | 16 | 0.438 | |||||||||||
7 | A | 6 | 5 | 1.00 | 14 | 0.357 | |||||||||||
8 | A | 5 | 4 | 1.00 | 12 | 0.333 | |||||||||||
9 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
10 | A | 7 | 5 | 1.00 | 35 | 0.143 | |||||||||||
11 | A | 12 | 7 | 1.00 | 13 | 0.538 | |||||||||||
12 | A | 6 | 5 | 1.00 | 11 | 0.454 | |||||||||||
13 | A | 5 | 4 | 1.00 | 9 | 0.444 | |||||||||||
14 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
15 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
16 | A | 14 | 8 | 1.00 | 17 | 0.471 | |||||||||||
17 | A | 8 | 6 | 1.00 | 15 | 0.400 | |||||||||||
18 | A | 7 | 5 | 1.00 | 13 | 0.385 | |||||||||||
19 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
20 | A | 14 | 8 | 1.00 | 18 | 0.444 | |||||||||||
21 | A | 8 | 6 | 1.00 | 16 | 0.375 | |||||||||||
22 | A | 7 | 5 | 1.00 | 14 | 0.357 | |||||||||||
23 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
24 | A | 14 | 8 | 1.00 | 15 | 0.533 | |||||||||||
25 | A | 8 | 6 | 1.00 | 13 | 0.462 | |||||||||||
26 | A | 7 | 5 | 1.00 | 11 | 0.454 | |||||||||||
27 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
28 | A | 12 | 7 | 1.00 | 19 | 0.368 | |||||||||||
29 | A | 6 | 5 | 1.00 | 17 | 0.294 | |||||||||||
30 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
31 | A | 14 | 8 | 1.00 | 21 | 0.381 | |||||||||||
32 | A | 8 | 6 | 1.00 | 19 | 0.316 | |||||||||||
33 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||