Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 16 | 17 | 22 | 29 | 17 | 18 | 22 |
N.S. |
1 | 1.00 | 0.64 | 0.68 | 0.88 | 1.16 | 0.68 | 0.72 | 0.88 |
time (sec) |
N/A | 0.152 | 0.011 | 0.180 | 0.206 | 0.227 | 0.040 | 0.284 | 0.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 33 | 32 | 39 | 31 | 45 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.89 | 1.08 | 0.86 | 1.25 | 0.89 |
time (sec) |
N/A | 0.160 | 0.016 | 0.171 | 0.204 | 0.252 | 0.030 | 0.278 | 0.038 |
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 | 41 | 41 | 37 | 25 | 30 | 45 | 31 | 27 | 30 |
N.S. |
1 | 1.00 | 0.90 | 0.61 | 0.73 | 1.10 | 0.76 | 0.66 | 0.73 |
time (sec) |
N/A | 0.203 | 0.022 | 0.042 | 0.216 | 0.244 | 0.064 | 0.266 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 28 | 29 | 45 | 26 | 37 | 29 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.07 | 1.67 | 0.96 | 1.37 | 1.07 |
time (sec) |
N/A | 0.196 | 0.018 | 0.193 | 0.206 | 0.271 | 0.052 | 0.294 | 0.269 |
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 | 39 | 44 | 47 | 31 | 29 | 45 | 32 | 35 | 31 |
N.S. |
1 | 1.13 | 1.21 | 0.79 | 0.74 | 1.15 | 0.82 | 0.90 | 0.79 |
time (sec) |
N/A | 0.206 | 0.019 | 0.211 | 0.220 | 0.252 | 0.063 | 0.282 | 0.054 |
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 | 46 | 46 | 40 | 35 | 40 | 65 | 37 | 40 | 40 |
N.S. |
1 | 1.00 | 0.87 | 0.76 | 0.87 | 1.41 | 0.80 | 0.87 | 0.87 |
time (sec) |
N/A | 0.208 | 0.018 | 0.049 | 0.206 | 0.239 | 0.068 | 0.290 | 0.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 24 | 23 | 23 | 22 | 24 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.79 | 0.79 | 0.76 | 0.83 | 1.00 |
time (sec) |
N/A | 0.179 | 0.008 | 0.072 | 0.313 | 0.237 | 0.055 | 0.268 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 22 | 21 | 21 | 22 | 23 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.78 | 0.78 | 0.81 | 0.85 | 1.00 |
time (sec) |
N/A | 0.160 | 0.009 | 0.233 | 0.326 | 0.242 | 0.080 | 0.292 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 32 | 26 | 25 | 25 | 29 | 27 | 17 |
N.S. |
1 | 1.00 | 1.33 | 1.08 | 1.04 | 1.04 | 1.21 | 1.12 | 0.71 |
time (sec) |
N/A | 0.142 | 0.012 | 0.049 | 0.309 | 0.242 | 0.061 | 0.279 | 0.065 |
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 | 41 | 41 | 41 | 33 | 32 | 44 | 39 | 33 | 49 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.78 | 1.07 | 0.95 | 0.80 | 1.20 |
time (sec) |
N/A | 0.240 | 0.025 | 0.053 | 0.312 | 0.238 | 0.063 | 0.291 | 0.336 |
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 | 46 | 46 | 40 | 35 | 36 | 57 | 37 | 62 | 38 |
N.S. |
1 | 1.00 | 0.87 | 0.76 | 0.78 | 1.24 | 0.80 | 1.35 | 0.83 |
time (sec) |
N/A | 0.231 | 0.021 | 0.276 | 0.330 | 0.241 | 0.089 | 0.288 | 0.223 |
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 | 47 | 47 | 37 | 31 | 36 | 59 | 36 | 32 | 42 |
N.S. |
1 | 1.00 | 0.79 | 0.66 | 0.77 | 1.26 | 0.77 | 0.68 | 0.89 |
time (sec) |
N/A | 0.204 | 0.028 | 0.253 | 0.295 | 0.245 | 0.076 | 0.279 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 71 | 73 | 54 | 53 | 53 | 70 | 53 | 47 |
N.S. |
1 | 1.06 | 1.09 | 0.81 | 0.79 | 0.79 | 1.04 | 0.79 | 0.70 |
time (sec) |
N/A | 0.214 | 0.064 | 0.030 | 0.295 | 0.241 | 0.086 | 0.294 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 67 | 46 | 54 | 58 | 306 | 64 | 73 |
N.S. |
1 | 1.00 | 1.40 | 0.96 | 1.12 | 1.21 | 6.38 | 1.33 | 1.52 |
time (sec) |
N/A | 0.227 | 0.020 | 0.244 | 0.298 | 0.239 | 0.286 | 0.297 | 0.181 |
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 | 58 | 58 | 46 | 38 | 43 | 66 | 46 | 39 | 44 |
N.S. |
1 | 1.00 | 0.79 | 0.66 | 0.74 | 1.14 | 0.79 | 0.67 | 0.76 |
time (sec) |
N/A | 0.226 | 0.027 | 0.369 | 0.285 | 0.239 | 0.078 | 0.284 | 0.229 |
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 | 51 | 51 | 47 | 36 | 35 | 35 | 44 | 35 | 35 |
N.S. |
1 | 1.00 | 0.92 | 0.71 | 0.69 | 0.69 | 0.86 | 0.69 | 0.69 |
time (sec) |
N/A | 0.409 | 0.029 | 0.316 | 0.291 | 0.243 | 0.205 | 0.271 | 0.301 |
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 | 41 | 45 | 41 | 34 | 33 | 33 | 32 | 33 | 33 |
N.S. |
1 | 1.10 | 1.00 | 0.83 | 0.80 | 0.80 | 0.78 | 0.80 | 0.80 |
time (sec) |
N/A | 0.410 | 0.010 | 0.243 | 0.198 | 0.245 | 0.076 | 0.277 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 58 | 52 | 51 | 49 | 45 | 73 | 50 | 64 |
N.S. |
1 | 1.04 | 0.93 | 0.91 | 0.88 | 0.80 | 1.30 | 0.89 | 1.14 |
time (sec) |
N/A | 0.194 | 0.016 | 0.226 | 0.280 | 0.240 | 0.058 | 0.308 | 0.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 58 | 50 | 43 | 49 | 43 | 71 | 50 | 68 |
N.S. |
1 | 1.04 | 0.89 | 0.77 | 0.88 | 0.77 | 1.27 | 0.89 | 1.21 |
time (sec) |
N/A | 0.197 | 0.010 | 0.207 | 0.287 | 0.238 | 0.050 | 0.280 | 0.123 |
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 | 12 | 11 | 10 | 10 | 8 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.92 | 0.83 |
time (sec) |
N/A | 0.124 | 0.003 | 0.193 | 0.193 | 0.236 | 0.038 | 0.287 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 26 | 22 | 21 | 23 | 18 | 19 | 22 | 18 |
N.S. |
1 | 1.18 | 1.00 | 0.95 | 1.05 | 0.82 | 0.86 | 1.00 | 0.82 |
time (sec) |
N/A | 0.141 | 0.006 | 0.200 | 0.201 | 0.230 | 0.096 | 0.325 | 0.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 72 | 60 | 60 | 57 | 53 | 83 | 58 | 88 |
N.S. |
1 | 1.14 | 0.95 | 0.95 | 0.90 | 0.84 | 1.32 | 0.92 | 1.40 |
time (sec) |
N/A | 0.221 | 0.019 | 0.230 | 0.276 | 0.238 | 0.071 | 0.296 | 0.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 74 | 68 | 60 | 57 | 62 | 80 | 58 | 86 |
N.S. |
1 | 1.14 | 1.05 | 0.92 | 0.88 | 0.95 | 1.23 | 0.89 | 1.32 |
time (sec) |
N/A | 0.216 | 0.021 | 0.234 | 0.285 | 0.241 | 0.091 | 0.299 | 0.301 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 34 | 33 | 34 | 31 | 33 | 29 | 40 | 29 |
N.S. |
1 | 1.03 | 1.00 | 1.03 | 0.94 | 1.00 | 0.88 | 1.21 | 0.88 |
time (sec) |
N/A | 0.176 | 0.007 | 0.207 | 0.198 | 0.235 | 0.125 | 0.271 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 88 | 74 | 66 | 66 | 68 | 90 | 67 | 99 |
N.S. |
1 | 1.21 | 1.01 | 0.90 | 0.90 | 0.93 | 1.23 | 0.92 | 1.36 |
time (sec) |
N/A | 0.235 | 0.017 | 0.227 | 0.284 | 0.242 | 0.098 | 0.273 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 45 | 0 | 0 | 0 | 92 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 2.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.149 | 0.142 | 0.000 | 0.000 | 0.000 | 1.229 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 38 | 33 | 32 | 26 | 37 | 34 | 18 |
N.S. |
1 | 1.00 | 1.41 | 1.22 | 1.19 | 0.96 | 1.37 | 1.26 | 0.67 |
time (sec) |
N/A | 0.145 | 0.012 | 0.249 | 0.288 | 0.244 | 0.065 | 0.277 | 0.093 |
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 | 15 | 15 | 15 | 27 | 29 | 26 | 24 | 30 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.80 | 1.93 | 1.73 | 1.60 | 2.00 | 0.87 |
time (sec) |
N/A | 0.135 | 0.005 | 0.205 | 0.191 | 0.239 | 0.063 | 0.287 | 0.054 |
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 | 28 | 24 | 23 | 25 | 20 | 19 | 26 | 20 |
N.S. |
1 | 1.17 | 1.00 | 0.96 | 1.04 | 0.83 | 0.79 | 1.08 | 0.83 |
time (sec) |
N/A | 0.142 | 0.008 | 0.203 | 0.196 | 0.231 | 0.120 | 0.284 | 0.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 40 | 46 | 41 | 40 | 36 | 44 | 42 | 31 |
N.S. |
1 | 1.14 | 1.31 | 1.17 | 1.14 | 1.03 | 1.26 | 1.20 | 0.89 |
time (sec) |
N/A | 0.157 | 0.012 | 0.256 | 0.285 | 0.243 | 0.089 | 0.285 | 0.270 |
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 | 26 | 25 | 50 | 42 | 37 | 41 | 34 | 38 | 22 |
N.S. |
1 | 0.96 | 1.92 | 1.62 | 1.42 | 1.58 | 1.31 | 1.46 | 0.85 |
time (sec) |
N/A | 0.147 | 0.009 | 0.216 | 0.210 | 0.236 | 0.098 | 0.275 | 0.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 42 | 48 | 41 | 40 | 45 | 48 | 42 | 31 |
N.S. |
1 | 1.14 | 1.30 | 1.11 | 1.08 | 1.22 | 1.30 | 1.14 | 0.84 |
time (sec) |
N/A | 0.153 | 0.015 | 0.254 | 0.292 | 0.242 | 0.104 | 0.281 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 44 | 0 | 0 | 0 | 95 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 2.11 | 0.00 | 0.00 |
time (sec) |
N/A | 0.150 | 0.234 | 0.000 | 0.000 | 0.000 | 0.497 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 13 | 29 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 1.93 | 0.87 | 0.87 |
time (sec) |
N/A | 0.136 | 0.005 | 0.237 | 0.278 | 0.245 | 0.068 | 0.322 | 0.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 114 | 79 | 24 | 98 | 96 | 19 | 114 | 33 |
N.S. |
1 | 1.05 | 0.72 | 0.22 | 0.90 | 0.88 | 0.17 | 1.05 | 0.30 |
time (sec) |
N/A | 0.271 | 0.034 | 0.232 | 0.295 | 0.243 | 0.059 | 0.301 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 201 | 202 | 204 | 55 | 180 | 11094 | 39 | 177 | 174 |
N.S. |
1 | 1.00 | 1.01 | 0.27 | 0.90 | 55.19 | 0.19 | 0.88 | 0.87 |
time (sec) |
N/A | 0.423 | 0.183 | 0.230 | 0.293 | 0.962 | 0.058 | 0.290 | 0.714 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 201 | 203 | 204 | 60 | 160 | 18781 | 41 | 177 | 182 |
N.S. |
1 | 1.01 | 1.01 | 0.30 | 0.80 | 93.44 | 0.20 | 0.88 | 0.91 |
time (sec) |
N/A | 0.386 | 0.067 | 0.211 | 0.285 | 0.985 | 0.054 | 0.304 | 0.690 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 201 | 220 | 204 | 58 | 160 | 12656 | 41 | 177 | 202 |
N.S. |
1 | 1.09 | 1.01 | 0.29 | 0.80 | 62.97 | 0.20 | 0.88 | 1.00 |
time (sec) |
N/A | 0.373 | 0.072 | 0.210 | 0.298 | 0.964 | 0.062 | 0.316 | 0.954 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 201 | 202 | 204 | 73 | 180 | 17865 | 39 | 177 | 202 |
N.S. |
1 | 1.00 | 1.01 | 0.36 | 0.90 | 88.88 | 0.19 | 0.88 | 1.00 |
time (sec) |
N/A | 0.370 | 0.041 | 0.213 | 0.285 | 0.972 | 0.062 | 0.288 | 0.427 |
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 | 12 | 11 | 10 | 10 | 8 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.92 | 0.83 |
time (sec) |
N/A | 0.127 | 0.003 | 0.204 | 0.196 | 0.227 | 0.042 | 0.298 | 0.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 26 | 22 | 21 | 23 | 18 | 19 | 22 | 18 |
N.S. |
1 | 1.18 | 1.00 | 0.95 | 1.05 | 0.82 | 0.86 | 1.00 | 0.82 |
time (sec) |
N/A | 0.139 | 0.007 | 0.205 | 0.201 | 0.229 | 0.119 | 0.291 | 0.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 209 | 216 | 172 | 76 | 192 | 15275 | 48 | 185 | 210 |
N.S. |
1 | 1.03 | 0.82 | 0.36 | 0.92 | 73.09 | 0.23 | 0.89 | 1.00 |
time (sec) |
N/A | 0.389 | 0.180 | 0.233 | 0.290 | 0.977 | 0.080 | 0.317 | 0.415 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 211 | 236 | 174 | 78 | 173 | 15499 | 51 | 185 | 210 |
N.S. |
1 | 1.12 | 0.82 | 0.37 | 0.82 | 73.45 | 0.24 | 0.88 | 1.00 |
time (sec) |
N/A | 0.384 | 0.171 | 0.227 | 0.290 | 1.018 | 0.097 | 0.303 | 0.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 211 | 219 | 175 | 81 | 172 | 15501 | 51 | 185 | 214 |
N.S. |
1 | 1.04 | 0.83 | 0.38 | 0.82 | 73.46 | 0.24 | 0.88 | 1.01 |
time (sec) |
N/A | 0.387 | 0.129 | 0.226 | 0.283 | 0.973 | 0.091 | 0.320 | 0.763 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 45 | 0 | 0 | 0 | 92 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 2.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.151 | 0.263 | 0.000 | 0.000 | 0.000 | 8.408 | 0.000 | 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 | 35 | 35 | 21 | 10 | 27 | 9 | 8 | 27 | 9 |
N.S. |
1 | 1.00 | 0.60 | 0.29 | 0.77 | 0.26 | 0.23 | 0.77 | 0.26 |
time (sec) |
N/A | 0.488 | 0.008 | 0.240 | 0.282 | 0.239 | 0.051 | 0.269 | 0.034 |
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 | 60 | 65 | 51 | 44 | 54 | 71 | 63 | 44 | 45 |
N.S. |
1 | 1.08 | 0.85 | 0.73 | 0.90 | 1.18 | 1.05 | 0.73 | 0.75 |
time (sec) |
N/A | 0.179 | 0.031 | 0.812 | 0.274 | 0.251 | 0.072 | 0.285 | 0.081 |
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 | 43 | 53 | 30 | 28 | 38 | 52 | 36 | 28 | 27 |
N.S. |
1 | 1.23 | 0.70 | 0.65 | 0.88 | 1.21 | 0.84 | 0.65 | 0.63 |
time (sec) |
N/A | 0.162 | 0.014 | 0.234 | 0.274 | 0.253 | 0.059 | 0.287 | 0.227 |
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 | 90 | 96 | 88 | 103 | 0 | 448 | 323 | 92 | 159 |
N.S. |
1 | 1.07 | 0.98 | 1.14 | 0.00 | 4.98 | 3.59 | 1.02 | 1.77 |
time (sec) |
N/A | 0.222 | 0.085 | 0.536 | 0.000 | 0.267 | 0.541 | 0.282 | 0.336 |
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 | 38 | 42 | 38 | 35 | 33 | 50 | 31 | 33 | 41 |
N.S. |
1 | 1.11 | 1.00 | 0.92 | 0.87 | 1.32 | 0.82 | 0.87 | 1.08 |
time (sec) |
N/A | 0.212 | 0.015 | 0.322 | 0.278 | 0.241 | 0.050 | 0.289 | 0.218 |
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 | 57 | 65 | 49 | 41 | 42 | 58 | 53 | 43 | 60 |
N.S. |
1 | 1.14 | 0.86 | 0.72 | 0.74 | 1.02 | 0.93 | 0.75 | 1.05 |
time (sec) |
N/A | 0.198 | 0.024 | 0.205 | 0.280 | 0.238 | 0.063 | 0.277 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 44 | 33 | 29 | 31 | 40 | 32 | 28 | 29 |
N.S. |
1 | 1.22 | 0.92 | 0.81 | 0.86 | 1.11 | 0.89 | 0.78 | 0.81 |
time (sec) |
N/A | 0.170 | 0.017 | 0.234 | 0.268 | 0.226 | 0.063 | 0.278 | 0.217 |
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 | 49 | 55 | 78 | 39 | 40 | 40 | 46 | 40 | 52 |
N.S. |
1 | 1.12 | 1.59 | 0.80 | 0.82 | 0.82 | 0.94 | 0.82 | 1.06 |
time (sec) |
N/A | 0.201 | 0.017 | 0.221 | 0.282 | 0.246 | 0.056 | 0.293 | 0.101 |
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 | 13 | 39 | 13 | 14 | 14 | 13 | 14 | 0 | 14 |
N.S. |
1 | 3.00 | 1.00 | 1.08 | 1.08 | 1.00 | 1.08 | 0.00 | 1.08 |
time (sec) |
N/A | 0.209 | 0.028 | 0.290 | 0.204 | 0.246 | 0.784 | 0.000 | 0.370 |
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 | 41 | 48 | 38 | 35 | 34 | 34 | 42 | 34 | 34 |
N.S. |
1 | 1.17 | 0.93 | 0.85 | 0.83 | 0.83 | 1.02 | 0.83 | 0.83 |
time (sec) |
N/A | 0.192 | 0.013 | 0.053 | 0.280 | 0.245 | 0.048 | 0.429 | 0.228 |
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 | 32 | 36 | 32 | 25 | 24 | 24 | 24 | 25 | 22 |
N.S. |
1 | 1.12 | 1.00 | 0.78 | 0.75 | 0.75 | 0.75 | 0.78 | 0.69 |
time (sec) |
N/A | 0.177 | 0.007 | 0.051 | 0.189 | 0.249 | 0.049 | 0.311 | 0.087 |
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 | 29 | 25 | 18 | 17 | 17 | 15 | 19 | 16 |
N.S. |
1 | 1.16 | 1.00 | 0.72 | 0.68 | 0.68 | 0.60 | 0.76 | 0.64 |
time (sec) |
N/A | 0.173 | 0.006 | 0.048 | 0.191 | 0.242 | 0.040 | 0.303 | 0.614 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 24 | 22 | 32 | 46 | 29 | 23 | 22 |
N.S. |
1 | 1.00 | 0.67 | 0.61 | 0.89 | 1.28 | 0.81 | 0.64 | 0.61 |
time (sec) |
N/A | 0.180 | 0.015 | 0.197 | 0.188 | 0.240 | 0.043 | 0.303 | 0.042 |
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 | 45 | 45 | 24 | 22 | 72 | 72 | 70 | 22 | 29 |
N.S. |
1 | 1.00 | 0.53 | 0.49 | 1.60 | 1.60 | 1.56 | 0.49 | 0.64 |
time (sec) |
N/A | 0.160 | 0.008 | 0.198 | 0.192 | 0.232 | 0.061 | 0.284 | 0.100 |
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 | 55 | 55 | 41 | 34 | 48 | 67 | 42 | 55 | 43 |
N.S. |
1 | 1.00 | 0.75 | 0.62 | 0.87 | 1.22 | 0.76 | 1.00 | 0.78 |
time (sec) |
N/A | 0.220 | 0.014 | 0.191 | 0.188 | 0.238 | 0.051 | 0.274 | 0.053 |
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 | 36 | 36 | 38 | 35 | 38 | 59 | 41 | 43 | 31 |
N.S. |
1 | 1.00 | 1.06 | 0.97 | 1.06 | 1.64 | 1.14 | 1.19 | 0.86 |
time (sec) |
N/A | 0.159 | 0.024 | 0.207 | 0.197 | 0.240 | 0.056 | 0.287 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 31 | 28 | 31 | 48 | 29 | 40 | 34 |
N.S. |
1 | 1.00 | 0.89 | 0.80 | 0.89 | 1.37 | 0.83 | 1.14 | 0.97 |
time (sec) |
N/A | 0.157 | 0.019 | 0.237 | 0.188 | 0.250 | 0.053 | 0.312 | 0.257 |
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 | 61 | 59 | 46 | 40 | 50 | 85 | 51 | 42 | 45 |
N.S. |
1 | 0.97 | 0.75 | 0.66 | 0.82 | 1.39 | 0.84 | 0.69 | 0.74 |
time (sec) |
N/A | 0.185 | 0.025 | 0.243 | 0.205 | 0.246 | 0.069 | 0.284 | 0.137 |
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 | 51 | 58 | 36 | 36 | 44 | 62 | 42 | 34 | 39 |
N.S. |
1 | 1.14 | 0.71 | 0.71 | 0.86 | 1.22 | 0.82 | 0.67 | 0.76 |
time (sec) |
N/A | 0.177 | 0.018 | 0.546 | 0.282 | 0.240 | 0.071 | 0.277 | 0.254 |
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 | 54 | 54 | 54 | 45 | 60 | 105 | 58 | 47 | 55 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.11 | 1.94 | 1.07 | 0.87 | 1.02 |
time (sec) |
N/A | 0.175 | 0.018 | 0.196 | 0.191 | 0.235 | 0.069 | 0.279 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 47 | 53 | 32 | 40 | 53 | 49 | 48 | 33 |
N.S. |
1 | 1.31 | 1.47 | 0.89 | 1.11 | 1.47 | 1.36 | 1.33 | 0.92 |
time (sec) |
N/A | 0.166 | 0.040 | 0.226 | 0.275 | 0.244 | 0.036 | 0.301 | 0.273 |
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 | 58 | 67 | 40 | 31 | 41 | 59 | 39 | 31 | 40 |
N.S. |
1 | 1.16 | 0.69 | 0.53 | 0.71 | 1.02 | 0.67 | 0.53 | 0.69 |
time (sec) |
N/A | 0.165 | 0.021 | 0.237 | 0.291 | 0.241 | 0.051 | 0.281 | 0.077 |
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 | 43 | 46 | 43 | 34 | 36 | 45 | 42 | 36 | 36 |
N.S. |
1 | 1.07 | 1.00 | 0.79 | 0.84 | 1.05 | 0.98 | 0.84 | 0.84 |
time (sec) |
N/A | 0.159 | 0.037 | 0.856 | 0.289 | 0.244 | 0.061 | 0.279 | 0.222 |
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 | 43 | 69 | 62 | 37 | 47 | 68 | 58 | 51 | 34 |
N.S. |
1 | 1.60 | 1.44 | 0.86 | 1.09 | 1.58 | 1.35 | 1.19 | 0.79 |
time (sec) |
N/A | 0.209 | 0.041 | 0.313 | 0.291 | 0.232 | 0.061 | 0.289 | 0.262 |
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 | 37 | 46 | 25 | 27 | 30 | 38 | 24 | 40 | 32 |
N.S. |
1 | 1.24 | 0.68 | 0.73 | 0.81 | 1.03 | 0.65 | 1.08 | 0.86 |
time (sec) |
N/A | 0.159 | 0.013 | 0.247 | 0.284 | 0.239 | 0.059 | 0.309 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 43 | 26 | 29 | 28 | 38 | 26 | 32 | 28 |
N.S. |
1 | 1.34 | 0.81 | 0.91 | 0.88 | 1.19 | 0.81 | 1.00 | 0.88 |
time (sec) |
N/A | 0.176 | 0.017 | 0.183 | 0.205 | 0.230 | 0.047 | 0.485 | 0.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 19 | 20 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.46 | 1.54 | 0.85 | 0.85 |
time (sec) |
N/A | 0.128 | 0.005 | 0.217 | 0.205 | 0.230 | 0.115 | 0.275 | 0.229 |
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 | 54 | 55 | 46 | 45 | 57 | 81 | 51 | 56 | 52 |
N.S. |
1 | 1.02 | 0.85 | 0.83 | 1.06 | 1.50 | 0.94 | 1.04 | 0.96 |
time (sec) |
N/A | 0.180 | 0.027 | 0.221 | 0.195 | 0.245 | 0.219 | 0.310 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 182 | 134 | 75 | 147 | 227 | 66 | 150 | 76 |
N.S. |
1 | 1.16 | 0.85 | 0.48 | 0.94 | 1.45 | 0.42 | 0.96 | 0.48 |
time (sec) |
N/A | 0.361 | 0.112 | 0.273 | 0.275 | 0.239 | 0.205 | 0.294 | 0.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 80 | 75 | 53 | 60 | 78 | 78 | 50 | 53 |
N.S. |
1 | 1.25 | 1.17 | 0.83 | 0.94 | 1.22 | 1.22 | 0.78 | 0.83 |
time (sec) |
N/A | 0.184 | 0.051 | 0.279 | 0.288 | 0.236 | 0.226 | 0.294 | 0.263 |
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 | 39 | 43 | 33 | 29 | 34 | 45 | 27 | 30 | 29 |
N.S. |
1 | 1.10 | 0.85 | 0.74 | 0.87 | 1.15 | 0.69 | 0.77 | 0.74 |
time (sec) |
N/A | 0.164 | 0.016 | 0.215 | 0.190 | 0.225 | 0.058 | 0.320 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 319 | 347 | 293 | 47 | 335 | 1751 | 37 | 250 | 285 |
N.S. |
1 | 1.09 | 0.92 | 0.15 | 1.05 | 5.49 | 0.12 | 0.78 | 0.89 |
time (sec) |
N/A | 0.572 | 0.351 | 0.247 | 0.280 | 2.695 | 0.113 | 0.590 | 1.704 |
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 | 59 | 75 | 65 | 39 | 56 | 73 | 58 | 55 | 41 |
N.S. |
1 | 1.27 | 1.10 | 0.66 | 0.95 | 1.24 | 0.98 | 0.93 | 0.69 |
time (sec) |
N/A | 0.162 | 0.074 | 0.222 | 0.301 | 0.232 | 0.070 | 0.292 | 0.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 44 | 33 | 29 | 31 | 40 | 32 | 28 | 29 |
N.S. |
1 | 1.22 | 0.92 | 0.81 | 0.86 | 1.11 | 0.89 | 0.78 | 0.81 |
time (sec) |
N/A | 0.174 | 0.016 | 0.228 | 0.292 | 0.237 | 0.059 | 0.301 | 0.004 |
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 | 38 | 38 | 32 | 31 | 38 | 65 | 36 | 35 | 33 |
N.S. |
1 | 1.00 | 0.84 | 0.82 | 1.00 | 1.71 | 0.95 | 0.92 | 0.87 |
time (sec) |
N/A | 0.218 | 0.025 | 0.050 | 0.221 | 0.226 | 0.057 | 0.288 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 69 | 65 | 50 | 50 | 73 | 60 | 60 | 63 |
N.S. |
1 | 1.08 | 1.02 | 0.78 | 0.78 | 1.14 | 0.94 | 0.94 | 0.98 |
time (sec) |
N/A | 0.272 | 0.032 | 0.225 | 0.301 | 0.238 | 0.098 | 0.307 | 0.111 |
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 | 63 | 66 | 63 | 54 | 59 | 97 | 68 | 72 | 73 |
N.S. |
1 | 1.05 | 1.00 | 0.86 | 0.94 | 1.54 | 1.08 | 1.14 | 1.16 |
time (sec) |
N/A | 0.291 | 0.039 | 0.471 | 0.279 | 0.248 | 0.083 | 0.303 | 0.284 |
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 | 43 | 43 | 46 | 32 | 36 | 55 | 34 | 33 | 25 |
N.S. |
1 | 1.00 | 1.07 | 0.74 | 0.84 | 1.28 | 0.79 | 0.77 | 0.58 |
time (sec) |
N/A | 0.160 | 0.020 | 0.226 | 0.198 | 0.234 | 0.068 | 0.290 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 31 | 20 | 18 | 43 | 43 | 39 | 18 | 18 |
N.S. |
1 | 1.15 | 0.74 | 0.67 | 1.59 | 1.59 | 1.44 | 0.67 | 0.67 |
time (sec) |
N/A | 0.155 | 0.011 | 0.210 | 0.202 | 0.229 | 0.067 | 0.302 | 0.119 |
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 | 46 | 50 | 44 | 34 | 39 | 55 | 36 | 40 | 34 |
N.S. |
1 | 1.09 | 0.96 | 0.74 | 0.85 | 1.20 | 0.78 | 0.87 | 0.74 |
time (sec) |
N/A | 0.166 | 0.018 | 0.200 | 0.185 | 0.225 | 0.045 | 0.306 | 0.220 |
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 | 44 | 50 | 39 | 35 | 37 | 56 | 34 | 43 | 33 |
N.S. |
1 | 1.14 | 0.89 | 0.80 | 0.84 | 1.27 | 0.77 | 0.98 | 0.75 |
time (sec) |
N/A | 0.167 | 0.024 | 0.200 | 0.189 | 0.230 | 0.061 | 0.288 | 0.050 |
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 | 54 | 54 | 54 | 45 | 60 | 105 | 58 | 47 | 55 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.11 | 1.94 | 1.07 | 0.87 | 1.02 |
time (sec) |
N/A | 0.173 | 0.009 | 0.187 | 0.186 | 0.233 | 0.069 | 0.278 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 33 | 32 | 39 | 31 | 45 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.89 | 1.08 | 0.86 | 1.25 | 0.89 |
time (sec) |
N/A | 0.157 | 0.015 | 0.182 | 0.182 | 0.237 | 0.025 | 0.299 | 0.002 |
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 | 44 | 44 | 41 | 38 | 38 | 38 | 39 | 39 | 37 |
N.S. |
1 | 1.00 | 0.93 | 0.86 | 0.86 | 0.86 | 0.89 | 0.89 | 0.84 |
time (sec) |
N/A | 0.188 | 0.013 | 0.074 | 0.182 | 0.241 | 0.021 | 0.299 | 0.049 |
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 | 96 | 96 | 91 | 89 | 91 | 91 | 100 | 98 | 88 |
N.S. |
1 | 1.00 | 0.95 | 0.93 | 0.95 | 0.95 | 1.04 | 1.02 | 0.92 |
time (sec) |
N/A | 0.263 | 0.030 | 0.362 | 0.194 | 0.234 | 0.022 | 0.277 | 0.218 |
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 | 167 | 167 | 167 | 165 | 171 | 171 | 189 | 188 | 164 |
N.S. |
1 | 1.00 | 1.00 | 0.99 | 1.02 | 1.02 | 1.13 | 1.13 | 0.98 |
time (sec) |
N/A | 0.364 | 0.032 | 0.342 | 0.180 | 0.223 | 0.030 | 0.288 | 0.242 |
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 | 263 | 263 | 263 | 264 | 273 | 273 | 313 | 307 | 263 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.04 | 1.04 | 1.19 | 1.17 | 1.00 |
time (sec) |
N/A | 0.524 | 0.061 | 0.350 | 0.189 | 0.246 | 0.036 | 0.282 | 0.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 267 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.252 | 0.673 | 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 | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 71 | 66 | 63 | 0 | 203 | 246 | 60 | 155 |
N.S. |
1 | 1.09 | 1.02 | 0.97 | 0.00 | 3.12 | 3.78 | 0.92 | 2.38 |
time (sec) |
N/A | 0.203 | 0.046 | 0.463 | 0.000 | 0.248 | 0.401 | 0.293 | 0.308 |
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 | 89 | 95 | 88 | 103 | 0 | 447 | 323 | 92 | 159 |
N.S. |
1 | 1.07 | 0.99 | 1.16 | 0.00 | 5.02 | 3.63 | 1.03 | 1.79 |
time (sec) |
N/A | 0.207 | 0.073 | 0.464 | 0.000 | 0.259 | 0.522 | 0.292 | 0.304 |
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 | 130 | 143 | 127 | 155 | 0 | 1104 | 622 | 194 | 360 |
N.S. |
1 | 1.10 | 0.98 | 1.19 | 0.00 | 8.49 | 4.78 | 1.49 | 2.77 |
time (sec) |
N/A | 0.249 | 0.127 | 0.457 | 0.000 | 0.269 | 0.996 | 0.289 | 0.528 |
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 | 173 | 191 | 168 | 206 | 0 | 1950 | 1027 | 363 | 640 |
N.S. |
1 | 1.10 | 0.97 | 1.19 | 0.00 | 11.27 | 5.94 | 2.10 | 3.70 |
time (sec) |
N/A | 0.280 | 0.190 | 0.478 | 0.000 | 0.298 | 1.528 | 0.306 | 0.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 264 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.238 | 0.791 | 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 | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 51 | 44 | 31 | 41 | 52 | 46 | 46 | 36 |
N.S. |
1 | 1.04 | 0.90 | 0.63 | 0.84 | 1.06 | 0.94 | 0.94 | 0.73 |
time (sec) |
N/A | 0.187 | 0.026 | 0.263 | 0.262 | 0.232 | 0.041 | 0.294 | 0.176 |
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 | 61 | 93 | 70 | 56 | 67 | 97 | 76 | 61 | 53 |
N.S. |
1 | 1.52 | 1.15 | 0.92 | 1.10 | 1.59 | 1.25 | 1.00 | 0.87 |
time (sec) |
N/A | 0.226 | 0.051 | 0.261 | 0.278 | 0.239 | 0.066 | 0.290 | 0.249 |