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 | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 219 | 181 | 622 | 0 | 1045 | 0 | 328 | 780 | 0 |
N.S. |
1 | 1.00 | 0.82 | 2.83 | 0.00 | 4.75 | 0.00 | 1.49 | 3.55 | 0.00 |
time (sec) |
N/A | 0.775 | 0.787 | 2.207 | 0.000 | 0.112 | 0.000 | 0.361 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 284 | 246 | 1025 | 0 | 1606 | 0 | 587 | 1302 | 0 |
N.S. |
1 | 0.96 | 0.83 | 3.46 | 0.00 | 5.43 | 0.00 | 1.98 | 4.40 | 0.00 |
time (sec) |
N/A | 0.911 | 1.384 | 2.202 | 0.000 | 0.155 | 0.000 | 0.379 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 375 | 360 | 330 | 1533 | 0 | 2258 | 0 | 1013 | 1916 | 0 |
N.S. |
1 | 0.96 | 0.88 | 4.09 | 0.00 | 6.02 | 0.00 | 2.70 | 5.11 | 0.00 |
time (sec) |
N/A | 1.056 | 1.756 | 2.271 | 0.000 | 0.242 | 0.000 | 0.372 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 421 | 388 | 364 | 529 | 875 | 880 | 0 | 12772 | 944 | 863 |
N.S. |
1 | 0.92 | 0.86 | 1.26 | 2.08 | 2.09 | 0.00 | 30.34 | 2.24 | 2.05 |
time (sec) |
N/A | 1.112 | 0.479 | 2.106 | 0.107 | 0.127 | 0.000 | 0.480 | 0.228 | 12.978 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 343 | 322 | 264 | 361 | 676 | 678 | 0 | 7604 | 704 | 637 |
N.S. |
1 | 0.94 | 0.77 | 1.05 | 1.97 | 1.98 | 0.00 | 22.17 | 2.05 | 1.86 |
time (sec) |
N/A | 0.984 | 0.345 | 2.020 | 0.113 | 0.109 | 0.000 | 0.410 | 0.240 | 12.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 254 | 183 | 229 | 502 | 505 | 0 | 3758 | 500 | 441 |
N.S. |
1 | 0.95 | 0.69 | 0.86 | 1.88 | 1.89 | 0.00 | 14.07 | 1.87 | 1.65 |
time (sec) |
N/A | 0.813 | 0.240 | 2.020 | 0.097 | 0.090 | 0.000 | 0.373 | 0.250 | 12.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 188 | 121 | 133 | 320 | 354 | 0 | 1123 | 332 | 239 |
N.S. |
1 | 0.99 | 0.64 | 0.70 | 1.68 | 1.86 | 0.00 | 5.91 | 1.75 | 1.26 |
time (sec) |
N/A | 0.694 | 0.161 | 1.963 | 0.080 | 0.098 | 0.000 | 0.383 | 0.221 | 11.753 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 118 | 78 | 73 | 197 | 229 | 0 | 540 | 200 | 133 |
N.S. |
1 | 1.02 | 0.67 | 0.63 | 1.70 | 1.97 | 0.00 | 4.66 | 1.72 | 1.15 |
time (sec) |
N/A | 0.558 | 0.119 | 2.122 | 0.079 | 0.088 | 0.000 | 0.354 | 0.233 | 11.450 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 241 | 194 | 593 | 0 | 658 | 0 | 316 | 392 | 0 |
N.S. |
1 | 0.96 | 0.78 | 2.37 | 0.00 | 2.63 | 0.00 | 1.26 | 1.57 | 0.00 |
time (sec) |
N/A | 0.843 | 0.544 | 1.717 | 0.000 | 0.109 | 0.000 | 0.340 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 276 | 192 | 687 | 0 | 641 | 0 | 323 | 442 | 0 |
N.S. |
1 | 1.07 | 0.74 | 2.66 | 0.00 | 2.48 | 0.00 | 1.25 | 1.71 | 0.00 |
time (sec) |
N/A | 0.924 | 0.707 | 1.625 | 0.000 | 0.115 | 0.000 | 0.372 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 270 | 192 | 657 | 0 | 1000 | 0 | 334 | 788 | 0 |
N.S. |
1 | 1.05 | 0.75 | 2.56 | 0.00 | 3.89 | 0.00 | 1.30 | 3.07 | 0.00 |
time (sec) |
N/A | 0.939 | 0.785 | 1.538 | 0.000 | 0.119 | 0.000 | 0.388 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 272 | 255 | 991 | 0 | 1456 | 0 | 592 | 1239 | 0 |
N.S. |
1 | 0.95 | 0.89 | 3.48 | 0.00 | 5.11 | 0.00 | 2.08 | 4.35 | 0.00 |
time (sec) |
N/A | 0.892 | 1.386 | 1.563 | 0.000 | 0.136 | 0.000 | 0.437 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 338 | 339 | 1509 | 0 | 2106 | 0 | 983 | 1836 | 0 |
N.S. |
1 | 0.93 | 0.93 | 4.13 | 0.00 | 5.77 | 0.00 | 2.69 | 5.03 | 0.00 |
time (sec) |
N/A | 1.044 | 2.327 | 1.501 | 0.000 | 0.215 | 0.000 | 0.394 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 496 | 456 | 484 | 733 | 1364 | 1370 | 0 | 29765 | 1532 | 1307 |
N.S. |
1 | 0.92 | 0.98 | 1.48 | 2.75 | 2.76 | 0.00 | 60.01 | 3.09 | 2.64 |
time (sec) |
N/A | 1.297 | 0.694 | 2.119 | 0.127 | 0.208 | 0.000 | 0.629 | 0.232 | 14.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 421 | 389 | 367 | 529 | 1108 | 1112 | 0 | 21712 | 1220 | 1023 |
N.S. |
1 | 0.92 | 0.87 | 1.26 | 2.63 | 2.64 | 0.00 | 51.57 | 2.90 | 2.43 |
time (sec) |
N/A | 1.150 | 0.537 | 1.955 | 0.109 | 0.158 | 0.000 | 0.519 | 0.223 | 13.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 343 | 321 | 264 | 361 | 878 | 881 | 0 | 11336 | 944 | 769 |
N.S. |
1 | 0.94 | 0.77 | 1.05 | 2.56 | 2.57 | 0.00 | 33.05 | 2.75 | 2.24 |
time (sec) |
N/A | 0.999 | 0.376 | 1.993 | 0.120 | 0.122 | 0.000 | 0.430 | 0.261 | 12.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 255 | 183 | 229 | 638 | 675 | 0 | 5116 | 704 | 491 |
N.S. |
1 | 0.96 | 0.69 | 0.86 | 2.39 | 2.53 | 0.00 | 19.16 | 2.64 | 1.84 |
time (sec) |
N/A | 0.843 | 0.321 | 2.089 | 0.074 | 0.110 | 0.000 | 0.460 | 0.212 | 11.697 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 188 | 121 | 133 | 465 | 500 | 0 | 3083 | 500 | 320 |
N.S. |
1 | 0.99 | 0.64 | 0.70 | 2.45 | 2.63 | 0.00 | 16.23 | 2.63 | 1.68 |
time (sec) |
N/A | 0.718 | 0.202 | 2.009 | 0.078 | 0.095 | 0.000 | 0.411 | 0.204 | 11.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 118 | 78 | 73 | 314 | 345 | 0 | 1540 | 331 | 170 |
N.S. |
1 | 1.02 | 0.67 | 0.63 | 2.71 | 2.97 | 0.00 | 13.28 | 2.85 | 1.47 |
time (sec) |
N/A | 0.570 | 0.162 | 1.961 | 0.076 | 0.089 | 0.000 | 0.435 | 0.205 | 11.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 316 | 299 | 253 | 948 | 0 | 951 | 0 | 560 | 688 | 0 |
N.S. |
1 | 0.95 | 0.80 | 3.00 | 0.00 | 3.01 | 0.00 | 1.77 | 2.18 | 0.00 |
time (sec) |
N/A | 0.975 | 0.677 | 1.578 | 0.000 | 0.108 | 0.000 | 0.405 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 334 | 254 | 1128 | 0 | 992 | 0 | 579 | 836 | 0 |
N.S. |
1 | 1.01 | 0.77 | 3.41 | 0.00 | 3.00 | 0.00 | 1.75 | 2.53 | 0.00 |
time (sec) |
N/A | 1.067 | 0.964 | 1.497 | 0.000 | 0.111 | 0.000 | 0.426 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 341 | 329 | 254 | 1181 | 0 | 961 | 0 | 572 | 809 | 0 |
N.S. |
1 | 0.96 | 0.74 | 3.46 | 0.00 | 2.82 | 0.00 | 1.68 | 2.37 | 0.00 |
time (sec) |
N/A | 1.074 | 1.260 | 1.542 | 0.000 | 0.127 | 0.000 | 0.393 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 323 | 257 | 1062 | 0 | 1390 | 0 | 596 | 1230 | 0 |
N.S. |
1 | 0.99 | 0.79 | 3.27 | 0.00 | 4.28 | 0.00 | 1.83 | 3.78 | 0.00 |
time (sec) |
N/A | 1.051 | 1.415 | 1.500 | 0.000 | 0.167 | 0.000 | 0.409 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 353 | 325 | 343 | 1509 | 0 | 1912 | 0 | 956 | 1756 | 0 |
N.S. |
1 | 0.92 | 0.97 | 4.27 | 0.00 | 5.42 | 0.00 | 2.71 | 4.97 | 0.00 |
time (sec) |
N/A | 1.030 | 2.244 | 1.491 | 0.000 | 0.183 | 0.000 | 0.424 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 430 | 391 | 442 | 2079 | 0 | 2652 | 0 | 1449 | 2434 | 0 |
N.S. |
1 | 0.91 | 1.03 | 4.83 | 0.00 | 6.17 | 0.00 | 3.37 | 5.66 | 0.00 |
time (sec) |
N/A | 1.199 | 3.335 | 1.527 | 0.000 | 0.314 | 0.000 | 0.486 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 255 | 181 | 215 | 319 | 235 | 0 | 405 | 200 | 246 |
N.S. |
1 | 0.96 | 0.68 | 0.81 | 1.20 | 0.89 | 0.00 | 1.53 | 0.75 | 0.93 |
time (sec) |
N/A | 0.839 | 0.196 | 1.863 | 0.083 | 0.080 | 0.000 | 0.330 | 0.216 | 11.422 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 188 | 118 | 119 | 201 | 143 | 0 | 188 | 104 | 149 |
N.S. |
1 | 1.00 | 0.63 | 0.63 | 1.07 | 0.76 | 0.00 | 1.00 | 0.55 | 0.79 |
time (sec) |
N/A | 0.690 | 0.121 | 1.947 | 0.064 | 0.082 | 0.000 | 0.331 | 0.218 | 11.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 117 | 63 | 59 | 110 | 79 | 0 | 68 | 44 | 89 |
N.S. |
1 | 1.03 | 0.55 | 0.52 | 0.96 | 0.69 | 0.00 | 0.60 | 0.39 | 0.78 |
time (sec) |
N/A | 0.557 | 0.088 | 1.473 | 0.059 | 0.077 | 0.000 | 0.340 | 0.222 | 10.911 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 137 | 153 | 0 | 444 | 0 | 81 | 138 | 0 |
N.S. |
1 | 1.00 | 1.05 | 1.17 | 0.00 | 3.39 | 0.00 | 0.62 | 1.05 | 0.00 |
time (sec) |
N/A | 0.581 | 0.282 | 1.491 | 0.000 | 0.087 | 0.000 | 0.315 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 153 | 320 | 0 | 700 | 0 | 156 | 398 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.09 | 0.00 | 4.58 | 0.00 | 1.02 | 2.60 | 0.00 |
time (sec) |
N/A | 0.644 | 0.579 | 1.678 | 0.000 | 0.096 | 0.000 | 0.295 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 232 | 196 | 622 | 0 | 1170 | 0 | 357 | 828 | 0 |
N.S. |
1 | 1.00 | 0.84 | 2.67 | 0.00 | 5.02 | 0.00 | 1.53 | 3.55 | 0.00 |
time (sec) |
N/A | 0.797 | 0.771 | 1.555 | 0.000 | 0.132 | 0.000 | 0.323 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 337 | 353 | 245 | 361 | 317 | 374 | 0 | 692 | 334 | 398 |
N.S. |
1 | 1.05 | 0.73 | 1.07 | 0.94 | 1.11 | 0.00 | 2.05 | 0.99 | 1.18 |
time (sec) |
N/A | 1.007 | 0.293 | 1.567 | 0.088 | 0.094 | 0.000 | 0.357 | 0.213 | 11.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 286 | 168 | 229 | 203 | 257 | 0 | 393 | 202 | 267 |
N.S. |
1 | 1.09 | 0.64 | 0.87 | 0.77 | 0.98 | 0.00 | 1.49 | 0.77 | 1.02 |
time (sec) |
N/A | 0.879 | 0.197 | 1.515 | 0.084 | 0.088 | 0.000 | 0.358 | 0.244 | 11.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 219 | 105 | 133 | 112 | 165 | 0 | 196 | 106 | 167 |
N.S. |
1 | 1.18 | 0.56 | 0.72 | 0.60 | 0.89 | 0.00 | 1.05 | 0.57 | 0.90 |
time (sec) |
N/A | 0.713 | 0.124 | 1.669 | 0.080 | 0.084 | 0.000 | 0.305 | 0.267 | 10.811 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 148 | 60 | 72 | 62 | 102 | 0 | 73 | 45 | 107 |
N.S. |
1 | 1.32 | 0.54 | 0.64 | 0.55 | 0.91 | 0.00 | 0.65 | 0.40 | 0.96 |
time (sec) |
N/A | 0.555 | 0.078 | 1.621 | 0.072 | 0.084 | 0.000 | 0.294 | 0.216 | 10.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 138 | 199 | 0 | 778 | 0 | 121 | 198 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.28 | 0.00 | 5.02 | 0.00 | 0.78 | 1.28 | 0.00 |
time (sec) |
N/A | 0.599 | 0.310 | 1.644 | 0.000 | 0.103 | 0.000 | 0.336 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 228 | 172 | 471 | 0 | 1353 | 0 | 288 | 550 | 0 |
N.S. |
1 | 1.02 | 0.77 | 2.11 | 0.00 | 6.07 | 0.00 | 1.29 | 2.47 | 0.00 |
time (sec) |
N/A | 0.766 | 0.687 | 1.738 | 0.000 | 0.168 | 0.000 | 0.369 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 304 | 255 | 816 | 0 | 1978 | 0 | 467 | 992 | 0 |
N.S. |
1 | 1.00 | 0.84 | 2.69 | 0.00 | 6.53 | 0.00 | 1.54 | 3.27 | 0.00 |
time (sec) |
N/A | 0.904 | 1.341 | 1.629 | 0.000 | 0.317 | 0.000 | 0.373 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 382 | 379 | 339 | 1216 | 0 | 2834 | 0 | 776 | 1500 | 0 |
N.S. |
1 | 0.99 | 0.89 | 3.18 | 0.00 | 7.42 | 0.00 | 2.03 | 3.93 | 0.00 |
time (sec) |
N/A | 1.056 | 2.050 | 1.665 | 0.000 | 0.675 | 0.000 | 0.351 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 417 | 420 | 366 | 529 | 511 | 578 | 0 | 975 | 516 | 596 |
N.S. |
1 | 1.01 | 0.88 | 1.27 | 1.23 | 1.39 | 0.00 | 2.34 | 1.24 | 1.43 |
time (sec) |
N/A | 1.193 | 0.486 | 1.581 | 0.103 | 0.258 | 0.000 | 0.387 | 0.224 | 12.565 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 339 | 353 | 263 | 361 | 363 | 428 | 0 | 616 | 348 | 435 |
N.S. |
1 | 1.04 | 0.78 | 1.06 | 1.07 | 1.26 | 0.00 | 1.82 | 1.03 | 1.28 |
time (sec) |
N/A | 1.056 | 0.321 | 1.575 | 0.111 | 0.197 | 0.000 | 0.370 | 0.260 | 12.346 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 283 | 180 | 229 | 246 | 308 | 0 | 358 | 215 | 314 |
N.S. |
1 | 1.08 | 0.68 | 0.87 | 0.94 | 1.17 | 0.00 | 1.36 | 0.82 | 1.19 |
time (sec) |
N/A | 0.875 | 0.224 | 1.678 | 0.087 | 0.137 | 0.000 | 0.356 | 0.230 | 12.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 218 | 117 | 132 | 157 | 216 | 0 | 178 | 119 | 214 |
N.S. |
1 | 1.17 | 0.63 | 0.71 | 0.84 | 1.16 | 0.00 | 0.96 | 0.64 | 1.15 |
time (sec) |
N/A | 0.716 | 0.142 | 1.533 | 0.087 | 0.102 | 0.000 | 0.338 | 0.237 | 11.971 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 152 | 76 | 72 | 103 | 154 | 0 | 76 | 60 | 154 |
N.S. |
1 | 1.33 | 0.67 | 0.63 | 0.90 | 1.35 | 0.00 | 0.67 | 0.53 | 1.35 |
time (sec) |
N/A | 0.564 | 0.098 | 1.563 | 0.100 | 0.091 | 0.000 | 0.362 | 0.257 | 11.920 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 229 | 185 | 477 | 0 | 1439 | 0 | 233 | 588 | 0 |
N.S. |
1 | 1.04 | 0.84 | 2.16 | 0.00 | 6.51 | 0.00 | 1.05 | 2.66 | 0.00 |
time (sec) |
N/A | 0.734 | 0.695 | 1.538 | 0.000 | 0.211 | 0.000 | 0.377 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 316 | 248 | 896 | 0 | 2108 | 0 | 370 | 1124 | 0 |
N.S. |
1 | 1.09 | 0.85 | 3.08 | 0.00 | 7.24 | 0.00 | 1.27 | 3.86 | 0.00 |
time (sec) |
N/A | 0.933 | 1.265 | 1.608 | 0.000 | 0.442 | 0.000 | 0.362 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 377 | 377 | 329 | 1520 | 0 | 3098 | 0 | 614 | 1902 | 0 |
N.S. |
1 | 1.00 | 0.87 | 4.03 | 0.00 | 8.22 | 0.00 | 1.63 | 5.05 | 0.00 |
time (sec) |
N/A | 1.115 | 1.832 | 1.612 | 0.000 | 1.577 | 0.000 | 0.362 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 459 | 452 | 438 | 2003 | 0 | 4086 | 0 | 1067 | 2504 | 0 |
N.S. |
1 | 0.98 | 0.95 | 4.36 | 0.00 | 8.90 | 0.00 | 2.32 | 5.46 | 0.00 |
time (sec) |
N/A | 1.262 | 3.219 | 1.576 | 0.000 | 3.368 | 0.000 | 0.391 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 149 | 42 | 0 | 25 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 2.92 | 0.82 | 0.00 | 0.49 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.289 | 31.539 | 1.115 | 0.000 | 0.073 | 0.000 | 0.000 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 226 | 170 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.30 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.879 | 1.193 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.097 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 215 | 149 | 0 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.24 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.879 | 0.719 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 212 | 155 | 0 | 0 | 0 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.24 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.840 | 0.750 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.472 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 210 | 176 | 0 | 0 | 0 | 0 | 0 | 242 | 0 |
N.S. |
1 | 1.18 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.819 | 0.851 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.652 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 229 | 185 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.27 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.528 | 1.110 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 232 | 193 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.29 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.505 | 1.420 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 34 | 56 | 64 | 66 | 173 | 162 | 67 | 79 |
N.S. |
1 | 1.00 | 0.81 | 1.33 | 1.52 | 1.57 | 4.12 | 3.86 | 1.60 | 1.88 |
time (sec) |
N/A | 0.194 | 0.653 | 5.302 | 0.097 | 0.088 | 7.797 | 0.372 | 0.206 | 10.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 48 | 91 | 0 | 132 | 0 | 412 | 254 | 138 |
N.S. |
1 | 1.00 | 0.75 | 1.42 | 0.00 | 2.06 | 0.00 | 6.44 | 3.97 | 2.16 |
time (sec) |
N/A | 0.201 | 0.542 | 5.491 | 0.000 | 0.091 | 0.000 | 0.371 | 0.195 | 11.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 153 | 153 | 217 | 268 | 448 | 0 | 299 | 1017 | 224 |
N.S. |
1 | 1.07 | 1.07 | 1.52 | 1.87 | 3.13 | 0.00 | 2.09 | 7.11 | 1.57 |
time (sec) |
N/A | 0.426 | 0.122 | 1.505 | 0.061 | 0.101 | 0.000 | 0.280 | 0.196 | 11.386 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 527 | 562 | 472 | 1323 | 0 | 1274 | 0 | 635 | 44 | 0 |
N.S. |
1 | 1.07 | 0.90 | 2.51 | 0.00 | 2.42 | 0.00 | 1.20 | 0.08 | 0.00 |
time (sec) |
N/A | 1.036 | 13.948 | 2.259 | 0.000 | 0.637 | 0.000 | 0.344 | 200.043 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 341 | 367 | 691 | 0 | 812 | 0 | 366 | 846 | 0 |
N.S. |
1 | 1.09 | 1.17 | 2.20 | 0.00 | 2.59 | 0.00 | 1.17 | 2.69 | 0.00 |
time (sec) |
N/A | 0.637 | 11.326 | 2.023 | 0.000 | 0.199 | 0.000 | 0.322 | 0.357 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 186 | 193 | 299 | 0 | 502 | 0 | 192 | 398 | 0 |
N.S. |
1 | 1.09 | 1.13 | 1.75 | 0.00 | 2.94 | 0.00 | 1.12 | 2.33 | 0.00 |
time (sec) |
N/A | 0.342 | 1.307 | 1.812 | 0.000 | 0.100 | 0.000 | 0.321 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 131 | 112 | 131 | 0 | 337 | 0 | 114 | 135 | 0 |
N.S. |
1 | 1.15 | 0.98 | 1.15 | 0.00 | 2.96 | 0.00 | 1.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.255 | 0.098 | 1.850 | 0.000 | 0.089 | 0.000 | 0.306 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 199 | 247 | 660 | 0 | 1689 | 0 | 216 | 410 | 0 |
N.S. |
1 | 1.21 | 1.50 | 4.00 | 0.00 | 10.24 | 0.00 | 1.31 | 2.48 | 0.00 |
time (sec) |
N/A | 0.414 | 1.076 | 2.351 | 0.000 | 8.908 | 0.000 | 0.447 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 191 | 147 | 1748 | 0 | 1113 | 0 | 744 | 1453 | 0 |
N.S. |
1 | 1.27 | 0.98 | 11.65 | 0.00 | 7.42 | 0.00 | 4.96 | 9.69 | 0.00 |
time (sec) |
N/A | 0.416 | 10.213 | 2.507 | 0.000 | 0.971 | 0.000 | 0.728 | 0.413 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 309 | 235 | 3574 | 0 | 2441 | 0 | 1848 | 11755 | 0 |
N.S. |
1 | 1.20 | 0.91 | 13.85 | 0.00 | 9.46 | 0.00 | 7.16 | 45.56 | 0.00 |
time (sec) |
N/A | 0.616 | 10.480 | 3.046 | 0.000 | 14.732 | 0.000 | 0.387 | 2.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 400 | 479 | 352 | 5581 | 0 | 0 | 0 | 6024 | 25163 | 0 |
N.S. |
1 | 1.20 | 0.88 | 13.95 | 0.00 | 0.00 | 0.00 | 15.06 | 62.91 | 0.00 |
time (sec) |
N/A | 0.988 | 11.223 | 3.740 | 0.000 | 0.000 | 0.000 | 0.553 | 17.695 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 716 | 650 | 753 | 1980 | 0 | 2430 | 0 | 1337 | 44 | 0 |
N.S. |
1 | 0.91 | 1.05 | 2.77 | 0.00 | 3.39 | 0.00 | 1.87 | 0.06 | 0.00 |
time (sec) |
N/A | 1.192 | 3.647 | 2.475 | 0.000 | 1.280 | 0.000 | 0.417 | 200.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 449 | 430 | 493 | 1069 | 0 | 1592 | 3509 | 828 | 44 | 0 |
N.S. |
1 | 0.96 | 1.10 | 2.38 | 0.00 | 3.55 | 7.82 | 1.84 | 0.10 | 0.00 |
time (sec) |
N/A | 0.747 | 2.341 | 2.197 | 0.000 | 0.583 | 66.022 | 0.350 | 200.036 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 275 | 299 | 491 | 0 | 960 | 1853 | 449 | 1003 | 0 |
N.S. |
1 | 1.03 | 1.12 | 1.84 | 0.00 | 3.60 | 6.94 | 1.68 | 3.76 | 0.00 |
time (sec) |
N/A | 0.425 | 1.063 | 1.806 | 0.000 | 0.159 | 8.107 | 0.330 | 0.322 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 215 | 180 | 230 | 0 | 532 | 751 | 229 | 400 | 0 |
N.S. |
1 | 1.16 | 0.97 | 1.24 | 0.00 | 2.86 | 4.04 | 1.23 | 2.15 | 0.00 |
time (sec) |
N/A | 0.324 | 0.106 | 1.859 | 0.000 | 0.096 | 2.958 | 0.315 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 294 | 358 | 302 | 1240 | 0 | 0 | 0 | 0 | 1106 | 0 |
N.S. |
1 | 1.22 | 1.03 | 4.22 | 0.00 | 0.00 | 0.00 | 0.00 | 3.76 | 0.00 |
time (sec) |
N/A | 0.943 | 1.213 | 2.294 | 0.000 | 0.000 | 0.000 | 0.000 | 0.803 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 325 | 258 | 3015 | 0 | 0 | 0 | 0 | 2635 | 0 |
N.S. |
1 | 1.25 | 0.99 | 11.55 | 0.00 | 0.00 | 0.00 | 0.00 | 10.10 | 0.00 |
time (sec) |
N/A | 0.704 | 1.671 | 2.671 | 0.000 | 0.000 | 0.000 | 0.000 | 19.715 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 364 | 447 | 322 | 6009 | 0 | 0 | 0 | 2052 | 14401 | 0 |
N.S. |
1 | 1.23 | 0.88 | 16.51 | 0.00 | 0.00 | 0.00 | 5.64 | 39.56 | 0.00 |
time (sec) |
N/A | 0.917 | 2.572 | 3.046 | 0.000 | 0.000 | 0.000 | 1.177 | 9.330 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 272 | 326 | 314 | 10984 | 0 | 3425 | 0 | 5573 | 44 | 0 |
N.S. |
1 | 1.20 | 1.15 | 40.38 | 0.00 | 12.59 | 0.00 | 20.49 | 0.16 | 0.00 |
time (sec) |
N/A | 0.556 | 2.787 | 3.487 | 0.000 | 90.330 | 0.000 | 2.403 | 200.075 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 348 | 362 | 353 | 1458 | 0 | 997 | 1282 | 527 | 1678 | 0 |
N.S. |
1 | 1.04 | 1.01 | 4.19 | 0.00 | 2.86 | 3.68 | 1.51 | 4.82 | 0.00 |
time (sec) |
N/A | 0.742 | 1.193 | 2.761 | 0.000 | 0.414 | 1.288 | 0.406 | 16.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 248 | 223 | 773 | 0 | 585 | 660 | 282 | 839 | 0 |
N.S. |
1 | 1.22 | 1.10 | 3.81 | 0.00 | 2.88 | 3.25 | 1.39 | 4.13 | 0.00 |
time (sec) |
N/A | 0.499 | 0.276 | 2.022 | 0.000 | 0.182 | 1.367 | 0.370 | 0.449 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 172 | 162 | 378 | 0 | 339 | 354 | 151 | 315 | 0 |
N.S. |
1 | 1.41 | 1.33 | 3.10 | 0.00 | 2.78 | 2.90 | 1.24 | 2.58 | 0.00 |
time (sec) |
N/A | 0.311 | 0.416 | 1.743 | 0.000 | 0.100 | 1.061 | 0.369 | 0.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 258 | 276 | 482 | 0 | 0 | 0 | 0 | 2483 | 0 |
N.S. |
1 | 1.22 | 1.31 | 2.28 | 0.00 | 0.00 | 0.00 | 0.00 | 11.77 | 0.00 |
time (sec) |
N/A | 0.628 | 0.988 | 2.141 | 0.000 | 0.000 | 0.000 | 0.000 | 0.471 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 314 | 279 | 746 | 0 | 0 | 0 | 0 | 6230 | 0 |
N.S. |
1 | 1.30 | 1.16 | 3.10 | 0.00 | 0.00 | 0.00 | 0.00 | 25.85 | 0.00 |
time (sec) |
N/A | 0.684 | 1.375 | 2.168 | 0.000 | 0.000 | 0.000 | 0.000 | 0.620 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 313 | 254 | 1561 | 0 | 2302 | 0 | 4728 | 15967 | 0 |
N.S. |
1 | 1.18 | 0.96 | 5.89 | 0.00 | 8.69 | 0.00 | 17.84 | 60.25 | 0.00 |
time (sec) |
N/A | 0.655 | 1.271 | 2.572 | 0.000 | 4.479 | 0.000 | 11.778 | 3.906 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 410 | 472 | 466 | 2826 | 0 | 5060 | 0 | 0 | 38018 | 0 |
N.S. |
1 | 1.15 | 1.14 | 6.89 | 0.00 | 12.34 | 0.00 | 0.00 | 92.73 | 0.00 |
time (sec) |
N/A | 0.976 | 4.353 | 3.227 | 0.000 | 53.141 | 0.000 | 0.000 | 32.365 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 453 | 499 | 393 | 3171 | 0 | 1402 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.10 | 0.87 | 7.00 | 0.00 | 3.09 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.590 | 1.637 | 3.309 | 0.000 | 1.648 | 0.000 | 0.000 | 200.050 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 315 | 244 | 1800 | 0 | 872 | 0 | 0 | 725 | 0 |
N.S. |
1 | 1.09 | 0.84 | 6.21 | 0.00 | 3.01 | 0.00 | 0.00 | 2.50 | 0.00 |
time (sec) |
N/A | 0.781 | 0.856 | 2.518 | 0.000 | 0.753 | 0.000 | 0.000 | 0.662 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 199 | 151 | 970 | 0 | 512 | 0 | 0 | 324 | 0 |
N.S. |
1 | 1.12 | 0.85 | 5.45 | 0.00 | 2.88 | 0.00 | 0.00 | 1.82 | 0.00 |
time (sec) |
N/A | 0.424 | 0.382 | 2.059 | 0.000 | 0.442 | 0.000 | 0.000 | 0.508 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 125 | 113 | 485 | 0 | 349 | 0 | 0 | 104 | 0 |
N.S. |
1 | 1.13 | 1.02 | 4.37 | 0.00 | 3.14 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.253 | 0.062 | 1.833 | 0.000 | 0.124 | 0.000 | 0.000 | 0.455 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 177 | 139 | 953 | 0 | 758 | 0 | 0 | 438 | 0 |
N.S. |
1 | 1.27 | 1.00 | 6.86 | 0.00 | 5.45 | 0.00 | 0.00 | 3.15 | 0.00 |
time (sec) |
N/A | 0.432 | 0.425 | 2.067 | 0.000 | 1.345 | 0.000 | 0.000 | 2.388 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 254 | 189 | 1795 | 0 | 1923 | 0 | 2888 | 4829 | 0 |
N.S. |
1 | 1.21 | 0.90 | 8.55 | 0.00 | 9.16 | 0.00 | 13.75 | 23.00 | 0.00 |
time (sec) |
N/A | 0.877 | 1.248 | 2.168 | 0.000 | 9.975 | 0.000 | 8.485 | 8.601 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 342 | 427 | 342 | 3621 | 0 | 4347 | 0 | 0 | 14503 | 0 |
N.S. |
1 | 1.25 | 1.00 | 10.59 | 0.00 | 12.71 | 0.00 | 0.00 | 42.41 | 0.00 |
time (sec) |
N/A | 2.552 | 3.360 | 2.447 | 0.000 | 126.402 | 0.000 | 0.000 | 14.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 332 | 345 | 4501 | 0 | 1718 | 0 | 0 | 2000 | 0 |
N.S. |
1 | 1.12 | 1.16 | 15.15 | 0.00 | 5.78 | 0.00 | 0.00 | 6.73 | 0.00 |
time (sec) |
N/A | 1.218 | 1.301 | 3.339 | 0.000 | 4.632 | 0.000 | 0.000 | 0.617 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 276 | 203 | 2629 | 0 | 1058 | 0 | 0 | 943 | 0 |
N.S. |
1 | 1.19 | 0.88 | 11.38 | 0.00 | 4.58 | 0.00 | 0.00 | 4.08 | 0.00 |
time (sec) |
N/A | 0.574 | 0.595 | 2.549 | 0.000 | 4.088 | 0.000 | 0.000 | 0.533 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 148 | 78 | 109 | 0 | 184 | 0 | 0 | 329 | 96 |
N.S. |
1 | 1.06 | 0.56 | 0.78 | 0.00 | 1.31 | 0.00 | 0.00 | 2.35 | 0.69 |
time (sec) |
N/A | 0.330 | 0.190 | 2.098 | 0.000 | 2.538 | 0.000 | 0.000 | 0.552 | 10.932 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 59 | 85 | 0 | 156 | 0 | 0 | 168 | 72 |
N.S. |
1 | 1.00 | 0.51 | 0.73 | 0.00 | 1.34 | 0.00 | 0.00 | 1.45 | 0.62 |
time (sec) |
N/A | 0.239 | 0.116 | 1.580 | 0.000 | 0.446 | 0.000 | 0.000 | 0.507 | 10.711 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 324 | 219 | 1783 | 0 | 3059 | 0 | 0 | 3593 | 0 |
N.S. |
1 | 1.20 | 0.81 | 6.60 | 0.00 | 11.33 | 0.00 | 0.00 | 13.31 | 0.00 |
time (sec) |
N/A | 0.645 | 0.880 | 2.048 | 0.000 | 12.549 | 0.000 | 0.000 | 3.921 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 424 | 416 | 434 | 3247 | 0 | 6793 | 0 | 0 | 44 | 0 |
N.S. |
1 | 0.98 | 1.02 | 7.66 | 0.00 | 16.02 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 2.520 | 2.982 | 2.033 | 0.000 | 68.333 | 0.000 | 0.000 | 200.058 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 109 | 127 | 233 | 146 | 0 | 585 | 144 | 185 |
N.S. |
1 | 1.00 | 0.74 | 0.86 | 1.57 | 0.99 | 0.00 | 3.95 | 0.97 | 1.25 |
time (sec) |
N/A | 0.306 | 1.823 | 1.173 | 0.167 | 0.075 | 0.000 | 0.500 | 0.218 | 0.435 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 82 | 82 | 156 | 94 | 0 | 359 | 88 | 81 |
N.S. |
1 | 1.00 | 0.77 | 0.77 | 1.46 | 0.88 | 0.00 | 3.36 | 0.82 | 0.76 |
time (sec) |
N/A | 0.275 | 1.016 | 1.187 | 0.165 | 0.074 | 0.000 | 0.272 | 0.225 | 0.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 77 | 59 | 48 | 90 | 55 | 0 | 184 | 43 | 47 |
N.S. |
1 | 1.07 | 0.82 | 0.67 | 1.25 | 0.76 | 0.00 | 2.56 | 0.60 | 0.65 |
time (sec) |
N/A | 0.243 | 0.488 | 1.138 | 0.144 | 0.075 | 0.000 | 0.261 | 0.198 | 11.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 42 | 32 | 38 | 31 | 0 | 31 | 20 | 31 |
N.S. |
1 | 1.00 | 1.08 | 0.82 | 0.97 | 0.79 | 0.00 | 0.79 | 0.51 | 0.79 |
time (sec) |
N/A | 0.180 | 0.229 | 1.043 | 0.126 | 0.068 | 0.000 | 0.232 | 0.247 | 10.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 97 | 130 | 166 | 0 | 309 | 0 | 99 | 112 | 0 |
N.S. |
1 | 0.92 | 1.23 | 1.57 | 0.00 | 2.92 | 0.00 | 0.93 | 1.06 | 0.00 |
time (sec) |
N/A | 0.266 | 0.812 | 1.391 | 0.000 | 0.084 | 0.000 | 0.282 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 127 | 127 | 182 | 0 | 396 | 0 | 104 | 243 | 0 |
N.S. |
1 | 1.15 | 1.15 | 1.65 | 0.00 | 3.60 | 0.00 | 0.95 | 2.21 | 0.00 |
time (sec) |
N/A | 0.289 | 1.235 | 1.330 | 0.000 | 0.082 | 0.000 | 0.295 | 0.208 | 0.000 |