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 | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 114 | 91 | 74 | 580 | 89 | 0 | 0 | 62 | 103 |
N.S. |
1 | 1.04 | 0.83 | 0.67 | 5.27 | 0.81 | 0.00 | 0.00 | 0.56 | 0.94 |
time (sec) |
N/A | 0.535 | 0.674 | 2.624 | 0.472 | 0.087 | 0.000 | 0.000 | 0.193 | 3.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 57 | 48 | 0 | 53 | 0 | 0 | 58 | 98 |
N.S. |
1 | 1.00 | 0.83 | 0.70 | 0.00 | 0.77 | 0.00 | 0.00 | 0.84 | 1.42 |
time (sec) |
N/A | 0.324 | 0.363 | 2.446 | 0.000 | 0.080 | 0.000 | 0.000 | 0.190 | 1.727 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 29 | 201 | 40 | 0 | 0 | 53 | 60 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 6.48 | 1.29 | 0.00 | 0.00 | 1.71 | 1.94 |
time (sec) |
N/A | 0.238 | 0.308 | 3.855 | 0.192 | 0.085 | 0.000 | 0.000 | 0.184 | 0.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 123 | 101 | 735 | 884 | 222 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.01 | 0.83 | 6.02 | 7.25 | 1.82 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.514 | 0.913 | 4.890 | 0.279 | 0.083 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 203 | 160 | 795 | 0 | 274 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.06 | 0.83 | 4.14 | 0.00 | 1.43 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.845 | 1.387 | 4.830 | 0.000 | 0.097 | 0.000 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 102 | 73 | 82 | 76 | 190 | 0 | 0 | 97 | 626 |
N.S. |
1 | 0.87 | 0.62 | 0.70 | 0.65 | 1.62 | 0.00 | 0.00 | 0.83 | 5.35 |
time (sec) |
N/A | 0.289 | 0.487 | 0.192 | 0.037 | 0.123 | 0.000 | 0.000 | 0.231 | 12.903 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 78 | 61 | 63 | 58 | 152 | 0 | 0 | 97 | 498 |
N.S. |
1 | 0.89 | 0.69 | 0.72 | 0.66 | 1.73 | 0.00 | 0.00 | 1.10 | 5.66 |
time (sec) |
N/A | 0.275 | 0.292 | 0.162 | 0.038 | 0.096 | 0.000 | 0.000 | 0.242 | 8.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 54 | 51 | 44 | 40 | 114 | 0 | 0 | 97 | 370 |
N.S. |
1 | 0.92 | 0.86 | 0.75 | 0.68 | 1.93 | 0.00 | 0.00 | 1.64 | 6.27 |
time (sec) |
N/A | 0.270 | 0.237 | 100.755 | 0.038 | 0.106 | 0.000 | 0.000 | 0.226 | 3.765 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 24 | 21 | 73 | 0 | 0 | 97 | 242 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.72 | 2.52 | 0.00 | 0.00 | 3.34 | 8.34 |
time (sec) |
N/A | 0.242 | 0.136 | 2.279 | 0.028 | 0.093 | 0.000 | 0.000 | 0.221 | 3.699 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 76 | 83 | 425 | 98 | 236 | 0 | 0 | 92 | 0 |
N.S. |
1 | 0.85 | 0.93 | 4.78 | 1.10 | 2.65 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.274 | 0.440 | 6.140 | 0.118 | 0.116 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 131 | 53 | 472 | 140 | 263 | 0 | 0 | 92 | 0 |
N.S. |
1 | 0.93 | 0.38 | 3.35 | 0.99 | 1.87 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.303 | 0.080 | 67.116 | 0.115 | 0.089 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 206 | 53 | 1315 | 194 | 309 | 0 | 0 | 92 | 0 |
N.S. |
1 | 0.94 | 0.24 | 6.03 | 0.89 | 1.42 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.323 | 0.108 | 2.571 | 0.114 | 0.097 | 0.000 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 155 | 103 | 92 | 0 | 121 | 0 | 0 | 97 | 301 |
N.S. |
1 | 1.05 | 0.70 | 0.63 | 0.00 | 0.82 | 0.00 | 0.00 | 0.66 | 2.05 |
time (sec) |
N/A | 0.716 | 1.102 | 21.631 | 0.000 | 0.097 | 0.000 | 0.000 | 0.239 | 5.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 108 | 93 | 66 | 0 | 83 | 0 | 0 | 91 | 105 |
N.S. |
1 | 1.04 | 0.89 | 0.63 | 0.00 | 0.80 | 0.00 | 0.00 | 0.88 | 1.01 |
time (sec) |
N/A | 0.445 | 0.528 | 2.594 | 0.000 | 0.086 | 0.000 | 0.000 | 0.207 | 3.410 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 46 | 41 | 331 | 45 | 0 | 0 | 86 | 64 |
N.S. |
1 | 1.00 | 0.71 | 0.63 | 5.09 | 0.69 | 0.00 | 0.00 | 1.32 | 0.98 |
time (sec) |
N/A | 0.358 | 0.460 | 6.200 | 0.219 | 0.080 | 0.000 | 0.000 | 0.201 | 0.451 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 69 | 51 | 328 | 59 | 0 | 0 | 92 | 89 |
N.S. |
1 | 1.00 | 1.97 | 1.46 | 9.37 | 1.69 | 0.00 | 0.00 | 2.63 | 2.54 |
time (sec) |
N/A | 0.246 | 0.689 | 14.982 | 0.216 | 0.094 | 0.000 | 0.000 | 0.211 | 0.977 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 163 | 118 | 1279 | 1076 | 244 | 0 | 0 | 92 | 0 |
N.S. |
1 | 1.03 | 0.74 | 8.04 | 6.77 | 1.53 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.674 | 1.262 | 285.869 | 0.288 | 0.091 | 0.000 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 243 | 155 | 1343 | 0 | 300 | 0 | 0 | 92 | 0 |
N.S. |
1 | 1.05 | 0.67 | 5.81 | 0.00 | 1.30 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 1.043 | 1.688 | 3.422 | 0.000 | 0.102 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 102 | 73 | 82 | 76 | 202 | 0 | 0 | 131 | 690 |
N.S. |
1 | 0.87 | 0.62 | 0.70 | 0.65 | 1.73 | 0.00 | 0.00 | 1.12 | 5.90 |
time (sec) |
N/A | 0.280 | 0.424 | 0.176 | 0.050 | 0.144 | 0.000 | 0.000 | 0.299 | 12.769 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 78 | 63 | 63 | 58 | 164 | 0 | 0 | 131 | 562 |
N.S. |
1 | 0.89 | 0.72 | 0.72 | 0.66 | 1.86 | 0.00 | 0.00 | 1.49 | 6.39 |
time (sec) |
N/A | 0.266 | 0.383 | 0.154 | 0.041 | 0.104 | 0.000 | 0.000 | 0.275 | 13.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 54 | 51 | 44 | 40 | 126 | 0 | 0 | 131 | 434 |
N.S. |
1 | 0.92 | 0.86 | 0.75 | 0.68 | 2.14 | 0.00 | 0.00 | 2.22 | 7.36 |
time (sec) |
N/A | 0.265 | 0.229 | 100.940 | 0.037 | 0.102 | 0.000 | 0.000 | 0.265 | 4.970 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 24 | 21 | 85 | 0 | 0 | 131 | 306 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.72 | 2.93 | 0.00 | 0.00 | 4.52 | 10.55 |
time (sec) |
N/A | 0.248 | 0.170 | 2.286 | 0.032 | 0.084 | 0.000 | 0.000 | 0.240 | 3.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 100 | 51 | 462 | 117 | 235 | 0 | 0 | 125 | 0 |
N.S. |
1 | 0.86 | 0.44 | 3.98 | 1.01 | 2.03 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.287 | 0.123 | 10.759 | 0.124 | 0.093 | 0.000 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 125 | 53 | 485 | 138 | 261 | 0 | 0 | 125 | 0 |
N.S. |
1 | 0.89 | 0.38 | 3.44 | 0.98 | 1.85 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.300 | 0.105 | 66.063 | 0.139 | 0.082 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 178 | 53 | 532 | 176 | 277 | 0 | 0 | 125 | 0 |
N.S. |
1 | 0.94 | 0.28 | 2.81 | 0.93 | 1.47 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.310 | 0.106 | 2.202 | 0.126 | 0.113 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 147 | 109 | 76 | 0 | 109 | 0 | 0 | 123 | 286 |
N.S. |
1 | 1.06 | 0.78 | 0.55 | 0.00 | 0.78 | 0.00 | 0.00 | 0.88 | 2.06 |
time (sec) |
N/A | 0.608 | 0.965 | 2.756 | 0.000 | 0.085 | 0.000 | 0.000 | 0.278 | 3.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 59 | 50 | 418 | 71 | 0 | 0 | 117 | 102 |
N.S. |
1 | 1.00 | 0.57 | 0.48 | 4.02 | 0.68 | 0.00 | 0.00 | 1.12 | 0.98 |
time (sec) |
N/A | 0.478 | 0.723 | 7.050 | 0.226 | 0.085 | 0.000 | 0.000 | 0.263 | 1.923 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 86 | 61 | 504 | 59 | 0 | 0 | 125 | 85 |
N.S. |
1 | 1.00 | 1.21 | 0.86 | 7.10 | 0.83 | 0.00 | 0.00 | 1.76 | 1.20 |
time (sec) |
N/A | 0.380 | 0.951 | 15.208 | 0.231 | 0.080 | 0.000 | 0.000 | 0.257 | 0.919 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 73 | 62 | 454 | 73 | 0 | 0 | 125 | 112 |
N.S. |
1 | 1.00 | 2.09 | 1.77 | 12.97 | 2.09 | 0.00 | 0.00 | 3.57 | 3.20 |
time (sec) |
N/A | 0.250 | 1.292 | 3.248 | 0.276 | 0.086 | 0.000 | 0.000 | 0.258 | 2.497 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 203 | 131 | 1926 | 1253 | 258 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.04 | 0.67 | 9.83 | 6.39 | 1.32 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.879 | 2.320 | 3.976 | 0.432 | 0.097 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 283 | 188 | 2005 | 0 | 314 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.06 | 0.70 | 7.48 | 0.00 | 1.17 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 1.292 | 3.548 | 6.883 | 0.000 | 0.114 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 342 | 365 | 194 | 2085 | 0 | 342 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.07 | 0.57 | 6.10 | 0.00 | 1.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 1.748 | 5.750 | 7.722 | 0.000 | 0.145 | 0.000 | 0.000 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 102 | 73 | 82 | 297 | 150 | 0 | 0 | 139 | 434 |
N.S. |
1 | 0.87 | 0.62 | 0.70 | 2.54 | 1.28 | 0.00 | 0.00 | 1.19 | 3.71 |
time (sec) |
N/A | 0.272 | 0.271 | 1.130 | 0.045 | 0.098 | 0.000 | 0.000 | 0.229 | 6.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 78 | 63 | 63 | 169 | 113 | 0 | 0 | 139 | 306 |
N.S. |
1 | 0.89 | 0.72 | 0.72 | 1.92 | 1.28 | 0.00 | 0.00 | 1.58 | 3.48 |
time (sec) |
N/A | 0.262 | 0.167 | 1.135 | 0.049 | 0.085 | 0.000 | 0.000 | 0.240 | 3.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 54 | 49 | 44 | 79 | 76 | 0 | 0 | 139 | 155 |
N.S. |
1 | 0.92 | 0.83 | 0.75 | 1.34 | 1.29 | 0.00 | 0.00 | 2.36 | 2.63 |
time (sec) |
N/A | 0.259 | 0.118 | 1.120 | 0.042 | 0.083 | 0.000 | 0.000 | 0.233 | 1.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 24 | 21 | 37 | 0 | 0 | 42 | 47 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 1.37 | 0.00 | 0.00 | 1.56 | 1.74 |
time (sec) |
N/A | 0.233 | 0.065 | 0.826 | 0.028 | 0.076 | 0.000 | 0.000 | 0.214 | 0.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 144 | 51 | 304 | 138 | 271 | 0 | 0 | 84 | 0 |
N.S. |
1 | 0.96 | 0.34 | 2.03 | 0.92 | 1.81 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.293 | 0.116 | 9.303 | 0.117 | 0.093 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 223 | 53 | 312 | 192 | 293 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.00 | 0.24 | 1.40 | 0.86 | 1.31 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.336 | 0.193 | 7.745 | 0.127 | 0.093 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 300 | 302 | 53 | 350 | 246 | 315 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.01 | 0.18 | 1.17 | 0.82 | 1.05 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.367 | 0.325 | 7.716 | 0.129 | 0.093 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 155 | 95 | 111 | 608 | 153 | 0 | 0 | 139 | 301 |
N.S. |
1 | 1.05 | 0.65 | 0.76 | 4.14 | 1.04 | 0.00 | 0.00 | 0.95 | 2.05 |
time (sec) |
N/A | 0.749 | 1.084 | 6.714 | 0.259 | 0.140 | 0.000 | 0.000 | 0.175 | 6.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 114 | 77 | 91 | 474 | 116 | 0 | 0 | 139 | 105 |
N.S. |
1 | 1.04 | 0.70 | 0.83 | 4.31 | 1.05 | 0.00 | 0.00 | 1.26 | 0.95 |
time (sec) |
N/A | 0.540 | 0.755 | 4.909 | 0.216 | 0.103 | 0.000 | 0.000 | 0.185 | 3.360 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 65 | 72 | 340 | 79 | 0 | 0 | 139 | 91 |
N.S. |
1 | 1.00 | 0.89 | 0.99 | 4.66 | 1.08 | 0.00 | 0.00 | 1.90 | 1.25 |
time (sec) |
N/A | 0.392 | 0.535 | 4.631 | 0.182 | 0.094 | 0.000 | 0.000 | 0.216 | 5.908 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 40 | 44 | 206 | 40 | 0 | 0 | 137 | 98 |
N.S. |
1 | 1.00 | 1.14 | 1.26 | 5.89 | 1.14 | 0.00 | 0.00 | 3.91 | 2.80 |
time (sec) |
N/A | 0.235 | 0.359 | 4.516 | 0.133 | 0.078 | 0.000 | 0.000 | 0.221 | 1.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 70 | 108 | 0 | 149 | 0 | 0 | 130 | 0 |
N.S. |
1 | 1.00 | 1.35 | 2.08 | 0.00 | 2.87 | 0.00 | 0.00 | 2.50 | 0.00 |
time (sec) |
N/A | 0.235 | 0.399 | 6.551 | 0.000 | 0.113 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 123 | 96 | 322 | 837 | 245 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.01 | 0.79 | 2.64 | 6.86 | 2.01 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.491 | 0.567 | 9.281 | 0.251 | 0.087 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 205 | 117 | 361 | 1938 | 267 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.06 | 0.61 | 1.87 | 10.04 | 1.38 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.857 | 0.743 | 9.387 | 0.382 | 0.102 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 102 | 73 | 82 | 76 | 149 | 0 | 0 | 310 | 370 |
N.S. |
1 | 0.87 | 0.62 | 0.70 | 0.65 | 1.27 | 0.00 | 0.00 | 2.65 | 3.16 |
time (sec) |
N/A | 0.277 | 0.350 | 1.021 | 0.039 | 0.086 | 0.000 | 0.000 | 0.390 | 5.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 78 | 59 | 63 | 58 | 108 | 0 | 0 | 310 | 242 |
N.S. |
1 | 0.89 | 0.67 | 0.72 | 0.66 | 1.23 | 0.00 | 0.00 | 3.52 | 2.75 |
time (sec) |
N/A | 0.282 | 0.189 | 1.004 | 0.044 | 0.088 | 0.000 | 0.000 | 0.420 | 3.941 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 52 | 37 | 44 | 38 | 67 | 0 | 0 | 310 | 85 |
N.S. |
1 | 0.91 | 0.65 | 0.77 | 0.67 | 1.18 | 0.00 | 0.00 | 5.44 | 1.49 |
time (sec) |
N/A | 0.274 | 0.100 | 0.942 | 0.048 | 0.077 | 0.000 | 0.000 | 0.427 | 0.783 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 24 | 21 | 49 | 0 | 0 | 52 | 67 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 1.81 | 0.00 | 0.00 | 1.93 | 2.48 |
time (sec) |
N/A | 0.245 | 0.067 | 0.990 | 0.039 | 0.084 | 0.000 | 0.000 | 0.166 | 0.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 176 | 51 | 378 | 153 | 294 | 0 | 0 | 52 | 0 |
N.S. |
1 | 0.98 | 0.28 | 2.11 | 0.85 | 1.64 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.323 | 0.183 | 9.458 | 0.126 | 0.088 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 255 | 53 | 421 | 207 | 316 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.01 | 0.21 | 1.67 | 0.82 | 1.25 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.353 | 0.313 | 8.864 | 0.131 | 0.088 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 334 | 53 | 462 | 261 | 338 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.02 | 0.16 | 1.40 | 0.79 | 1.03 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.379 | 0.474 | 9.948 | 0.142 | 0.133 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 155 | 108 | 134 | 764 | 184 | 0 | 0 | 310 | 301 |
N.S. |
1 | 1.05 | 0.73 | 0.91 | 5.20 | 1.25 | 0.00 | 0.00 | 2.11 | 2.05 |
time (sec) |
N/A | 0.751 | 1.839 | 9.916 | 0.300 | 0.149 | 0.000 | 0.000 | 0.415 | 7.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 114 | 92 | 114 | 626 | 143 | 0 | 0 | 310 | 105 |
N.S. |
1 | 1.04 | 0.84 | 1.04 | 5.69 | 1.30 | 0.00 | 0.00 | 2.82 | 0.95 |
time (sec) |
N/A | 0.530 | 1.402 | 5.385 | 0.252 | 0.116 | 0.000 | 0.000 | 0.399 | 5.757 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 80 | 86 | 488 | 102 | 0 | 0 | 310 | 91 |
N.S. |
1 | 1.00 | 1.10 | 1.18 | 6.68 | 1.40 | 0.00 | 0.00 | 4.25 | 1.25 |
time (sec) |
N/A | 0.398 | 0.955 | 4.786 | 0.217 | 0.130 | 0.000 | 0.000 | 0.382 | 3.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 59 | 51 | 350 | 59 | 0 | 0 | 310 | 139 |
N.S. |
1 | 1.00 | 1.69 | 1.46 | 10.00 | 1.69 | 0.00 | 0.00 | 8.86 | 3.97 |
time (sec) |
N/A | 0.250 | 0.679 | 4.635 | 0.180 | 0.112 | 0.000 | 0.000 | 0.364 | 1.872 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 101 | 169 | 813 | 196 | 0 | 0 | 308 | 0 |
N.S. |
1 | 1.00 | 1.17 | 1.97 | 9.45 | 2.28 | 0.00 | 0.00 | 3.58 | 0.00 |
time (sec) |
N/A | 0.389 | 0.900 | 6.523 | 0.259 | 0.089 | 0.000 | 0.000 | 0.394 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 95 | 343 | 0 | 246 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 1.09 | 3.94 | 0.00 | 2.83 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.358 | 0.672 | 7.804 | 0.000 | 0.094 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 163 | 120 | 374 | 1821 | 270 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.04 | 0.76 | 2.38 | 11.60 | 1.72 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.684 | 1.002 | 9.346 | 0.304 | 0.085 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 247 | 145 | 413 | 2632 | 292 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.06 | 0.62 | 1.77 | 11.30 | 1.25 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.070 | 1.651 | 9.938 | 0.414 | 0.096 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 126 | 85 | 101 | 94 | 175 | 0 | 0 | 76 | 434 |
N.S. |
1 | 0.86 | 0.58 | 0.69 | 0.64 | 1.20 | 0.00 | 0.00 | 0.52 | 2.97 |
time (sec) |
N/A | 0.305 | 0.338 | 1.074 | 0.039 | 0.102 | 0.000 | 0.000 | 0.202 | 6.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 102 | 73 | 82 | 76 | 134 | 0 | 0 | 76 | 306 |
N.S. |
1 | 0.87 | 0.62 | 0.70 | 0.65 | 1.15 | 0.00 | 0.00 | 0.65 | 2.62 |
time (sec) |
N/A | 0.291 | 0.279 | 1.054 | 0.034 | 0.093 | 0.000 | 0.000 | 0.162 | 4.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 76 | 51 | 63 | 58 | 93 | 0 | 0 | 76 | 155 |
N.S. |
1 | 0.88 | 0.59 | 0.73 | 0.67 | 1.08 | 0.00 | 0.00 | 0.88 | 1.80 |
time (sec) |
N/A | 0.280 | 0.160 | 0.959 | 0.043 | 0.090 | 0.000 | 0.000 | 0.164 | 1.369 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 50 | 36 | 42 | 44 | 50 | 0 | 0 | 76 | 72 |
N.S. |
1 | 0.91 | 0.65 | 0.76 | 0.80 | 0.91 | 0.00 | 0.00 | 1.38 | 1.31 |
time (sec) |
N/A | 0.265 | 0.114 | 0.953 | 0.031 | 0.097 | 0.000 | 0.000 | 0.164 | 0.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 24 | 21 | 61 | 0 | 0 | 76 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.72 | 2.10 | 0.00 | 0.00 | 2.62 | 0.79 |
time (sec) |
N/A | 0.257 | 0.102 | 0.965 | 0.037 | 0.079 | 0.000 | 0.000 | 0.184 | 0.747 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 208 | 51 | 449 | 175 | 305 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.00 | 0.25 | 2.16 | 0.84 | 1.47 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.340 | 0.171 | 10.184 | 0.121 | 0.085 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 287 | 53 | 489 | 229 | 327 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.02 | 0.19 | 1.74 | 0.81 | 1.16 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.360 | 0.454 | 9.479 | 0.118 | 0.091 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 155 | 112 | 145 | 902 | 199 | 0 | 0 | 76 | 301 |
N.S. |
1 | 1.05 | 0.76 | 0.99 | 6.14 | 1.35 | 0.00 | 0.00 | 0.52 | 2.05 |
time (sec) |
N/A | 0.718 | 1.897 | 25.754 | 0.366 | 0.181 | 0.000 | 0.000 | 0.160 | 9.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 114 | 94 | 125 | 764 | 158 | 0 | 0 | 76 | 105 |
N.S. |
1 | 1.04 | 0.85 | 1.14 | 6.95 | 1.44 | 0.00 | 0.00 | 0.69 | 0.95 |
time (sec) |
N/A | 0.554 | 1.678 | 6.645 | 0.392 | 0.136 | 0.000 | 0.000 | 0.159 | 6.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 80 | 102 | 626 | 117 | 0 | 0 | 76 | 91 |
N.S. |
1 | 1.00 | 1.10 | 1.40 | 8.58 | 1.60 | 0.00 | 0.00 | 1.04 | 1.25 |
time (sec) |
N/A | 0.373 | 1.544 | 5.165 | 0.273 | 0.108 | 0.000 | 0.000 | 0.215 | 3.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 57 | 75 | 488 | 74 | 0 | 0 | 76 | 50 |
N.S. |
1 | 1.00 | 1.63 | 2.14 | 13.94 | 2.11 | 0.00 | 0.00 | 2.17 | 1.43 |
time (sec) |
N/A | 0.240 | 1.357 | 4.891 | 0.211 | 0.096 | 0.000 | 0.000 | 0.216 | 2.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 129 | 82 | 232 | 1074 | 270 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.05 | 0.67 | 1.89 | 8.73 | 2.20 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.550 | 1.264 | 6.995 | 0.323 | 0.082 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 126 | 149 | 260 | 827 | 245 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.47 | 1.73 | 3.02 | 9.62 | 2.85 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.505 | 1.330 | 7.180 | 0.318 | 0.089 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 127 | 121 | 413 | 0 | 267 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.04 | 0.99 | 3.39 | 0.00 | 2.19 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.475 | 0.936 | 7.970 | 0.000 | 0.084 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 203 | 143 | 433 | 2297 | 289 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.06 | 0.74 | 2.26 | 11.96 | 1.51 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.820 | 1.219 | 9.645 | 0.326 | 0.086 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 289 | 165 | 480 | 3789 | 311 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.07 | 0.61 | 1.78 | 14.03 | 1.15 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 1.272 | 1.687 | 9.088 | 0.432 | 0.092 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 126 | 81 | 101 | 94 | 160 | 0 | 0 | 0 | 370 |
N.S. |
1 | 0.86 | 0.55 | 0.69 | 0.64 | 1.10 | 0.00 | 0.00 | 0.00 | 2.53 |
time (sec) |
N/A | 0.288 | 0.406 | 1.077 | 0.043 | 0.098 | 0.000 | 0.000 | 1.338 | 5.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 98 | 61 | 82 | 76 | 119 | 0 | 0 | 0 | 242 |
N.S. |
1 | 0.87 | 0.54 | 0.73 | 0.67 | 1.05 | 0.00 | 0.00 | 0.00 | 2.14 |
time (sec) |
N/A | 0.286 | 0.251 | 1.017 | 0.045 | 0.081 | 0.000 | 0.000 | 1.353 | 4.650 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 74 | 49 | 63 | 62 | 77 | 0 | 0 | 939 | 110 |
N.S. |
1 | 0.88 | 0.58 | 0.75 | 0.74 | 0.92 | 0.00 | 0.00 | 11.18 | 1.31 |
time (sec) |
N/A | 0.274 | 0.127 | 0.984 | 0.049 | 0.081 | 0.000 | 0.000 | 1.379 | 0.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 52 | 52 | 44 | 32 | 61 | 0 | 0 | 759 | 0 |
N.S. |
1 | 0.91 | 0.91 | 0.77 | 0.56 | 1.07 | 0.00 | 0.00 | 13.32 | 0.00 |
time (sec) |
N/A | 0.271 | 0.148 | 1.069 | 0.051 | 0.083 | 0.000 | 0.000 | 1.048 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 24 | 21 | 72 | 0 | 0 | 1123 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.72 | 2.48 | 0.00 | 0.00 | 38.72 | 0.79 |
time (sec) |
N/A | 0.243 | 0.139 | 1.010 | 0.037 | 0.080 | 0.000 | 0.000 | 1.049 | 0.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 240 | 51 | 455 | 195 | 316 | 0 | 0 | 169 | 0 |
N.S. |
1 | 1.01 | 0.22 | 1.92 | 0.82 | 1.33 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.342 | 0.420 | 9.445 | 0.125 | 0.087 | 0.000 | 0.000 | 0.480 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 319 | 53 | 501 | 249 | 338 | 0 | 0 | 169 | 0 |
N.S. |
1 | 1.03 | 0.17 | 1.62 | 0.80 | 1.09 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.353 | 0.672 | 10.430 | 0.120 | 0.106 | 0.000 | 0.000 | 0.500 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 114 | 92 | 143 | 902 | 173 | 0 | 0 | 0 | 105 |
N.S. |
1 | 1.04 | 0.84 | 1.30 | 8.20 | 1.57 | 0.00 | 0.00 | 0.00 | 0.95 |
time (sec) |
N/A | 0.550 | 1.900 | 10.074 | 0.504 | 0.158 | 0.000 | 0.000 | 1.264 | 6.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 82 | 113 | 764 | 132 | 0 | 0 | 0 | 91 |
N.S. |
1 | 1.00 | 1.12 | 1.55 | 10.47 | 1.81 | 0.00 | 0.00 | 0.00 | 1.25 |
time (sec) |
N/A | 0.384 | 1.702 | 5.570 | 0.380 | 0.121 | 0.000 | 0.000 | 1.286 | 3.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 59 | 86 | 626 | 89 | 0 | 0 | 0 | 50 |
N.S. |
1 | 1.00 | 1.69 | 2.46 | 17.89 | 2.54 | 0.00 | 0.00 | 0.00 | 1.43 |
time (sec) |
N/A | 0.241 | 1.509 | 5.033 | 0.258 | 0.097 | 0.000 | 0.000 | 1.292 | 3.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 172 | 130 | 235 | 1164 | 326 | 0 | 0 | 939 | 0 |
N.S. |
1 | 1.08 | 0.81 | 1.47 | 7.28 | 2.04 | 0.00 | 0.00 | 5.87 | 0.00 |
time (sec) |
N/A | 0.729 | 1.987 | 7.227 | 0.333 | 0.114 | 0.000 | 0.000 | 1.015 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 167 | 126 | 267 | 0 | 245 | 0 | 0 | 939 | 0 |
N.S. |
1 | 1.38 | 1.04 | 2.21 | 0.00 | 2.02 | 0.00 | 0.00 | 7.76 | 0.00 |
time (sec) |
N/A | 0.686 | 1.806 | 7.261 | 0.000 | 0.089 | 0.000 | 0.000 | 1.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 170 | 120 | 469 | 977 | 267 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.36 | 0.96 | 3.75 | 7.82 | 2.14 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.643 | 1.706 | 8.435 | 0.301 | 0.084 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 167 | 119 | 471 | 0 | 278 | 0 | 0 | 1457 | 0 |
N.S. |
1 | 1.06 | 0.76 | 3.00 | 0.00 | 1.77 | 0.00 | 0.00 | 9.28 | 0.00 |
time (sec) |
N/A | 0.604 | 1.479 | 8.057 | 0.000 | 0.108 | 0.000 | 0.000 | 1.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 243 | 141 | 492 | 2779 | 300 | 0 | 0 | 165 | 0 |
N.S. |
1 | 1.07 | 0.62 | 2.17 | 12.24 | 1.32 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 1.013 | 2.018 | 10.003 | 0.357 | 0.093 | 0.000 | 0.000 | 128.992 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 331 | 175 | 552 | 5821 | 322 | 0 | 0 | 169 | 0 |
N.S. |
1 | 1.08 | 0.57 | 1.80 | 18.96 | 1.05 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 1.481 | 2.964 | 9.763 | 0.540 | 0.100 | 0.000 | 0.000 | 0.498 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 398 | 413 | 373 | 265 | 1870 | 418 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.04 | 0.94 | 0.67 | 4.70 | 1.05 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.914 | 1.848 | 7.923 | 0.440 | 0.088 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 333 | 277 | 204 | 1400 | 323 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.38 | 1.15 | 0.85 | 5.81 | 1.34 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.489 | 1.704 | 7.778 | 0.360 | 0.085 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 31 | 76 | 64 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 2.11 | 1.78 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.234 | 0.596 | 8.365 | 0.268 | 0.074 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 48 | 51 | 54 | 75 | 0 | 0 | 37 | 86 |
N.S. |
1 | 1.00 | 0.59 | 0.63 | 0.67 | 0.93 | 0.00 | 0.00 | 0.46 | 1.06 |
time (sec) |
N/A | 0.379 | 0.620 | 6.457 | 0.338 | 0.071 | 0.000 | 0.000 | 0.158 | 1.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 127 | 63 | 62 | 130 | 86 | 0 | 0 | 37 | 101 |
N.S. |
1 | 1.04 | 0.52 | 0.51 | 1.07 | 0.70 | 0.00 | 0.00 | 0.30 | 0.83 |
time (sec) |
N/A | 0.537 | 0.824 | 6.589 | 0.262 | 0.070 | 0.000 | 0.000 | 0.160 | 1.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 174 | 80 | 79 | 178 | 97 | 0 | 0 | 37 | 109 |
N.S. |
1 | 1.06 | 0.49 | 0.48 | 1.09 | 0.59 | 0.00 | 0.00 | 0.23 | 0.66 |
time (sec) |
N/A | 0.784 | 1.095 | 6.569 | 0.246 | 0.074 | 0.000 | 0.000 | 0.159 | 2.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 369 | 465 | 376 | 316 | 3005 | 644 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.26 | 1.02 | 0.86 | 8.14 | 1.75 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.074 | 3.734 | 7.582 | 0.578 | 0.098 | 0.000 | 0.000 | 0.290 | 0.000 |