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 | 11 | 11 | 11 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.91 | 0.91 | 0.73 | 0.91 | 0.91 |
time (sec) |
N/A | 0.008 | 0.016 | 0.590 | 0.192 | 0.246 | 0.046 | 0.252 | 0.063 |
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 | 29 | 0 | 16 | 18 | 19 | 16 | 14 | 16 | 17 |
N.S. |
1 | 0.00 | 0.55 | 0.62 | 0.66 | 0.55 | 0.48 | 0.55 | 0.59 |
time (sec) |
N/A | 0.000 | 0.163 | 5.539 | 0.343 | 0.249 | 0.100 | 0.274 | 9.515 |
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 | 7 | 7 | 8 | 7 | 10 | 3 | 7 | 7 |
N.S. |
1 | 0.33 | 0.33 | 0.38 | 0.33 | 0.48 | 0.14 | 0.33 | 0.33 |
time (sec) |
N/A | 0.002 | 0.001 | 0.248 | 0.188 | 0.232 | 0.025 | 0.243 | 0.023 |
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 | 24 | 21 | 21 | 18 | 23 | 42 | 17 | 23 | 17 |
N.S. |
1 | 0.88 | 0.88 | 0.75 | 0.96 | 1.75 | 0.71 | 0.96 | 0.71 |
time (sec) |
N/A | 0.042 | 0.035 | 1.586 | 0.194 | 0.250 | 0.162 | 0.251 | 0.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 49 | 18 | 15 | 117 | 37 | 0 | 37 | 42 |
N.S. |
1 | 2.72 | 1.00 | 0.83 | 6.50 | 2.06 | 0.00 | 2.06 | 2.33 |
time (sec) |
N/A | 0.066 | 0.036 | 11.067 | 0.443 | 0.233 | 0.000 | 0.279 | 9.482 |
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 | 19 | 19 | 19 | 19 | 19 | 17 | 19 | 19 |
N.S. |
1 | 0.70 | 0.70 | 0.70 | 0.70 | 0.70 | 0.63 | 0.70 | 0.70 |
time (sec) |
N/A | 0.002 | 0.000 | 0.205 | 0.199 | 0.224 | 0.025 | 0.253 | 0.035 |
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 | 32 | 27 | 31 | 31 | 21 | 50 | 22 | 26 | 41 |
N.S. |
1 | 0.84 | 0.97 | 0.97 | 0.66 | 1.56 | 0.69 | 0.81 | 1.28 |
time (sec) |
N/A | 0.077 | 0.074 | 2.477 | 0.192 | 0.248 | 0.073 | 0.262 | 0.221 |
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 | 22 | 22 | 19 | 18 | 23 | 19 | 23 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.05 | 0.86 | 1.05 | 0.86 |
time (sec) |
N/A | 0.014 | 0.013 | 0.429 | 0.197 | 0.250 | 0.075 | 0.252 | 0.083 |
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 | 30 | 352 | 206 | 185 | 184 | 186 | 224 | 187 | 43 |
N.S. |
1 | 11.73 | 6.87 | 6.17 | 6.13 | 6.20 | 7.47 | 6.23 | 1.43 |
time (sec) |
N/A | 0.362 | 6.814 | 1.053 | 0.299 | 0.236 | 0.237 | 0.259 | 9.290 |
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 | 41 | 21 | 17 | 30 | 16 | 29 | 16 | 16 |
N.S. |
1 | 1.95 | 1.00 | 0.81 | 1.43 | 0.76 | 1.38 | 0.76 | 0.76 |
time (sec) |
N/A | 0.020 | 0.064 | 0.344 | 0.199 | 0.233 | 0.108 | 0.251 | 0.094 |
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 | 23 | 19 | 23 | 18 | 0 | 23 | 15 | 45 | 18 |
N.S. |
1 | 0.83 | 1.00 | 0.78 | 0.00 | 1.00 | 0.65 | 1.96 | 0.78 |
time (sec) |
N/A | 0.333 | 0.808 | 3.992 | 0.000 | 0.265 | 6.505 | 0.261 | 9.480 |
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 | 19 | 21 | 28 | 24 | 29 | 24 | 27 | 21 |
N.S. |
1 | 0.66 | 0.72 | 0.97 | 0.83 | 1.00 | 0.83 | 0.93 | 0.72 |
time (sec) |
N/A | 0.011 | 0.013 | 0.431 | 0.185 | 0.234 | 0.060 | 0.249 | 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 | 20 | 15 | 18 | 14 | 13 | 13 | 14 | 14 | 13 |
N.S. |
1 | 0.75 | 0.90 | 0.70 | 0.65 | 0.65 | 0.70 | 0.70 | 0.65 |
time (sec) |
N/A | 0.006 | 0.010 | 1.204 | 0.187 | 0.231 | 0.041 | 0.253 | 9.034 |
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 | 18 | 88 | 16 | 20 | 29 | 19 | 15 | 19 | 16 |
N.S. |
1 | 4.89 | 0.89 | 1.11 | 1.61 | 1.06 | 0.83 | 1.06 | 0.89 |
time (sec) |
N/A | 0.667 | 0.193 | 1.505 | 0.248 | 0.237 | 0.053 | 0.257 | 0.192 |
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 | 25 | 29 | 27 | 28 | 30 | 22 | 33 | 25 |
N.S. |
1 | 1.04 | 1.21 | 1.12 | 1.17 | 1.25 | 0.92 | 1.38 | 1.04 |
time (sec) |
N/A | 0.024 | 0.009 | 0.284 | 0.189 | 0.243 | 0.116 | 0.248 | 9.126 |
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 | 31 | 31 | 32 | 31 | 31 | 31 | 31 | 27 |
N.S. |
1 | 1.29 | 1.29 | 1.33 | 1.29 | 1.29 | 1.29 | 1.29 | 1.12 |
time (sec) |
N/A | 0.004 | 0.005 | 0.197 | 0.184 | 0.236 | 0.050 | 0.253 | 9.117 |
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 | 19 | 60 | 14 | 14 | 14 | 16 | 8 | 16 | 13 |
N.S. |
1 | 3.16 | 0.74 | 0.74 | 0.74 | 0.84 | 0.42 | 0.84 | 0.68 |
time (sec) |
N/A | 0.179 | 0.226 | 0.317 | 0.208 | 0.240 | 0.054 | 0.251 | 0.083 |
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 | 33 | 84 | 94 | 76 | 69 | 107 | 82 | 68 | 106 |
N.S. |
1 | 2.55 | 2.85 | 2.30 | 2.09 | 3.24 | 2.48 | 2.06 | 3.21 |
time (sec) |
N/A | 0.095 | 0.082 | 0.880 | 0.193 | 0.245 | 0.317 | 0.249 | 9.264 |
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 | 26 | 16 | 15 | 21 | 17 | 21 | 15 |
N.S. |
1 | 0.00 | 1.37 | 0.84 | 0.79 | 1.11 | 0.89 | 1.11 | 0.79 |
time (sec) |
N/A | 0.000 | 0.391 | 0.289 | 0.234 | 0.259 | 0.077 | 0.254 | 0.160 |
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 | 26 | 27 | 25 | 39 | 26 | 34 | 31 | 39 | 0 |
N.S. |
1 | 1.04 | 0.96 | 1.50 | 1.00 | 1.31 | 1.19 | 1.50 | 0.00 |
time (sec) |
N/A | 0.481 | 0.080 | 40.869 | 0.335 | 0.249 | 0.298 | 0.471 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 98 | 58 | 40 | 50 | 50 | 88 | 50 | 102 |
N.S. |
1 | 4.08 | 2.42 | 1.67 | 2.08 | 2.08 | 3.67 | 2.08 | 4.25 |
time (sec) |
N/A | 0.013 | 0.007 | 0.409 | 0.188 | 0.243 | 0.033 | 0.249 | 9.046 |
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 | 20 | 21 | 16 | 15 | 15 | 15 | 15 | 17 |
N.S. |
1 | 0.80 | 0.84 | 0.64 | 0.60 | 0.60 | 0.60 | 0.60 | 0.68 |
time (sec) |
N/A | 0.003 | 0.003 | 0.188 | 0.196 | 0.227 | 0.025 | 0.245 | 0.070 |
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 | 18 | 26 | 20 | 24 | 22 | 17 |
N.S. |
1 | 1.18 | 1.14 | 0.82 | 1.18 | 0.91 | 1.09 | 1.00 | 0.77 |
time (sec) |
N/A | 0.525 | 0.069 | 6.010 | 0.252 | 0.245 | 0.194 | 0.270 | 9.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F(-1) | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 0 | 83 | 89 | 113 | 113 | 110 | 131 | 0 |
N.S. |
1 | 0.00 | 2.13 | 2.28 | 2.90 | 2.90 | 2.82 | 3.36 | 0.00 |
time (sec) |
N/A | 0.000 | 7.170 | 1.642 | 0.370 | 0.257 | 0.426 | 3.482 | 0.000 |
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 | 36 | 29 | 26 | 23 | 0 | 24 | 22 | 27 | 29 |
N.S. |
1 | 0.81 | 0.72 | 0.64 | 0.00 | 0.67 | 0.61 | 0.75 | 0.81 |
time (sec) |
N/A | 6.645 | 1.077 | 10.833 | 0.000 | 0.262 | 8.535 | 1.160 | 9.427 |
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 | 20 | 0 | 20 | 17 | 16 | 16 | 20 | 16 | 110 |
N.S. |
1 | 0.00 | 1.00 | 0.85 | 0.80 | 0.80 | 1.00 | 0.80 | 5.50 |
time (sec) |
N/A | 0.000 | 0.207 | 1.031 | 0.221 | 0.257 | 0.090 | 0.263 | 9.866 |
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 | 35 | 48 | 37 | 38 | 58 | 39 | 29 | 40 | 38 |
N.S. |
1 | 1.37 | 1.06 | 1.09 | 1.66 | 1.11 | 0.83 | 1.14 | 1.09 |
time (sec) |
N/A | 0.407 | 0.128 | 3.638 | 0.244 | 0.250 | 0.294 | 0.257 | 9.245 |
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 | 33 | 13 | 13 | 11 | 10 | 10 | 7 | 10 | 10 |
N.S. |
1 | 0.39 | 0.39 | 0.33 | 0.30 | 0.30 | 0.21 | 0.30 | 0.30 |
time (sec) |
N/A | 0.003 | 0.007 | 0.239 | 0.182 | 0.234 | 0.050 | 0.248 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 87 | 35 | 31 | 65 | 28 | 29 | 33 | 35 |
N.S. |
1 | 3.00 | 1.21 | 1.07 | 2.24 | 0.97 | 1.00 | 1.14 | 1.21 |
time (sec) |
N/A | 1.007 | 0.154 | 0.753 | 0.220 | 0.248 | 0.146 | 0.252 | 9.185 |
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 | 24 | 24 | 27 | 23 | 27 | 20 | 26 | 24 |
N.S. |
1 | 0.89 | 0.89 | 1.00 | 0.85 | 1.00 | 0.74 | 0.96 | 0.89 |
time (sec) |
N/A | 0.009 | 0.009 | 0.344 | 0.191 | 0.237 | 0.048 | 0.249 | 0.052 |
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 | 18 | 37 | 20 | 18 | 35 | 36 | 34 | 35 | 29 |
N.S. |
1 | 2.06 | 1.11 | 1.00 | 1.94 | 2.00 | 1.89 | 1.94 | 1.61 |
time (sec) |
N/A | 0.010 | 0.003 | 0.496 | 0.192 | 0.233 | 0.039 | 0.252 | 9.014 |
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 | 8 | 8 | 9 | 8 | 8 | 5 | 8 | 8 |
N.S. |
1 | 0.30 | 0.30 | 0.33 | 0.30 | 0.30 | 0.19 | 0.30 | 0.30 |
time (sec) |
N/A | 0.002 | 0.000 | 0.196 | 0.193 | 0.221 | 0.018 | 0.259 | 0.002 |
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 | 21 | 27 | 23 | 248 | 213 | 179 | 182 | 213 | 248 |
N.S. |
1 | 1.29 | 1.10 | 11.81 | 10.14 | 8.52 | 8.67 | 10.14 | 11.81 |
time (sec) |
N/A | 96.301 | 1.527 | 0.099 | 40.870 | 0.247 | 1.127 | 0.398 | 9.989 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 81 | 33 | 114 | 68 | 76 | 133 | 0 |
N.S. |
1 | 0.00 | 2.89 | 1.18 | 4.07 | 2.43 | 2.71 | 4.75 | 0.00 |
time (sec) |
N/A | 0.000 | 0.347 | 5.221 | 0.794 | 0.247 | 0.318 | 0.799 | 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 | 25 | 25 | 30 | 30 | 26 | 30 | 31 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.20 | 1.20 | 1.04 | 1.20 | 1.24 |
time (sec) |
N/A | 0.000 | 0.103 | 7.921 | 0.341 | 0.246 | 0.247 | 0.375 | 0.407 |
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 | 27 | 0 | 27 | 25 | 27 | 25 | 0 | 0 | 30 |
N.S. |
1 | 0.00 | 1.00 | 0.93 | 1.00 | 0.93 | 0.00 | 0.00 | 1.11 |
time (sec) |
N/A | 0.000 | 4.111 | 14.009 | 0.365 | 0.261 | 0.000 | 0.000 | 0.260 |
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 | 13 | 13 | 12 | 11 | 20 | 8 | 11 | 11 |
N.S. |
1 | 0.59 | 0.59 | 0.55 | 0.50 | 0.91 | 0.36 | 0.50 | 0.50 |
time (sec) |
N/A | 0.005 | 0.011 | 0.145 | 0.189 | 0.265 | 0.082 | 0.247 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 54 | 60 | 56 | 69 | 0 | 68 | 27623 |
N.S. |
1 | 0.00 | 1.54 | 1.71 | 1.60 | 1.97 | 0.00 | 1.94 | 789.23 |
time (sec) |
N/A | 0.000 | 3.058 | 4.451 | 0.341 | 0.247 | 0.000 | 0.315 | 12.984 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F(-1) | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 43 | 36 | 43 | 44 | 39 | 39 | 34 |
N.S. |
1 | 0.00 | 1.30 | 1.09 | 1.30 | 1.33 | 1.18 | 1.18 | 1.03 |
time (sec) |
N/A | 0.000 | 0.154 | 45.052 | 0.296 | 0.263 | 1.262 | 0.279 | 9.641 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | C | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 70 | 32 | 62 | 66 | 71 | 69 |
N.S. |
1 | 0.00 | 0.95 | 3.18 | 1.45 | 2.82 | 3.00 | 3.23 | 3.14 |
time (sec) |
N/A | 0.000 | 0.369 | 2.255 | 0.334 | 0.256 | 0.571 | 0.323 | 10.263 |
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 | 24 | 24 | 22 | 21 | 57 | 31 | 20 | 28 | 28 |
N.S. |
1 | 1.00 | 0.92 | 0.88 | 2.38 | 1.29 | 0.83 | 1.17 | 1.17 |
time (sec) |
N/A | 0.249 | 0.178 | 2.463 | 0.669 | 0.235 | 0.223 | 0.269 | 9.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 0 | 15 | 30 | 29 | 27 | 14 | 27 | 14 |
N.S. |
1 | 0.00 | 1.00 | 2.00 | 1.93 | 1.80 | 0.93 | 1.80 | 0.93 |
time (sec) |
N/A | 0.000 | 0.060 | 5.125 | 0.277 | 0.247 | 0.594 | 0.549 | 9.453 |
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 | 25 | 26 | 25 | 24 | 24 | 19 | 24 | 25 |
N.S. |
1 | 0.86 | 0.90 | 0.86 | 0.83 | 0.83 | 0.66 | 0.83 | 0.86 |
time (sec) |
N/A | 0.274 | 3.608 | 4.301 | 0.266 | 0.254 | 0.102 | 0.320 | 21.938 |
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 | 30 | 34 | 35 | 43 | 27 | 35 | 35 |
N.S. |
1 | 1.44 | 1.20 | 1.36 | 1.40 | 1.72 | 1.08 | 1.40 | 1.40 |
time (sec) |
N/A | 0.058 | 0.037 | 0.532 | 0.207 | 0.237 | 0.247 | 0.249 | 0.122 |
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 | 24 | 21 | 21 | 20 | 75 | 19 | 17 | 19 | 19 |
N.S. |
1 | 0.88 | 0.88 | 0.83 | 3.12 | 0.79 | 0.71 | 0.79 | 0.79 |
time (sec) |
N/A | 0.096 | 0.060 | 1.694 | 0.228 | 0.248 | 0.073 | 0.261 | 9.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 172 | 31 | 30 | 115 | 29 | 42 | 29 | 29 |
N.S. |
1 | 5.55 | 1.00 | 0.97 | 3.71 | 0.94 | 1.35 | 0.94 | 0.94 |
time (sec) |
N/A | 0.868 | 0.393 | 2.061 | 0.715 | 0.250 | 0.154 | 0.262 | 9.546 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 53 | 53 | 45 | 55 | 49 | 0 | 49 | 50 |
N.S. |
1 | 1.83 | 1.83 | 1.55 | 1.90 | 1.69 | 0.00 | 1.69 | 1.72 |
time (sec) |
N/A | 6.696 | 0.321 | 24.537 | 0.353 | 0.257 | 0.000 | 15.792 | 9.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 58 | 68 | 63 | 69 | 71 | 0 | 76 |
N.S. |
1 | 0.00 | 1.81 | 2.12 | 1.97 | 2.16 | 2.22 | 0.00 | 2.38 |
time (sec) |
N/A | 0.000 | 0.201 | 1.434 | 0.616 | 0.252 | 0.344 | 0.000 | 9.375 |
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 | 38 | 37 | 33 | 31 | 31 | 39 | 31 | 34 |
N.S. |
1 | 1.41 | 1.37 | 1.22 | 1.15 | 1.15 | 1.44 | 1.15 | 1.26 |
time (sec) |
N/A | 0.012 | 0.005 | 0.363 | 0.207 | 0.238 | 0.039 | 0.253 | 9.150 |
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 | 17 | 17 | 22 | 17 | 23 | 20 | 23 | 17 |
N.S. |
1 | 0.63 | 0.63 | 0.81 | 0.63 | 0.85 | 0.74 | 0.85 | 0.63 |
time (sec) |
N/A | 0.090 | 0.085 | 1.968 | 0.249 | 0.247 | 0.075 | 0.269 | 9.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | F(-1) | B | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 0 | 61 | 0 | 60 | 58 | 221 | 229 |
N.S. |
1 | 0.00 | 0.00 | 3.05 | 0.00 | 3.00 | 2.90 | 11.05 | 11.45 |
time (sec) |
N/A | 0.000 | 0.000 | 1.892 | 0.000 | 0.237 | 0.140 | 0.281 | 0.400 |
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 | 30 | 28 | 29 | 28 | 27 | 28 | 28 |
N.S. |
1 | 0.00 | 1.25 | 1.17 | 1.21 | 1.17 | 1.12 | 1.17 | 1.17 |
time (sec) |
N/A | 0.000 | 1.000 | 0.507 | 0.309 | 0.274 | 0.149 | 0.270 | 9.406 |
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 | 24 | 22 | 23 | 38 | 38 | 20 | 41 | 44 |
N.S. |
1 | 1.00 | 0.92 | 0.96 | 1.58 | 1.58 | 0.83 | 1.71 | 1.83 |
time (sec) |
N/A | 0.238 | 0.027 | 1.435 | 0.235 | 0.256 | 0.226 | 0.284 | 9.859 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 17 | 17 | 13 | 12 | 32 | 14 | 0 | 12 |
N.S. |
1 | 0.85 | 0.85 | 0.65 | 0.60 | 1.60 | 0.70 | 0.00 | 0.60 |
time (sec) |
N/A | 0.040 | 0.182 | 0.460 | 0.196 | 0.236 | 0.127 | 0.000 | 0.155 |
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 | 14 | 58 | 16 | 15 | 22 | 14 | 14 | 22 | 14 |
N.S. |
1 | 4.14 | 1.14 | 1.07 | 1.57 | 1.00 | 1.00 | 1.57 | 1.00 |
time (sec) |
N/A | 0.270 | 0.152 | 2.075 | 0.321 | 0.228 | 0.052 | 0.255 | 9.520 |
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 | 28 | 0 | 26 | 36 | 66 | 35 | 29 | 70 | 69 |
N.S. |
1 | 0.00 | 0.93 | 1.29 | 2.36 | 1.25 | 1.04 | 2.50 | 2.46 |
time (sec) |
N/A | 0.000 | 0.133 | 0.885 | 0.341 | 0.263 | 0.242 | 0.813 | 0.332 |
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 | 13 | 13 | 13 | 12 | 12 | 12 | 12 | 12 |
N.S. |
1 | 0.65 | 0.65 | 0.65 | 0.60 | 0.60 | 0.60 | 0.60 | 0.60 |
time (sec) |
N/A | 0.007 | 0.006 | 0.155 | 0.194 | 0.242 | 0.058 | 0.246 | 0.042 |
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 | 30 | 117 | 28 | 83 | 81 | 81 | 80 | 81 | 25 |
N.S. |
1 | 3.90 | 0.93 | 2.77 | 2.70 | 2.70 | 2.67 | 2.70 | 0.83 |
time (sec) |
N/A | 0.257 | 2.846 | 1.052 | 0.197 | 0.234 | 0.078 | 0.255 | 9.306 |
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 | 30 | 0 | 30 | 26 | 31 | 25 | 26 | 121 | 64 |
N.S. |
1 | 0.00 | 1.00 | 0.87 | 1.03 | 0.83 | 0.87 | 4.03 | 2.13 |
time (sec) |
N/A | 0.000 | 0.074 | 15.348 | 0.330 | 0.241 | 0.144 | 0.539 | 9.960 |
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 | 27 | 0 | 33 | 27 | 28 | 33 | 32 | 0 | 29 |
N.S. |
1 | 0.00 | 1.22 | 1.00 | 1.04 | 1.22 | 1.19 | 0.00 | 1.07 |
time (sec) |
N/A | 0.000 | 0.233 | 3.020 | 0.238 | 0.250 | 0.066 | 0.000 | 9.390 |
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 | 30 | 26 | 19 | 21 | 18 | 20 | 24 | 16 |
N.S. |
1 | 1.50 | 1.30 | 0.95 | 1.05 | 0.90 | 1.00 | 1.20 | 0.80 |
time (sec) |
N/A | 0.156 | 0.030 | 2.033 | 0.326 | 0.254 | 0.144 | 0.262 | 9.256 |
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 | 8 | 7 | 10 | 8 | 10 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.17 | 1.67 | 1.33 | 1.67 | 1.17 |
time (sec) |
N/A | 0.001 | 0.000 | 0.398 | 0.192 | 0.234 | 0.020 | 0.251 | 9.088 |
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 | 27 | 42 | 43 | 40 | 48 | 41 | 37 | 44 | 40 |
N.S. |
1 | 1.56 | 1.59 | 1.48 | 1.78 | 1.52 | 1.37 | 1.63 | 1.48 |
time (sec) |
N/A | 0.080 | 0.074 | 1.048 | 0.225 | 0.245 | 0.137 | 0.259 | 0.138 |
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 | 13 | 13 | 14 | 13 | 13 | 12 | 13 | 11 |
N.S. |
1 | 0.76 | 0.76 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.65 |
time (sec) |
N/A | 0.002 | 0.001 | 0.117 | 0.195 | 0.242 | 0.048 | 0.248 | 9.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 32 | 28 | 31 | 34 | 30 | 0 | 32 | 30 |
N.S. |
1 | 1.39 | 1.22 | 1.35 | 1.48 | 1.30 | 0.00 | 1.39 | 1.30 |
time (sec) |
N/A | 0.575 | 0.234 | 3.891 | 0.336 | 0.258 | 0.000 | 0.270 | 9.480 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 25 | 24 | 24 | 22 | 24 | 24 |
N.S. |
1 | 0.00 | 0.00 | 1.14 | 1.09 | 1.09 | 1.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.000 | 0.000 | 3.142 | 0.317 | 0.241 | 0.221 | 0.297 | 9.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | A | A | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 20 | 20 | 0 | 18 | 17 | 17 | 18 | 17 |
N.S. |
1 | 0.91 | 0.91 | 0.00 | 0.82 | 0.77 | 0.77 | 0.82 | 0.77 |
time (sec) |
N/A | 0.086 | 0.178 | 0.000 | 0.282 | 0.237 | 0.317 | 0.262 | 10.879 |
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 | 24 | 22 | 50 | 42 | 60 | 51 | 57 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 2.08 | 1.75 | 2.50 | 2.12 | 2.38 |
time (sec) |
N/A | 0.000 | 0.190 | 2.373 | 0.247 | 0.270 | 0.117 | 0.275 | 0.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 22 | 20 | 24 | 22 | 21 | 22 | 0 | 20 |
N.S. |
1 | 0.79 | 0.71 | 0.86 | 0.79 | 0.75 | 0.79 | 0.00 | 0.71 |
time (sec) |
N/A | 0.103 | 0.037 | 3.426 | 0.320 | 0.254 | 0.178 | 0.000 | 10.305 |
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 | 36 | 35 | 35 | 32 | 33 | 33 | 32 | 35 | 31 |
N.S. |
1 | 0.97 | 0.97 | 0.89 | 0.92 | 0.92 | 0.89 | 0.97 | 0.86 |
time (sec) |
N/A | 0.060 | 0.014 | 0.681 | 0.193 | 0.243 | 0.064 | 0.259 | 8.812 |
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 | 25 | 41 | 41 | 20 | 24 | 28 |
N.S. |
1 | 0.00 | 0.91 | 1.09 | 1.78 | 1.78 | 0.87 | 1.04 | 1.22 |
time (sec) |
N/A | 0.000 | 0.185 | 2.250 | 0.220 | 0.248 | 0.073 | 0.261 | 8.896 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 34 | 27 | 25 | 29 | 20 | 27 | 24 | 24 |
N.S. |
1 | 2.00 | 1.59 | 1.47 | 1.71 | 1.18 | 1.59 | 1.41 | 1.41 |
time (sec) |
N/A | 0.021 | 0.012 | 0.696 | 0.196 | 0.249 | 0.089 | 0.252 | 8.703 |
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 | 24 | 0 | 23 | 19 | 0 | 19 | 19 | 32 | 18 |
N.S. |
1 | 0.00 | 0.96 | 0.79 | 0.00 | 0.79 | 0.79 | 1.33 | 0.75 |
time (sec) |
N/A | 0.000 | 0.111 | 2.462 | 0.000 | 0.243 | 0.131 | 0.257 | 8.790 |
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 | 20 | 0 | 16 | 16 | 20 | 15 | 20 | 24 | 15 |
N.S. |
1 | 0.00 | 0.80 | 0.80 | 1.00 | 0.75 | 1.00 | 1.20 | 0.75 |
time (sec) |
N/A | 0.000 | 0.558 | 0.497 | 0.245 | 0.232 | 0.104 | 0.256 | 8.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 48 | 62 | 57 | 71 | 55 | 61 | 77 | 62 |
N.S. |
1 | 1.66 | 2.14 | 1.97 | 2.45 | 1.90 | 2.10 | 2.66 | 2.14 |
time (sec) |
N/A | 0.124 | 0.077 | 0.696 | 0.235 | 0.246 | 0.073 | 0.266 | 8.888 |
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 | 40 | 40 | 28 | 27 | 27 | 26 | 27 | 107 |
N.S. |
1 | 1.60 | 1.60 | 1.12 | 1.08 | 1.08 | 1.04 | 1.08 | 4.28 |
time (sec) |
N/A | 0.508 | 5.061 | 1.825 | 0.318 | 0.251 | 0.411 | 0.282 | 1.280 |
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 | 20 | 30 | 19 | 18 | 18 | 17 | 19 | 18 |
N.S. |
1 | 1.11 | 1.67 | 1.06 | 1.00 | 1.00 | 0.94 | 1.06 | 1.00 |
time (sec) |
N/A | 0.014 | 0.015 | 1.393 | 0.198 | 0.240 | 0.056 | 0.250 | 8.943 |
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 | 25 | 41 | 20 | 38 | 0 | 27 | 34 | 30 | 18 |
N.S. |
1 | 1.64 | 0.80 | 1.52 | 0.00 | 1.08 | 1.36 | 1.20 | 0.72 |
time (sec) |
N/A | 0.082 | 0.155 | 2.287 | 0.000 | 0.241 | 0.153 | 0.283 | 9.158 |
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 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.93 | 0.93 | 0.86 | 0.93 | 0.93 |
time (sec) |
N/A | 0.003 | 0.000 | 0.822 | 0.185 | 0.246 | 0.024 | 0.250 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 121 | 116 | 71 | 841 | 60 | 75 | 0 | 88 |
N.S. |
1 | 4.65 | 4.46 | 2.73 | 32.35 | 2.31 | 2.88 | 0.00 | 3.38 |
time (sec) |
N/A | 0.816 | 0.224 | 3.738 | 0.336 | 0.245 | 1.975 | 0.000 | 9.854 |
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 | 23 | 23 | 18 | 22 | 21 | 15 | 25 | 17 |
N.S. |
1 | 1.28 | 1.28 | 1.00 | 1.22 | 1.17 | 0.83 | 1.39 | 0.94 |
time (sec) |
N/A | 0.222 | 0.424 | 0.540 | 0.233 | 0.250 | 0.105 | 0.254 | 9.006 |
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 | 13 | 13 | 16 | 15 | 15 | 10 | 15 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.23 | 1.15 | 1.15 | 0.77 | 1.15 | 0.92 |
time (sec) |
N/A | 0.071 | 0.026 | 1.036 | 0.308 | 0.248 | 0.066 | 0.257 | 8.928 |
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 | 11 | 10 | 17 | 10 | 10 | 12 |
N.S. |
1 | 0.75 | 0.75 | 0.69 | 0.62 | 1.06 | 0.62 | 0.62 | 0.75 |
time (sec) |
N/A | 0.003 | 0.001 | 0.207 | 0.189 | 0.235 | 0.047 | 0.251 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 20 | 16 | 15 | 30 | 17 | 0 | 15 |
N.S. |
1 | 1.00 | 0.91 | 0.73 | 0.68 | 1.36 | 0.77 | 0.00 | 0.68 |
time (sec) |
N/A | 0.091 | 0.028 | 5.205 | 1.158 | 0.250 | 1.091 | 0.000 | 8.821 |
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 | 32 | 25 | 20 | 29 | 29 | 24 | 29 | 24 |
N.S. |
1 | 1.39 | 1.09 | 0.87 | 1.26 | 1.26 | 1.04 | 1.26 | 1.04 |
time (sec) |
N/A | 0.007 | 0.007 | 0.545 | 0.200 | 0.259 | 0.029 | 0.245 | 0.062 |
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 | 11 | 9 | 10 | 9 | 9 | 8 | 10 | 9 |
N.S. |
1 | 0.65 | 0.53 | 0.59 | 0.53 | 0.53 | 0.47 | 0.59 | 0.53 |
time (sec) |
N/A | 0.005 | 0.005 | 0.114 | 0.191 | 0.236 | 0.047 | 0.264 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | B | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 0 | 27 | 168 | 49 | 48 | 169 | 429 |
N.S. |
1 | 0.00 | 0.00 | 1.35 | 8.40 | 2.45 | 2.40 | 8.45 | 21.45 |
time (sec) |
N/A | 0.000 | 0.000 | 6.420 | 0.662 | 0.255 | 0.421 | 2.372 | 9.569 |
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 | 17 | 17 | 18 | 18 | 21 | 17 | 19 | 18 |
N.S. |
1 | 0.81 | 0.81 | 0.86 | 0.86 | 1.00 | 0.81 | 0.90 | 0.86 |
time (sec) |
N/A | 0.033 | 0.009 | 2.575 | 0.214 | 0.243 | 0.338 | 0.257 | 0.072 |
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 | 43 | 31 | 29 | 28 | 28 | 26 | 28 | 28 |
N.S. |
1 | 1.08 | 0.78 | 0.72 | 0.70 | 0.70 | 0.65 | 0.70 | 0.70 |
time (sec) |
N/A | 0.602 | 0.193 | 1.230 | 0.235 | 0.254 | 0.142 | 0.272 | 9.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 27 | 25 | 24 | 26 | 34 | 0 | 26 | 0 |
N.S. |
1 | 1.08 | 1.00 | 0.96 | 1.04 | 1.36 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.252 | 0.056 | 3.102 | 0.385 | 0.256 | 0.000 | 0.284 | 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 | 17 | 0 | 11 | 13 | 14 | 12 | 12 | 12 | 12 |
N.S. |
1 | 0.00 | 0.65 | 0.76 | 0.82 | 0.71 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.000 | 0.067 | 2.983 | 0.331 | 0.251 | 0.078 | 0.248 | 8.915 |
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 | 9 | 3 | 3 | 4 | 3 | 3 | 2 | 3 | 3 |
N.S. |
1 | 0.33 | 0.33 | 0.44 | 0.33 | 0.33 | 0.22 | 0.33 | 0.33 |
time (sec) |
N/A | 0.000 | 0.000 | 0.227 | 0.206 | 0.232 | 0.023 | 0.247 | 0.012 |
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 | 30 | 51 | 30 | 34 | 32 | 30 | 34 | 34 | 28 |
N.S. |
1 | 1.70 | 1.00 | 1.13 | 1.07 | 1.00 | 1.13 | 1.13 | 0.93 |
time (sec) |
N/A | 0.095 | 0.033 | 1.101 | 0.209 | 0.233 | 0.516 | 0.256 | 8.984 |
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 | 23 | 23 | 21 | 20 | 29 | 27 | 20 | 20 |
N.S. |
1 | 0.92 | 0.92 | 0.84 | 0.80 | 1.16 | 1.08 | 0.80 | 0.80 |
time (sec) |
N/A | 0.009 | 0.014 | 0.870 | 0.201 | 0.236 | 0.063 | 0.252 | 8.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 174 | 95 | 80 | 131 | 85 | 88 | 100 | 81 |
N.S. |
1 | 5.80 | 3.17 | 2.67 | 4.37 | 2.83 | 2.93 | 3.33 | 2.70 |
time (sec) |
N/A | 0.218 | 0.149 | 0.853 | 0.235 | 0.264 | 0.129 | 0.266 | 9.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | B | F(-2) | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 0 | 47 | 57 | 41 | 0 | 48 | 46 |
N.S. |
1 | 0.00 | 0.00 | 2.24 | 2.71 | 1.95 | 0.00 | 2.29 | 2.19 |
time (sec) |
N/A | 0.000 | 0.000 | 7.964 | 0.354 | 0.250 | 0.000 | 1.492 | 9.453 |
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 | 33 | 34 | 40 | 28 | 35 | 35 | 32 | 36 | 35 |
N.S. |
1 | 1.03 | 1.21 | 0.85 | 1.06 | 1.06 | 0.97 | 1.09 | 1.06 |
time (sec) |
N/A | 0.051 | 0.027 | 0.696 | 0.195 | 0.234 | 0.176 | 0.255 | 9.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | C | A | A | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 19 | 567 | 74 | 27 | 20 | 76 | 18 |
N.S. |
1 | 0.00 | 0.90 | 27.00 | 3.52 | 1.29 | 0.95 | 3.62 | 0.86 |
time (sec) |
N/A | 0.000 | 0.073 | 4.967 | 0.383 | 0.245 | 0.852 | 0.354 | 9.583 |
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 | 28 | 21 | 20 | 120 | 20 | 14 | 81 | 29 |
N.S. |
1 | 1.04 | 0.78 | 0.74 | 4.44 | 0.74 | 0.52 | 3.00 | 1.07 |
time (sec) |
N/A | 0.807 | 0.308 | 4.273 | 0.200 | 0.239 | 0.103 | 1.669 | 0.371 |
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 | 17 | 21 | 23 | 23 | 20 | 23 | 24 |
N.S. |
1 | 1.74 | 0.63 | 0.78 | 0.85 | 0.85 | 0.74 | 0.85 | 0.89 |
time (sec) |
N/A | 0.027 | 0.076 | 0.438 | 0.191 | 0.240 | 0.063 | 0.259 | 0.070 |