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 | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 71 | 62 | 45 | 68 | 113 | 139 | 60 | 58 |
N.S. |
1 | 0.86 | 0.75 | 0.54 | 0.82 | 1.36 | 1.67 | 0.72 | 0.70 |
time (sec) |
N/A | 0.201 | 0.037 | 1.637 | 0.180 | 0.276 | 2.058 | 0.263 | 0.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 47 | 45 | 47 | 53 | 95 | 207 | 57 | 42 |
N.S. |
1 | 0.82 | 0.79 | 0.82 | 0.93 | 1.67 | 3.63 | 1.00 | 0.74 |
time (sec) |
N/A | 0.204 | 0.030 | 0.707 | 0.214 | 0.278 | 0.835 | 0.272 | 1.513 |
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 | 49 | 43 | 39 | 35 | 40 | 54 | 78 | 34 | 36 |
N.S. |
1 | 0.88 | 0.80 | 0.71 | 0.82 | 1.10 | 1.59 | 0.69 | 0.73 |
time (sec) |
N/A | 0.197 | 0.019 | 0.326 | 0.207 | 0.311 | 0.393 | 0.259 | 1.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 32 | 23 | 19 | 24 | 50 | 63 | 24 | 18 |
N.S. |
1 | 1.39 | 1.00 | 0.83 | 1.04 | 2.17 | 2.74 | 1.04 | 0.78 |
time (sec) |
N/A | 0.183 | 0.012 | 0.173 | 0.185 | 0.275 | 0.184 | 0.305 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 17 | 27 | 30 | 0 | 24 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.42 | 1.58 | 0.00 | 1.26 | 0.84 |
time (sec) |
N/A | 0.169 | 0.011 | 0.124 | 0.180 | 0.263 | 0.000 | 0.275 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 45 | 37 | 25 | 52 | 157 | 0 | 48 | 52 |
N.S. |
1 | 1.07 | 0.88 | 0.60 | 1.24 | 3.74 | 0.00 | 1.14 | 1.24 |
time (sec) |
N/A | 0.187 | 0.042 | 0.369 | 0.190 | 0.275 | 0.000 | 0.271 | 1.347 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 29 | 24 | 68 | 88 | 0 | 31 | 31 |
N.S. |
1 | 1.00 | 0.94 | 0.77 | 2.19 | 2.84 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.178 | 0.014 | 1.562 | 0.210 | 0.269 | 0.000 | 0.264 | 1.307 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 112 | 75 | 37 | 100 | 705 | 0 | 75 | 135 |
N.S. |
1 | 1.11 | 0.74 | 0.37 | 0.99 | 6.98 | 0.00 | 0.74 | 1.34 |
time (sec) |
N/A | 0.208 | 0.048 | 2.311 | 0.214 | 0.276 | 0.000 | 0.272 | 1.320 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 44 | 35 | 172 | 233 | 0 | 42 | 42 |
N.S. |
1 | 1.00 | 0.67 | 0.53 | 2.61 | 3.53 | 0.00 | 0.64 | 0.64 |
time (sec) |
N/A | 0.220 | 0.038 | 3.417 | 0.214 | 0.262 | 0.000 | 0.270 | 1.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 28 | 26 | 17 | 17 | 47 | 42 | 17 | 17 |
N.S. |
1 | 1.08 | 1.00 | 0.65 | 0.65 | 1.81 | 1.62 | 0.65 | 0.65 |
time (sec) |
N/A | 0.183 | 0.013 | 1.589 | 0.209 | 0.279 | 0.156 | 0.264 | 0.101 |
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 | 19 | 16 | 14 | 13 | 26 | 20 | 13 | 12 |
N.S. |
1 | 1.00 | 0.84 | 0.74 | 0.68 | 1.37 | 1.05 | 0.68 | 0.63 |
time (sec) |
N/A | 0.175 | 0.008 | 0.346 | 0.209 | 0.279 | 0.096 | 0.257 | 1.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 19 | 11 | 34 | 18 | 25 | 0 | 19 | 26 |
N.S. |
1 | 1.73 | 1.00 | 3.09 | 1.64 | 2.27 | 0.00 | 1.73 | 2.36 |
time (sec) |
N/A | 0.168 | 0.011 | 0.874 | 0.296 | 0.283 | 0.000 | 0.259 | 0.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 42 | 32 | 46 | 32 | 182 | 0 | 33 | 36 |
N.S. |
1 | 1.31 | 1.00 | 1.44 | 1.00 | 5.69 | 0.00 | 1.03 | 1.12 |
time (sec) |
N/A | 0.190 | 0.056 | 0.647 | 0.296 | 0.281 | 0.000 | 0.259 | 1.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 28 | 26 | 17 | 17 | 67 | 42 | 17 | 17 |
N.S. |
1 | 1.08 | 1.00 | 0.65 | 0.65 | 2.58 | 1.62 | 0.65 | 0.65 |
time (sec) |
N/A | 0.180 | 0.013 | 0.556 | 0.215 | 0.272 | 0.152 | 0.262 | 1.318 |
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 | 19 | 23 | 16 | 14 | 13 | 40 | 20 | 13 | 12 |
N.S. |
1 | 1.21 | 0.84 | 0.74 | 0.68 | 2.11 | 1.05 | 0.68 | 0.63 |
time (sec) |
N/A | 0.179 | 0.012 | 0.635 | 0.208 | 0.268 | 0.095 | 0.277 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | A | A | F | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 56 | 22 | 79 | 73 | 83 | 0 | 43 | 65 |
N.S. |
1 | 1.04 | 0.41 | 1.46 | 1.35 | 1.54 | 0.00 | 0.80 | 1.20 |
time (sec) |
N/A | 0.241 | 0.011 | 0.630 | 0.305 | 0.287 | 0.000 | 0.269 | 0.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 118 | 34 | 148 | 85 | 560 | 0 | 86 | 91 |
N.S. |
1 | 1.12 | 0.32 | 1.41 | 0.81 | 5.33 | 0.00 | 0.82 | 0.87 |
time (sec) |
N/A | 0.300 | 0.020 | 0.740 | 0.300 | 0.283 | 0.000 | 0.270 | 0.394 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 28 | 26 | 17 | 17 | 87 | 42 | 17 | 17 |
N.S. |
1 | 1.08 | 1.00 | 0.65 | 0.65 | 3.35 | 1.62 | 0.65 | 0.65 |
time (sec) |
N/A | 0.181 | 0.014 | 0.638 | 0.198 | 0.281 | 0.152 | 0.266 | 0.081 |
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 | 19 | 23 | 19 | 14 | 13 | 46 | 20 | 13 | 13 |
N.S. |
1 | 1.21 | 1.00 | 0.74 | 0.68 | 2.42 | 1.05 | 0.68 | 0.68 |
time (sec) |
N/A | 0.179 | 0.011 | 0.229 | 0.189 | 0.273 | 0.097 | 0.258 | 1.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | A | C | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 130 | 22 | 56 | 95 | 107 | 0 | 96 | 106 |
N.S. |
1 | 1.15 | 0.19 | 0.50 | 0.84 | 0.95 | 0.00 | 0.85 | 0.94 |
time (sec) |
N/A | 0.353 | 0.010 | 0.934 | 0.276 | 0.281 | 0.000 | 0.262 | 0.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | A | C | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 153 | 34 | 68 | 107 | 855 | 0 | 108 | 120 |
N.S. |
1 | 1.17 | 0.26 | 0.52 | 0.82 | 6.53 | 0.00 | 0.82 | 0.92 |
time (sec) |
N/A | 0.370 | 0.025 | 0.745 | 0.279 | 0.298 | 0.000 | 0.273 | 1.646 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 202 | 190 | 157 | 147 | 134 | 2228 | 1525 | 1211 | 166 |
N.S. |
1 | 0.94 | 0.78 | 0.73 | 0.66 | 11.03 | 7.55 | 6.00 | 0.82 |
time (sec) |
N/A | 0.400 | 0.508 | 1.609 | 0.199 | 0.358 | 7.771 | 0.318 | 2.330 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 86 | 90 | 94 | 703 | 709 | 890 | 97 |
N.S. |
1 | 1.00 | 0.65 | 0.68 | 0.71 | 5.33 | 5.37 | 6.74 | 0.73 |
time (sec) |
N/A | 0.296 | 0.128 | 0.850 | 0.224 | 0.284 | 1.070 | 0.297 | 1.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 50 | 51 | 63 | 244 | 323 | 598 | 73 |
N.S. |
1 | 1.00 | 0.67 | 0.68 | 0.84 | 3.25 | 4.31 | 7.97 | 0.97 |
time (sec) |
N/A | 0.220 | 0.075 | 0.161 | 0.226 | 0.287 | 0.580 | 0.293 | 1.383 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 79 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.211 | 2.619 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 87 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.221 | 0.908 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 122 | 137 | 281 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 2.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.345 | 14.380 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 131 | 146 | 163 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.358 | 1.579 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 250 | 102 | 109 | 88 | 90 | 218 | 0 | 269 | 0 |
N.S. |
1 | 0.41 | 0.44 | 0.35 | 0.36 | 0.87 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.433 | 0.078 | 6.257 | 0.311 | 0.293 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 162 | 74 | 76 | 75 | 62 | 126 | 0 | 195 | 0 |
N.S. |
1 | 0.46 | 0.47 | 0.46 | 0.38 | 0.78 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.378 | 0.044 | 0.571 | 0.313 | 0.294 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | B | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 74 | 61 | 48 | 60 | 36 | 66 | 158 | 71 | 77 |
N.S. |
1 | 0.82 | 0.65 | 0.81 | 0.49 | 0.89 | 2.14 | 0.96 | 1.04 |
time (sec) |
N/A | 0.343 | 0.033 | 0.588 | 0.308 | 0.273 | 1.568 | 0.285 | 1.369 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 44 | 29 | 39 | 42 | 0 | 85 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.63 | 0.85 | 0.91 | 0.00 | 1.85 | 0.00 |
time (sec) |
N/A | 0.320 | 0.042 | 0.639 | 0.298 | 0.263 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 46 | 42 | 84 | 121 | 0 | 87 | 76 |
N.S. |
1 | 1.00 | 0.79 | 0.72 | 1.45 | 2.09 | 0.00 | 1.50 | 1.31 |
time (sec) |
N/A | 0.334 | 0.056 | 1.311 | 0.307 | 0.269 | 0.000 | 0.289 | 1.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 147 | 93 | 72 | 66 | 209 | 315 | 0 | 122 | 89 |
N.S. |
1 | 0.63 | 0.49 | 0.45 | 1.42 | 2.14 | 0.00 | 0.83 | 0.61 |
time (sec) |
N/A | 0.407 | 0.050 | 0.681 | 0.308 | 0.283 | 0.000 | 0.302 | 1.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 199 | 113 | 84 | 91 | 386 | 592 | 0 | 161 | 353 |
N.S. |
1 | 0.57 | 0.42 | 0.46 | 1.94 | 2.97 | 0.00 | 0.81 | 1.77 |
time (sec) |
N/A | 0.437 | 0.059 | 0.871 | 0.317 | 0.291 | 0.000 | 0.308 | 1.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 28 | 28 | 0 | 42 | 99 | 32 | 45 |
N.S. |
1 | 1.00 | 0.68 | 0.68 | 0.00 | 1.02 | 2.41 | 0.78 | 1.10 |
time (sec) |
N/A | 0.191 | 0.038 | 0.674 | 0.000 | 0.267 | 0.230 | 0.274 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 80 | 72 | 65 | 103 | 0 | 73 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.85 | 0.76 | 1.21 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.275 | 0.067 | 0.847 | 0.206 | 0.271 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 92 | 97 | 81 | 129 | 0 | 91 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.96 | 0.80 | 1.28 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.337 | 0.123 | 0.943 | 0.226 | 0.279 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 51 | 52 | 45 | 72 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.80 | 0.69 | 1.11 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.260 | 0.050 | 1.089 | 0.183 | 0.281 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 72 | 48 | 47 | 75 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.74 | 0.72 | 1.15 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.280 | 0.080 | 1.554 | 0.187 | 0.281 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 123 | 105 | 89 | 164 | 0 | 101 | 0 |
N.S. |
1 | 1.00 | 1.07 | 0.91 | 0.77 | 1.43 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.363 | 0.285 | 1.300 | 0.190 | 0.280 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 103 | 100 | 90 | 213 | 0 | 106 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.91 | 0.82 | 1.94 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.353 | 0.112 | 0.677 | 0.190 | 0.294 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 149 | 126 | 127 | 278 | 0 | 356 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.85 | 0.86 | 1.88 | 0.00 | 2.41 | 0.00 |
time (sec) |
N/A | 0.401 | 0.559 | 0.770 | 0.262 | 0.309 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 239 | 239 | 287 | 207 | 200 | 445 | 0 | 223 | 0 |
N.S. |
1 | 1.00 | 1.20 | 0.87 | 0.84 | 1.86 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.539 | 0.299 | 1.541 | 0.269 | 0.316 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 124 | 126 | 102 | 253 | 0 | 132 | 0 |
N.S. |
1 | 1.00 | 1.08 | 1.10 | 0.89 | 2.20 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.436 | 0.194 | 0.492 | 0.186 | 0.295 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 220 | 158 | 143 | 334 | 0 | 388 | 0 |
N.S. |
1 | 1.00 | 1.37 | 0.98 | 0.89 | 2.07 | 0.00 | 2.41 | 0.00 |
time (sec) |
N/A | 0.508 | 0.448 | 0.892 | 0.263 | 0.300 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 257 | 257 | 354 | 265 | 228 | 541 | 0 | 281 | 0 |
N.S. |
1 | 1.00 | 1.38 | 1.03 | 0.89 | 2.11 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.725 | 0.594 | 1.379 | 0.268 | 0.296 | 0.000 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 104 | 117 | 105 | 217 | 0 | 132 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.88 | 0.79 | 1.63 | 0.00 | 0.99 | 0.00 |
time (sec) |
N/A | 0.399 | 0.127 | 0.427 | 0.186 | 0.298 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 131 | 139 | 131 | 244 | 0 | 150 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.86 | 0.81 | 1.52 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.430 | 0.196 | 0.353 | 0.191 | 0.347 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 271 | 271 | 214 | 234 | 211 | 427 | 0 | 264 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.86 | 0.78 | 1.58 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.588 | 0.346 | 0.978 | 0.198 | 0.306 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 76 | 70 | 69 | 146 | 0 | 75 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.86 | 0.85 | 1.80 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.358 | 0.254 | 0.192 | 0.188 | 0.305 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 179 | 101 | 100 | 254 | 0 | 107 | 0 |
N.S. |
1 | 1.00 | 1.40 | 0.79 | 0.78 | 1.98 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.419 | 0.383 | 0.309 | 0.185 | 0.291 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 171 | 272 | 144 | 143 | 492 | 0 | 155 | 0 |
N.S. |
1 | 1.00 | 1.59 | 0.84 | 0.84 | 2.88 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.526 | 0.905 | 0.799 | 0.198 | 0.286 | 0.000 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 166 | 147 | 127 | 322 | 0 | 172 | 0 |
N.S. |
1 | 1.00 | 1.19 | 1.05 | 0.91 | 2.30 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.497 | 0.520 | 0.271 | 0.196 | 0.310 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 183 | 183 | 258 | 177 | 161 | 422 | 0 | 198 | 0 |
N.S. |
1 | 1.00 | 1.41 | 0.97 | 0.88 | 2.31 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.596 | 1.026 | 0.398 | 0.202 | 0.277 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 300 | 300 | 480 | 302 | 263 | 848 | 0 | 352 | 0 |
N.S. |
1 | 1.00 | 1.60 | 1.01 | 0.88 | 2.83 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.843 | 4.321 | 1.171 | 0.231 | 0.355 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 135 | 162 | 129 | 263 | 0 | 167 | 0 |
N.S. |
1 | 1.00 | 0.88 | 1.06 | 0.84 | 1.72 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.506 | 0.231 | 0.339 | 0.248 | 0.308 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 219 | 219 | 183 | 210 | 185 | 343 | 0 | 223 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.96 | 0.84 | 1.57 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.579 | 0.412 | 0.420 | 0.239 | 0.280 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 315 | 315 | 263 | 326 | 263 | 527 | 0 | 339 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.03 | 0.83 | 1.67 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.723 | 0.641 | 0.997 | 0.240 | 0.343 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 154 | 154 | 179 | 160 | 139 | 325 | 0 | 181 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.04 | 0.90 | 2.11 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.535 | 0.574 | 0.230 | 0.205 | 0.303 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 225 | 225 | 257 | 217 | 199 | 466 | 0 | 239 | 0 |
N.S. |
1 | 1.00 | 1.14 | 0.96 | 0.88 | 2.07 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.650 | 1.530 | 0.405 | 0.207 | 0.321 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 323 | 323 | 503 | 326 | 287 | 852 | 0 | 369 | 0 |
N.S. |
1 | 1.00 | 1.56 | 1.01 | 0.89 | 2.64 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.824 | 4.729 | 1.095 | 0.210 | 0.302 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 252 | 186 | 151 | 363 | 0 | 207 | 0 |
N.S. |
1 | 1.00 | 1.57 | 1.16 | 0.94 | 2.25 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.641 | 1.084 | 0.236 | 0.228 | 0.295 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 239 | 239 | 339 | 249 | 215 | 516 | 0 | 271 | 0 |
N.S. |
1 | 1.00 | 1.42 | 1.04 | 0.90 | 2.16 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 0.828 | 4.455 | 0.602 | 0.207 | 0.293 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 344 | 344 | 2991 | 384 | 315 | 940 | 0 | 427 | 0 |
N.S. |
1 | 1.00 | 8.69 | 1.12 | 0.92 | 2.73 | 0.00 | 1.24 | 0.00 |
time (sec) |
N/A | 1.044 | 6.459 | 1.403 | 0.211 | 0.303 | 0.000 | 0.297 | 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 | 30 | 30 | 30 | 25 | 35 | 22 | 41 | 35 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.17 | 0.73 | 1.37 | 1.17 | 0.80 |
time (sec) |
N/A | 0.219 | 0.044 | 0.344 | 0.195 | 0.277 | 0.060 | 0.250 | 1.287 |
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 | 56 | 56 | 48 | 48 | 81 | 58 | 85 | 75 | 46 |
N.S. |
1 | 1.00 | 0.86 | 0.86 | 1.45 | 1.04 | 1.52 | 1.34 | 0.82 |
time (sec) |
N/A | 0.267 | 0.063 | 0.416 | 0.229 | 0.277 | 0.089 | 0.252 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 213 | 213 | 167 | 212 | 0 | 316 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.78 | 1.00 | 0.00 | 1.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.715 | 0.547 | 0.796 | 0.000 | 0.303 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 271 | 271 | 220 | 376 | 0 | 671 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.81 | 1.39 | 0.00 | 2.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.008 | 1.131 | 1.880 | 0.000 | 0.289 | 0.000 | 0.000 | 0.000 |