A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 31 }
B grade: { }
C grade: { }
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 24, 26, 27, 28, 29, 31 }
B grade: { 12 }
A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 21, 22, 24, 26, 27, 29, 31 }
B grade: { 9, 10, 11, 13, 14, 28 }
C grade: { 12, 15, 16, 17, 18, 19, 20, 23, 30 }
F grade: { 25 }
A grade: { 1, 2, 3, 4, 6, 7, 8, 21, 22, 24, 26, 28, 29, 31 }
B grade: { }
C grade: { }
F grade: { 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 25, 27, 30 }
A grade: { 1, 2, 3, 4, 6, 26, 27 }
C grade: { }
F grade: { 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 28, 29, 30, 31 }
A grade: { 1, 2, 3, 4, 6, 7, 8, 21, 22, 28, 29 }
B grade: { }
C grade: { }
F grade: { 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 30, 31 }
A grade: { 21, 22, 26, 27, 28, 29 }
B grade: { 24 }
C grade: { }
F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 25, 30, 31 }
B grade: { 1, 2, 3, 4, 6, 7, 21, 22, 24, 28, 29, 31 }
C grade: { }
F grade: { 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 25, 30 }
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 | A | A | A | F | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 184 | 255 | 283 | 252 | 264 | 345 | 0 | 273 |
normalized size | 1 | 1.00 | 1.39 | 1.54 | 1.37 | 1.43 | 1.88 | 0.00 | 1.48 |
time (sec) | N/A | 0.143 | 0.493 | 0.031 | 0.412 | 0.482 | 2.735 | 0.000 | 1.049 |
Problem 2 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 218 | 207 | 186 | 196 | 262 | 0 | 197 |
normalized size | 1 | 1.00 | 1.51 | 1.44 | 1.29 | 1.36 | 1.82 | 0.00 | 1.37 |
time (sec) | N/A | 0.123 | 0.462 | 0.034 | 0.411 | 0.920 | 1.846 | 0.000 | 0.802 |
Problem 3 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 163 | 137 | 126 | 133 | 160 | 0 | 127 |
normalized size | 1 | 1.00 | 1.58 | 1.33 | 1.22 | 1.29 | 1.55 | 0.00 | 1.23 |
time (sec) | N/A | 0.090 | 0.352 | 0.033 | 0.411 | 3.000 | 1.046 | 0.000 | 0.353 |
Problem 4 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 77 | 68 | 71 | 71 | 87 | 0 | 67 |
normalized size | 1 | 1.00 | 1.01 | 0.89 | 0.93 | 0.93 | 1.14 | 0.00 | 0.88 |
time (sec) | N/A | 0.061 | 0.006 | 0.033 | 0.468 | 1.419 | 0.590 | 0.000 | 0.410 |
Problem 5 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 138 | 168 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.083 | 0.065 | 0.061 | 0.000 | 0.742 | 0.000 | 0.000 | 0.000 |
Problem 6 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 111 | 118 | 107 | 116 | 695 | 0 | 112 |
normalized size | 1 | 1.00 | 1.13 | 1.20 | 1.09 | 1.18 | 7.09 | 0.00 | 1.14 |
time (sec) | N/A | 0.053 | 0.197 | 0.036 | 0.421 | 0.527 | 4.256 | 0.000 | 3.460 |
Problem 7 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | B | A | F | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 146 | 192 | 184 | 214 | 313 | 2887 | 0 | 591 |
normalized size | 1 | 1.00 | 1.32 | 1.26 | 1.47 | 2.14 | 19.77 | 0.00 | 4.05 |
time (sec) | N/A | 0.123 | 0.332 | 0.040 | 0.417 | 0.690 | 9.645 | 0.000 | 4.428 |
Problem 8 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | B | A | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 206 | 254 | 282 | 374 | 642 | 9229 | 0 | -1 |
normalized size | 1 | 1.00 | 1.23 | 1.37 | 1.82 | 3.12 | 44.80 | 0.00 | -0.00 |
time (sec) | N/A | 0.182 | 0.651 | 0.040 | 0.435 | 1.868 | 20.036 | 0.000 | 0.000 |
Problem 9 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 376 | 376 | 472 | 948 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.26 | 2.52 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.573 | 1.001 | 0.108 | 0.000 | 0.538 | 0.000 | 0.000 | 0.000 |
Problem 10 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 270 | 312 | 750 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.16 | 2.78 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.399 | 0.595 | 0.109 | 0.000 | 0.956 | 0.000 | 0.000 | 0.000 |
Problem 11 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 171 | 172 | 360 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.01 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.298 | 0.285 | 0.101 | 0.000 | 1.352 | 0.000 | 0.000 | 0.000 |
Problem 12 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | B | C | F | F | F | F(-1) | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 223 | 741 | 1297 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 3.32 | 5.82 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.049 | 15.116 | 1.234 | 0.000 | 0.661 | 0.000 | 0.000 | 0.000 |
Problem 13 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F | F | F | F(-1) | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 341 | 341 | 300 | 698 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.88 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.370 | 3.397 | 0.115 | 0.000 | 1.097 | 0.000 | 0.000 | 0.000 |
Problem 14 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F(-1) | F | F(-1) | F(-1) | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 496 | 496 | 479 | 961 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.97 | 1.94 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.539 | 7.083 | 0.113 | 0.000 | 1.295 | 0.000 | 0.000 | 0.000 |
Problem 15 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | C | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 652 | 652 | 855 | 3577 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.31 | 5.49 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.202 | 2.233 | 18.815 | 0.000 | 0.639 | 0.000 | 0.000 | 0.000 |
Problem 16 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | C | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 411 | 411 | 621 | 3022 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.51 | 7.35 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.774 | 1.318 | 9.025 | 0.000 | 0.597 | 0.000 | 0.000 | 0.000 |
Problem 17 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | C | F | F | F | F | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 264 | 342 | 7462 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.30 | 28.27 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.580 | 0.709 | 1.417 | 0.000 | 0.412 | 0.000 | 0.000 | 0.000 |
Problem 18 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | F | C | F | F | F | F(-1) | F |
verified | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 320 | 320 | 0 | 2616 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 8.18 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.057 | 102.459 | 0.594 | 0.000 | 0.409 | 0.000 | 0.000 | 0.000 |
Problem 19 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | C | F | F | F | F(-1) | F |
verified | N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 499 | 499 | 770 | 2960 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 1.54 | 5.93 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.530 | 21.653 | 1.231 | 0.000 | 0.425 | 0.000 | 0.000 | 0.000 |
Problem 20 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | F | C | F(-1) | F | F(-1) | F(-1) | F |
verified | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 936 | 936 | 0 | 41269 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.00 | 44.09 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.090 | 69.396 | 23.156 | 0.000 | 0.475 | 0.000 | 0.000 | 0.000 |
Problem 21 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | B | A | A | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 250 | 252 | 381 | 323 | 4861 | 464 | 303 | 419 |
normalized size | 1 | 1.00 | 1.01 | 1.52 | 1.29 | 19.44 | 1.86 | 1.21 | 1.68 |
time (sec) | N/A | 0.303 | 3.480 | 0.048 | 0.418 | 0.653 | 25.999 | 34.881 | 3.366 |
Problem 22 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | B | A | A | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 191 | 153 | 167 | 168 | 534 | 1734 | 201 | 203 |
normalized size | 1 | 0.99 | 0.80 | 0.87 | 0.88 | 2.78 | 9.03 | 1.05 | 1.06 |
time (sec) | N/A | 0.209 | 0.099 | 0.028 | 0.412 | 0.492 | 18.146 | 5.099 | 2.534 |
Problem 23 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | F | C | C | F | F | F(-1) | F | F |
verified | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 501 | 0 | 326 | 138 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.65 | 0.28 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.064 | 34.979 | 0.139 | 0.000 | 0.406 | 0.000 | 0.000 | 0.000 |
Problem 24 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | F(-1) | F(-1) | B | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 328 | 328 | 321 | 433 | 287 | 0 | 0 | 1443 | 883 |
normalized size | 1 | 1.00 | 0.98 | 1.32 | 0.88 | 0.00 | 0.00 | 4.40 | 2.69 |
time (sec) | N/A | 0.522 | 0.803 | 0.043 | 0.545 | 0.000 | 0.000 | 3.691 | 0.661 |
Problem 25 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | C | F | F | F | F | F | F |
verified | N/A | NO | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1325 | 1554 | 5591 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.17 | 4.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 3.099 | 31.403 | 0.425 | 0.000 | 0.753 | 0.000 | 0.000 | 0.000 |
Problem 26 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
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 | 23 | 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 | -0.04 |
time (sec) | N/A | 0.123 | 75.978 | 1.092 | 0.000 | 1.615 | 0.000 | 0.000 | 0.000 |
Problem 27 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | N/A | A | A | A | F(-1) | A | F(-1) | A | A |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 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 | -0.04 |
time (sec) | N/A | 0.656 | 66.472 | 0.710 | 0.000 | 0.600 | 0.000 | 0.000 | 0.000 |
Problem 28 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | A | F(-1) | A | A | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 331 | 297 | 536 | 280 | 0 | 151 | 326 | 988 |
normalized size | 1 | 1.05 | 0.94 | 1.70 | 0.89 | 0.00 | 0.48 | 1.03 | 3.14 |
time (sec) | N/A | 0.709 | 168.707 | 0.175 | 0.411 | 0.000 | 50.144 | 2.451 | 0.517 |
Problem 29 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | F(-2) | A | A | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 285 | 310 | 314 | 232 | 0 | 3068 | 257 | 485 |
normalized size | 1 | 1.00 | 1.09 | 1.10 | 0.81 | 0.00 | 10.76 | 0.90 | 1.70 |
time (sec) | N/A | 0.603 | 0.096 | 0.122 | 0.412 | 0.000 | 46.474 | 0.986 | 0.436 |
Problem 30 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | F | F(-1) | C | F | F | F(-1) | F | F |
verified | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 739 | 0 | 0 | 172 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.00 | 0.00 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.063 | 180.003 | 0.149 | 0.000 | 0.405 | 0.000 | 0.000 | 0.000 |
Problem 31 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | F(-1) | F(-1) | F(-1) | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 906 | 906 | 536 | 1220 | 464 | 0 | 0 | 0 | 2105 |
normalized size | 1 | 1.00 | 0.59 | 1.35 | 0.51 | 0.00 | 0.00 | 0.00 | 2.32 |
time (sec) | N/A | 1.484 | 16.809 | 0.229 | 0.411 | 0.000 | 0.000 | 0.000 | 0.776 |
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 [25] had the largest ratio of [2.556]
# | grade |
|
|
|
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) | |||||||||||
1 | A | 6 | 5 | 1.00 | 16 | 0.312 | |||||||||||
2 | A | 6 | 5 | 1.00 | 16 | 0.312 | |||||||||||
3 | A | 6 | 5 | 1.00 | 16 | 0.312 | |||||||||||
4 | A | 6 | 5 | 1.00 | 14 | 0.357 | |||||||||||
5 | A | 4 | 4 | 1.00 | 16 | 0.250 | |||||||||||
6 | A | 6 | 6 | 1.00 | 16 | 0.375 | |||||||||||
7 | A | 7 | 6 | 1.00 | 16 | 0.375 | |||||||||||
8 | A | 7 | 6 | 1.00 | 16 | 0.375 | |||||||||||
9 | A | 19 | 14 | 1.00 | 18 | 0.778 | |||||||||||
10 | A | 15 | 12 | 1.00 | 18 | 0.667 | |||||||||||
11 | A | 12 | 9 | 1.00 | 16 | 0.562 | |||||||||||
12 | A | 1 | 1 | 1.00 | 18 | 0.056 | |||||||||||
13 | A | 13 | 9 | 1.00 | 18 | 0.500 | |||||||||||
14 | A | 19 | 15 | 1.00 | 18 | 0.833 | |||||||||||
15 | A | 29 | 15 | 1.00 | 18 | 0.833 | |||||||||||
16 | A | 20 | 13 | 1.00 | 18 | 0.722 | |||||||||||
17 | A | 14 | 10 | 1.00 | 16 | 0.625 | |||||||||||
18 | A | 1 | 1 | 1.00 | 18 | 0.056 | |||||||||||
19 | A | 10 | 8 | 1.00 | 18 | 0.444 | |||||||||||
20 | A | 23 | 12 | 1.00 | 18 | 0.667 | |||||||||||
21 | A | 18 | 14 | 1.00 | 18 | 0.778 | |||||||||||
22 | A | 16 | 10 | 0.99 | 16 | 0.625 | |||||||||||
23 | F | 0 | 0 | N/A | 0 | N/A | |||||||||||
24 | A | 19 | 14 | 1.00 | 18 | 0.778 | |||||||||||
25 | A | 110 | 46 | 1.17 | 18 | 2.556 | |||||||||||
26 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
27 | A | 0 | 0 | 0.00 | 0 | 0.000 | |||||||||||
28 | A | 25 | 14 | 1.05 | 18 | 0.778 | |||||||||||
29 | A | 23 | 13 | 1.00 | 16 | 0.812 | |||||||||||
30 | F | 0 | 0 | N/A | 0 | N/A | |||||||||||
31 | A | 35 | 16 | 1.00 | 18 | 0.889 | |||||||||||