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 | 15 | 14 | 6 | 6 | 12 | 5 | 5 | 5 | 5 |
N.S. |
1 | 0.93 | 0.40 | 0.40 | 0.80 | 0.33 | 0.33 | 0.33 | 0.33 |
time (sec) |
N/A | 0.167 | 0.001 | 0.111 | 0.224 | 0.254 | 0.039 | 0.269 | 0.020 |
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 | 9 | 8 | 7 | 7 | 5 | 7 | 7 |
N.S. |
1 | 0.55 | 0.45 | 0.40 | 0.35 | 0.35 | 0.25 | 0.35 | 0.35 |
time (sec) |
N/A | 0.138 | 0.001 | 0.124 | 0.184 | 0.230 | 0.026 | 0.264 | 0.019 |
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 | 29 | 27 | 25 | 37 | 46 | 40 | 49 | 40 | 42 |
N.S. |
1 | 0.93 | 0.86 | 1.28 | 1.59 | 1.38 | 1.69 | 1.38 | 1.45 |
time (sec) |
N/A | 3.101 | 0.165 | 85.537 | 0.700 | 0.239 | 1.416 | 8.554 | 14.685 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 24 | 23 | 0 | 25 | 34 | 24 | 24 |
N.S. |
1 | 0.00 | 0.89 | 0.85 | 0.00 | 0.93 | 1.26 | 0.89 | 0.89 |
time (sec) |
N/A | 0.000 | 1.773 | 0.314 | 0.000 | 0.235 | 0.107 | 0.273 | 0.294 |
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 | 17 | 17 | 17 | 17 | 16 | 16 | 19 | 16 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.94 | 0.94 | 1.12 | 0.94 | 0.00 |
time (sec) |
N/A | 0.556 | 0.086 | 29.048 | 0.278 | 0.246 | 0.129 | 0.278 | 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 | 14 | 17 | 13 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. |
1 | 1.21 | 0.93 | 0.79 | 0.71 | 0.71 | 0.57 | 0.71 | 0.71 |
time (sec) |
N/A | 0.136 | 0.011 | 0.649 | 0.185 | 0.228 | 0.035 | 0.269 | 13.876 |
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 | 29 | 30 | 32 | 27 | 29 | 29 | 26 | 32 | 26 |
N.S. |
1 | 1.03 | 1.10 | 0.93 | 1.00 | 1.00 | 0.90 | 1.10 | 0.90 |
time (sec) |
N/A | 0.201 | 0.033 | 0.576 | 0.208 | 0.239 | 0.092 | 0.276 | 13.872 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 41 | 22 | 23 | 37 | 28 | 20 | 71 | 22 |
N.S. |
1 | 1.71 | 0.92 | 0.96 | 1.54 | 1.17 | 0.83 | 2.96 | 0.92 |
time (sec) |
N/A | 0.222 | 0.162 | 0.588 | 0.194 | 0.232 | 0.072 | 0.262 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F(-1) | C | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 18 | 0 | 24 | 18 | 15 | 20 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 1.33 | 1.00 | 0.83 | 1.11 | 0.00 |
time (sec) |
N/A | 0.000 | 1.042 | 0.000 | 0.313 | 0.239 | 0.272 | 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 | 23 | 0 | 25 | 21 | 20 | 34 | 22 | 21 | 22 |
N.S. |
1 | 0.00 | 1.09 | 0.91 | 0.87 | 1.48 | 0.96 | 0.91 | 0.96 |
time (sec) |
N/A | 0.000 | 0.882 | 3.204 | 0.248 | 0.238 | 0.267 | 0.350 | 14.940 |
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 | 20 | 19 | 23 | 31 | 30 | 20 | 21 | 26 |
N.S. |
1 | 0.87 | 0.83 | 1.00 | 1.35 | 1.30 | 0.87 | 0.91 | 1.13 |
time (sec) |
N/A | 0.441 | 0.167 | 2.328 | 0.228 | 0.239 | 0.169 | 0.267 | 14.769 |
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 | 19 | 18 | 19 | 32 | 14 | 35 | 17 |
N.S. |
1 | 0.00 | 0.68 | 0.64 | 0.68 | 1.14 | 0.50 | 1.25 | 0.61 |
time (sec) |
N/A | 0.000 | 2.019 | 1.745 | 0.224 | 0.250 | 0.062 | 0.283 | 14.967 |
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 | 36 | 28 | 24 | 28 | 24 | 22 | 25 | 27 |
N.S. |
1 | 1.29 | 1.00 | 0.86 | 1.00 | 0.86 | 0.79 | 0.89 | 0.96 |
time (sec) |
N/A | 0.208 | 0.010 | 0.111 | 0.190 | 0.239 | 0.072 | 0.274 | 14.766 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 29 | 27 | 24 | 53 | 45 | 31 | 67 | 28 |
N.S. |
1 | 1.21 | 1.12 | 1.00 | 2.21 | 1.88 | 1.29 | 2.79 | 1.17 |
time (sec) |
N/A | 0.838 | 0.046 | 2.665 | 0.229 | 0.243 | 0.168 | 0.270 | 15.935 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 119 | 28 | 35 | 38 | 30 | 39 | 0 | 33 |
N.S. |
1 | 4.96 | 1.17 | 1.46 | 1.58 | 1.25 | 1.62 | 0.00 | 1.38 |
time (sec) |
N/A | 0.516 | 0.048 | 1.450 | 0.199 | 0.232 | 0.598 | 0.000 | 15.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 24 | 22 | 16 | 0 | 17 | 15 | 18 | 18 |
N.S. |
1 | 1.33 | 1.22 | 0.89 | 0.00 | 0.94 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.349 | 0.097 | 1.478 | 0.000 | 0.243 | 0.059 | 0.265 | 15.315 |
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 | 20 | 24 | 17 | 18 | 18 | 17 | 21 | 16 |
N.S. |
1 | 0.91 | 1.09 | 0.77 | 0.82 | 0.82 | 0.77 | 0.95 | 0.73 |
time (sec) |
N/A | 0.209 | 0.008 | 1.827 | 0.201 | 0.239 | 0.060 | 0.265 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 66 | 26 | 21 | 28 | 22 | 19 | 22 | 20 |
N.S. |
1 | 2.44 | 0.96 | 0.78 | 1.04 | 0.81 | 0.70 | 0.81 | 0.74 |
time (sec) |
N/A | 0.369 | 0.240 | 0.584 | 0.221 | 0.240 | 0.074 | 0.264 | 15.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 113 | 52 | 128 | 104 | 111 | 0 | 139 | 0 |
N.S. |
1 | 2.97 | 1.37 | 3.37 | 2.74 | 2.92 | 0.00 | 3.66 | 0.00 |
time (sec) |
N/A | 8.850 | 0.517 | 0.149 | 0.637 | 0.253 | 0.000 | 2.443 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 33 | 37 | 59 | 79 | 34 | 82 | 0 |
N.S. |
1 | 0.00 | 1.10 | 1.23 | 1.97 | 2.63 | 1.13 | 2.73 | 0.00 |
time (sec) |
N/A | 0.000 | 7.812 | 0.760 | 0.302 | 0.312 | 0.196 | 0.660 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | F | A | F | A | A | F | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 104 | 0 | 24 | 0 | 21 | 20 | 0 | 21 |
N.S. |
1 | 4.33 | 0.00 | 1.00 | 0.00 | 0.88 | 0.83 | 0.00 | 0.88 |
time (sec) |
N/A | 0.414 | 0.000 | 29.651 | 0.000 | 0.282 | 0.319 | 0.000 | 16.370 |
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 | 26 | 25 | 42 | 42 | 20 | 42 | 24 |
N.S. |
1 | 0.00 | 1.04 | 1.00 | 1.68 | 1.68 | 0.80 | 1.68 | 0.96 |
time (sec) |
N/A | 0.000 | 0.075 | 0.315 | 0.227 | 0.297 | 0.095 | 0.291 | 15.490 |
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 | 30 | 28 | 35 | 25 | 41 | 26 | 24 | 24 | 24 |
N.S. |
1 | 0.93 | 1.17 | 0.83 | 1.37 | 0.87 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.209 | 0.013 | 0.045 | 0.190 | 0.255 | 0.119 | 0.269 | 15.421 |
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 | 13 | 13 | 13 | 12 | 30 | 11 | 10 | 11 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 2.31 | 0.85 | 0.77 | 0.85 | 1.00 |
time (sec) |
N/A | 0.148 | 0.005 | 0.011 | 0.204 | 0.260 | 0.074 | 0.271 | 16.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 17 | 17 | 35 | 35 | 17 | 35 | 30 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 2.06 | 2.06 | 1.00 | 2.06 | 1.76 |
time (sec) |
N/A | 0.000 | 0.355 | 0.059 | 0.231 | 0.275 | 0.132 | 0.333 | 16.993 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 26 | 24 | 45 | 53 | 55 | 46 | 53 | 33 |
N.S. |
1 | 1.04 | 0.96 | 1.80 | 2.12 | 2.20 | 1.84 | 2.12 | 1.32 |
time (sec) |
N/A | 0.475 | 0.399 | 0.046 | 0.205 | 0.258 | 0.120 | 0.283 | 16.233 |
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 | 16 | 19 | 13 | 15 | 15 | 17 | 15 | 12 |
N.S. |
1 | 0.70 | 0.83 | 0.57 | 0.65 | 0.65 | 0.74 | 0.65 | 0.52 |
time (sec) |
N/A | 0.144 | 0.002 | 0.016 | 0.203 | 0.245 | 0.030 | 0.274 | 0.044 |
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 | 11 | 11 | 9 | 9 | 9 | 8 | 9 | 8 |
N.S. |
1 | 0.52 | 0.52 | 0.43 | 0.43 | 0.43 | 0.38 | 0.43 | 0.38 |
time (sec) |
N/A | 0.123 | 0.001 | 0.008 | 0.185 | 0.237 | 0.024 | 0.276 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 47 | 27 | 34 | 354 | 119 | 34 | 36 | 58 |
N.S. |
1 | 1.74 | 1.00 | 1.26 | 13.11 | 4.41 | 1.26 | 1.33 | 2.15 |
time (sec) |
N/A | 0.461 | 0.040 | 2.186 | 0.411 | 0.276 | 0.173 | 0.297 | 15.888 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 144 | 26 | 36 | 0 | 33 | 17 | 40 | 21 |
N.S. |
1 | 6.00 | 1.08 | 1.50 | 0.00 | 1.38 | 0.71 | 1.67 | 0.88 |
time (sec) |
N/A | 0.944 | 0.568 | 0.185 | 0.000 | 0.273 | 0.098 | 0.275 | 0.236 |
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 | 27 | 24 | 25 | 25 | 22 | 25 | 50 |
N.S. |
1 | 0.00 | 1.08 | 0.96 | 1.00 | 1.00 | 0.88 | 1.00 | 2.00 |
time (sec) |
N/A | 0.000 | 9.446 | 0.538 | 0.228 | 0.238 | 0.081 | 0.271 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 42 | 33 | 104 | 37 | 37 | 0 | 41 |
N.S. |
1 | 0.00 | 1.40 | 1.10 | 3.47 | 1.23 | 1.23 | 0.00 | 1.37 |
time (sec) |
N/A | 0.000 | 0.157 | 230.601 | 0.339 | 0.252 | 0.560 | 0.000 | 15.963 |
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 | 13 | 13 | 14 | 13 | 14 | 10 | 13 | 13 |
N.S. |
1 | 0.45 | 0.45 | 0.48 | 0.45 | 0.48 | 0.34 | 0.45 | 0.45 |
time (sec) |
N/A | 0.478 | 0.097 | 0.050 | 0.227 | 0.254 | 0.074 | 0.269 | 15.699 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 27 | 62 | 22 | 22 | 21 | 22 | 24 | 21 |
N.S. |
1 | 1.35 | 3.10 | 1.10 | 1.10 | 1.05 | 1.10 | 1.20 | 1.05 |
time (sec) |
N/A | 0.302 | 0.029 | 0.050 | 0.194 | 0.239 | 0.231 | 0.267 | 15.792 |
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 | 32 | 18 | 17 | 30 | 16 | 12 | 16 | 16 |
N.S. |
1 | 1.52 | 0.86 | 0.81 | 1.43 | 0.76 | 0.57 | 0.76 | 0.76 |
time (sec) |
N/A | 0.718 | 0.285 | 0.062 | 0.230 | 0.255 | 0.073 | 0.274 | 15.362 |
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 | 17 | 13 | 15 | 14 | 20 | 12 | 14 | 14 |
N.S. |
1 | 0.77 | 0.59 | 0.68 | 0.64 | 0.91 | 0.55 | 0.64 | 0.64 |
time (sec) |
N/A | 0.173 | 0.014 | 0.085 | 0.192 | 0.235 | 0.051 | 0.260 | 14.592 |
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 | 32 | 36 | 23 | 20 | 35 | 35 | 39 | 35 | 36 |
N.S. |
1 | 1.12 | 0.72 | 0.62 | 1.09 | 1.09 | 1.22 | 1.09 | 1.12 |
time (sec) |
N/A | 0.179 | 0.011 | 0.023 | 0.191 | 0.256 | 0.040 | 0.274 | 0.090 |
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 | 22 | 32 | 23 | 19 | 23 | 23 |
N.S. |
1 | 0.00 | 0.92 | 0.88 | 1.28 | 0.92 | 0.76 | 0.92 | 0.92 |
time (sec) |
N/A | 0.000 | 0.165 | 0.180 | 0.284 | 0.240 | 0.123 | 0.263 | 15.500 |
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 | 33 | 0 | 30 | 28 | 30 | 30 | 26 | 30 | 32 |
N.S. |
1 | 0.00 | 0.91 | 0.85 | 0.91 | 0.91 | 0.79 | 0.91 | 0.97 |
time (sec) |
N/A | 0.000 | 3.516 | 0.069 | 0.238 | 0.260 | 0.082 | 0.268 | 15.229 |
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 | 21 | 19 | 18 | 18 | 19 | 18 | 18 |
N.S. |
1 | 0.00 | 0.95 | 0.86 | 0.82 | 0.82 | 0.86 | 0.82 | 0.82 |
time (sec) |
N/A | 0.000 | 1.304 | 0.031 | 0.222 | 0.267 | 0.137 | 0.280 | 0.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 32 | 43 | 35 | 35 | 41 | 0 | 47 |
N.S. |
1 | 0.00 | 0.94 | 1.26 | 1.03 | 1.03 | 1.21 | 0.00 | 1.38 |
time (sec) |
N/A | 0.000 | 3.790 | 0.224 | 0.243 | 0.279 | 0.232 | 0.000 | 0.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 129 | 53 | 55 | 0 | 64 | 58 | 69 | 52 |
N.S. |
1 | 4.96 | 2.04 | 2.12 | 0.00 | 2.46 | 2.23 | 2.65 | 2.00 |
time (sec) |
N/A | 1.447 | 1.142 | 0.255 | 0.000 | 0.257 | 0.232 | 0.289 | 16.034 |
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 | 26 | 57 | 29 | 32 | 34 | 36 | 31 | 43 | 40 |
N.S. |
1 | 2.19 | 1.12 | 1.23 | 1.31 | 1.38 | 1.19 | 1.65 | 1.54 |
time (sec) |
N/A | 0.528 | 0.933 | 0.187 | 0.244 | 0.249 | 0.081 | 0.268 | 14.840 |
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 | 26 | 34 | 27 | 33 | 19 | 15 | 17 | 18 |
N.S. |
1 | 1.04 | 1.36 | 1.08 | 1.32 | 0.76 | 0.60 | 0.68 | 0.72 |
time (sec) |
N/A | 0.190 | 0.011 | 0.047 | 0.202 | 0.254 | 0.075 | 0.271 | 15.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 16 | 22 | 12 | 31 | 20 | 12 | 13 |
N.S. |
1 | 0.00 | 1.00 | 1.38 | 0.75 | 1.94 | 1.25 | 0.75 | 0.81 |
time (sec) |
N/A | 0.000 | 0.110 | 0.137 | 0.343 | 0.252 | 0.146 | 0.266 | 16.012 |
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 | 12 | 12 | 13 | 12 | 16 | 10 | 12 | 12 |
N.S. |
1 | 0.75 | 0.75 | 0.81 | 0.75 | 1.00 | 0.62 | 0.75 | 0.75 |
time (sec) |
N/A | 0.151 | 0.002 | 0.013 | 0.189 | 0.243 | 0.041 | 0.268 | 0.031 |
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 | 34 | 0 | 27 | 26 | 34 | 33 | 29 | 34 | 116 |
N.S. |
1 | 0.00 | 0.79 | 0.76 | 1.00 | 0.97 | 0.85 | 1.00 | 3.41 |
time (sec) |
N/A | 0.000 | 5.148 | 1.095 | 0.277 | 0.259 | 0.265 | 0.525 | 15.698 |
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 | 11 | 9 | 13 | 10 | 12 | 12 | 12 | 12 |
N.S. |
1 | 0.69 | 0.56 | 0.81 | 0.62 | 0.75 | 0.75 | 0.75 | 0.75 |
time (sec) |
N/A | 0.260 | 0.045 | 0.044 | 0.308 | 0.277 | 0.080 | 0.278 | 0.553 |
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 | 21 | 46 | 83 | 61 | 59 | 95 | 63 | 50 | 126 |
N.S. |
1 | 2.19 | 3.95 | 2.90 | 2.81 | 4.52 | 3.00 | 2.38 | 6.00 |
time (sec) |
N/A | 0.354 | 0.091 | 0.117 | 0.189 | 0.279 | 0.330 | 0.275 | 14.677 |
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 | 71 | 22 | 23 | 22 | 30 | 24 | 0 | 23 |
N.S. |
1 | 3.23 | 1.00 | 1.05 | 1.00 | 1.36 | 1.09 | 0.00 | 1.05 |
time (sec) |
N/A | 0.672 | 0.110 | 0.312 | 0.275 | 0.247 | 0.107 | 0.000 | 14.748 |
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 | 18 | 24 | 23 | 23 | 45 | 24 | 19 | 19 | 22 |
N.S. |
1 | 1.33 | 1.28 | 1.28 | 2.50 | 1.33 | 1.06 | 1.06 | 1.22 |
time (sec) |
N/A | 0.259 | 0.126 | 0.025 | 0.197 | 0.248 | 0.061 | 0.269 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 76 | 22 | 20 | 290 | 37 | 32 | 37 | 38 |
N.S. |
1 | 3.30 | 0.96 | 0.87 | 12.61 | 1.61 | 1.39 | 1.61 | 1.65 |
time (sec) |
N/A | 1.402 | 0.168 | 1.133 | 0.440 | 0.262 | 0.269 | 0.306 | 14.779 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 28 | 18 | 0 | 17 | 20 | 17 | 17 |
N.S. |
1 | 0.00 | 1.12 | 0.72 | 0.00 | 0.68 | 0.80 | 0.68 | 0.68 |
time (sec) |
N/A | 0.000 | 0.065 | 0.088 | 0.000 | 0.258 | 0.132 | 0.270 | 0.088 |
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 | 3 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 2 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.67 | 0.67 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.123 | 0.000 | 0.010 | 0.203 | 0.241 | 0.035 | 0.273 | 0.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 50 | 22 | 20 | 40 | 30 | 24 | 37 | 19 |
N.S. |
1 | 2.27 | 1.00 | 0.91 | 1.82 | 1.36 | 1.09 | 1.68 | 0.86 |
time (sec) |
N/A | 0.188 | 0.077 | 0.058 | 0.195 | 0.240 | 0.113 | 0.267 | 0.094 |
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 | 18 | 0 | 21 | 26 | 25 | 31 | 26 | 25 | 24 |
N.S. |
1 | 0.00 | 1.17 | 1.44 | 1.39 | 1.72 | 1.44 | 1.39 | 1.33 |
time (sec) |
N/A | 0.000 | 0.134 | 0.232 | 0.320 | 0.259 | 0.072 | 0.291 | 14.882 |
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 | 30 | 30 | 21 | 20 | 20 | 20 | 24 | 20 |
N.S. |
1 | 1.20 | 1.20 | 0.84 | 0.80 | 0.80 | 0.80 | 0.96 | 0.80 |
time (sec) |
N/A | 0.643 | 0.160 | 0.219 | 0.234 | 0.247 | 0.113 | 0.273 | 14.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 91 | 33 | 51 | 391 | 30 | 53 | 53 | 49 |
N.S. |
1 | 3.14 | 1.14 | 1.76 | 13.48 | 1.03 | 1.83 | 1.83 | 1.69 |
time (sec) |
N/A | 2.212 | 0.085 | 0.745 | 0.271 | 0.255 | 2.654 | 0.354 | 16.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 75 | 82 | 121 | 112 | 73 | 282 | 122 |
N.S. |
1 | 0.00 | 2.68 | 2.93 | 4.32 | 4.00 | 2.61 | 10.07 | 4.36 |
time (sec) |
N/A | 0.000 | 0.420 | 14.809 | 0.460 | 0.268 | 0.639 | 0.829 | 15.924 |
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 | 25 | 0 | 23 | 26 | 28 | 28 | 20 | 62 | 21 |
N.S. |
1 | 0.00 | 0.92 | 1.04 | 1.12 | 1.12 | 0.80 | 2.48 | 0.84 |
time (sec) |
N/A | 0.000 | 4.735 | 0.151 | 0.246 | 0.268 | 0.096 | 0.280 | 14.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 25 | 21 | 0 | 21 | 26 | 21 | 21 |
N.S. |
1 | 0.00 | 0.86 | 0.72 | 0.00 | 0.72 | 0.90 | 0.72 | 0.72 |
time (sec) |
N/A | 0.000 | 0.597 | 0.111 | 0.000 | 0.255 | 0.166 | 0.275 | 0.195 |
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 | 22 | 0 | 22 | 19 | 18 | 30 | 19 | 18 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.86 | 0.82 | 1.36 | 0.86 | 0.82 | 0.00 |
time (sec) |
N/A | 0.000 | 2.187 | 0.135 | 0.237 | 0.250 | 0.100 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 23 | 23 | 36 | 49 | 38 | 0 | 38 | 36 |
N.S. |
1 | 0.92 | 0.92 | 1.44 | 1.96 | 1.52 | 0.00 | 1.52 | 1.44 |
time (sec) |
N/A | 4.286 | 0.179 | 3.644 | 0.251 | 0.257 | 0.000 | 2.406 | 14.240 |
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 | 20 | 23 | 19 | 21 | 577 | 20 | 19 | 24 | 22 |
N.S. |
1 | 1.15 | 0.95 | 1.05 | 28.85 | 1.00 | 0.95 | 1.20 | 1.10 |
time (sec) |
N/A | 0.332 | 0.088 | 0.204 | 0.295 | 0.278 | 0.106 | 0.269 | 14.705 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 28 | 31 | 66 | 54 | 26 | 72 | 58 |
N.S. |
1 | 0.00 | 0.90 | 1.00 | 2.13 | 1.74 | 0.84 | 2.32 | 1.87 |
time (sec) |
N/A | 0.000 | 0.105 | 0.194 | 0.323 | 0.269 | 0.131 | 0.302 | 15.832 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 40 | 37 | 45 | 39 | 44 | 36 | 34 |
N.S. |
1 | 0.00 | 1.48 | 1.37 | 1.67 | 1.44 | 1.63 | 1.33 | 1.26 |
time (sec) |
N/A | 0.000 | 5.053 | 0.084 | 0.317 | 0.259 | 0.287 | 0.262 | 16.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 34 | 439 | 33 | 34 | 37 | 16 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 25.82 | 1.94 | 2.00 | 2.18 | 0.94 |
time (sec) |
N/A | 0.401 | 0.032 | 0.510 | 0.481 | 0.253 | 0.115 | 0.283 | 0.441 |
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 | 14 | 15 | 14 | 14 | 12 | 16 | 14 |
N.S. |
1 | 0.93 | 0.93 | 1.00 | 0.93 | 0.93 | 0.80 | 1.07 | 0.93 |
time (sec) |
N/A | 0.171 | 0.005 | 0.184 | 0.215 | 0.240 | 0.073 | 0.277 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 49 | 60 | 42 | 35 | 40 | 60 | 53 | 41 |
N.S. |
1 | 1.96 | 2.40 | 1.68 | 1.40 | 1.60 | 2.40 | 2.12 | 1.64 |
time (sec) |
N/A | 0.489 | 0.013 | 5.917 | 0.257 | 0.249 | 0.179 | 0.269 | 15.353 |
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 | 16 | 17 | 22 | 25 | 17 | 22 | 21 |
N.S. |
1 | 0.75 | 0.67 | 0.71 | 0.92 | 1.04 | 0.71 | 0.92 | 0.88 |
time (sec) |
N/A | 0.237 | 0.011 | 0.020 | 0.201 | 0.242 | 0.046 | 0.254 | 0.058 |
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 | 16 | 16 | 16 | 15 | 19 | 12 | 20 | 15 |
N.S. |
1 | 0.80 | 0.80 | 0.80 | 0.75 | 0.95 | 0.60 | 1.00 | 0.75 |
time (sec) |
N/A | 0.270 | 0.004 | 0.033 | 0.213 | 0.284 | 0.039 | 0.269 | 15.604 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | B | A | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 42 | 67 | 67 | 44 | 73 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.62 | 2.58 | 2.58 | 1.69 | 2.81 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.261 | 0.352 | 0.263 | 0.178 | 0.298 | 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 | 15 | 15 | 15 | 17 | 18 | 22 | 19 | 18 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.13 | 1.20 | 1.47 | 1.27 | 1.20 | 1.07 |
time (sec) |
N/A | 0.772 | 0.352 | 0.187 | 0.325 | 0.261 | 0.076 | 0.272 | 0.166 |
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 | 12 | 11 | 11 | 11 | 10 | 10 | 7 | 10 | 10 |
N.S. |
1 | 0.92 | 0.92 | 0.92 | 0.83 | 0.83 | 0.58 | 0.83 | 0.83 |
time (sec) |
N/A | 0.138 | 0.008 | 0.010 | 0.202 | 0.249 | 0.061 | 0.259 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 22 | 19 | 18 | 18 | 20 | 0 | 22 |
N.S. |
1 | 0.00 | 0.85 | 0.73 | 0.69 | 0.69 | 0.77 | 0.00 | 0.85 |
time (sec) |
N/A | 0.000 | 0.042 | 0.307 | 0.330 | 0.259 | 0.108 | 0.000 | 16.328 |
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 | 21 | 26 | 21 | 23 | 19 | 33 | 24 | 19 | 18 |
N.S. |
1 | 1.24 | 1.00 | 1.10 | 0.90 | 1.57 | 1.14 | 0.90 | 0.86 |
time (sec) |
N/A | 0.165 | 0.037 | 0.057 | 0.195 | 0.256 | 0.124 | 0.263 | 0.181 |
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 | 25 | 23 | 23 | 25 | 57 | 24 | 27 | 24 | 24 |
N.S. |
1 | 0.92 | 0.92 | 1.00 | 2.28 | 0.96 | 1.08 | 0.96 | 0.96 |
time (sec) |
N/A | 0.912 | 1.093 | 5.399 | 0.364 | 0.287 | 1.562 | 0.464 | 16.844 |
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 | 9 | 9 | 10 | 9 | 9 | 8 | 10 | 9 |
N.S. |
1 | 0.47 | 0.47 | 0.53 | 0.47 | 0.47 | 0.42 | 0.53 | 0.47 |
time (sec) |
N/A | 0.129 | 0.004 | 0.173 | 0.205 | 0.243 | 0.035 | 0.272 | 15.702 |
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 | 20 | 41 | 19 | 19 | 21 | 23 | 17 | 23 | 21 |
N.S. |
1 | 2.05 | 0.95 | 0.95 | 1.05 | 1.15 | 0.85 | 1.15 | 1.05 |
time (sec) |
N/A | 0.204 | 0.074 | 0.051 | 0.251 | 0.242 | 0.086 | 0.283 | 15.603 |
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 | 15 | 16 | 15 | 14 | 19 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 0.93 | 1.27 | 1.00 | 1.00 |
time (sec) |
N/A | 0.155 | 0.003 | 0.031 | 0.187 | 0.254 | 0.100 | 0.257 | 16.483 |
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 | 28 | 29 | 44 | 44 | 26 | 28 | 28 |
N.S. |
1 | 0.00 | 1.27 | 1.32 | 2.00 | 2.00 | 1.18 | 1.27 | 1.27 |
time (sec) |
N/A | 0.000 | 0.049 | 0.293 | 0.241 | 0.267 | 0.106 | 0.317 | 16.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 39 | 27 | 41 | 68 | 53 | 20 | 235 | 44 |
N.S. |
1 | 1.44 | 1.00 | 1.52 | 2.52 | 1.96 | 0.74 | 8.70 | 1.63 |
time (sec) |
N/A | 0.861 | 0.291 | 15.226 | 0.375 | 0.265 | 0.321 | 0.622 | 15.988 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 40 | 37 | 35 | 36 | 41 | 36 | 41 |
N.S. |
1 | 0.00 | 1.48 | 1.37 | 1.30 | 1.33 | 1.52 | 1.33 | 1.52 |
time (sec) |
N/A | 0.000 | 0.320 | 0.377 | 0.260 | 0.266 | 0.178 | 0.272 | 15.582 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 24 | 22 | 26 | 33 | 29 | 26 | 27 |
N.S. |
1 | 0.00 | 1.26 | 1.16 | 1.37 | 1.74 | 1.53 | 1.37 | 1.42 |
time (sec) |
N/A | 0.000 | 3.438 | 0.326 | 0.377 | 0.258 | 0.210 | 0.272 | 15.829 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 17 | 23 | 58 | 19 | 0 | 25 |
N.S. |
1 | 0.00 | 1.00 | 0.77 | 1.05 | 2.64 | 0.86 | 0.00 | 1.14 |
time (sec) |
N/A | 0.000 | 5.068 | 4.996 | 0.562 | 0.254 | 0.730 | 0.000 | 19.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 34 | 69 | 34 | 34 | 33 | 34 | 71 | 2558 |
N.S. |
1 | 1.26 | 2.56 | 1.26 | 1.26 | 1.22 | 1.26 | 2.63 | 94.74 |
time (sec) |
N/A | 0.317 | 0.053 | 0.078 | 0.202 | 0.261 | 0.866 | 0.270 | 19.670 |
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 | 21 | 30 | 25 | 23 | 23 | 27 | 23 | 29 |
N.S. |
1 | 1.40 | 2.00 | 1.67 | 1.53 | 1.53 | 1.80 | 1.53 | 1.93 |
time (sec) |
N/A | 0.149 | 0.003 | 0.012 | 0.204 | 0.246 | 0.031 | 0.265 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 22 | 25 | 24 | 467 | 23 | 22 | 181 | 156 |
N.S. |
1 | 1.22 | 1.39 | 1.33 | 25.94 | 1.28 | 1.22 | 10.06 | 8.67 |
time (sec) |
N/A | 0.403 | 0.090 | 0.243 | 0.288 | 0.274 | 0.120 | 0.276 | 32.533 |
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 | 26 | 21 | 25 | 29 | 24 | 26 | 30 | 24 |
N.S. |
1 | 1.24 | 1.00 | 1.19 | 1.38 | 1.14 | 1.24 | 1.43 | 1.14 |
time (sec) |
N/A | 0.297 | 0.334 | 0.732 | 0.310 | 0.268 | 0.282 | 0.286 | 19.649 |
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 | 18 | 0 | 18 | 23 | 22 | 20 | 17 | 20 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.28 | 1.22 | 1.11 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.000 | 0.340 | 0.282 | 0.237 | 0.248 | 0.112 | 0.279 | 17.864 |
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 | 21 | 95 | 22 | 21 | 20 | 20 | 20 | 0 | 23 |
N.S. |
1 | 4.52 | 1.05 | 1.00 | 0.95 | 0.95 | 0.95 | 0.00 | 1.10 |
time (sec) |
N/A | 0.803 | 0.425 | 0.143 | 0.278 | 0.284 | 129.131 | 0.000 | 17.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | F(-1) | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 0 | 19 | 28 | 18 | 0 | 0 | 16 |
N.S. |
1 | 0.00 | 0.00 | 0.95 | 1.40 | 0.90 | 0.00 | 0.00 | 0.80 |
time (sec) |
N/A | 0.000 | 0.000 | 0.041 | 0.371 | 0.274 | 0.000 | 0.000 | 18.130 |
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 | 23 | 15 | 15 | 22 | 22 | 14 | 22 | 14 |
N.S. |
1 | 1.53 | 1.00 | 1.00 | 1.47 | 1.47 | 0.93 | 1.47 | 0.93 |
time (sec) |
N/A | 0.157 | 0.003 | 0.029 | 0.184 | 0.237 | 0.020 | 0.273 | 0.039 |
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 | 19 | 19 | 26 | 26 | 20 | 25 | 27 |
N.S. |
1 | 0.00 | 0.76 | 0.76 | 1.04 | 1.04 | 0.80 | 1.00 | 1.08 |
time (sec) |
N/A | 0.000 | 1.164 | 0.072 | 0.248 | 0.252 | 0.080 | 0.287 | 16.708 |
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 | 20 | 15 | 14 | 20 | 14 | 14 | 20 | 13 |
N.S. |
1 | 1.33 | 1.00 | 0.93 | 1.33 | 0.93 | 0.93 | 1.33 | 0.87 |
time (sec) |
N/A | 0.197 | 0.115 | 0.233 | 0.202 | 0.251 | 0.064 | 0.273 | 0.640 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | B | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 4186 | 57 | 112 | 2515 | 58 | 36 | 115 | 0 |
N.S. |
1 | 123.12 | 1.68 | 3.29 | 73.97 | 1.71 | 1.06 | 3.38 | 0.00 |
time (sec) |
N/A | 22.328 | 0.185 | 3.336 | 0.341 | 0.271 | 0.318 | 0.337 | 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 | 23 | 16 | 16 | 19 | 15 | 15 | 17 | 11 |
N.S. |
1 | 1.77 | 1.23 | 1.23 | 1.46 | 1.15 | 1.15 | 1.31 | 0.85 |
time (sec) |
N/A | 0.156 | 0.005 | 0.025 | 0.206 | 0.261 | 0.062 | 0.266 | 16.421 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 730 | 22 | 24 | 27 | 25 | 24 | 27 | 0 |
N.S. |
1 | 31.74 | 0.96 | 1.04 | 1.17 | 1.09 | 1.04 | 1.17 | 0.00 |
time (sec) |
N/A | 1.751 | 0.817 | 0.194 | 0.323 | 0.258 | 0.146 | 0.283 | 0.000 |
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 | 32 | 29 | 29 | 27 | 28 | 47 | 22 | 57 | 26 |
N.S. |
1 | 0.91 | 0.91 | 0.84 | 0.88 | 1.47 | 0.69 | 1.78 | 0.81 |
time (sec) |
N/A | 0.248 | 0.037 | 0.079 | 0.239 | 0.253 | 0.149 | 0.262 | 17.130 |
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 | 27 | 0 | 35 | 31 | 24 | 30 | 26 | 66 | 39 |
N.S. |
1 | 0.00 | 1.30 | 1.15 | 0.89 | 1.11 | 0.96 | 2.44 | 1.44 |
time (sec) |
N/A | 0.000 | 2.315 | 0.204 | 0.484 | 0.256 | 0.311 | 0.265 | 17.964 |