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 | 429 | 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 | 0.136 | 0.308 | 0.129 | 0.653 | 0.511 | 0.000 | 0.147 | 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 | 344 | 0 | 121 | -1 |
normalized size | 1 | 1.00 | 1.17 | 1.12 | 5.50 | 3.10 | 0.00 | 1.09 | -0.01 |
time (sec) | N/A | 0.048 | 0.152 | 0.099 | 0.611 | 0.511 | 0.000 | 0.122 | 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 | 112 | 0 | 79 | -1 |
normalized size | 1 | 1.00 | 1.15 | 0.91 | 5.10 | 1.23 | 0.00 | 0.87 | -0.01 |
time (sec) | N/A | 0.034 | 0.067 | 0.105 | 0.546 | 0.740 | 0.000 | 0.149 | 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 | 0.596 | 0.108 | 0.000 | 0.565 | 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 | 330 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.23 | 0.00 | 0.00 | 3.08 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.086 | 8.269 | 0.394 | 0.000 | 0.900 | 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 | 466 | 0 | 167 | -1 |
normalized size | 1 | 1.00 | 0.67 | 1.07 | 3.67 | 2.05 | 0.00 | 0.74 | -0.00 |
time (sec) | N/A | 0.142 | 0.306 | 0.117 | 0.661 | 0.769 | 0.000 | 0.127 | 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 | 384 | 0 | 123 | -1 |
normalized size | 1 | 1.00 | 1.20 | 1.07 | 6.02 | 3.43 | 0.00 | 1.10 | -0.01 |
time (sec) | N/A | 0.053 | 0.152 | 0.102 | 0.629 | 0.505 | 0.000 | 0.125 | 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 | 511 | 116 | 0 | 81 | -1 |
normalized size | 1 | 1.00 | 1.20 | 0.87 | 5.62 | 1.27 | 0.00 | 0.89 | -0.01 |
time (sec) | N/A | 0.034 | 0.071 | 0.094 | 0.650 | 0.543 | 0.000 | 0.117 | 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 | 0.011 | 1.282 | 0.106 | 0.000 | 0.482 | 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 | 370 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.26 | 0.00 | 0.00 | 3.43 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.089 | 9.924 | 0.372 | 0.000 | 0.644 | 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 | 60 | 0 | 53 | -1 |
normalized size | 1 | 1.00 | 1.09 | 1.14 | 2.77 | 0.91 | 0.00 | 0.80 | -0.02 |
time (sec) | N/A | 0.057 | 0.167 | 0.127 | 0.445 | 0.529 | 0.000 | 0.127 | 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 | 76 | 49 | 123 | 48 | 0 | 43 | -1 |
normalized size | 1 | 1.00 | 1.46 | 0.94 | 2.37 | 0.92 | 0.00 | 0.83 | -0.02 |
time (sec) | N/A | 0.025 | 0.079 | 0.120 | 0.472 | 0.688 | 0.000 | 0.141 | 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 | 22 | 25 | 94 | 14 | 0 | 21 | -1 |
normalized size | 1 | 1.00 | 0.56 | 0.64 | 2.41 | 0.36 | 0.00 | 0.54 | -0.03 |
time (sec) | N/A | 0.016 | 0.025 | 0.115 | 0.432 | 0.550 | 0.000 | 0.124 | 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 | 7.631 | 0.128 | 0.000 | 0.442 | 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 | 0.040 | 9.946 | 0.136 | 0.000 | 0.455 | 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 | 0.235 | 0.795 | 0.235 | 0.472 | 0.892 | 0.000 | 0.155 | 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 | 647 | 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 | 0.093 | 0.416 | 0.192 | 0.428 | 0.597 | 0.000 | 0.148 | 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 | 0.066 | 0.148 | 0.177 | 0.403 | 0.606 | 0.000 | 0.126 | 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 | 0.033 | 35.246 | 0.206 | 0.000 | 0.592 | 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 | 0.235 | 0.769 | 0.229 | 0.493 | 0.557 | 0.000 | 0.158 | 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 | 161 | 137 | 216 | 729 | 0 | 144 | -1 |
normalized size | 1 | 1.00 | 1.18 | 1.01 | 1.59 | 5.36 | 0.00 | 1.06 | -0.01 |
time (sec) | N/A | 0.093 | 0.412 | 0.199 | 0.435 | 0.515 | 0.000 | 0.152 | 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 | 0.066 | 0.148 | 0.167 | 0.395 | 0.806 | 0.000 | 0.144 | 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 | 0.033 | 37.112 | 0.193 | 0.000 | 0.473 | 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 | 0.099 | 0.219 | 0.264 | 0.443 | 0.882 | 0.000 | 0.133 | 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 | 91 | 0 | 70 | -1 |
normalized size | 1 | 1.00 | 1.17 | 1.00 | 1.61 | 1.21 | 0.00 | 0.93 | -0.01 |
time (sec) | N/A | 0.054 | 0.214 | 0.251 | 0.459 | 0.631 | 0.000 | 0.136 | 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 | 0.034 | 0.077 | 0.233 | 0.416 | 0.411 | 0.000 | 0.134 | 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 | 0.032 | 11.107 | 0.262 | 0.000 | 0.563 | 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 | 633 | 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 | 0.172 | 0.555 | 0.132 | 0.576 | 0.496 | 0.000 | 0.143 | 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 | 412 | 0 | 209 | -1 |
normalized size | 1 | 1.00 | 1.14 | 1.65 | 1.98 | 3.22 | 0.00 | 1.63 | -0.01 |
time (sec) | N/A | 0.060 | 0.245 | 0.108 | 0.442 | 0.565 | 0.000 | 0.128 | 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 | 2.613 | 0.173 | 0.000 | 0.537 | 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 | 603 | 1142 | 0 | 450 | -1 |
normalized size | 1 | 1.00 | 0.77 | 1.79 | 1.94 | 3.67 | 0.00 | 1.45 | -0.00 |
time (sec) | N/A | 0.386 | 1.416 | 0.237 | 0.667 | 0.768 | 0.000 | 0.150 | 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 | 301 | 777 | 0 | 248 | -1 |
normalized size | 1 | 1.00 | 1.11 | 1.51 | 1.88 | 4.86 | 0.00 | 1.55 | -0.01 |
time (sec) | N/A | 0.146 | 0.684 | 0.223 | 0.537 | 0.499 | 0.000 | 0.146 | 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 | 0.047 | 8.942 | 0.288 | 0.000 | 0.599 | 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 | |||||||||||