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, 34 }
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, 34 }
B grade: { }
C grade: { }
F grade: { }
A grade: { 2, 3, 4, 11, 12, 13, 19, 20, 21 }
B grade: { 1, 5, 6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 22, 23, 24, 25, 26, 27, 28 }
C grade: { }
F grade: { 29, 30, 31, 32, 33, 34 }
A grade: { 1, 2, 3, 4, 10, 11, 12, 13, 18, 19, 20, 21, 28 }
C grade: { }
F grade: { 5, 6, 7, 8, 9, 14, 15, 16, 17, 22, 23, 24, 29, 30, 31, 32, 33, 34 }
A grade: { 1, 2, 3, 4, 5, 10, 11, 12, 13, 18, 19, 20, 21 }
B grade: { 6, 7, 8, 9, 14, 15, 16, 17, 22, 23, 24, 25, 26, 27, 28 }
C grade: { }
F grade: { 29, 30, 31, 32, 33, 34 }
A grade: { 2, 3, 4, 5, 11, 12, 13, 14, 20, 21, 22, 27, 28 }
B grade: { }
C grade: { }
F grade: { 1, 6, 7, 8, 9, 10, 15, 16, 17, 18, 19, 23, 24, 25, 26, 29, 30, 31, 32, 33, 34 }
A grade: { 2, 3, 4, 5, 6, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24 }
B grade: { 1, 7, 8, 9, 10, 11, 17, 18, 19, 25, 26, 27, 28 }
C grade: { }
F grade: { 29, 30, 31, 32, 33, 34 }
A grade: { }
C grade: { }
F grade: { 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, 34 }
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 | B | A | A | F(-1) | B | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 436 | 436 | 391 | 841 | 621 | 668 | 0 | 854 | 713 |
normalized size | 1 | 1.00 | 0.90 | 1.93 | 1.42 | 1.53 | 0.00 | 1.96 | 1.64 |
time (sec) | N/A | 0.408 | 1.309 | 0.009 | 0.475 | 0.757 | 0.000 | 1.305 | 3.903 |
Problem 2 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | A | A | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 324 | 287 | 505 | 387 | 410 | 1510 | 558 | 514 |
normalized size | 1 | 1.00 | 0.89 | 1.56 | 1.19 | 1.27 | 4.66 | 1.72 | 1.59 |
time (sec) | N/A | 0.272 | 0.690 | 0.007 | 0.473 | 0.680 | 157.827 | 1.281 | 3.488 |
Problem 3 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | A | A | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 212 | 184 | 241 | 198 | 204 | 848 | 309 | 351 |
normalized size | 1 | 1.00 | 0.87 | 1.14 | 0.93 | 0.96 | 4.00 | 1.46 | 1.66 |
time (sec) | N/A | 0.173 | 0.314 | 0.006 | 0.441 | 0.688 | 87.368 | 1.247 | 3.301 |
Problem 4 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | A | A | B |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 82 | 91 | 128 | 90 | 354 | 128 | 128 |
normalized size | 1 | 1.00 | 0.71 | 0.79 | 1.11 | 0.78 | 3.08 | 1.11 | 1.11 |
time (sec) | N/A | 0.072 | 0.097 | 0.006 | 0.437 | 0.538 | 18.094 | 1.209 | 2.846 |
Problem 5 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F(-2) | A | A | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 188 | 185 | 338 | 0 | 565 | 192 | 248 | -1 |
normalized size | 1 | 1.00 | 0.98 | 1.80 | 0.00 | 3.01 | 1.02 | 1.32 | -0.01 |
time (sec) | N/A | 0.206 | 0.270 | 0.015 | 0.000 | 0.726 | 66.262 | 1.261 | 0.000 |
Problem 6 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F(-2) | B | F(-1) | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 201 | 244 | 566 | 0 | 1004 | 0 | 271 | -1 |
normalized size | 1 | 1.00 | 1.21 | 2.82 | 0.00 | 5.00 | 0.00 | 1.35 | -0.00 |
time (sec) | N/A | 0.518 | 0.442 | 0.022 | 0.000 | 0.824 | 0.000 | 1.321 | 0.000 |
Problem 7 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F(-2) | B | F(-1) | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 279 | 359 | 1207 | 0 | 1661 | 0 | 529 | -1 |
normalized size | 1 | 1.00 | 1.29 | 4.33 | 0.00 | 5.95 | 0.00 | 1.90 | -0.00 |
time (sec) | N/A | 0.741 | 0.866 | 0.030 | 0.000 | 1.019 | 0.000 | 1.239 | 0.000 |
Problem 8 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F(-2) | B | F(-1) | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 375 | 375 | 493 | 1186 | 0 | 2446 | 0 | 976 | -1 |
normalized size | 1 | 1.00 | 1.31 | 3.16 | 0.00 | 6.52 | 0.00 | 2.60 | -0.00 |
time (sec) | N/A | 0.821 | 1.394 | 0.029 | 0.000 | 1.077 | 0.000 | 1.564 | 0.000 |
Problem 9 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F(-2) | B | F(-1) | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 495 | 495 | 621 | 3252 | 0 | 3624 | 0 | 1512 | -1 |
normalized size | 1 | 1.00 | 1.25 | 6.57 | 0.00 | 7.32 | 0.00 | 3.05 | -0.00 |
time (sec) | N/A | 1.009 | 2.419 | 0.030 | 0.000 | 1.208 | 0.000 | 1.654 | 0.000 |
Problem 10 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | A | A | F(-1) | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 434 | 434 | 391 | 841 | 629 | 677 | 0 | 1067 | -1 |
normalized size | 1 | 1.00 | 0.90 | 1.94 | 1.45 | 1.56 | 0.00 | 2.46 | -0.00 |
time (sec) | N/A | 0.359 | 1.161 | 0.010 | 0.472 | 1.222 | 0.000 | 1.489 | 0.000 |
Problem 11 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | A | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 322 | 287 | 505 | 395 | 419 | 435 | 651 | -1 |
normalized size | 1 | 1.00 | 0.89 | 1.57 | 1.23 | 1.30 | 1.35 | 2.02 | -0.00 |
time (sec) | N/A | 0.259 | 0.667 | 0.009 | 0.465 | 0.877 | 148.595 | 1.373 | 0.000 |
Problem 12 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | A | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 188 | 241 | 206 | 213 | 230 | 323 | -1 |
normalized size | 1 | 1.00 | 0.90 | 1.15 | 0.98 | 1.01 | 1.10 | 1.54 | -0.00 |
time (sec) | N/A | 0.166 | 0.328 | 0.007 | 0.458 | 0.748 | 60.709 | 1.269 | 0.000 |
Problem 13 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | A | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 82 | 91 | 102 | 100 | 114 | 127 | -1 |
normalized size | 1 | 1.00 | 0.73 | 0.81 | 0.90 | 0.88 | 1.01 | 1.12 | -0.01 |
time (sec) | N/A | 0.081 | 0.093 | 0.005 | 0.434 | 0.814 | 20.138 | 1.288 | 0.000 |
Problem 14 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F(-2) | B | A | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 193 | 174 | 366 | 0 | 866 | 172 | 200 | -1 |
normalized size | 1 | 1.00 | 0.90 | 1.90 | 0.00 | 4.49 | 0.89 | 1.04 | -0.01 |
time (sec) | N/A | 0.240 | 0.527 | 0.017 | 0.000 | 0.968 | 85.725 | 1.332 | 0.000 |
Problem 15 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F(-2) | B | F(-1) | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 253 | 283 | 604 | 0 | 1583 | 0 | 388 | -1 |
normalized size | 1 | 1.00 | 1.12 | 2.39 | 0.00 | 6.26 | 0.00 | 1.53 | -0.00 |
time (sec) | N/A | 0.601 | 0.720 | 0.028 | 0.000 | 1.001 | 0.000 | 1.328 | 0.000 |
Problem 16 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F(-2) | B | F(-1) | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 350 | 350 | 482 | 1225 | 0 | 2594 | 0 | 617 | -1 |
normalized size | 1 | 1.00 | 1.38 | 3.50 | 0.00 | 7.41 | 0.00 | 1.76 | -0.00 |
time (sec) | N/A | 0.832 | 1.418 | 0.033 | 0.000 | 1.164 | 0.000 | 1.413 | 0.000 |
Problem 17 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F(-2) | B | F(-1) | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 463 | 463 | 697 | 2108 | 0 | 3834 | 0 | 1085 | -1 |
normalized size | 1 | 1.00 | 1.51 | 4.55 | 0.00 | 8.28 | 0.00 | 2.34 | -0.00 |
time (sec) | N/A | 1.150 | 2.344 | 0.041 | 0.000 | 1.246 | 0.000 | 1.558 | 0.000 |
Problem 18 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | A | A | F(-1) | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 434 | 434 | 391 | 841 | 627 | 689 | 0 | 1030 | -1 |
normalized size | 1 | 1.00 | 0.90 | 1.94 | 1.44 | 1.59 | 0.00 | 2.37 | -0.00 |
time (sec) | N/A | 0.353 | 0.727 | 0.010 | 0.476 | 0.932 | 0.000 | 1.451 | 0.000 |
Problem 19 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | F(-1) | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 322 | 287 | 505 | 393 | 431 | 0 | 622 | -1 |
normalized size | 1 | 1.00 | 0.89 | 1.57 | 1.22 | 1.34 | 0.00 | 1.93 | -0.00 |
time (sec) | N/A | 0.243 | 0.703 | 0.009 | 0.474 | 0.783 | 0.000 | 1.393 | 0.000 |
Problem 20 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | A | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 177 | 241 | 204 | 225 | 230 | 302 | -1 |
normalized size | 1 | 1.00 | 0.84 | 1.15 | 0.97 | 1.07 | 1.10 | 1.44 | -0.00 |
time (sec) | N/A | 0.172 | 0.309 | 0.007 | 0.456 | 0.668 | 82.476 | 1.217 | 0.000 |
Problem 21 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | A | A | A | A | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 75 | 90 | 98 | 110 | 425 | 115 | -1 |
normalized size | 1 | 1.00 | 0.66 | 0.80 | 0.87 | 0.97 | 3.76 | 1.02 | -0.01 |
time (sec) | N/A | 0.072 | 0.094 | 0.005 | 0.439 | 1.036 | 1.418 | 1.229 | 0.000 |
Problem 22 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F(-2) | B | A | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 210 | 464 | 0 | 1287 | 214 | 281 | -1 |
normalized size | 1 | 1.00 | 1.00 | 2.21 | 0.00 | 6.13 | 1.02 | 1.34 | -0.00 |
time (sec) | N/A | 0.313 | 0.661 | 0.019 | 0.000 | 0.767 | 153.497 | 1.313 | 0.000 |
Problem 23 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F(-2) | B | F(-1) | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 336 | 336 | 334 | 730 | 0 | 2444 | 0 | 439 | -1 |
normalized size | 1 | 1.00 | 0.99 | 2.17 | 0.00 | 7.27 | 0.00 | 1.31 | -0.00 |
time (sec) | N/A | 0.791 | 1.045 | 0.028 | 0.000 | 1.056 | 0.000 | 1.417 | 0.000 |
Problem 24 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | F(-2) | B | F(-1) | A | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 438 | 438 | 536 | 1376 | 0 | 3889 | 0 | 767 | -1 |
normalized size | 1 | 1.00 | 1.22 | 3.14 | 0.00 | 8.88 | 0.00 | 1.75 | -0.00 |
time (sec) | N/A | 1.214 | 2.097 | 0.037 | 0.000 | 1.257 | 0.000 | 1.450 | 0.000 |
Problem 25 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | B | B | F(-1) | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 455 | 455 | 418 | 5003 | 1802 | 4115 | 0 | 9032 | -1 |
normalized size | 1 | 1.00 | 0.92 | 11.00 | 3.96 | 9.04 | 0.00 | 19.85 | -0.00 |
time (sec) | N/A | 0.338 | 0.680 | 0.035 | 0.764 | 1.067 | 0.000 | 1.865 | 0.000 |
Problem 26 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | B | B | F(-1) | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 338 | 338 | 308 | 2588 | 1118 | 2258 | 0 | 4972 | -1 |
normalized size | 1 | 1.00 | 0.91 | 7.66 | 3.31 | 6.68 | 0.00 | 14.71 | -0.00 |
time (sec) | N/A | 0.247 | 0.486 | 0.021 | 0.640 | 0.735 | 0.000 | 1.477 | 0.000 |
Problem 27 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | B | B | A | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 226 | 199 | 1039 | 596 | 988 | 13522 | 2224 | -1 |
normalized size | 1 | 1.00 | 0.88 | 4.60 | 2.64 | 4.37 | 59.83 | 9.84 | -0.00 |
time (sec) | N/A | 0.161 | 0.270 | 0.012 | 0.559 | 0.942 | 12.514 | 1.390 | 0.000 |
Problem 28 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | B | A | B | A | B | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 108 | 308 | 234 | 394 | 3798 | 728 | -1 |
normalized size | 1 | 1.00 | 0.86 | 2.44 | 1.86 | 3.13 | 30.14 | 5.78 | -0.01 |
time (sec) | N/A | 0.072 | 0.113 | 0.008 | 0.485 | 0.940 | 4.322 | 1.316 | 0.000 |
Problem 29 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | F | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 203 | 181 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.180 | 0.259 | 0.244 | 0.000 | 1.022 | 0.000 | 0.000 | 0.000 |
Problem 30 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | F | F(-2) | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 220 | 180 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.524 | 0.202 | 0.242 | 0.000 | 0.828 | 0.000 | 0.000 | 0.000 |
Problem 31 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | F | F | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 329 | 188 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.619 | 0.196 | 0.243 | 0.000 | 0.883 | 0.000 | 0.000 | 0.000 |
Problem 32 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | F | F(-2) | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 117 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 1.00 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) | N/A | 0.089 | 0.110 | 0.243 | 0.000 | 0.825 | 0.000 | 0.000 | 0.000 |
Problem 33 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | F | F(-2) | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 266 | 187 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 0.309 | 0.209 | 0.245 | 0.000 | 0.789 | 0.000 | 0.000 | 0.000 |
Problem 34 | Optimal | Rubi | Mathematica | Maple | Maxima | Fricas | Sympy | Giac | Mupad |
grade | A | A | A | F | F | F | F(-2) | F | F |
verified | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 610 | 605 | 254 | 0 | 0 | 0 | 0 | 0 | -1 |
normalized size | 1 | 0.99 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 |
time (sec) | N/A | 1.069 | 0.265 | 0.256 | 0.000 | 1.126 | 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 [9] had the largest ratio of [.1875]
# | grade |
|
|
|
|
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\) | |||||||||||
1 | A | 2 | 1 | 1.00 | 32 | 0.031 | |||||||||||
2 | A | 2 | 1 | 1.00 | 32 | 0.031 | |||||||||||
3 | A | 2 | 1 | 1.00 | 30 | 0.033 | |||||||||||
4 | A | 2 | 1 | 1.00 | 25 | 0.040 | |||||||||||
5 | A | 4 | 3 | 1.00 | 32 | 0.094 | |||||||||||
6 | A | 5 | 4 | 1.00 | 32 | 0.125 | |||||||||||
7 | A | 5 | 5 | 1.00 | 32 | 0.156 | |||||||||||
8 | A | 5 | 5 | 1.00 | 32 | 0.156 | |||||||||||
9 | A | 6 | 6 | 1.00 | 32 | 0.188 | |||||||||||
10 | A | 2 | 1 | 1.00 | 32 | 0.031 | |||||||||||
11 | A | 2 | 1 | 1.00 | 32 | 0.031 | |||||||||||
12 | A | 2 | 1 | 1.00 | 30 | 0.033 | |||||||||||
13 | A | 2 | 1 | 1.00 | 25 | 0.040 | |||||||||||
14 | A | 6 | 4 | 1.00 | 32 | 0.125 | |||||||||||
15 | A | 5 | 4 | 1.00 | 32 | 0.125 | |||||||||||
16 | A | 5 | 5 | 1.00 | 32 | 0.156 | |||||||||||
17 | A | 6 | 6 | 1.00 | 32 | 0.188 | |||||||||||
18 | A | 2 | 1 | 1.00 | 32 | 0.031 | |||||||||||
19 | A | 2 | 1 | 1.00 | 32 | 0.031 | |||||||||||
20 | A | 2 | 1 | 1.00 | 30 | 0.033 | |||||||||||
21 | A | 2 | 1 | 1.00 | 25 | 0.040 | |||||||||||
22 | A | 4 | 3 | 1.00 | 32 | 0.094 | |||||||||||
23 | A | 5 | 4 | 1.00 | 32 | 0.125 | |||||||||||
24 | A | 6 | 5 | 1.00 | 32 | 0.156 | |||||||||||
25 | A | 2 | 1 | 1.00 | 30 | 0.033 | |||||||||||
26 | A | 2 | 1 | 1.00 | 30 | 0.033 | |||||||||||
27 | A | 2 | 1 | 1.00 | 28 | 0.036 | |||||||||||
28 | A | 2 | 1 | 1.00 | 23 | 0.043 | |||||||||||
29 | A | 3 | 2 | 1.00 | 30 | 0.067 | |||||||||||
30 | A | 4 | 4 | 1.00 | 30 | 0.133 | |||||||||||
31 | A | 4 | 4 | 1.00 | 30 | 0.133 | |||||||||||
32 | A | 3 | 3 | 1.00 | 20 | 0.150 | |||||||||||
33 | A | 4 | 4 | 0.99 | 25 | 0.160 | |||||||||||
34 | A | 5 | 5 | 0.99 | 30 | 0.167 | |||||||||||