Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 25 | 27 | 28 | 26 | 28 | 26 | 28 | 27 |
N.S. |
1 | 1.19 | 1.29 | 1.33 | 1.24 | 1.33 | 1.24 | 1.33 | 1.29 |
time (sec) |
N/A | 10.452 | 0.025 | 0.319 | 0.199 | 0.252 | 0.874 | 0.276 | 11.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 46 | 19 | 18 | 17 | 17 | 15 | 0 | 19 |
N.S. |
1 | 2.09 | 0.86 | 0.82 | 0.77 | 0.77 | 0.68 | 0.00 | 0.86 |
time (sec) |
N/A | 0.220 | 0.075 | 0.164 | 0.238 | 0.249 | 2.942 | 0.000 | 11.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 103 | 58 | 112 | 244 | 250 | 144 | 360 | 783 |
N.S. |
1 | 2.86 | 1.61 | 3.11 | 6.78 | 6.94 | 4.00 | 10.00 | 21.75 |
time (sec) |
N/A | 7.013 | 0.198 | 0.611 | 0.298 | 0.246 | 0.267 | 0.342 | 12.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 20 | 29 | 32 | 32 | 32 | 36 | 27 | 37 |
N.S. |
1 | 0.91 | 1.32 | 1.45 | 1.45 | 1.45 | 1.64 | 1.23 | 1.68 |
time (sec) |
N/A | 0.156 | 0.011 | 0.068 | 0.198 | 0.227 | 0.075 | 0.271 | 0.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 22 | 22 | 14 | 19 | 19 | 12 | 13 |
N.S. |
1 | 0.00 | 0.85 | 0.85 | 0.54 | 0.73 | 0.73 | 0.46 | 0.50 |
time (sec) |
N/A | 0.000 | 0.108 | 2.565 | 0.314 | 0.227 | 0.134 | 0.273 | 11.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 52 | 31 | 97 | 91 | 107 | 148 | 0 |
N.S. |
1 | 0.00 | 2.00 | 1.19 | 3.73 | 3.50 | 4.12 | 5.69 | 0.00 |
time (sec) |
N/A | 0.000 | 0.472 | 3.382 | 0.355 | 0.235 | 0.217 | 0.317 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 27 | 27 | 34 | 25 | 32 | 25 | 24 |
N.S. |
1 | 0.00 | 0.90 | 0.90 | 1.13 | 0.83 | 1.07 | 0.83 | 0.80 |
time (sec) |
N/A | 0.000 | 0.118 | 13.368 | 0.316 | 0.244 | 0.169 | 0.342 | 11.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 6 | 6 | 5 | 5 | 5 | 5 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.122 | 0.000 | 0.021 | 0.197 | 0.216 | 0.017 | 0.269 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 228 | 23 | 69 | 68 | 145 | 76 | 0 | 68 |
N.S. |
1 | 9.12 | 0.92 | 2.76 | 2.72 | 5.80 | 3.04 | 0.00 | 2.72 |
time (sec) |
N/A | 0.722 | 0.908 | 6.222 | 0.293 | 0.237 | 4.258 | 0.000 | 0.421 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 22 | 24 | 23 | 34 | 30 | 29 | 24 | 22 |
N.S. |
1 | 1.05 | 1.14 | 1.10 | 1.62 | 1.43 | 1.38 | 1.14 | 1.05 |
time (sec) |
N/A | 0.229 | 0.071 | 0.384 | 0.220 | 0.237 | 0.113 | 0.273 | 10.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 112 | 22 | 21 | 0 | 25 | 22 | 35 | 0 |
N.S. |
1 | 4.48 | 0.88 | 0.84 | 0.00 | 1.00 | 0.88 | 1.40 | 0.00 |
time (sec) |
N/A | 2.091 | 2.000 | 14.929 | 0.000 | 0.239 | 0.144 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 365 | 51 | 47 | 0 | 57 | 60 | 64 | 0 |
N.S. |
1 | 14.04 | 1.96 | 1.81 | 0.00 | 2.19 | 2.31 | 2.46 | 0.00 |
time (sec) |
N/A | 3.392 | 0.134 | 0.936 | 0.000 | 0.232 | 0.231 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 46 | 31 | 24 | 23 | 23 | 29 | 23 | 23 |
N.S. |
1 | 2.19 | 1.48 | 1.14 | 1.10 | 1.10 | 1.38 | 1.10 | 1.10 |
time (sec) |
N/A | 0.210 | 0.023 | 0.044 | 0.189 | 0.235 | 0.065 | 0.277 | 11.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 65 | 30 | 26 | 24 | 26 | 24 | 0 | 23 |
N.S. |
1 | 2.10 | 0.97 | 0.84 | 0.77 | 0.84 | 0.77 | 0.00 | 0.74 |
time (sec) |
N/A | 0.395 | 2.047 | 5.087 | 0.375 | 0.228 | 0.211 | 0.000 | 11.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 26 | 26 | 42 | 24 | 3058 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.90 | 0.90 | 1.45 | 0.83 | 105.45 | 0.00 |
time (sec) |
N/A | 0.000 | 0.185 | 22.950 | 0.273 | 0.231 | 0.682 | 35.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 18 | 16 | 13 | 12 | 17 | 10 | 12 | 14 |
N.S. |
1 | 0.64 | 0.57 | 0.46 | 0.43 | 0.61 | 0.36 | 0.43 | 0.50 |
time (sec) |
N/A | 0.160 | 0.002 | 0.025 | 0.190 | 0.221 | 0.027 | 0.276 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 86 | 81 | 114 | 136 | 90 | 0 | 79 |
N.S. |
1 | 0.00 | 2.77 | 2.61 | 3.68 | 4.39 | 2.90 | 0.00 | 2.55 |
time (sec) |
N/A | 0.000 | 0.193 | 0.889 | 0.299 | 0.257 | 0.323 | 0.000 | 11.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 33 | 18 | 20 | 17 | 19 | 19 | 19 | 21 |
N.S. |
1 | 1.50 | 0.82 | 0.91 | 0.77 | 0.86 | 0.86 | 0.86 | 0.95 |
time (sec) |
N/A | 0.473 | 0.110 | 0.400 | 0.220 | 0.223 | 0.049 | 0.282 | 10.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 27 | 27 | 27 | 28 | 30 | 26 | 31 | 26 |
N.S. |
1 | 0.96 | 0.96 | 0.96 | 1.00 | 1.07 | 0.93 | 1.11 | 0.93 |
time (sec) |
N/A | 0.486 | 0.562 | 1.675 | 0.222 | 0.234 | 0.226 | 0.293 | 14.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 56 | 19 | 40 | 46 | 51 | 44 | 55 | 40 |
N.S. |
1 | 2.67 | 0.90 | 1.90 | 2.19 | 2.43 | 2.10 | 2.62 | 1.90 |
time (sec) |
N/A | 0.285 | 0.647 | 0.118 | 0.259 | 0.238 | 0.086 | 0.270 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | B | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 46 | 470 | 30 | 32 | 48 | 56 | 32 |
N.S. |
1 | 0.00 | 1.77 | 18.08 | 1.15 | 1.23 | 1.85 | 2.15 | 1.23 |
time (sec) |
N/A | 0.000 | 0.337 | 0.026 | 0.276 | 0.237 | 19.044 | 0.721 | 11.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 36 | 22 | 19 | 43 | 18 | 17 | 31 | 12 |
N.S. |
1 | 1.57 | 0.96 | 0.83 | 1.87 | 0.78 | 0.74 | 1.35 | 0.52 |
time (sec) |
N/A | 0.250 | 0.029 | 0.098 | 0.208 | 0.236 | 0.061 | 0.268 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 33 | 26 | 30 | 25 | 22 | 26 | 18 |
N.S. |
1 | 0.00 | 1.27 | 1.00 | 1.15 | 0.96 | 0.85 | 1.00 | 0.69 |
time (sec) |
N/A | 0.000 | 0.258 | 0.465 | 0.303 | 0.232 | 0.261 | 0.309 | 0.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 20 | 16 | 16 | 15 | 15 | 17 | 15 | 15 |
N.S. |
1 | 1.18 | 0.94 | 0.94 | 0.88 | 0.88 | 1.00 | 0.88 | 0.88 |
time (sec) |
N/A | 0.217 | 0.166 | 0.076 | 0.177 | 0.257 | 0.093 | 0.283 | 10.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 45 | 30 | 27 | 68 | 31 | 56 | 32 | 32 |
N.S. |
1 | 1.73 | 1.15 | 1.04 | 2.62 | 1.19 | 2.15 | 1.23 | 1.23 |
time (sec) |
N/A | 0.259 | 0.216 | 0.059 | 0.224 | 0.251 | 0.097 | 0.278 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 26 | 36 | 0 | 34 | 29 | 0 | 0 |
N.S. |
1 | 0.00 | 0.76 | 1.06 | 0.00 | 1.00 | 0.85 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.128 | 13.175 | 0.000 | 0.239 | 8.722 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 173 | 42 | 43 | 108 | 82 | 51 | 93 | 178 |
N.S. |
1 | 6.65 | 1.62 | 1.65 | 4.15 | 3.15 | 1.96 | 3.58 | 6.85 |
time (sec) |
N/A | 1.537 | 0.145 | 0.357 | 0.226 | 0.253 | 0.086 | 0.284 | 10.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 27 | 20 | 20 | 17 | 17 | 22 | 38 | 22 |
N.S. |
1 | 1.17 | 0.87 | 0.87 | 0.74 | 0.74 | 0.96 | 1.65 | 0.96 |
time (sec) |
N/A | 0.169 | 0.028 | 0.087 | 0.232 | 0.231 | 0.302 | 0.272 | 10.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 53 | 27 | 56 | 28 | 24 | 28 | 0 |
N.S. |
1 | 0.00 | 1.96 | 1.00 | 2.07 | 1.04 | 0.89 | 1.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.941 | 0.129 | 0.260 | 0.243 | 0.121 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 30 | 34 | 32 | 33 | 36 | 42 | 32 | 31 |
N.S. |
1 | 1.03 | 1.17 | 1.10 | 1.14 | 1.24 | 1.45 | 1.10 | 1.07 |
time (sec) |
N/A | 0.214 | 0.033 | 0.071 | 0.178 | 0.229 | 0.056 | 0.285 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 21 | 19 | 21 | 22 | 19 | 23 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 0.86 | 0.95 | 1.00 | 0.86 | 1.05 |
time (sec) |
N/A | 0.000 | 0.263 | 0.393 | 0.222 | 0.230 | 0.302 | 0.290 | 11.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 36 | 27 | 25 | 44 | 37 | 27 | 35 | 30 |
N.S. |
1 | 1.71 | 1.29 | 1.19 | 2.10 | 1.76 | 1.29 | 1.67 | 1.43 |
time (sec) |
N/A | 0.409 | 0.193 | 0.120 | 0.216 | 0.247 | 0.082 | 0.278 | 11.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 21 | 21 | 22 | 20 | 20 | 22 | 20 |
N.S. |
1 | 0.00 | 0.91 | 0.91 | 0.96 | 0.87 | 0.87 | 0.96 | 0.87 |
time (sec) |
N/A | 0.000 | 0.463 | 0.107 | 0.211 | 0.240 | 0.115 | 0.270 | 11.179 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 39 | 27 | 33 | 44 | 48 | 48 | 47 | 40 |
N.S. |
1 | 1.39 | 0.96 | 1.18 | 1.57 | 1.71 | 1.71 | 1.68 | 1.43 |
time (sec) |
N/A | 0.314 | 0.038 | 0.087 | 0.179 | 0.230 | 0.539 | 0.271 | 10.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | A | A | F(-1) | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 31 | 0 | 32 | 34 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.03 | 0.00 | 1.07 | 1.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.156 | 0.000 | 0.370 | 0.246 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 138 | 312 | 107 | 119 | 92 | 128 | 113 | 494 |
N.S. |
1 | 7.67 | 17.33 | 5.94 | 6.61 | 5.11 | 7.11 | 6.28 | 27.44 |
time (sec) |
N/A | 0.522 | 0.212 | 0.158 | 0.198 | 0.236 | 3.972 | 0.279 | 0.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 47 | 26 | 25 | 24 | 24 | 20 | 26 | 34 |
N.S. |
1 | 1.74 | 0.96 | 0.93 | 0.89 | 0.89 | 0.74 | 0.96 | 1.26 |
time (sec) |
N/A | 0.334 | 0.011 | 0.082 | 0.179 | 0.224 | 0.117 | 0.293 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 42 | 42 | 41 | 40 | 40 | 0 | 40 | 0 |
N.S. |
1 | 1.40 | 1.40 | 1.37 | 1.33 | 1.33 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 1.474 | 0.092 | 0.476 | 0.233 | 0.248 | 0.000 | 0.354 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 23 | 27 | 25 | 25 | 22 | 25 | 21 |
N.S. |
1 | 0.00 | 0.92 | 1.08 | 1.00 | 1.00 | 0.88 | 1.00 | 0.84 |
time (sec) |
N/A | 0.000 | 0.666 | 0.235 | 0.224 | 0.244 | 0.085 | 0.293 | 11.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 55 | 45 | 82 | 82 | 0 | 82 | 78 |
N.S. |
1 | 0.00 | 1.77 | 1.45 | 2.65 | 2.65 | 0.00 | 2.65 | 2.52 |
time (sec) |
N/A | 0.000 | 0.762 | 1.389 | 0.526 | 0.244 | 0.000 | 0.406 | 11.836 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 43 | 34 | 28 | 42 | 53 | 85 |
N.S. |
1 | 0.00 | 1.00 | 1.39 | 1.10 | 0.90 | 1.35 | 1.71 | 2.74 |
time (sec) |
N/A | 0.000 | 0.114 | 8.489 | 0.319 | 0.238 | 32.089 | 0.528 | 10.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 12 | 14 | 10 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 0.86 | 1.00 | 0.71 | 1.00 | 1.00 |
time (sec) |
N/A | 0.193 | 0.012 | 0.048 | 0.227 | 0.224 | 0.077 | 0.274 | 10.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 26 | 30 | 24 | 29 | 24 | 28 | 25 |
N.S. |
1 | 0.00 | 0.84 | 0.97 | 0.77 | 0.94 | 0.77 | 0.90 | 0.81 |
time (sec) |
N/A | 0.000 | 0.389 | 0.582 | 0.228 | 0.250 | 0.332 | 0.343 | 10.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 60 | 65 | 56 | 48 | 77 | 61 | 57 | 55 |
N.S. |
1 | 2.14 | 2.32 | 2.00 | 1.71 | 2.75 | 2.18 | 2.04 | 1.96 |
time (sec) |
N/A | 1.099 | 0.131 | 0.460 | 0.271 | 0.238 | 0.429 | 0.388 | 12.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 26 | 25 | 25 | 24 | 30 | 32 | 24 | 20 |
N.S. |
1 | 1.18 | 1.14 | 1.14 | 1.09 | 1.36 | 1.45 | 1.09 | 0.91 |
time (sec) |
N/A | 0.212 | 0.086 | 0.061 | 0.283 | 0.230 | 0.075 | 0.261 | 10.783 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 22 | 24 | 66 | 66 | 54 | 79 | 236 |
N.S. |
1 | 0.00 | 0.92 | 1.00 | 2.75 | 2.75 | 2.25 | 3.29 | 9.83 |
time (sec) |
N/A | 0.000 | 0.186 | 0.855 | 0.246 | 0.234 | 0.089 | 0.312 | 11.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 16 | 18 | 15 | 14 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.90 | 0.75 | 0.70 | 0.85 | 0.75 |
time (sec) |
N/A | 0.237 | 2.531 | 0.918 | 0.294 | 0.242 | 0.060 | 0.274 | 10.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 20 | 17 | 15 | 16 | 16 | 15 | 16 | 16 |
N.S. |
1 | 1.54 | 1.31 | 1.15 | 1.23 | 1.23 | 1.15 | 1.23 | 1.23 |
time (sec) |
N/A | 0.133 | 0.001 | 0.023 | 0.187 | 0.220 | 0.018 | 0.279 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 108 | 25 | 28 | 29 | 29 | 24 | 0 | 32 |
N.S. |
1 | 4.00 | 0.93 | 1.04 | 1.07 | 1.07 | 0.89 | 0.00 | 1.19 |
time (sec) |
N/A | 0.453 | 0.503 | 0.422 | 0.341 | 0.254 | 2.273 | 0.000 | 10.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 29 | 50 | 28 | 24 | 50 | 24 |
N.S. |
1 | 0.00 | 0.00 | 1.21 | 2.08 | 1.17 | 1.00 | 2.08 | 1.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.490 | 0.295 | 0.237 | 0.202 | 0.309 | 11.538 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 6 | 4 | 4 | 5 | 4 | 4 | 3 | 5 | 4 |
N.S. |
1 | 0.67 | 0.67 | 0.83 | 0.67 | 0.67 | 0.50 | 0.83 | 0.67 |
time (sec) |
N/A | 0.114 | 0.000 | 0.019 | 0.185 | 0.225 | 0.018 | 0.287 | 0.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 25 | 25 | 47 | 34 | 39 | 34 | 57 |
N.S. |
1 | 0.00 | 1.04 | 1.04 | 1.96 | 1.42 | 1.62 | 1.42 | 2.38 |
time (sec) |
N/A | 0.000 | 2.410 | 109.948 | 0.327 | 0.233 | 0.140 | 0.311 | 11.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 61 | 45 | 78 | 42 | 42 | 74 | 67 |
N.S. |
1 | 0.00 | 2.26 | 1.67 | 2.89 | 1.56 | 1.56 | 2.74 | 2.48 |
time (sec) |
N/A | 0.000 | 2.231 | 0.593 | 0.346 | 0.226 | 0.186 | 1.033 | 0.835 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 25 | 27 | 22 | 0 | 0 | 29 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.08 | 0.88 | 0.00 | 0.00 | 1.16 |
time (sec) |
N/A | 0.000 | 5.228 | 34.555 | 0.271 | 0.235 | 0.000 | 0.000 | 11.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 21 | 23 | 20 | 39 | 26 | 15 | 19 | 19 |
N.S. |
1 | 1.11 | 1.21 | 1.05 | 2.05 | 1.37 | 0.79 | 1.00 | 1.00 |
time (sec) |
N/A | 0.308 | 0.098 | 0.144 | 0.296 | 0.292 | 0.050 | 0.267 | 10.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 17 | 17 | 18 | 18 | 20 | 20 | 16 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 1.00 | 1.00 | 1.11 | 1.11 | 0.89 |
time (sec) |
N/A | 0.222 | 0.011 | 0.128 | 0.192 | 0.226 | 0.307 | 0.259 | 0.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 18 | 14 | 12 | 12 | 12 | 10 | 12 | 11 |
N.S. |
1 | 0.75 | 0.58 | 0.50 | 0.50 | 0.50 | 0.42 | 0.50 | 0.46 |
time (sec) |
N/A | 0.128 | 0.000 | 0.023 | 0.181 | 0.220 | 0.020 | 0.260 | 10.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 43 | 37 | 49 | 58 | 45 | 71 | 65 | 45 |
N.S. |
1 | 1.54 | 1.32 | 1.75 | 2.07 | 1.61 | 2.54 | 2.32 | 1.61 |
time (sec) |
N/A | 9.847 | 0.142 | 5.490 | 0.307 | 0.239 | 0.685 | 0.581 | 11.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 48 | 48 | 36 | 34 | 34 | 36 | 35 | 32 |
N.S. |
1 | 2.29 | 2.29 | 1.71 | 1.62 | 1.62 | 1.71 | 1.67 | 1.52 |
time (sec) |
N/A | 0.171 | 0.011 | 0.050 | 0.177 | 0.247 | 0.058 | 0.265 | 10.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 182 | 26 | 26 | 31 | 25 | 29 | 123 | 0 |
N.S. |
1 | 6.50 | 0.93 | 0.93 | 1.11 | 0.89 | 1.04 | 4.39 | 0.00 |
time (sec) |
N/A | 0.803 | 0.461 | 0.702 | 0.297 | 0.252 | 0.189 | 0.395 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 50 | 51 | 45 | 42 | 44 | 41 | 45 | 43 |
N.S. |
1 | 1.25 | 1.28 | 1.12 | 1.05 | 1.10 | 1.02 | 1.12 | 1.08 |
time (sec) |
N/A | 0.219 | 0.018 | 0.060 | 0.180 | 0.226 | 0.077 | 0.259 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 15 | 13 | 11 | 15 | 9 | 8 | 13 | 9 |
N.S. |
1 | 1.36 | 1.18 | 1.00 | 1.36 | 0.82 | 0.73 | 1.18 | 0.82 |
time (sec) |
N/A | 0.146 | 0.001 | 0.026 | 0.175 | 0.256 | 0.049 | 0.263 | 10.726 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 9 | 15 | 8 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.67 | 0.89 | 0.89 | 0.89 | 0.89 |
time (sec) |
N/A | 0.158 | 0.043 | 0.136 | 0.206 | 0.246 | 0.047 | 0.277 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 40 | 21 | 18 | 17 | 17 | 15 | 20 | 20 |
N.S. |
1 | 2.50 | 1.31 | 1.12 | 1.06 | 1.06 | 0.94 | 1.25 | 1.25 |
time (sec) |
N/A | 0.170 | 0.004 | 0.081 | 0.185 | 0.231 | 0.056 | 0.321 | 10.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 91 | 30 | 28 | 280 | 46 | 63 | 54 | 50 |
N.S. |
1 | 3.64 | 1.20 | 1.12 | 11.20 | 1.84 | 2.52 | 2.16 | 2.00 |
time (sec) |
N/A | 0.623 | 0.121 | 0.086 | 0.205 | 0.228 | 0.104 | 0.269 | 10.968 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 11 | 11 | 11 | 21 | 21 | 20 | 21 | 25 |
N.S. |
1 | 0.55 | 0.55 | 0.55 | 1.05 | 1.05 | 1.00 | 1.05 | 1.25 |
time (sec) |
N/A | 0.284 | 0.024 | 0.057 | 0.182 | 0.238 | 0.052 | 0.271 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 36 | 46 | 32 | 34 | 35 | 32 | 38 | 41 |
N.S. |
1 | 1.44 | 1.84 | 1.28 | 1.36 | 1.40 | 1.28 | 1.52 | 1.64 |
time (sec) |
N/A | 0.376 | 0.961 | 0.121 | 0.207 | 0.247 | 0.071 | 0.267 | 11.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 74 | 49 | 51 | 136 | 38 | 46 | 48 | 53 |
N.S. |
1 | 3.22 | 2.13 | 2.22 | 5.91 | 1.65 | 2.00 | 2.09 | 2.30 |
time (sec) |
N/A | 0.629 | 0.154 | 0.191 | 0.225 | 0.254 | 0.358 | 0.285 | 11.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 47 | 35 | 32 | 97 | 81 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.74 | 1.30 | 1.19 | 3.59 | 3.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.300 | 2.769 | 0.305 | 0.251 | 0.322 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 16 | 19 | 18 | 20 | 17 | 20 | 18 |
N.S. |
1 | 0.00 | 0.84 | 1.00 | 0.95 | 1.05 | 0.89 | 1.05 | 0.95 |
time (sec) |
N/A | 0.000 | 0.121 | 0.375 | 0.304 | 0.245 | 0.093 | 0.267 | 11.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 31 | 28 | 25 | 25 | 22 | 25 | 0 |
N.S. |
1 | 0.00 | 0.97 | 0.88 | 0.78 | 0.78 | 0.69 | 0.78 | 0.00 |
time (sec) |
N/A | 0.000 | 5.090 | 0.409 | 0.320 | 0.231 | 0.095 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 18 | 17 | 13 | 12 | 12 | 10 | 13 | 12 |
N.S. |
1 | 1.12 | 1.06 | 0.81 | 0.75 | 0.75 | 0.62 | 0.81 | 0.75 |
time (sec) |
N/A | 0.147 | 0.010 | 0.100 | 0.185 | 0.226 | 0.029 | 0.266 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 14 | 22 | 21 | 23 | 23 | 17 | 23 | 18 |
N.S. |
1 | 0.93 | 1.47 | 1.40 | 1.53 | 1.53 | 1.13 | 1.53 | 1.20 |
time (sec) |
N/A | 0.158 | 0.000 | 0.046 | 0.187 | 0.233 | 0.020 | 0.269 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 14 | 14 | 13 | 13 | 12 | 0 | 13 |
N.S. |
1 | 1.00 | 0.88 | 0.88 | 0.81 | 0.81 | 0.75 | 0.00 | 0.81 |
time (sec) |
N/A | 0.168 | 0.016 | 0.042 | 0.237 | 0.241 | 0.073 | 0.000 | 10.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 31 | 60 | 64 | 106 | 112 | 573 | 562 |
N.S. |
1 | 0.00 | 1.15 | 2.22 | 2.37 | 3.93 | 4.15 | 21.22 | 20.81 |
time (sec) |
N/A | 0.000 | 0.060 | 3.753 | 0.332 | 0.251 | 0.146 | 4.692 | 11.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 18 | 16 | 17 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.20 | 1.07 | 1.13 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.201 | 0.037 | 0.187 | 0.196 | 0.237 | 0.075 | 0.274 | 10.843 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 61 | 54 | 83 | 83 | 0 | 96 | 0 |
N.S. |
1 | 0.00 | 1.85 | 1.64 | 2.52 | 2.52 | 0.00 | 2.91 | 0.00 |
time (sec) |
N/A | 0.000 | 0.127 | 0.485 | 0.268 | 0.259 | 0.000 | 0.334 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 4 | 4 | 5 | 4 | 4 | 3 | 5 | 4 |
N.S. |
1 | 0.31 | 0.31 | 0.38 | 0.31 | 0.31 | 0.23 | 0.38 | 0.31 |
time (sec) |
N/A | 0.121 | 0.000 | 0.017 | 0.189 | 0.224 | 0.018 | 0.271 | 0.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 13 | 14 | 17 | 13 | 14 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 0.81 | 0.88 | 1.06 | 0.81 | 0.88 |
time (sec) |
N/A | 0.134 | 0.000 | 0.014 | 0.187 | 0.223 | 0.016 | 0.265 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 23 | 15 | 12 | 19 | 26 | 14 | 19 | 12 |
N.S. |
1 | 1.35 | 0.88 | 0.71 | 1.12 | 1.53 | 0.82 | 1.12 | 0.71 |
time (sec) |
N/A | 0.160 | 0.023 | 0.145 | 0.191 | 0.247 | 0.079 | 0.305 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 25 | 24 | 47 | 47 | 48 | 51 | 45 |
N.S. |
1 | 0.00 | 0.89 | 0.86 | 1.68 | 1.68 | 1.71 | 1.82 | 1.61 |
time (sec) |
N/A | 0.000 | 0.619 | 199.639 | 0.314 | 0.250 | 0.164 | 0.359 | 11.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 230 | 48 | 159 | 722 | 163 | 168 | 150 | 208 |
N.S. |
1 | 7.19 | 1.50 | 4.97 | 22.56 | 5.09 | 5.25 | 4.69 | 6.50 |
time (sec) |
N/A | 3.745 | 10.145 | 0.489 | 0.222 | 0.249 | 0.182 | 0.282 | 11.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 30 | 38 | 49 | 72 | 34 | 136 | 66 |
N.S. |
1 | 0.00 | 0.97 | 1.23 | 1.58 | 2.32 | 1.10 | 4.39 | 2.13 |
time (sec) |
N/A | 0.000 | 1.562 | 0.404 | 0.532 | 0.263 | 0.213 | 0.291 | 12.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 16 | 16 | 16 | 36 | 18 | 12 | 18 | 15 |
N.S. |
1 | 0.76 | 0.76 | 0.76 | 1.71 | 0.86 | 0.57 | 0.86 | 0.71 |
time (sec) |
N/A | 0.201 | 0.086 | 0.047 | 0.210 | 0.250 | 0.046 | 0.264 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | A | A | A | A | A | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 39 | 0 | 27 | 26 | 29 | 29 | 29 | 27 |
N.S. |
1 | 1.22 | 0.00 | 0.84 | 0.81 | 0.91 | 0.91 | 0.91 | 0.84 |
time (sec) |
N/A | 0.448 | 0.000 | 0.204 | 0.273 | 0.260 | 0.294 | 0.319 | 10.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 39 | 37 | 26 | 0 | 33 | 26 | 54 | 32 |
N.S. |
1 | 1.34 | 1.28 | 0.90 | 0.00 | 1.14 | 0.90 | 1.86 | 1.10 |
time (sec) |
N/A | 0.806 | 5.111 | 0.196 | 0.000 | 0.255 | 0.162 | 0.296 | 11.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | B | A | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 0 | 72 | 125 | 62 | 126 | 150 | 124 |
N.S. |
1 | 0.00 | 0.00 | 2.06 | 3.57 | 1.77 | 3.60 | 4.29 | 3.54 |
time (sec) |
N/A | 0.000 | 0.000 | 4.091 | 0.304 | 0.270 | 1.016 | 0.464 | 11.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 18 | 18 | 16 | 94 | 15 | 17 | 15 | 15 |
N.S. |
1 | 0.86 | 0.86 | 0.76 | 4.48 | 0.71 | 0.81 | 0.71 | 0.71 |
time (sec) |
N/A | 0.503 | 0.176 | 0.596 | 0.310 | 0.237 | 0.097 | 0.288 | 10.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | F | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 57 | 79 | 0 | 77 | 104 | 102 | 87 |
N.S. |
1 | 0.00 | 2.19 | 3.04 | 0.00 | 2.96 | 4.00 | 3.92 | 3.35 |
time (sec) |
N/A | 0.000 | 0.479 | 0.078 | 0.000 | 0.252 | 0.170 | 0.301 | 11.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 28 | 28 | 30 | 26 | 30 | 27 | 30 | 0 |
N.S. |
1 | 1.12 | 1.12 | 1.20 | 1.04 | 1.20 | 1.08 | 1.20 | 0.00 |
time (sec) |
N/A | 0.382 | 0.246 | 0.302 | 0.298 | 0.254 | 0.127 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 19 | 11 | 11 | 14 | 10 | 7 | 10 | 12 |
N.S. |
1 | 1.06 | 0.61 | 0.61 | 0.78 | 0.56 | 0.39 | 0.56 | 0.67 |
time (sec) |
N/A | 0.149 | 0.028 | 0.018 | 0.176 | 0.243 | 0.034 | 0.265 | 10.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 28 | 17 | 12 | 11 | 20 | 8 | 11 | 13 |
N.S. |
1 | 1.75 | 1.06 | 0.75 | 0.69 | 1.25 | 0.50 | 0.69 | 0.81 |
time (sec) |
N/A | 0.515 | 0.049 | 0.045 | 0.181 | 0.258 | 0.062 | 0.260 | 10.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 32 | 24 | 0 | 25 | 0 | 48 | 26 |
N.S. |
1 | 0.00 | 1.14 | 0.86 | 0.00 | 0.89 | 0.00 | 1.71 | 0.93 |
time (sec) |
N/A | 0.000 | 6.958 | 0.170 | 0.000 | 0.254 | 0.000 | 0.285 | 10.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 58 | 18 | 28 | 57 | 29 | 29 | 57 | 27 |
N.S. |
1 | 2.64 | 0.82 | 1.27 | 2.59 | 1.32 | 1.32 | 2.59 | 1.23 |
time (sec) |
N/A | 0.273 | 0.151 | 0.246 | 0.190 | 0.256 | 0.128 | 0.266 | 10.224 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 17 | 17 | 15 | 17 | 17 | 14 | 26 | 17 |
N.S. |
1 | 0.89 | 0.89 | 0.79 | 0.89 | 0.89 | 0.74 | 1.37 | 0.89 |
time (sec) |
N/A | 0.175 | 0.013 | 0.094 | 0.179 | 0.235 | 0.111 | 0.259 | 0.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 21 | 22 | 23 | 23 | 26 | 23 | 21 |
N.S. |
1 | 0.96 | 0.78 | 0.81 | 0.85 | 0.85 | 0.96 | 0.85 | 0.78 |
time (sec) |
N/A | 0.188 | 0.111 | 0.036 | 0.189 | 0.238 | 0.052 | 0.264 | 10.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 52 | 64 | 68 | 68 | 63 | 65 | 0 |
N.S. |
1 | 0.00 | 1.68 | 2.06 | 2.19 | 2.19 | 2.03 | 2.10 | 0.00 |
time (sec) |
N/A | 0.000 | 0.093 | 0.786 | 0.307 | 0.252 | 0.226 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 23 | 28 | 19 | 23 | 29 | 19 | 22 | 21 |
N.S. |
1 | 1.10 | 1.33 | 0.90 | 1.10 | 1.38 | 0.90 | 1.05 | 1.00 |
time (sec) |
N/A | 0.222 | 0.020 | 0.198 | 0.183 | 0.237 | 0.068 | 0.262 | 10.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 26 | 24 | 24 | 24 | 26 | 31 | 23 |
N.S. |
1 | 0.00 | 1.24 | 1.14 | 1.14 | 1.14 | 1.24 | 1.48 | 1.10 |
time (sec) |
N/A | 0.000 | 4.226 | 0.656 | 0.227 | 0.275 | 0.131 | 0.298 | 11.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 28 | 27 | 30 | 25 | 37 | 27 | 28 | 26 |
N.S. |
1 | 1.27 | 1.23 | 1.36 | 1.14 | 1.68 | 1.23 | 1.27 | 1.18 |
time (sec) |
N/A | 0.233 | 0.040 | 0.166 | 0.187 | 0.247 | 0.095 | 0.266 | 10.665 |