Detailed conclusion table per each integral is given by the 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 as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 323 | 323 | 410 | 372 | 0 | 8169 | 0 | 0 | 39682 |
N.S. |
1 | 1.00 | 1.27 | 1.15 | 0.00 | 25.29 | 0.00 | 0.00 | 122.85 |
time (sec) |
N/A | 2.244 | 1.223 | 3.041 | 0.000 | 4.768 | 0.000 | 0.000 | 25.962 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 298 | 298 | 358 | 305 | 0 | 6531 | 0 | 0 | 21407 |
N.S. |
1 | 1.00 | 1.20 | 1.02 | 0.00 | 21.92 | 0.00 | 0.00 | 71.84 |
time (sec) |
N/A | 2.268 | 0.748 | 2.213 | 0.000 | 2.255 | 0.000 | 0.000 | 25.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 253 | 253 | 310 | 252 | 0 | 4985 | 0 | 0 | 15461 |
N.S. |
1 | 1.00 | 1.23 | 1.00 | 0.00 | 19.70 | 0.00 | 0.00 | 61.11 |
time (sec) |
N/A | 1.018 | 1.364 | 1.612 | 0.000 | 0.981 | 0.000 | 0.000 | 28.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 226 | 226 | 268 | 217 | 0 | 3519 | 0 | 0 | 5048 |
N.S. |
1 | 1.00 | 1.19 | 0.96 | 0.00 | 15.57 | 0.00 | 0.00 | 22.34 |
time (sec) |
N/A | 0.700 | 1.370 | 1.042 | 0.000 | 0.572 | 0.000 | 0.000 | 24.568 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 221 | 229 | 233 | 247 | 0 | 3495 | 0 | 0 | 5064 |
N.S. |
1 | 1.04 | 1.05 | 1.12 | 0.00 | 15.81 | 0.00 | 0.00 | 22.91 |
time (sec) |
N/A | 0.486 | 0.997 | 1.015 | 0.000 | 0.508 | 0.000 | 0.000 | 24.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 244 | 244 | 306 | 284 | 0 | 5296 | 0 | 0 | 11540 |
N.S. |
1 | 1.00 | 1.25 | 1.16 | 0.00 | 21.70 | 0.00 | 0.00 | 47.30 |
time (sec) |
N/A | 0.828 | 1.390 | 1.995 | 0.000 | 73.246 | 0.000 | 0.000 | 26.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 271 | 271 | 388 | 337 | 0 | 6851 | 0 | 0 | 16102 |
N.S. |
1 | 1.00 | 1.43 | 1.24 | 0.00 | 25.28 | 0.00 | 0.00 | 59.42 |
time (sec) |
N/A | 0.962 | 2.521 | 2.834 | 0.000 | 258.462 | 0.000 | 0.000 | 25.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 331 | 331 | 481 | 414 | 0 | 0 | 0 | 0 | 21909 |
N.S. |
1 | 1.00 | 1.45 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 66.19 |
time (sec) |
N/A | 2.367 | 2.945 | 4.324 | 0.000 | 0.000 | 0.000 | 0.000 | 24.743 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 73 | 79 | 0 | 276 | 0 | 78 | 229 |
N.S. |
1 | 1.00 | 0.96 | 1.04 | 0.00 | 3.63 | 0.00 | 1.03 | 3.01 |
time (sec) |
N/A | 0.329 | 0.129 | 0.923 | 0.000 | 0.383 | 0.000 | 0.319 | 0.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 230 | 230 | 314 | 178 | 0 | 971 | 0 | 0 | 11164 |
N.S. |
1 | 1.00 | 1.37 | 0.77 | 0.00 | 4.22 | 0.00 | 0.00 | 48.54 |
time (sec) |
N/A | 0.747 | 0.582 | 0.908 | 0.000 | 0.388 | 0.000 | 0.000 | 29.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 36 | 0 | 139 | 99 | 35 | 47 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 0.00 | 3.97 | 2.83 | 1.00 | 1.34 |
time (sec) |
N/A | 0.213 | 0.017 | 0.523 | 0.000 | 0.348 | 1.487 | 0.305 | 15.685 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 125 | 119 | 118 | 0 | 482 | 0 | 131 | 1001 |
N.S. |
1 | 0.98 | 0.93 | 0.92 | 0.00 | 3.77 | 0.00 | 1.02 | 7.82 |
time (sec) |
N/A | 0.396 | 0.237 | 0.855 | 0.000 | 0.789 | 0.000 | 0.317 | 18.912 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 324 | 324 | 407 | 417 | 0 | 16739 | 0 | 0 | 37118 |
N.S. |
1 | 1.00 | 1.26 | 1.29 | 0.00 | 51.66 | 0.00 | 0.00 | 114.56 |
time (sec) |
N/A | 1.580 | 1.200 | 7.063 | 0.000 | 3.952 | 0.000 | 0.000 | 28.270 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 206 | 203 | 202 | 236 | 0 | 1244 | 0 | 377 | 2743 |
N.S. |
1 | 0.99 | 0.98 | 1.15 | 0.00 | 6.04 | 0.00 | 1.83 | 13.32 |
time (sec) |
N/A | 0.575 | 0.762 | 2.186 | 0.000 | 5.874 | 0.000 | 0.362 | 34.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 15 | 16 | 15 | 17 | 15 | 17 | 9 |
N.S. |
1 | 1.00 | 0.71 | 0.76 | 0.71 | 0.81 | 0.71 | 0.81 | 0.43 |
time (sec) |
N/A | 0.216 | 0.011 | 0.497 | 0.227 | 0.268 | 0.088 | 0.337 | 0.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 9 | 14 | 13 | 17 | 12 | 17 | 9 |
N.S. |
1 | 1.00 | 0.53 | 0.82 | 0.76 | 1.00 | 0.71 | 1.00 | 0.53 |
time (sec) |
N/A | 0.216 | 0.112 | 0.401 | 0.246 | 0.280 | 0.093 | 0.380 | 15.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 15 | 16 | 15 | 17 | 15 | 17 | 9 |
N.S. |
1 | 1.00 | 0.71 | 0.76 | 0.71 | 0.81 | 0.71 | 0.81 | 0.43 |
time (sec) |
N/A | 0.216 | 0.100 | 0.490 | 0.239 | 0.306 | 0.090 | 0.352 | 0.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 11 | 9 | 6 | 5 | 5 | 5 | 5 | 5 |
N.S. |
1 | 1.22 | 1.00 | 0.67 | 0.56 | 0.56 | 0.56 | 0.56 | 0.56 |
time (sec) |
N/A | 0.196 | 0.012 | 2.259 | 0.314 | 0.284 | 0.110 | 0.306 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 5 | 5 | 5 | 6 | 5 | 5 | 5 | 5 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.196 | 0.012 | 1.743 | 0.360 | 0.270 | 0.103 | 0.285 | 0.073 |