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 | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 190 | 20 | 19 | 437 | 32 | 17 | 359 | 18 |
N.S. |
1 | 8.26 | 0.87 | 0.83 | 19.00 | 1.39 | 0.74 | 15.61 | 0.78 |
time (sec) |
N/A | 0.965 | 0.232 | 0.230 | 0.272 | 0.268 | 0.060 | 0.269 | 8.826 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 21 | 14 | 12 | 16 | 19 | 15 | 16 | 12 |
N.S. |
1 | 1.40 | 0.93 | 0.80 | 1.07 | 1.27 | 1.00 | 1.07 | 0.80 |
time (sec) |
N/A | 0.156 | 0.026 | 0.044 | 0.178 | 0.247 | 0.050 | 0.258 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 19 | 19 | 20 | 19 | 28 | 17 | 21 | 17 |
N.S. |
1 | 0.61 | 0.61 | 0.65 | 0.61 | 0.90 | 0.55 | 0.68 | 0.55 |
time (sec) |
N/A | 0.219 | 0.011 | 0.148 | 0.180 | 0.245 | 0.052 | 0.258 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 23 | 29 | 26 | 27 | 27 | 24 | 27 | 24 |
N.S. |
1 | 1.10 | 1.38 | 1.24 | 1.29 | 1.29 | 1.14 | 1.29 | 1.14 |
time (sec) |
N/A | 0.135 | 0.008 | 0.028 | 0.182 | 0.266 | 0.022 | 0.264 | 0.286 |
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 | 34 | 26 | 21 | 21 | 28 | 20 | 19 | 20 | 22 |
N.S. |
1 | 0.76 | 0.62 | 0.62 | 0.82 | 0.59 | 0.56 | 0.59 | 0.65 |
time (sec) |
N/A | 0.160 | 0.054 | 0.028 | 0.189 | 0.248 | 0.053 | 0.262 | 8.809 |
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 | 19 | 17 | 14 | 16 | 16 | 12 | 16 | 15 |
N.S. |
1 | 0.79 | 0.71 | 0.58 | 0.67 | 0.67 | 0.50 | 0.67 | 0.62 |
time (sec) |
N/A | 0.200 | 0.008 | 0.017 | 0.183 | 0.252 | 0.046 | 0.265 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 17 | 17 | 18 | 21 | 17 | 15 | 17 | 17 |
N.S. |
1 | 0.77 | 0.77 | 0.82 | 0.95 | 0.77 | 0.68 | 0.77 | 0.77 |
time (sec) |
N/A | 0.286 | 0.219 | 0.072 | 0.287 | 0.251 | 0.107 | 0.265 | 9.279 |
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 | 27 | 32 | 23 | 19 | 0 | 22 | 20 | 22 | 19 |
N.S. |
1 | 1.19 | 0.85 | 0.70 | 0.00 | 0.81 | 0.74 | 0.81 | 0.70 |
time (sec) |
N/A | 0.442 | 0.199 | 0.174 | 0.000 | 0.265 | 0.081 | 0.264 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 143 | 31 | 29 | 95 | 44 | 24 | 60 | 32 |
N.S. |
1 | 4.47 | 0.97 | 0.91 | 2.97 | 1.38 | 0.75 | 1.88 | 1.00 |
time (sec) |
N/A | 2.106 | 0.052 | 0.119 | 0.247 | 0.252 | 0.088 | 0.270 | 0.279 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 18 | 17 | 17 | 14 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.13 | 1.13 | 0.93 | 1.13 | 1.13 |
time (sec) |
N/A | 0.466 | 0.369 | 0.111 | 0.223 | 0.260 | 0.066 | 0.274 | 9.224 |
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 | 20 | 28 | 18 | 28 | 0 | 26 | 17 | 26 | 18 |
N.S. |
1 | 1.40 | 0.90 | 1.40 | 0.00 | 1.30 | 0.85 | 1.30 | 0.90 |
time (sec) |
N/A | 0.382 | 0.052 | 0.077 | 0.000 | 0.246 | 0.140 | 0.270 | 9.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 34 | 23 | 24 | 41 | 45 | 20 | 23 | 34 |
N.S. |
1 | 1.70 | 1.15 | 1.20 | 2.05 | 2.25 | 1.00 | 1.15 | 1.70 |
time (sec) |
N/A | 0.507 | 0.210 | 0.223 | 0.227 | 0.297 | 0.062 | 0.297 | 9.046 |
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 | 19 | 0 | 16 | 16 | 23 | 26 | 10 | 69 | 23 |
N.S. |
1 | 0.00 | 0.84 | 0.84 | 1.21 | 1.37 | 0.53 | 3.63 | 1.21 |
time (sec) |
N/A | 0.000 | 0.540 | 0.044 | 0.218 | 0.244 | 0.084 | 0.271 | 0.127 |
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 | 31 | 24 | 24 | 27 | 29 | 24 | 27 | 26 |
N.S. |
1 | 1.41 | 1.09 | 1.09 | 1.23 | 1.32 | 1.09 | 1.23 | 1.18 |
time (sec) |
N/A | 0.169 | 0.017 | 0.063 | 0.173 | 0.263 | 0.045 | 0.259 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 98 | 35 | 52 | 155 | 46 | 63 | 0 | 91 |
N.S. |
1 | 2.88 | 1.03 | 1.53 | 4.56 | 1.35 | 1.85 | 0.00 | 2.68 |
time (sec) |
N/A | 1.256 | 0.241 | 1.060 | 0.283 | 0.267 | 0.240 | 0.000 | 9.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | F | B | F(-2) | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 118 | 0 | 75 | 0 | 0 | 223 |
N.S. |
1 | 0.00 | 0.00 | 3.81 | 0.00 | 2.42 | 0.00 | 0.00 | 7.19 |
time (sec) |
N/A | 0.000 | 0.000 | 0.492 | 0.000 | 0.269 | 0.000 | 0.000 | 9.861 |
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 | 22 | 45 | 22 | 39 | 21 | 17 | 21 | 20 |
N.S. |
1 | 0.96 | 1.96 | 0.96 | 1.70 | 0.91 | 0.74 | 0.91 | 0.87 |
time (sec) |
N/A | 0.264 | 0.028 | 0.135 | 0.297 | 0.259 | 0.065 | 0.268 | 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 | 24 | 29 | 24 | 23 | 21 | 22 | 22 | 21 | 21 |
N.S. |
1 | 1.21 | 1.00 | 0.96 | 0.88 | 0.92 | 0.92 | 0.88 | 0.88 |
time (sec) |
N/A | 0.196 | 0.015 | 0.096 | 0.170 | 0.238 | 0.143 | 0.266 | 8.918 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 25 | 34 | 66 | 56 | 48 | 44 | 0 |
N.S. |
1 | 0.00 | 1.04 | 1.42 | 2.75 | 2.33 | 2.00 | 1.83 | 0.00 |
time (sec) |
N/A | 0.000 | 0.107 | 100.480 | 0.233 | 0.260 | 0.246 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 19 | 14 | 11 | 10 | 10 | 12 | 10 | 12 |
N.S. |
1 | 1.27 | 0.93 | 0.73 | 0.67 | 0.67 | 0.80 | 0.67 | 0.80 |
time (sec) |
N/A | 0.160 | 0.015 | 0.027 | 0.180 | 0.249 | 0.040 | 0.264 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | F | A | A | A | B | B | F(-1) |
verified |
N/A | No | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 1779 | 0 | 43 | 48 | 45 | 53 | 288 | 0 |
N.S. |
1 | 53.91 | 0.00 | 1.30 | 1.45 | 1.36 | 1.61 | 8.73 | 0.00 |
time (sec) |
N/A | 5.204 | 0.000 | 0.531 | 0.326 | 0.260 | 0.216 | 0.383 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 34 | 24 | 31 | 18 | 30 | 27 | 18 | 22 |
N.S. |
1 | 1.89 | 1.33 | 1.72 | 1.00 | 1.67 | 1.50 | 1.00 | 1.22 |
time (sec) |
N/A | 1.082 | 0.784 | 3.803 | 0.282 | 0.261 | 0.144 | 0.268 | 9.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 31 | 0 | 29 | 35 | 37 | 35 | 0 |
N.S. |
1 | 0.00 | 0.91 | 0.00 | 0.85 | 1.03 | 1.09 | 1.03 | 0.00 |
time (sec) |
N/A | 0.000 | 0.127 | 0.000 | 0.248 | 0.246 | 0.272 | 84.650 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 54 | 58 | 66 | 54 | 0 | 0 | 57 |
N.S. |
1 | 0.00 | 2.00 | 2.15 | 2.44 | 2.00 | 0.00 | 0.00 | 2.11 |
time (sec) |
N/A | 0.000 | 0.344 | 0.068 | 0.473 | 0.276 | 0.000 | 0.000 | 8.452 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 35 | 74 | 127 | 61 | 60 | 0 | 354 |
N.S. |
1 | 0.00 | 1.09 | 2.31 | 3.97 | 1.91 | 1.88 | 0.00 | 11.06 |
time (sec) |
N/A | 0.000 | 0.442 | 73.947 | 1.014 | 0.250 | 2.207 | 0.000 | 9.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 12 | 9 | 7 | 9 | 8 | 7 | 8 | 6 |
N.S. |
1 | 0.80 | 0.60 | 0.47 | 0.60 | 0.53 | 0.47 | 0.53 | 0.40 |
time (sec) |
N/A | 0.134 | 0.002 | 0.108 | 0.174 | 0.243 | 0.025 | 0.258 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 26 | 102 | 0 | 66 | 82 | 84 | 68 |
N.S. |
1 | 1.00 | 0.93 | 3.64 | 0.00 | 2.36 | 2.93 | 3.00 | 2.43 |
time (sec) |
N/A | 0.516 | 0.061 | 0.263 | 0.000 | 0.251 | 0.201 | 0.294 | 8.900 |
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 | 12 | 12 | 10 | 9 | 9 | 10 | 9 | 9 |
N.S. |
1 | 0.60 | 0.60 | 0.50 | 0.45 | 0.45 | 0.50 | 0.45 | 0.45 |
time (sec) |
N/A | 0.128 | 0.000 | 0.011 | 0.172 | 0.239 | 0.014 | 0.280 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 26 | 27 | 26 | 33 | 36 | 34 | 48 | 32 |
N.S. |
1 | 1.13 | 1.17 | 1.13 | 1.43 | 1.57 | 1.48 | 2.09 | 1.39 |
time (sec) |
N/A | 0.565 | 0.180 | 0.172 | 0.214 | 0.275 | 0.147 | 0.263 | 8.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 24 | 22 | 48 | 34 | 36 | 44 | 47 | 0 |
N.S. |
1 | 1.04 | 0.96 | 2.09 | 1.48 | 1.57 | 1.91 | 2.04 | 0.00 |
time (sec) |
N/A | 0.709 | 0.062 | 0.360 | 0.309 | 0.269 | 0.251 | 0.361 | 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 | 25 | 31 | 14 | 18 | 19 | 17 | 14 | 19 | 14 |
N.S. |
1 | 1.24 | 0.56 | 0.72 | 0.76 | 0.68 | 0.56 | 0.76 | 0.56 |
time (sec) |
N/A | 0.181 | 0.052 | 0.033 | 0.177 | 0.256 | 0.080 | 0.259 | 8.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 18 | 15 | 15 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.12 | 0.94 | 0.94 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.204 | 0.038 | 0.033 | 0.195 | 0.262 | 0.074 | 0.264 | 8.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 65 | 71 | 68 | 68 | 68 | 98 | 98 |
N.S. |
1 | 0.00 | 2.50 | 2.73 | 2.62 | 2.62 | 2.62 | 3.77 | 3.77 |
time (sec) |
N/A | 0.000 | 0.232 | 0.308 | 0.221 | 0.261 | 0.420 | 0.316 | 8.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 22 | 17 | 12 | 15 | 15 | 12 | 15 | 12 |
N.S. |
1 | 1.83 | 1.42 | 1.00 | 1.25 | 1.25 | 1.00 | 1.25 | 1.00 |
time (sec) |
N/A | 0.154 | 0.004 | 0.039 | 0.175 | 0.247 | 0.048 | 0.259 | 8.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 17 | 16 | 16 | 19 | 17 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.13 | 1.07 | 1.07 | 1.27 | 1.13 | 1.07 |
time (sec) |
N/A | 0.167 | 0.002 | 0.042 | 0.180 | 0.260 | 0.044 | 0.258 | 8.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 27 | 28 | 28 | 24 | 24 | 27 | 29 | 22 |
N.S. |
1 | 1.08 | 1.12 | 1.12 | 0.96 | 0.96 | 1.08 | 1.16 | 0.88 |
time (sec) |
N/A | 0.284 | 0.153 | 0.383 | 0.194 | 0.253 | 0.111 | 0.284 | 7.903 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | A | A | A | A | A | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 28 | 0 | 17 | 25 | 21 | 20 | 16 | 16 |
N.S. |
1 | 1.47 | 0.00 | 0.89 | 1.32 | 1.11 | 1.05 | 0.84 | 0.84 |
time (sec) |
N/A | 0.495 | 0.000 | 0.048 | 0.526 | 0.250 | 1.658 | 2.594 | 8.121 |
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 | 24 | 24 | 17 | 20 | 32 | 17 | 20 | 17 |
N.S. |
1 | 1.04 | 1.04 | 0.74 | 0.87 | 1.39 | 0.74 | 0.87 | 0.74 |
time (sec) |
N/A | 0.164 | 0.026 | 0.101 | 0.181 | 0.248 | 0.074 | 0.262 | 0.095 |
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 | 16 | 20 | 15 | 18 | 14 | 17 | 18 | 15 |
N.S. |
1 | 0.89 | 1.11 | 0.83 | 1.00 | 0.78 | 0.94 | 1.00 | 0.83 |
time (sec) |
N/A | 0.321 | 0.025 | 0.166 | 0.174 | 0.253 | 0.060 | 0.258 | 7.743 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | A | A | A | A | A | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 25 | 0 | 23 | 23 | 23 | 22 | 23 | 27 |
N.S. |
1 | 0.86 | 0.00 | 0.79 | 0.79 | 0.79 | 0.76 | 0.79 | 0.93 |
time (sec) |
N/A | 0.477 | 0.000 | 0.163 | 0.354 | 0.291 | 0.127 | 0.284 | 8.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | B | A | A | F | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 31 | 0 | 125 | 30 | 31 | 0 | 32 |
N.S. |
1 | 0.00 | 0.97 | 0.00 | 3.91 | 0.94 | 0.97 | 0.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.101 | 0.000 | 0.330 | 0.268 | 3.137 | 0.000 | 8.941 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 1706 | 65 | 48 | 1762 | 67 | 48 | 78 | 54 |
N.S. |
1 | 48.74 | 1.86 | 1.37 | 50.34 | 1.91 | 1.37 | 2.23 | 1.54 |
time (sec) |
N/A | 3.790 | 0.128 | 0.368 | 0.308 | 0.281 | 1.494 | 0.277 | 9.018 |
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 | 26 | 20 | 24 | 24 | 23 | 19 | 23 | 24 |
N.S. |
1 | 1.30 | 1.00 | 1.20 | 1.20 | 1.15 | 0.95 | 1.15 | 1.20 |
time (sec) |
N/A | 0.412 | 0.021 | 0.133 | 0.222 | 0.243 | 0.059 | 0.271 | 7.853 |
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 | 18 | 21 | 18 | 16 | 25 | 15 | 26 | 26 | 15 |
N.S. |
1 | 1.17 | 1.00 | 0.89 | 1.39 | 0.83 | 1.44 | 1.44 | 0.83 |
time (sec) |
N/A | 0.138 | 0.004 | 0.137 | 0.178 | 0.247 | 0.031 | 0.255 | 0.215 |
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 | 32 | 32 | 29 | 25 | 25 | 32 | 25 | 27 |
N.S. |
1 | 2.00 | 2.00 | 1.81 | 1.56 | 1.56 | 2.00 | 1.56 | 1.69 |
time (sec) |
N/A | 0.176 | 0.007 | 0.031 | 0.174 | 0.249 | 0.022 | 0.267 | 7.887 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 31 | 25 | 45 | 45 | 20 | 45 | 0 |
N.S. |
1 | 0.00 | 1.24 | 1.00 | 1.80 | 1.80 | 0.80 | 1.80 | 0.00 |
time (sec) |
N/A | 0.000 | 2.890 | 0.084 | 0.223 | 0.257 | 0.082 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 72 | 61 | 233 | 22 | 19 | 0 | 0 | 0 |
N.S. |
1 | 2.40 | 2.03 | 7.77 | 0.73 | 0.63 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.415 | 0.702 | 0.151 | 0.248 | 0.260 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 190 | 40 | 96 | 88 | 94 | 39 | 190805 |
N.S. |
1 | 0.00 | 6.33 | 1.33 | 3.20 | 2.93 | 3.13 | 1.30 | 6360.17 |
time (sec) |
N/A | 0.000 | 0.174 | 0.204 | 0.189 | 0.246 | 2.480 | 0.280 | 52.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | A | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 145 | 60 | 46 | 80 | 47 | 48 | 72 | 52 |
N.S. |
1 | 6.30 | 2.61 | 2.00 | 3.48 | 2.04 | 2.09 | 3.13 | 2.26 |
time (sec) |
N/A | 1.620 | 4.719 | 0.101 | 0.215 | 0.276 | 0.080 | 0.260 | 0.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | F | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 49 | 68 | 0 | 205 | 65 | 0 | 184 |
N.S. |
1 | 0.00 | 1.63 | 2.27 | 0.00 | 6.83 | 2.17 | 0.00 | 6.13 |
time (sec) |
N/A | 0.000 | 1.758 | 171.464 | 0.000 | 0.274 | 5.070 | 0.000 | 1.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 26 | 55 | 24 | 20 | 30 | 32 |
N.S. |
1 | 0.00 | 0.96 | 1.04 | 2.20 | 0.96 | 0.80 | 1.20 | 1.28 |
time (sec) |
N/A | 0.000 | 5.207 | 0.569 | 0.388 | 0.253 | 0.140 | 0.775 | 9.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 89 | 53 | 25 | 150 | 22 | 44 | 63 | 22 |
N.S. |
1 | 4.45 | 2.65 | 1.25 | 7.50 | 1.10 | 2.20 | 3.15 | 1.10 |
time (sec) |
N/A | 0.776 | 0.097 | 0.242 | 0.310 | 0.258 | 0.120 | 0.259 | 8.280 |
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 | 29 | 30 | 26 | 24 | 31 | 22 | 23 | 25 |
N.S. |
1 | 1.61 | 1.67 | 1.44 | 1.33 | 1.72 | 1.22 | 1.28 | 1.39 |
time (sec) |
N/A | 0.192 | 0.025 | 0.174 | 0.172 | 0.270 | 0.068 | 0.257 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 132 | 18 | 30 | 20 | 0 | 18 |
N.S. |
1 | 0.00 | 1.00 | 6.29 | 0.86 | 1.43 | 0.95 | 0.00 | 0.86 |
time (sec) |
N/A | 0.000 | 5.096 | 183.646 | 0.343 | 0.275 | 6.559 | 0.000 | 0.550 |
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 | 27 | 0 | 25 | 40 | 31 | 39 | 27 | 39 | 22 |
N.S. |
1 | 0.00 | 0.93 | 1.48 | 1.15 | 1.44 | 1.00 | 1.44 | 0.81 |
time (sec) |
N/A | 0.000 | 1.560 | 0.199 | 0.235 | 0.250 | 0.182 | 0.265 | 8.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | B | B | B | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 68 | 110 | 311 | 105 | 0 | 125 |
N.S. |
1 | 0.00 | 0.00 | 2.19 | 3.55 | 10.03 | 3.39 | 0.00 | 4.03 |
time (sec) |
N/A | 0.000 | 0.000 | 0.483 | 2.430 | 0.273 | 6.052 | 0.000 | 9.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 28 | 55 | 26 | 22 | 21 | 27 |
N.S. |
1 | 0.00 | 1.00 | 1.27 | 2.50 | 1.18 | 1.00 | 0.95 | 1.23 |
time (sec) |
N/A | 0.000 | 0.197 | 146.019 | 0.381 | 0.261 | 2.325 | 5.113 | 8.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | F(-2) | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 29 | 144 | 30 | 29 | 0 | 43 |
N.S. |
1 | 0.00 | 0.00 | 0.97 | 4.80 | 1.00 | 0.97 | 0.00 | 1.43 |
time (sec) |
N/A | 0.000 | 0.000 | 189.471 | 0.361 | 0.259 | 1.544 | 0.000 | 8.389 |
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 | 29 | 0 | 30 | 32 | 39 | 32 | 56 | 67 | 31 |
N.S. |
1 | 0.00 | 1.03 | 1.10 | 1.34 | 1.10 | 1.93 | 2.31 | 1.07 |
time (sec) |
N/A | 0.000 | 0.160 | 0.384 | 0.295 | 0.263 | 0.079 | 0.291 | 8.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | F | B | A | B | B | B | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 66 | 0 | 62 | 28 | 62 | 70 | 143 | 65 |
N.S. |
1 | 2.28 | 0.00 | 2.14 | 0.97 | 2.14 | 2.41 | 4.93 | 2.24 |
time (sec) |
N/A | 0.786 | 0.000 | 41.770 | 3.642 | 0.250 | 5.381 | 2.597 | 11.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 22 | 21 | 22 | 20 | 26 | 27 | 26 | 21 |
N.S. |
1 | 1.05 | 1.00 | 1.05 | 0.95 | 1.24 | 1.29 | 1.24 | 1.00 |
time (sec) |
N/A | 0.327 | 0.344 | 0.270 | 0.363 | 0.257 | 0.106 | 0.312 | 8.250 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 49 | 26 | 30 | 34 | 34 | 27 | 34 | 24 |
N.S. |
1 | 1.75 | 0.93 | 1.07 | 1.21 | 1.21 | 0.96 | 1.21 | 0.86 |
time (sec) |
N/A | 0.184 | 0.080 | 0.072 | 0.172 | 0.256 | 0.046 | 0.265 | 7.966 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 0 | 47 | 49 | 44 | 48 | 49 | 52 |
N.S. |
1 | 0.00 | 0.00 | 2.04 | 2.13 | 1.91 | 2.09 | 2.13 | 2.26 |
time (sec) |
N/A | 0.000 | 0.000 | 0.450 | 2.014 | 0.257 | 0.217 | 0.287 | 8.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 18 | 18 | 25 | 104 | 86 | 112 | 23 | 105 |
N.S. |
1 | 1.06 | 1.06 | 1.47 | 6.12 | 5.06 | 6.59 | 1.35 | 6.18 |
time (sec) |
N/A | 11.111 | 0.226 | 1.129 | 0.191 | 0.263 | 2.026 | 0.324 | 9.504 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 15 | 12 | 11 | 13 | 13 | 12 | 25 | 10 |
N.S. |
1 | 1.25 | 1.00 | 0.92 | 1.08 | 1.08 | 1.00 | 2.08 | 0.83 |
time (sec) |
N/A | 0.168 | 0.119 | 0.079 | 0.215 | 0.271 | 0.068 | 0.261 | 8.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 36 | 37 | 37 | 32 | 39 | 37 | 37 |
N.S. |
1 | 0.00 | 1.20 | 1.23 | 1.23 | 1.07 | 1.30 | 1.23 | 1.23 |
time (sec) |
N/A | 0.000 | 0.185 | 0.144 | 0.179 | 0.247 | 2.253 | 0.282 | 0.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 48 | 37 | 18 | 34 | 17 | 17 | 0 | 17 |
N.S. |
1 | 2.09 | 1.61 | 0.78 | 1.48 | 0.74 | 0.74 | 0.00 | 0.74 |
time (sec) |
N/A | 0.291 | 0.399 | 7.596 | 0.277 | 0.253 | 4.447 | 0.000 | 8.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 0 | 31 | 64 | 31 | 27 | 0 | 33 |
N.S. |
1 | 0.00 | 0.00 | 0.89 | 1.83 | 0.89 | 0.77 | 0.00 | 0.94 |
time (sec) |
N/A | 0.000 | 0.000 | 23.073 | 0.287 | 0.259 | 18.641 | 0.000 | 8.686 |
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 | 17 | 15 | 17 | 16 | 16 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 0.88 | 1.00 | 0.94 | 0.94 | 0.88 | 0.94 | 0.94 |
time (sec) |
N/A | 0.259 | 0.168 | 0.061 | 0.224 | 0.249 | 0.126 | 0.268 | 0.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 27 | 46 | 26 | 24 | 0 | 118 |
N.S. |
1 | 0.00 | 1.00 | 1.17 | 2.00 | 1.13 | 1.04 | 0.00 | 5.13 |
time (sec) |
N/A | 0.000 | 0.693 | 0.103 | 0.338 | 0.258 | 0.134 | 0.000 | 8.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 18 | 18 | 20 | 19 | 19 | 15 | 19 | 19 |
N.S. |
1 | 1.20 | 1.20 | 1.33 | 1.27 | 1.27 | 1.00 | 1.27 | 1.27 |
time (sec) |
N/A | 0.397 | 0.024 | 0.275 | 0.203 | 0.245 | 0.054 | 0.264 | 8.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 33 | 33 | 0 | 31 | 44 | 0 | 28 |
N.S. |
1 | 0.00 | 1.03 | 1.03 | 0.00 | 0.97 | 1.38 | 0.00 | 0.88 |
time (sec) |
N/A | 0.000 | 0.085 | 8.926 | 0.000 | 0.261 | 0.135 | 0.000 | 8.507 |
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 | 20 | 0 | 0 | 25 | 38 | 37 | 24 | 27 | 27 |
N.S. |
1 | 0.00 | 0.00 | 1.25 | 1.90 | 1.85 | 1.20 | 1.35 | 1.35 |
time (sec) |
N/A | 0.000 | 0.000 | 0.213 | 0.203 | 0.283 | 0.203 | 0.266 | 8.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 95 | 49 | 46 | 52 | 53 | 46 | 63 | 48 |
N.S. |
1 | 3.52 | 1.81 | 1.70 | 1.93 | 1.96 | 1.70 | 2.33 | 1.78 |
time (sec) |
N/A | 0.677 | 0.094 | 0.270 | 0.189 | 0.270 | 1.748 | 0.269 | 8.361 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 31 | 23 | 41 | 41 | 17 | 45 | 26 |
N.S. |
1 | 0.00 | 1.19 | 0.88 | 1.58 | 1.58 | 0.65 | 1.73 | 1.00 |
time (sec) |
N/A | 0.000 | 0.461 | 0.104 | 0.214 | 0.268 | 0.067 | 0.271 | 8.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 368 | 250 | 41 | 620 | 80 | 48 | 74 | 0 |
N.S. |
1 | 16.00 | 10.87 | 1.78 | 26.96 | 3.48 | 2.09 | 3.22 | 0.00 |
time (sec) |
N/A | 1.009 | 0.637 | 0.244 | 0.335 | 0.249 | 0.298 | 0.277 | 0.000 |
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 | 18 | 0 | 18 | 18 | 24 | 24 | 19 | 110 | 17 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.33 | 1.33 | 1.06 | 6.11 | 0.94 |
time (sec) |
N/A | 0.000 | 0.195 | 0.478 | 0.217 | 0.287 | 0.058 | 0.269 | 8.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 21 | 20 | 21 | 19 | 21 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.00 | 1.05 | 0.95 | 1.05 | 1.10 |
time (sec) |
N/A | 0.254 | 0.186 | 0.102 | 0.170 | 0.267 | 0.086 | 0.256 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 10 | 10 | 10 | 9 | 9 | 7 | 9 | 9 |
N.S. |
1 | 0.83 | 0.83 | 0.83 | 0.75 | 0.75 | 0.58 | 0.75 | 0.75 |
time (sec) |
N/A | 0.143 | 0.002 | 0.167 | 0.189 | 0.259 | 0.026 | 0.261 | 0.055 |
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 | 36 | 0 | 20 | 20 | 18 | 34 | 12 | 34 | 18 |
N.S. |
1 | 0.00 | 0.56 | 0.56 | 0.50 | 0.94 | 0.33 | 0.94 | 0.50 |
time (sec) |
N/A | 0.000 | 0.319 | 0.161 | 0.247 | 0.268 | 0.096 | 0.275 | 8.361 |
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 | 15 | 15 | 16 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.15 | 1.15 | 1.23 | 1.15 | 1.15 | 1.15 | 1.15 | 1.15 |
time (sec) |
N/A | 0.278 | 0.005 | 0.026 | 0.175 | 0.257 | 0.041 | 0.258 | 7.966 |
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 | 16 | 52 | 49 | 49 | 48 | 48 | 46 | 48 | 48 |
N.S. |
1 | 3.25 | 3.06 | 3.06 | 3.00 | 3.00 | 2.88 | 3.00 | 3.00 |
time (sec) |
N/A | 2.474 | 0.021 | 0.089 | 0.184 | 0.246 | 0.820 | 0.263 | 0.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | A | B | B | B |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 74 | 35 | 261 | 33 | 39 | 239 | 75 |
N.S. |
1 | 0.00 | 3.08 | 1.46 | 10.88 | 1.38 | 1.62 | 9.96 | 3.12 |
time (sec) |
N/A | 0.000 | 2.596 | 2.979 | 0.401 | 0.259 | 0.223 | 0.716 | 8.732 |
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 | 19 | 19 | 18 | 19 | 27 | 18 | 32 | 27 | 18 |
N.S. |
1 | 1.00 | 0.95 | 1.00 | 1.42 | 0.95 | 1.68 | 1.42 | 0.95 |
time (sec) |
N/A | 0.441 | 0.125 | 0.293 | 0.293 | 0.264 | 0.503 | 0.275 | 8.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 1749 | 33759 | 296 | 407 | 426 | 0 | 1494 | 0 |
N.S. |
1 | 60.31 | 1164.10 | 10.21 | 14.03 | 14.69 | 0.00 | 51.52 | 0.00 |
time (sec) |
N/A | 4.553 | 10.120 | 0.671 | 0.243 | 0.276 | 0.000 | 0.369 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 2131 | 32 | 32 | 34 | 34 | 53 | 34 | 34 |
N.S. |
1 | 78.93 | 1.19 | 1.19 | 1.26 | 1.26 | 1.96 | 1.26 | 1.26 |
time (sec) |
N/A | 10.086 | 0.016 | 0.043 | 0.185 | 0.254 | 0.630 | 0.264 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 30 | 20 | 31 | 25 | 20 | 14 | 50 | 30 |
N.S. |
1 | 1.36 | 0.91 | 1.41 | 1.14 | 0.91 | 0.64 | 2.27 | 1.36 |
time (sec) |
N/A | 0.423 | 0.186 | 0.264 | 0.306 | 0.252 | 0.105 | 0.274 | 0.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 19 | 18 | 17 | 56 | 17 | 0 | 17 |
N.S. |
1 | 0.00 | 0.95 | 0.90 | 0.85 | 2.80 | 0.85 | 0.00 | 0.85 |
time (sec) |
N/A | 0.000 | 0.188 | 0.111 | 0.279 | 0.257 | 0.099 | 0.000 | 8.276 |
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 | 30 | 27 | 27 | 22 | 27 | 23 |
N.S. |
1 | 0.00 | 0.00 | 1.36 | 1.23 | 1.23 | 1.00 | 1.23 | 1.05 |
time (sec) |
N/A | 0.000 | 0.000 | 0.776 | 0.302 | 0.266 | 0.230 | 0.318 | 9.404 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 10 | 9 | 8 | 8 | 7 | 9 | 8 |
N.S. |
1 | 1.00 | 0.83 | 0.75 | 0.67 | 0.67 | 0.58 | 0.75 | 0.67 |
time (sec) |
N/A | 0.142 | 0.001 | 0.024 | 0.185 | 0.257 | 0.033 | 0.254 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 40 | 18 | 33 | 42 | 42 | 44 | 42 | 20 |
N.S. |
1 | 1.67 | 0.75 | 1.38 | 1.75 | 1.75 | 1.83 | 1.75 | 0.83 |
time (sec) |
N/A | 0.170 | 0.019 | 0.051 | 0.181 | 0.254 | 0.022 | 0.273 | 0.086 |
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 | 27 | 130 | 43 | 100 | 100 | 99 | 110 | 121 | 103 |
N.S. |
1 | 4.81 | 1.59 | 3.70 | 3.70 | 3.67 | 4.07 | 4.48 | 3.81 |
time (sec) |
N/A | 0.289 | 0.119 | 0.062 | 0.180 | 0.264 | 0.118 | 0.258 | 8.051 |
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 | 15 | 16 | 16 | 18 | 15 | 34 | 15 |
N.S. |
1 | 0.00 | 0.65 | 0.70 | 0.70 | 0.78 | 0.65 | 1.48 | 0.65 |
time (sec) |
N/A | 0.000 | 0.197 | 0.118 | 0.211 | 0.254 | 0.052 | 0.260 | 0.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 60 | 58 | 38 | 0 | 54 | 44 | 58 | 35 |
N.S. |
1 | 2.22 | 2.15 | 1.41 | 0.00 | 2.00 | 1.63 | 2.15 | 1.30 |
time (sec) |
N/A | 0.452 | 0.037 | 0.071 | 0.000 | 0.262 | 0.090 | 0.260 | 8.100 |
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 | 25 | 58 | 40 | 41 | 27 | 33 | 106 |
N.S. |
1 | 0.00 | 0.86 | 2.00 | 1.38 | 1.41 | 0.93 | 1.14 | 3.66 |
time (sec) |
N/A | 0.000 | 0.299 | 1.203 | 0.294 | 0.263 | 0.086 | 0.389 | 8.562 |
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 | 8 | 7 | 7 | 7 | 6 | 6 | 7 | 7 | 6 |
N.S. |
1 | 0.88 | 0.88 | 0.88 | 0.75 | 0.75 | 0.88 | 0.88 | 0.75 |
time (sec) |
N/A | 0.120 | 0.001 | 0.018 | 0.185 | 0.262 | 0.022 | 0.246 | 8.023 |
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 | 25 | 24 | 23 | 31 | 29 | 0 | 46 |
N.S. |
1 | 0.00 | 0.93 | 0.89 | 0.85 | 1.15 | 1.07 | 0.00 | 1.70 |
time (sec) |
N/A | 0.000 | 2.610 | 1.107 | 0.312 | 0.270 | 0.189 | 0.000 | 8.511 |
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 | 21 | 21 | 20 | 19 | 30 | 22 | 30 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 1.43 | 1.05 | 1.43 | 0.90 |
time (sec) |
N/A | 0.197 | 0.020 | 0.068 | 0.201 | 0.261 | 0.068 | 0.259 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 37 | 36 | 0 | 37 | 0 | 0 | 30 |
N.S. |
1 | 0.00 | 1.19 | 1.16 | 0.00 | 1.19 | 0.00 | 0.00 | 0.97 |
time (sec) |
N/A | 0.000 | 0.269 | 19.274 | 0.000 | 0.268 | 0.000 | 0.000 | 8.125 |
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 | 31 | 43 | 25 | 25 | 24 | 27 | 27 | 24 | 34 |
N.S. |
1 | 1.39 | 0.81 | 0.81 | 0.77 | 0.87 | 0.87 | 0.77 | 1.10 |
time (sec) |
N/A | 0.231 | 0.019 | 0.968 | 0.184 | 0.267 | 0.529 | 0.253 | 0.149 |