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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 362 | 606 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 1.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.919 | 13.103 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.477 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 387 | 0 | 0 | 0 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.00 | 3.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.438 | 0.880 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 174 | 0 | 0 | 0 | 0 | 0 | 116 | 0 |
N.S. |
1 | 1.00 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.462 | 0.753 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 62 | 76 | 0 | 625 | 0 | 0 | 31 | 65 |
N.S. |
1 | 1.00 | 0.85 | 1.04 | 0.00 | 8.56 | 0.00 | 0.00 | 0.42 | 0.89 |
time (sec) |
N/A | 0.352 | 0.203 | 1.450 | 0.000 | 0.117 | 0.000 | 0.000 | 0.298 | 3.301 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 71 | 57 | 74 | 0 | 334 | 87 | 0 | 56 | 51 |
N.S. |
1 | 1.01 | 0.81 | 1.06 | 0.00 | 4.77 | 1.24 | 0.00 | 0.80 | 0.73 |
time (sec) |
N/A | 0.341 | 0.100 | 1.168 | 0.000 | 0.105 | 17.139 | 0.000 | 0.245 | 2.861 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 49 | 43 | 61 | 0 | 303 | 66 | 0 | 18 | 39 |
N.S. |
1 | 1.02 | 0.90 | 1.27 | 0.00 | 6.31 | 1.38 | 0.00 | 0.38 | 0.81 |
time (sec) |
N/A | 0.274 | 0.059 | 1.191 | 0.000 | 0.117 | 0.997 | 0.000 | 0.267 | 2.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 49 | 47 | 37 | 0 | 305 | 66 | 0 | 31 | 36 |
N.S. |
1 | 1.04 | 1.00 | 0.79 | 0.00 | 6.49 | 1.40 | 0.00 | 0.66 | 0.77 |
time (sec) |
N/A | 0.268 | 0.085 | 1.158 | 0.000 | 0.108 | 1.910 | 0.000 | 0.310 | 2.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 97 | 76 | 0 | 625 | 87 | 0 | 31 | 65 |
N.S. |
1 | 1.00 | 1.37 | 1.07 | 0.00 | 8.80 | 1.23 | 0.00 | 0.44 | 0.92 |
time (sec) |
N/A | 0.348 | 0.112 | 1.153 | 0.000 | 0.108 | 8.253 | 0.000 | 0.228 | 2.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 73 | 101 | 74 | 0 | 1110 | 0 | 0 | 31 | 64 |
N.S. |
1 | 1.01 | 1.40 | 1.03 | 0.00 | 15.42 | 0.00 | 0.00 | 0.43 | 0.89 |
time (sec) |
N/A | 0.340 | 0.176 | 1.154 | 0.000 | 0.154 | 0.000 | 0.000 | 0.321 | 3.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 92 | 136 | 149 | 0 | 8891 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.68 | 1.01 | 1.10 | 0.00 | 65.86 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.500 | 0.870 | 2.351 | 0.000 | 1.149 | 0.000 | 0.000 | 0.382 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 53 | 105 | 90 | 0 | 6663 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.50 | 1.00 | 0.86 | 0.00 | 63.46 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.438 | 0.051 | 2.131 | 0.000 | 0.842 | 0.000 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 29 | 58 | 52 | 0 | 1748 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.50 | 1.00 | 0.90 | 0.00 | 30.14 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.320 | 0.024 | 2.151 | 0.000 | 0.560 | 0.000 | 0.000 | 0.349 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 111 | 109 | 0 | 0 | 6705 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.05 | 1.03 | 0.00 | 0.00 | 63.25 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.458 | 0.241 | 0.000 | 0.000 | 0.831 | 0.000 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 191 | 142 | 0 | 0 | 9168 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.35 | 1.00 | 0.00 | 0.00 | 64.56 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.580 | 0.397 | 0.000 | 0.000 | 1.103 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 85 | 131 | 165 | 0 | 7896 | 0 | 0 | 502 | 0 |
N.S. |
1 | 0.64 | 0.99 | 1.25 | 0.00 | 59.82 | 0.00 | 0.00 | 3.80 | 0.00 |
time (sec) |
N/A | 0.779 | 0.211 | 2.221 | 0.000 | 1.353 | 0.000 | 0.000 | 0.422 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 95 | 76 | 92 | 94 | 604 | 0 | 68 | 159 | 155 |
N.S. |
1 | 0.89 | 0.71 | 0.86 | 0.88 | 5.64 | 0.00 | 0.64 | 1.49 | 1.45 |
time (sec) |
N/A | 0.412 | 0.098 | 0.796 | 0.120 | 0.104 | 0.000 | 0.272 | 0.245 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 68 | 60 | 80 | 69 | 339 | 0 | 52 | 112 | 93 |
N.S. |
1 | 0.88 | 0.78 | 1.04 | 0.90 | 4.40 | 0.00 | 0.68 | 1.45 | 1.21 |
time (sec) |
N/A | 0.362 | 0.065 | 0.708 | 0.127 | 0.088 | 0.000 | 0.116 | 0.240 | 2.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 45 | 40 | 48 | 47 | 147 | 0 | 41 | 68 | 58 |
N.S. |
1 | 0.88 | 0.78 | 0.94 | 0.92 | 2.88 | 0.00 | 0.80 | 1.33 | 1.14 |
time (sec) |
N/A | 0.339 | 0.066 | 0.390 | 0.119 | 0.115 | 0.000 | 0.114 | 0.216 | 0.082 |
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 | 25 | 22 | 22 | 27 | 23 | 38 | 0 | 23 | 22 | 34 |
N.S. |
1 | 0.88 | 0.88 | 1.08 | 0.92 | 1.52 | 0.00 | 0.92 | 0.88 | 1.36 |
time (sec) |
N/A | 0.297 | 0.013 | 0.378 | 0.120 | 0.086 | 0.000 | 0.110 | 0.238 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 22 | 22 | 27 | 38 | 49 | 0 | 32 | 34 | 38 |
N.S. |
1 | 0.88 | 0.88 | 1.08 | 1.52 | 1.96 | 0.00 | 1.28 | 1.36 | 1.52 |
time (sec) |
N/A | 0.296 | 0.015 | 0.365 | 0.039 | 0.099 | 0.000 | 0.113 | 0.268 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 47 | 179 | 48 | 62 | 198 | 0 | 56 | 103 | 62 |
N.S. |
1 | 0.89 | 3.38 | 0.91 | 1.17 | 3.74 | 0.00 | 1.06 | 1.94 | 1.17 |
time (sec) |
N/A | 0.351 | 1.440 | 0.388 | 0.039 | 0.090 | 0.000 | 0.125 | 0.246 | 2.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 72 | 286 | 77 | 88 | 459 | 0 | 72 | 177 | 97 |
N.S. |
1 | 0.89 | 3.53 | 0.95 | 1.09 | 5.67 | 0.00 | 0.89 | 2.19 | 1.20 |
time (sec) |
N/A | 0.263 | 1.792 | 0.691 | 0.035 | 0.097 | 0.000 | 0.143 | 0.271 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 101 | 115 | 88 | 110 | 796 | 0 | 83 | 245 | 160 |
N.S. |
1 | 0.89 | 1.02 | 0.78 | 0.97 | 7.04 | 0.00 | 0.73 | 2.17 | 1.42 |
time (sec) |
N/A | 0.258 | 10.083 | 0.752 | 0.038 | 0.108 | 0.000 | 0.127 | 0.228 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 113 | 48 | 35 | 89 | 393 | 0 | 89 | 193 | 86 |
N.S. |
1 | 1.28 | 0.55 | 0.40 | 1.01 | 4.47 | 0.00 | 1.01 | 2.19 | 0.98 |
time (sec) |
N/A | 0.283 | 0.041 | 0.603 | 0.111 | 0.113 | 0.000 | 0.111 | 0.267 | 0.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 108 | 95 | 24 | 78 | 94 | 0 | 78 | 79 | 81 |
N.S. |
1 | 1.59 | 1.40 | 0.35 | 1.15 | 1.38 | 0.00 | 1.15 | 1.16 | 1.19 |
time (sec) |
N/A | 0.330 | 0.026 | 0.485 | 0.128 | 0.097 | 0.000 | 0.105 | 0.244 | 2.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 23 | 16 | 36 | 22 | 31 | 0 | 23 | 26 | 26 |
N.S. |
1 | 1.44 | 1.00 | 2.25 | 1.38 | 1.94 | 0.00 | 1.44 | 1.62 | 1.62 |
time (sec) |
N/A | 0.192 | 0.011 | 0.503 | 0.121 | 0.088 | 0.000 | 0.107 | 0.225 | 0.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 113 | 48 | 34 | 230 | 0 | 35 | 81 | 38 |
N.S. |
1 | 1.00 | 3.23 | 1.37 | 0.97 | 6.57 | 0.00 | 1.00 | 2.31 | 1.09 |
time (sec) |
N/A | 0.209 | 1.125 | 0.591 | 0.113 | 0.098 | 0.000 | 0.104 | 0.277 | 0.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 76 | 62 | 61 | 1097 | 0 | 50 | 186 | 110 |
N.S. |
1 | 1.00 | 1.03 | 0.84 | 0.82 | 14.82 | 0.00 | 0.68 | 2.51 | 1.49 |
time (sec) |
N/A | 0.249 | 11.059 | 0.678 | 0.107 | 0.108 | 0.000 | 0.105 | 0.251 | 2.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 113 | 97 | 59 | 81 | 549 | 0 | 81 | 182 | 86 |
N.S. |
1 | 1.28 | 1.10 | 0.67 | 0.92 | 6.24 | 0.00 | 0.92 | 2.07 | 0.98 |
time (sec) |
N/A | 0.409 | 0.068 | 0.633 | 0.114 | 0.092 | 0.000 | 0.107 | 0.258 | 0.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 104 | 24 | 47 | 69 | 94 | 0 | 69 | 71 | 70 |
N.S. |
1 | 1.49 | 0.34 | 0.67 | 0.99 | 1.34 | 0.00 | 0.99 | 1.01 | 1.00 |
time (sec) |
N/A | 0.329 | 0.012 | 0.546 | 0.122 | 0.100 | 0.000 | 0.108 | 0.230 | 2.347 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 97 | 22 | 138 | 75 | 113 | 0 | 76 | 82 | 81 |
N.S. |
1 | 1.37 | 0.31 | 1.94 | 1.06 | 1.59 | 0.00 | 1.07 | 1.15 | 1.14 |
time (sec) |
N/A | 0.298 | 0.015 | 0.539 | 0.113 | 0.095 | 0.000 | 0.105 | 0.260 | 0.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 108 | 113 | 150 | 87 | 628 | 0 | 88 | 208 | 93 |
N.S. |
1 | 1.15 | 1.20 | 1.60 | 0.93 | 6.68 | 0.00 | 0.94 | 2.21 | 0.99 |
time (sec) |
N/A | 0.498 | 1.451 | 0.556 | 0.122 | 0.113 | 0.000 | 0.108 | 0.236 | 2.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 382 | 51 | 36 | 0 | 1303 | 0 | 263 | 513 | 474 |
N.S. |
1 | 1.29 | 0.17 | 0.12 | 0.00 | 4.40 | 0.00 | 0.89 | 1.73 | 1.60 |
time (sec) |
N/A | 1.120 | 0.047 | 0.689 | 0.000 | 0.143 | 0.000 | 0.122 | 0.285 | 5.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 373 | 24 | 24 | 0 | 171 | 0 | 251 | 230 | 457 |
N.S. |
1 | 1.33 | 0.09 | 0.09 | 0.00 | 0.61 | 0.00 | 0.90 | 0.82 | 1.63 |
time (sec) |
N/A | 1.115 | 0.011 | 0.540 | 0.000 | 0.099 | 0.000 | 0.117 | 0.287 | 4.844 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 134 | 22 | 56 | 97 | 120 | 0 | 98 | 101 | 104 |
N.S. |
1 | 1.47 | 0.24 | 0.62 | 1.07 | 1.32 | 0.00 | 1.08 | 1.11 | 1.14 |
time (sec) |
N/A | 0.381 | 0.014 | 0.560 | 0.117 | 0.120 | 0.000 | 0.106 | 0.227 | 2.464 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 134 | 113 | 68 | 109 | 943 | 0 | 110 | 252 | 122 |
N.S. |
1 | 1.23 | 1.04 | 0.62 | 1.00 | 8.65 | 0.00 | 1.01 | 2.31 | 1.12 |
time (sec) |
N/A | 0.295 | 1.231 | 0.618 | 0.118 | 0.119 | 0.000 | 0.113 | 0.258 | 2.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 109 | 81 | 70 | 0 | 406 | 0 | 328 | 230 | 163 |
N.S. |
1 | 1.02 | 0.76 | 0.65 | 0.00 | 3.79 | 0.00 | 3.07 | 2.15 | 1.52 |
time (sec) |
N/A | 0.305 | 0.056 | 0.944 | 0.000 | 0.103 | 0.000 | 0.107 | 0.274 | 2.437 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | C | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 107 | 215 | 0 | 1604 | 0 | 456 | 5067 | 280 |
N.S. |
1 | 1.00 | 0.69 | 1.39 | 0.00 | 10.35 | 0.00 | 2.94 | 32.69 | 1.81 |
time (sec) |
N/A | 0.386 | 0.127 | 1.077 | 0.000 | 0.119 | 0.000 | 0.113 | 0.267 | 24.354 |
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 | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 167 | 205 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.464 | 1.660 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.265 | 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 | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 169 | 0 | 0 | 0 | 0 | 0 | 439 | 0 |
N.S. |
1 | 1.00 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.75 | 0.00 |
time (sec) |
N/A | 0.372 | 0.830 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 141 | 0 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 2.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.286 | 0.176 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 134 | 0 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 2.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.290 | 0.777 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 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 | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 164 | 0 | 0 | 0 | 0 | 0 | 440 | 0 |
N.S. |
1 | 1.00 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.89 | 0.00 |
time (sec) |
N/A | 0.571 | 0.606 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.249 | 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 | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 210 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.686 | 1.122 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 161 | 133 | 195 | 145 | 1226 | 0 | 193 | 248 | 0 |
N.S. |
1 | 0.52 | 0.43 | 0.63 | 0.47 | 3.94 | 0.00 | 0.62 | 0.80 | 0.00 |
time (sec) |
N/A | 1.525 | 0.175 | 1.982 | 0.138 | 0.104 | 0.000 | 0.134 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 103 | 104 | 131 | 90 | 458 | 0 | 137 | 139 | 0 |
N.S. |
1 | 0.53 | 0.54 | 0.68 | 0.47 | 2.37 | 0.00 | 0.71 | 0.72 | 0.00 |
time (sec) |
N/A | 0.486 | 0.124 | 1.613 | 0.141 | 0.107 | 0.000 | 0.134 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 53 | 51 | 218 | 35 | 53 | 0 | 63 | 31 | 0 |
N.S. |
1 | 0.64 | 0.61 | 2.63 | 0.42 | 0.64 | 0.00 | 0.76 | 0.37 | 0.00 |
time (sec) |
N/A | 0.356 | 0.039 | 1.884 | 0.129 | 0.099 | 0.000 | 0.118 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 53 | 51 | 48 | 56 | 70 | 0 | 99 | 58 | 0 |
N.S. |
1 | 0.64 | 0.61 | 0.58 | 0.67 | 0.84 | 0.00 | 1.19 | 0.70 | 0.00 |
time (sec) |
N/A | 0.390 | 0.088 | 1.195 | 0.139 | 0.092 | 0.000 | 0.128 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 107 | 334 | 131 | 112 | 613 | 0 | 176 | 303 | 0 |
N.S. |
1 | 0.54 | 1.70 | 0.66 | 0.57 | 3.11 | 0.00 | 0.89 | 1.54 | 0.00 |
time (sec) |
N/A | 0.888 | 7.135 | 1.675 | 0.159 | 0.109 | 0.000 | 0.134 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 319 | 169 | 164 | 195 | 167 | 1617 | 0 | 230 | 830 | 0 |
N.S. |
1 | 0.53 | 0.51 | 0.61 | 0.52 | 5.07 | 0.00 | 0.72 | 2.60 | 0.00 |
time (sec) |
N/A | 1.764 | 11.478 | 1.831 | 0.137 | 0.112 | 0.000 | 0.143 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 137 | 124 | 118 | 0 | 697 | 0 | 0 | 11 | 0 |
N.S. |
1 | 0.87 | 0.79 | 0.75 | 0.00 | 4.44 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.004 | 0.382 | 1.779 | 0.000 | 0.126 | 0.000 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 101 | 88 | 88 | 0 | 230 | 0 | 0 | 11 | 0 |
N.S. |
1 | 0.88 | 0.77 | 0.77 | 0.00 | 2.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.646 | 0.327 | 0.860 | 0.000 | 0.115 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 69 | 59 | 58 | 0 | 215 | 0 | 0 | 9 | 0 |
N.S. |
1 | 0.90 | 0.77 | 0.75 | 0.00 | 2.79 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.353 | 0.132 | 0.555 | 0.000 | 0.106 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | F(-1) | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 9 | 0 | 9 | 9 | 8 | 9 | 9 | 11 |
N.S. |
1 | 1.00 | 1.29 | 0.00 | 1.29 | 1.29 | 1.14 | 1.29 | 1.29 | 1.57 |
time (sec) |
N/A | 0.324 | 1.907 | 0.000 | 0.470 | 0.100 | 10.144 | 0.177 | 0.273 | 3.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 137 | 124 | 118 | 0 | 698 | 0 | 0 | 11 | 0 |
N.S. |
1 | 0.87 | 0.79 | 0.75 | 0.00 | 4.45 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.608 | 0.459 | 1.716 | 0.000 | 0.141 | 0.000 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 101 | 88 | 88 | 0 | 230 | 0 | 0 | 11 | 0 |
N.S. |
1 | 0.88 | 0.77 | 0.77 | 0.00 | 2.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.682 | 0.368 | 0.839 | 0.000 | 0.093 | 0.000 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 69 | 62 | 58 | 0 | 216 | 0 | 0 | 9 | 0 |
N.S. |
1 | 0.90 | 0.81 | 0.75 | 0.00 | 2.81 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.588 | 0.130 | 0.566 | 0.000 | 0.102 | 0.000 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | F(-1) | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 9 | 0 | 9 | 9 | 8 | 9 | 9 | 11 |
N.S. |
1 | 1.00 | 1.29 | 0.00 | 1.29 | 1.29 | 1.14 | 1.29 | 1.29 | 1.57 |
time (sec) |
N/A | 0.532 | 3.648 | 0.000 | 0.215 | 0.096 | 2.013 | 0.191 | 0.244 | 2.852 |