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 | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 21 | 42 | 21 | 59 | 113 | 0 | 44 | 53 |
N.S. |
1 | 0.91 | 1.83 | 0.91 | 2.57 | 4.91 | 0.00 | 1.91 | 2.30 |
time (sec) |
N/A | 0.195 | 0.050 | 0.298 | 0.195 | 0.247 | 0.000 | 0.258 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 28 | 22 | 33 | 56 | 31 | 0 | 45 | 49 |
N.S. |
1 | 1.27 | 1.00 | 1.50 | 2.55 | 1.41 | 0.00 | 2.05 | 2.23 |
time (sec) |
N/A | 0.211 | 0.011 | 0.311 | 0.196 | 0.254 | 0.000 | 0.282 | 2.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 51 | 85 | 62 | 108 | 612 | 0 | 105 | 112 |
N.S. |
1 | 1.04 | 1.73 | 1.27 | 2.20 | 12.49 | 0.00 | 2.14 | 2.29 |
time (sec) |
N/A | 0.212 | 0.104 | 0.975 | 0.203 | 0.291 | 0.000 | 0.293 | 0.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 42 | 37 | 51 | 100 | 89 | 0 | 71 | 131 |
N.S. |
1 | 1.14 | 1.00 | 1.38 | 2.70 | 2.41 | 0.00 | 1.92 | 3.54 |
time (sec) |
N/A | 0.211 | 0.016 | 0.556 | 0.196 | 0.247 | 0.000 | 0.288 | 2.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 28 | 25 | 23 | 70 | 203 | 105 | 63 | 49 |
N.S. |
1 | 1.04 | 0.93 | 0.85 | 2.59 | 7.52 | 3.89 | 2.33 | 1.81 |
time (sec) |
N/A | 0.210 | 0.017 | 0.499 | 0.185 | 0.253 | 0.826 | 0.273 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 62 | 31 | 39 | 66 | 60 | 0 | 71 | 50 |
N.S. |
1 | 1.55 | 0.78 | 0.98 | 1.65 | 1.50 | 0.00 | 1.78 | 1.25 |
time (sec) |
N/A | 0.225 | 0.175 | 0.552 | 0.188 | 0.252 | 0.000 | 0.279 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | F | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 41 | 35 | 43 | 120 | 743 | 0 | 102 | 97 |
N.S. |
1 | 0.95 | 0.81 | 1.00 | 2.79 | 17.28 | 0.00 | 2.37 | 2.26 |
time (sec) |
N/A | 0.229 | 0.036 | 0.772 | 0.196 | 0.264 | 0.000 | 0.302 | 2.100 |
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 | 38 | 33 | 60 | 31 | 87 | 357 | 0 | 69 | 81 |
N.S. |
1 | 0.87 | 1.58 | 0.82 | 2.29 | 9.39 | 0.00 | 1.82 | 2.13 |
time (sec) |
N/A | 0.218 | 0.088 | 0.891 | 0.193 | 0.258 | 0.000 | 0.287 | 2.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 42 | 38 | 52 | 79 | 63 | 0 | 67 | 78 |
N.S. |
1 | 1.11 | 1.00 | 1.37 | 2.08 | 1.66 | 0.00 | 1.76 | 2.05 |
time (sec) |
N/A | 0.225 | 0.015 | 1.293 | 0.192 | 0.249 | 0.000 | 0.288 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 63 | 103 | 81 | 133 | 1077 | 0 | 123 | 140 |
N.S. |
1 | 0.95 | 1.56 | 1.23 | 2.02 | 16.32 | 0.00 | 1.86 | 2.12 |
time (sec) |
N/A | 0.244 | 0.126 | 2.700 | 0.189 | 0.282 | 0.000 | 0.318 | 2.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | F | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 41 | 35 | 33 | 95 | 457 | 0 | 85 | 77 |
N.S. |
1 | 1.05 | 0.90 | 0.85 | 2.44 | 11.72 | 0.00 | 2.18 | 1.97 |
time (sec) |
N/A | 0.221 | 0.024 | 2.310 | 0.199 | 0.257 | 0.000 | 0.275 | 0.112 |
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 | 11 | 11 | 11 | 12 | 25 | 56 | 17 | 25 | 24 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 2.27 | 5.09 | 1.55 | 2.27 | 2.18 |
time (sec) |
N/A | 0.188 | 0.008 | 0.144 | 0.209 | 0.232 | 0.779 | 0.281 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 86 | 22 | 27 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 5.73 | 1.47 | 1.80 | 0.87 |
time (sec) |
N/A | 0.199 | 0.010 | 0.164 | 0.186 | 0.247 | 1.558 | 0.278 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 17 | 53 | 115 | 36 | 0 | 31 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 3.31 | 7.19 | 2.25 | 0.00 | 1.94 |
time (sec) |
N/A | 0.203 | 0.016 | 0.324 | 0.349 | 0.254 | 2.192 | 0.000 | 2.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 139 | 0 | 31 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 9.27 | 0.00 | 2.07 | 2.07 |
time (sec) |
N/A | 0.198 | 0.003 | 0.191 | 0.187 | 0.247 | 0.000 | 0.309 | 2.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 208 | 0 | 37 | 231 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 13.87 | 0.00 | 2.47 | 15.40 |
time (sec) |
N/A | 0.200 | 0.004 | 0.214 | 0.197 | 0.245 | 0.000 | 0.318 | 2.086 |
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 | 20 | 20 | 20 | 21 | 20 | 70 | 0 | 39 | 43 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.00 | 3.50 | 0.00 | 1.95 | 2.15 |
time (sec) |
N/A | 0.213 | 0.017 | 2.002 | 0.196 | 0.255 | 0.000 | 0.293 | 2.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 32 | 27 | 24 | 148 | 171 | 0 | 49 | 48 |
N.S. |
1 | 1.19 | 1.00 | 0.89 | 5.48 | 6.33 | 0.00 | 1.81 | 1.78 |
time (sec) |
N/A | 0.208 | 0.011 | 0.212 | 0.199 | 0.250 | 0.000 | 0.306 | 2.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 36 | 31 | 27 | 214 | 343 | 0 | 49 | 252 |
N.S. |
1 | 1.16 | 1.00 | 0.87 | 6.90 | 11.06 | 0.00 | 1.58 | 8.13 |
time (sec) |
N/A | 0.218 | 0.018 | 0.356 | 0.191 | 0.243 | 0.000 | 0.330 | 2.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 37 | 35 | 34 | 479 | 414 | 216 | 0 | 0 | 100 |
N.S. |
1 | 0.95 | 0.92 | 12.95 | 11.19 | 5.84 | 0.00 | 0.00 | 2.70 |
time (sec) |
N/A | 0.236 | 0.050 | 0.855 | 0.340 | 0.263 | 0.000 | 0.000 | 2.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 42 | 75 | 45 | 84 | 387 | 0 | 84 | 87 |
N.S. |
1 | 1.24 | 2.21 | 1.32 | 2.47 | 11.38 | 0.00 | 2.47 | 2.56 |
time (sec) |
N/A | 0.260 | 0.088 | 0.915 | 0.186 | 0.258 | 0.000 | 0.279 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 70 | 113 | 58 | 129 | 1109 | 0 | 106 | 219 |
N.S. |
1 | 1.27 | 2.05 | 1.05 | 2.35 | 20.16 | 0.00 | 1.93 | 3.98 |
time (sec) |
N/A | 0.361 | 0.125 | 1.004 | 0.191 | 0.262 | 0.000 | 0.288 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 70 | 113 | 74 | 133 | 1114 | 0 | 110 | 190 |
N.S. |
1 | 1.27 | 2.05 | 1.35 | 2.42 | 20.25 | 0.00 | 2.00 | 3.45 |
time (sec) |
N/A | 0.369 | 0.110 | 0.968 | 0.191 | 0.264 | 0.000 | 0.318 | 2.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 25 | 27 | 14 | 149 | 164 | 0 | 30 | 144 |
N.S. |
1 | 1.47 | 1.59 | 0.82 | 8.76 | 9.65 | 0.00 | 1.76 | 8.47 |
time (sec) |
N/A | 0.208 | 0.035 | 0.476 | 0.191 | 0.248 | 0.000 | 0.263 | 2.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 22 | 139 | 222 | 0 | 29 | 210 |
N.S. |
1 | 1.00 | 1.00 | 1.29 | 8.18 | 13.06 | 0.00 | 1.71 | 12.35 |
time (sec) |
N/A | 0.211 | 0.010 | 0.500 | 0.196 | 0.244 | 0.000 | 0.255 | 2.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 35 | 30 | 33 | 368 | 114 | 0 | 0 | 87 |
N.S. |
1 | 1.35 | 1.15 | 1.27 | 14.15 | 4.38 | 0.00 | 0.00 | 3.35 |
time (sec) |
N/A | 0.226 | 0.080 | 34.492 | 0.321 | 0.268 | 0.000 | 0.000 | 2.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 60 | 95 | 46 | 98 | 1260 | 0 | 71 | 214 |
N.S. |
1 | 1.58 | 2.50 | 1.21 | 2.58 | 33.16 | 0.00 | 1.87 | 5.63 |
time (sec) |
N/A | 0.397 | 0.028 | 1.077 | 0.208 | 0.247 | 0.000 | 0.268 | 2.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 35 | 47 | 20 | 431 | 430 | 0 | 48 | 413 |
N.S. |
1 | 1.40 | 1.88 | 0.80 | 17.24 | 17.20 | 0.00 | 1.92 | 16.52 |
time (sec) |
N/A | 0.221 | 0.036 | 1.867 | 0.202 | 0.249 | 0.000 | 0.276 | 2.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 39 | 29 | 24 | 191 | 250 | 0 | 47 | 40 |
N.S. |
1 | 1.34 | 1.00 | 0.83 | 6.59 | 8.62 | 0.00 | 1.62 | 1.38 |
time (sec) |
N/A | 0.203 | 0.014 | 0.279 | 0.199 | 0.254 | 0.000 | 0.285 | 2.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 45 | 33 | 26 | 435 | 442 | 0 | 54 | 372 |
N.S. |
1 | 1.36 | 1.00 | 0.79 | 13.18 | 13.39 | 0.00 | 1.64 | 11.27 |
time (sec) |
N/A | 0.223 | 0.012 | 1.022 | 0.200 | 0.244 | 0.000 | 0.268 | 2.040 |
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 | 27 | 27 | 26 | 24 | 58 | 87 | 58 | 71 | 23 |
N.S. |
1 | 1.00 | 0.96 | 0.89 | 2.15 | 3.22 | 2.15 | 2.63 | 0.85 |
time (sec) |
N/A | 0.202 | 0.028 | 0.427 | 0.207 | 0.260 | 0.174 | 0.271 | 0.166 |
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 | 27 | 27 | 27 | 24 | 59 | 75 | 61 | 78 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 2.19 | 2.78 | 2.26 | 2.89 | 0.85 |
time (sec) |
N/A | 0.206 | 0.032 | 0.414 | 0.208 | 0.243 | 0.174 | 0.265 | 2.145 |
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 | 27 | 27 | 26 | 24 | 58 | 89 | 58 | 69 | 23 |
N.S. |
1 | 1.00 | 0.96 | 0.89 | 2.15 | 3.30 | 2.15 | 2.56 | 0.85 |
time (sec) |
N/A | 0.203 | 0.013 | 0.424 | 0.199 | 0.250 | 0.165 | 0.267 | 2.119 |
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 | 27 | 27 | 26 | 24 | 59 | 77 | 58 | 74 | 23 |
N.S. |
1 | 1.00 | 0.96 | 0.89 | 2.19 | 2.85 | 2.15 | 2.74 | 0.85 |
time (sec) |
N/A | 0.196 | 0.014 | 0.389 | 0.202 | 0.251 | 0.171 | 0.280 | 2.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 46 | 29 | 151 | 83 | 259 | 0 | 95 | 115 |
N.S. |
1 | 1.24 | 0.78 | 4.08 | 2.24 | 7.00 | 0.00 | 2.57 | 3.11 |
time (sec) |
N/A | 0.323 | 0.347 | 0.237 | 0.285 | 0.261 | 0.000 | 0.285 | 2.641 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 42 | 30 | 149 | 87 | 216 | 0 | 86 | 121 |
N.S. |
1 | 1.17 | 0.83 | 4.14 | 2.42 | 6.00 | 0.00 | 2.39 | 3.36 |
time (sec) |
N/A | 0.311 | 0.332 | 0.235 | 0.286 | 0.266 | 0.000 | 0.280 | 2.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 53 | 29 | 155 | 157 | 259 | 0 | 97 | 115 |
N.S. |
1 | 1.43 | 0.78 | 4.19 | 4.24 | 7.00 | 0.00 | 2.62 | 3.11 |
time (sec) |
N/A | 0.317 | 0.324 | 0.247 | 0.216 | 0.253 | 0.000 | 0.281 | 0.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 50 | 32 | 153 | 160 | 216 | 0 | 90 | 121 |
N.S. |
1 | 1.39 | 0.89 | 4.25 | 4.44 | 6.00 | 0.00 | 2.50 | 3.36 |
time (sec) |
N/A | 0.310 | 0.313 | 0.247 | 0.216 | 0.266 | 0.000 | 0.277 | 2.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 27 | 77 | 68 | 184 | 0 | 79 | 266 |
N.S. |
1 | 1.00 | 0.75 | 2.14 | 1.89 | 5.11 | 0.00 | 2.19 | 7.39 |
time (sec) |
N/A | 0.243 | 0.150 | 0.431 | 0.284 | 0.251 | 0.000 | 0.288 | 3.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 27 | 75 | 67 | 156 | 0 | 70 | 268 |
N.S. |
1 | 1.00 | 0.82 | 2.27 | 2.03 | 4.73 | 0.00 | 2.12 | 8.12 |
time (sec) |
N/A | 0.239 | 0.151 | 0.460 | 0.282 | 0.262 | 0.000 | 0.272 | 2.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 44 | 28 | 79 | 133 | 184 | 0 | 81 | 266 |
N.S. |
1 | 1.22 | 0.78 | 2.19 | 3.69 | 5.11 | 0.00 | 2.25 | 7.39 |
time (sec) |
N/A | 0.250 | 0.157 | 0.203 | 0.204 | 0.256 | 0.000 | 0.285 | 2.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 41 | 29 | 77 | 129 | 156 | 0 | 74 | 269 |
N.S. |
1 | 1.24 | 0.88 | 2.33 | 3.91 | 4.73 | 0.00 | 2.24 | 8.15 |
time (sec) |
N/A | 0.245 | 0.141 | 0.247 | 0.215 | 0.270 | 0.000 | 0.290 | 0.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 86 | 167 | 57 | 327 | 0 | 49 | 133 |
N.S. |
1 | 1.00 | 2.97 | 5.76 | 1.97 | 11.28 | 0.00 | 1.69 | 4.59 |
time (sec) |
N/A | 0.260 | 0.041 | 0.343 | 0.286 | 0.249 | 0.000 | 0.267 | 2.288 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 102 | 205 | 105 | 902 | 0 | 97 | 173 |
N.S. |
1 | 1.00 | 2.27 | 4.56 | 2.33 | 20.04 | 0.00 | 2.16 | 3.84 |
time (sec) |
N/A | 0.421 | 0.076 | 0.363 | 0.285 | 0.270 | 0.000 | 0.264 | 0.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 86 | 70 | 240 | 149 | 1737 | 0 | 120 | 0 |
N.S. |
1 | 1.19 | 0.97 | 3.33 | 2.07 | 24.12 | 0.00 | 1.67 | 0.00 |
time (sec) |
N/A | 0.713 | 0.232 | 0.396 | 0.292 | 0.277 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 93 | 155 | 94 | 439 | 0 | 93 | 139 |
N.S. |
1 | 1.00 | 3.21 | 5.34 | 3.24 | 15.14 | 0.00 | 3.21 | 4.79 |
time (sec) |
N/A | 0.258 | 0.042 | 0.327 | 0.210 | 0.247 | 0.000 | 0.260 | 0.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 110 | 197 | 140 | 1237 | 0 | 136 | 181 |
N.S. |
1 | 1.00 | 2.39 | 4.28 | 3.04 | 26.89 | 0.00 | 2.96 | 3.93 |
time (sec) |
N/A | 0.418 | 0.076 | 0.330 | 0.212 | 0.267 | 0.000 | 0.261 | 2.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 94 | 70 | 230 | 186 | 2372 | 0 | 169 | 0 |
N.S. |
1 | 1.29 | 0.96 | 3.15 | 2.55 | 32.49 | 0.00 | 2.32 | 0.00 |
time (sec) |
N/A | 0.737 | 0.238 | 0.387 | 0.197 | 0.269 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 148 | 49 | 87 | 0 | 49 | 65 |
N.S. |
1 | 1.00 | 1.00 | 5.69 | 1.88 | 3.35 | 0.00 | 1.88 | 2.50 |
time (sec) |
N/A | 0.230 | 0.086 | 0.416 | 0.208 | 0.266 | 0.000 | 0.261 | 0.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 83 | 181 | 70 | 405 | 0 | 68 | 150 |
N.S. |
1 | 1.00 | 2.37 | 5.17 | 2.00 | 11.57 | 0.00 | 1.94 | 4.29 |
time (sec) |
N/A | 0.289 | 0.068 | 1.136 | 0.291 | 0.258 | 0.000 | 0.265 | 2.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 35 | 42 | 120 | 246 | 0 | 51 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.11 | 3.16 | 6.47 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 0.314 | 0.119 | 0.988 | 0.204 | 0.257 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 30 | 26 | 150 | 84 | 86 | 0 | 51 | 65 |
N.S. |
1 | 1.15 | 1.00 | 5.77 | 3.23 | 3.31 | 0.00 | 1.96 | 2.50 |
time (sec) |
N/A | 0.233 | 0.080 | 0.186 | 0.206 | 0.272 | 0.000 | 0.268 | 2.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 90 | 172 | 103 | 617 | 0 | 104 | 156 |
N.S. |
1 | 1.00 | 2.50 | 4.78 | 2.86 | 17.14 | 0.00 | 2.89 | 4.33 |
time (sec) |
N/A | 0.295 | 0.058 | 0.311 | 0.203 | 0.257 | 0.000 | 0.269 | 0.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 35 | 57 | 131 | 246 | 0 | 53 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.46 | 3.36 | 6.31 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.320 | 0.126 | 0.554 | 0.199 | 0.242 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 86 | 167 | 59 | 327 | 0 | 53 | 133 |
N.S. |
1 | 1.00 | 2.97 | 5.76 | 2.03 | 11.28 | 0.00 | 1.83 | 4.59 |
time (sec) |
N/A | 0.260 | 0.040 | 0.361 | 0.276 | 0.262 | 0.000 | 0.267 | 0.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 102 | 207 | 103 | 902 | 0 | 97 | 173 |
N.S. |
1 | 1.00 | 2.27 | 4.60 | 2.29 | 20.04 | 0.00 | 2.16 | 3.84 |
time (sec) |
N/A | 0.401 | 0.075 | 0.392 | 0.287 | 0.260 | 0.000 | 0.266 | 0.213 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 86 | 115 | 238 | 149 | 1737 | 0 | 122 | 0 |
N.S. |
1 | 1.19 | 1.60 | 3.31 | 2.07 | 24.12 | 0.00 | 1.69 | 0.00 |
time (sec) |
N/A | 0.714 | 0.230 | 0.444 | 0.303 | 0.274 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 93 | 155 | 90 | 439 | 0 | 91 | 139 |
N.S. |
1 | 1.00 | 3.21 | 5.34 | 3.10 | 15.14 | 0.00 | 3.14 | 4.79 |
time (sec) |
N/A | 0.255 | 0.039 | 0.270 | 0.201 | 0.256 | 0.000 | 0.273 | 0.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 110 | 195 | 144 | 1237 | 0 | 142 | 183 |
N.S. |
1 | 1.00 | 2.39 | 4.24 | 3.13 | 26.89 | 0.00 | 3.09 | 3.98 |
time (sec) |
N/A | 0.411 | 0.073 | 0.312 | 0.221 | 0.263 | 0.000 | 0.268 | 2.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 94 | 70 | 228 | 184 | 2372 | 0 | 167 | 0 |
N.S. |
1 | 1.29 | 0.96 | 3.12 | 2.52 | 32.49 | 0.00 | 2.29 | 0.00 |
time (sec) |
N/A | 0.721 | 0.221 | 0.427 | 0.203 | 0.277 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 146 | 51 | 86 | 0 | 50 | 64 |
N.S. |
1 | 1.00 | 1.00 | 5.62 | 1.96 | 3.31 | 0.00 | 1.92 | 2.46 |
time (sec) |
N/A | 0.228 | 0.081 | 0.434 | 0.197 | 0.250 | 0.000 | 0.263 | 0.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 83 | 183 | 70 | 405 | 0 | 68 | 148 |
N.S. |
1 | 1.00 | 2.37 | 5.23 | 2.00 | 11.57 | 0.00 | 1.94 | 4.23 |
time (sec) |
N/A | 0.287 | 0.069 | 1.126 | 0.300 | 0.253 | 0.000 | 0.264 | 2.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 35 | 26 | 119 | 248 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.68 | 3.13 | 6.53 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.313 | 0.124 | 0.954 | 0.202 | 0.249 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 30 | 26 | 152 | 80 | 87 | 0 | 50 | 66 |
N.S. |
1 | 1.15 | 1.00 | 5.85 | 3.08 | 3.35 | 0.00 | 1.92 | 2.54 |
time (sec) |
N/A | 0.233 | 0.080 | 0.281 | 0.204 | 0.256 | 0.000 | 0.260 | 2.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 90 | 170 | 105 | 617 | 0 | 106 | 156 |
N.S. |
1 | 1.00 | 2.50 | 4.72 | 2.92 | 17.14 | 0.00 | 2.94 | 4.33 |
time (sec) |
N/A | 0.292 | 0.061 | 0.441 | 0.206 | 0.250 | 0.000 | 0.289 | 2.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 35 | 36 | 132 | 243 | 0 | 51 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.92 | 3.38 | 6.23 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.320 | 0.124 | 0.685 | 0.206 | 0.244 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 40 | 0 | 72 | 153 | 85 | 42 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.00 | 1.67 | 3.56 | 1.98 | 0.98 |
time (sec) |
N/A | 0.223 | 0.156 | 0.442 | 0.000 | 0.245 | 0.323 | 0.288 | 0.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 69 | 57 | 0 | 120 | 405 | 120 | 76 |
N.S. |
1 | 1.00 | 1.11 | 0.92 | 0.00 | 1.94 | 6.53 | 1.94 | 1.23 |
time (sec) |
N/A | 0.259 | 0.515 | 0.816 | 0.000 | 0.259 | 0.722 | 0.261 | 0.270 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 86 | 84 | 0 | 218 | 918 | 179 | 182 |
N.S. |
1 | 1.00 | 0.95 | 0.92 | 0.00 | 2.40 | 10.09 | 1.97 | 2.00 |
time (sec) |
N/A | 0.287 | 0.326 | 1.496 | 0.000 | 0.263 | 1.911 | 0.278 | 0.554 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 106 | 89 | 0 | 192 | 1027 | 156 | 152 |
N.S. |
1 | 1.00 | 1.20 | 1.01 | 0.00 | 2.18 | 11.67 | 1.77 | 1.73 |
time (sec) |
N/A | 0.276 | 0.501 | 1.815 | 0.000 | 0.265 | 1.557 | 0.294 | 2.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 158 | 133 | 0 | 414 | 2001 | 260 | 337 |
N.S. |
1 | 1.00 | 1.10 | 0.92 | 0.00 | 2.88 | 13.90 | 1.81 | 2.34 |
time (sec) |
N/A | 0.353 | 1.165 | 4.585 | 0.000 | 0.248 | 5.481 | 0.282 | 2.614 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 195 | 177 | 190 | 0 | 731 | 3580 | 373 | 906 |
N.S. |
1 | 1.00 | 0.91 | 0.97 | 0.00 | 3.75 | 18.36 | 1.91 | 4.65 |
time (sec) |
N/A | 0.399 | 1.082 | 10.555 | 0.000 | 0.273 | 16.688 | 0.282 | 2.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 40 | 0 | 71 | 153 | 85 | 42 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.00 | 1.65 | 3.56 | 1.98 | 0.98 |
time (sec) |
N/A | 0.225 | 0.117 | 0.381 | 0.000 | 0.247 | 0.317 | 0.265 | 0.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 69 | 57 | 0 | 115 | 408 | 120 | 68 |
N.S. |
1 | 1.00 | 1.11 | 0.92 | 0.00 | 1.85 | 6.58 | 1.94 | 1.10 |
time (sec) |
N/A | 0.246 | 0.484 | 0.808 | 0.000 | 0.255 | 0.703 | 0.265 | 0.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 85 | 84 | 0 | 217 | 921 | 179 | 180 |
N.S. |
1 | 1.00 | 0.93 | 0.92 | 0.00 | 2.38 | 10.12 | 1.97 | 1.98 |
time (sec) |
N/A | 0.277 | 0.285 | 1.477 | 0.000 | 0.287 | 1.881 | 0.272 | 2.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 105 | 89 | 0 | 192 | 1027 | 156 | 115 |
N.S. |
1 | 1.00 | 1.19 | 1.01 | 0.00 | 2.18 | 11.67 | 1.77 | 1.31 |
time (sec) |
N/A | 0.275 | 0.465 | 1.715 | 0.000 | 0.241 | 1.582 | 0.270 | 2.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 158 | 133 | 0 | 397 | 2008 | 260 | 337 |
N.S. |
1 | 1.00 | 1.10 | 0.92 | 0.00 | 2.76 | 13.94 | 1.81 | 2.34 |
time (sec) |
N/A | 0.327 | 1.084 | 4.770 | 0.000 | 0.253 | 5.288 | 0.277 | 2.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 195 | 176 | 190 | 0 | 726 | 3582 | 373 | 908 |
N.S. |
1 | 1.00 | 0.90 | 0.97 | 0.00 | 3.72 | 18.37 | 1.91 | 4.66 |
time (sec) |
N/A | 0.370 | 1.109 | 11.099 | 0.000 | 0.267 | 16.835 | 0.281 | 2.717 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 40 | 0 | 71 | 153 | 85 | 42 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.00 | 1.65 | 3.56 | 1.98 | 0.98 |
time (sec) |
N/A | 0.226 | 0.154 | 0.461 | 0.000 | 0.255 | 0.327 | 0.264 | 0.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 69 | 57 | 0 | 119 | 408 | 120 | 68 |
N.S. |
1 | 1.00 | 1.11 | 0.92 | 0.00 | 1.92 | 6.58 | 1.94 | 1.10 |
time (sec) |
N/A | 0.250 | 0.469 | 0.836 | 0.000 | 0.255 | 0.707 | 0.267 | 0.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 85 | 84 | 0 | 213 | 921 | 179 | 182 |
N.S. |
1 | 1.00 | 0.93 | 0.92 | 0.00 | 2.34 | 10.12 | 1.97 | 2.00 |
time (sec) |
N/A | 0.284 | 0.314 | 1.619 | 0.000 | 0.263 | 1.956 | 0.274 | 2.565 |
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 | 68 | 68 | 74 | 63 | 0 | 114 | 408 | 124 | 76 |
N.S. |
1 | 1.00 | 1.09 | 0.93 | 0.00 | 1.68 | 6.00 | 1.82 | 1.12 |
time (sec) |
N/A | 0.244 | 0.512 | 0.782 | 0.000 | 0.260 | 0.742 | 0.260 | 2.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 107 | 89 | 0 | 192 | 1027 | 156 | 135 |
N.S. |
1 | 1.00 | 1.22 | 1.01 | 0.00 | 2.18 | 11.67 | 1.77 | 1.53 |
time (sec) |
N/A | 0.269 | 0.461 | 1.965 | 0.000 | 0.262 | 1.558 | 0.261 | 2.615 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 158 | 133 | 0 | 398 | 2001 | 260 | 337 |
N.S. |
1 | 1.00 | 1.10 | 0.92 | 0.00 | 2.76 | 13.90 | 1.81 | 2.34 |
time (sec) |
N/A | 0.323 | 1.013 | 4.817 | 0.000 | 0.264 | 5.549 | 0.285 | 2.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 90 | 90 | 0 | 243 | 935 | 183 | 183 |
N.S. |
1 | 1.00 | 0.93 | 0.93 | 0.00 | 2.51 | 9.64 | 1.89 | 1.89 |
time (sec) |
N/A | 0.286 | 0.371 | 1.326 | 0.000 | 0.249 | 1.941 | 0.286 | 0.552 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 153 | 127 | 0 | 443 | 2030 | 256 | 337 |
N.S. |
1 | 1.00 | 1.11 | 0.92 | 0.00 | 3.21 | 14.71 | 1.86 | 2.44 |
time (sec) |
N/A | 0.335 | 1.126 | 4.009 | 0.000 | 0.262 | 5.342 | 0.278 | 2.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 195 | 176 | 190 | 0 | 729 | 3580 | 373 | 908 |
N.S. |
1 | 1.00 | 0.90 | 0.97 | 0.00 | 3.74 | 18.36 | 1.91 | 4.66 |
time (sec) |
N/A | 0.405 | 1.044 | 11.361 | 0.000 | 0.268 | 16.865 | 0.300 | 2.795 |
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 | 121 | 121 | 103 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.331 | 0.717 | 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 | 117 | 117 | 240 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.325 | 2.150 | 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 | 116 | 116 | 99 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.329 | 0.797 | 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 | 120 | 120 | 103 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.319 | 0.520 | 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 | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 15 | 15 | 12 | 27 | 17 | 20 | 25 | 6 |
N.S. |
1 | 1.88 | 1.88 | 1.50 | 3.38 | 2.12 | 2.50 | 3.12 | 0.75 |
time (sec) |
N/A | 0.181 | 0.026 | 0.322 | 0.194 | 0.253 | 0.127 | 0.266 | 0.071 |
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 | 17 | 17 | 17 | 14 | 27 | 22 | 20 | 27 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.59 | 1.29 | 1.18 | 1.59 | 0.76 |
time (sec) |
N/A | 0.180 | 0.044 | 0.416 | 0.197 | 0.261 | 0.133 | 0.268 | 0.061 |
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 | 17 | 17 | 17 | 14 | 27 | 36 | 20 | 27 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.59 | 2.12 | 1.18 | 1.59 | 0.82 |
time (sec) |
N/A | 0.182 | 0.025 | 0.361 | 0.193 | 0.328 | 0.131 | 0.263 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 25 | 28 | 0 | 42 | 78 | 59 | 26 |
N.S. |
1 | 1.00 | 0.71 | 0.80 | 0.00 | 1.20 | 2.23 | 1.69 | 0.74 |
time (sec) |
N/A | 0.213 | 0.038 | 0.324 | 0.000 | 0.244 | 0.253 | 0.261 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 23 | 15 | 12 | 27 | 19 | 20 | 25 | 11 |
N.S. |
1 | 1.53 | 1.00 | 0.80 | 1.80 | 1.27 | 1.33 | 1.67 | 0.73 |
time (sec) |
N/A | 0.190 | 0.031 | 0.315 | 0.194 | 0.246 | 0.128 | 0.270 | 2.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 25 | 17 | 14 | 27 | 33 | 20 | 26 | 11 |
N.S. |
1 | 1.47 | 1.00 | 0.82 | 1.59 | 1.94 | 1.18 | 1.53 | 0.65 |
time (sec) |
N/A | 0.184 | 0.030 | 0.399 | 0.187 | 0.244 | 0.129 | 0.258 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 25 | 17 | 14 | 27 | 38 | 20 | 27 | 15 |
N.S. |
1 | 1.47 | 1.00 | 0.82 | 1.59 | 2.24 | 1.18 | 1.59 | 0.88 |
time (sec) |
N/A | 0.183 | 0.030 | 0.413 | 0.196 | 0.258 | 0.127 | 0.256 | 2.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 25 | 28 | 0 | 42 | 37 | 59 | 26 |
N.S. |
1 | 1.00 | 0.71 | 0.80 | 0.00 | 1.20 | 1.06 | 1.69 | 0.74 |
time (sec) |
N/A | 0.213 | 0.046 | 0.324 | 0.000 | 0.254 | 0.265 | 0.270 | 2.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 27 | 19 | 16 | 53 | 115 | 0 | 36 | 47 |
N.S. |
1 | 1.42 | 1.00 | 0.84 | 2.79 | 6.05 | 0.00 | 1.89 | 2.47 |
time (sec) |
N/A | 0.203 | 0.012 | 0.177 | 0.277 | 0.262 | 0.000 | 0.261 | 2.262 |