Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 81 | 94 | 85 | 74 | 205 | 697 | 45 | 0 |
N.S. |
1 | 1.08 | 1.25 | 1.13 | 0.99 | 2.73 | 9.29 | 0.60 | 0.00 |
time (sec) |
N/A | 0.194 | 10.197 | 0.044 | 0.278 | 0.295 | 27.056 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 117 | 56 | 90 | 119 | 249 | 818 | 65 | 0 |
N.S. |
1 | 1.18 | 0.57 | 0.91 | 1.20 | 2.52 | 8.26 | 0.66 | 0.00 |
time (sec) |
N/A | 0.220 | 10.023 | 0.070 | 0.275 | 0.269 | 81.460 | 0.349 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 149 | 56 | 100 | 163 | 283 | 0 | 93 | 0 |
N.S. |
1 | 1.16 | 0.43 | 0.78 | 1.26 | 2.19 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.242 | 10.022 | 0.068 | 0.290 | 0.316 | 0.000 | 0.363 | 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 | 17 | 17 | 17 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.151 | 0.003 | 0.054 | 0.192 | 0.232 | 0.016 | 0.273 | 0.027 |
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 | 17 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.154 | 0.003 | 0.043 | 0.196 | 0.260 | 0.017 | 0.284 | 0.023 |
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 | 17 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.152 | 0.002 | 0.061 | 0.215 | 0.229 | 0.017 | 0.272 | 0.022 |
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 | 17 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.160 | 0.002 | 0.043 | 0.197 | 0.230 | 0.016 | 0.285 | 0.022 |
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 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 0.83 |
time (sec) |
N/A | 0.149 | 0.001 | 0.015 | 0.193 | 0.241 | 0.015 | 0.280 | 0.019 |
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 | 14 | 11 | 10 | 12 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.08 | 0.85 | 0.77 | 0.92 | 0.85 |
time (sec) |
N/A | 0.147 | 0.006 | 0.016 | 0.188 | 0.234 | 0.036 | 0.281 | 0.026 |
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 | 10 | 10 | 10 | 11 | 10 | 13 | 5 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.30 | 0.50 | 1.00 | 1.00 |
time (sec) |
N/A | 0.140 | 0.001 | 0.013 | 0.189 | 0.260 | 0.029 | 0.280 | 0.027 |
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 | 14 | 17 | 10 | 20 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.08 | 1.31 | 0.77 | 1.54 | 0.85 |
time (sec) |
N/A | 0.153 | 0.005 | 0.018 | 0.199 | 0.250 | 0.044 | 0.279 | 0.047 |
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 | 14 | 13 | 13 | 14 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.93 | 0.87 | 0.87 |
time (sec) |
N/A | 0.158 | 0.003 | 0.014 | 0.199 | 0.259 | 0.049 | 0.276 | 0.028 |
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 | 17 | 14 | 14 | 13 | 14 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.82 | 0.76 | 0.82 | 0.76 | 0.76 |
time (sec) |
N/A | 0.159 | 0.003 | 0.017 | 0.187 | 0.264 | 0.052 | 0.272 | 0.028 |
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 | 17 | 14 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.157 | 0.003 | 0.018 | 0.201 | 0.299 | 0.060 | 0.291 | 0.028 |
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 | 17 | 14 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.154 | 0.003 | 0.016 | 0.192 | 0.267 | 0.060 | 0.270 | 0.029 |
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 | 17 | 14 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.156 | 0.003 | 0.017 | 0.189 | 0.233 | 0.065 | 0.278 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 25 | 24 | 24 | 26 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.87 | 0.80 | 0.80 |
time (sec) |
N/A | 0.176 | 0.001 | 0.056 | 0.202 | 0.252 | 0.019 | 0.278 | 5.931 |
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 | 16 | 16 | 16 | 15 | 24 | 24 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.50 | 1.50 | 1.50 | 1.50 | 1.50 |
time (sec) |
N/A | 0.144 | 0.003 | 0.046 | 0.188 | 0.275 | 0.020 | 0.264 | 0.035 |
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 | 25 | 22 | 21 | 21 | 22 | 21 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.84 | 0.84 | 0.88 | 0.84 | 0.84 |
time (sec) |
N/A | 0.164 | 0.002 | 0.017 | 0.188 | 0.238 | 0.017 | 0.269 | 0.033 |
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 | 30 | 23 | 22 | 24 | 21 | 20 | 22 | 21 |
N.S. |
1 | 1.30 | 1.00 | 0.96 | 1.04 | 0.91 | 0.87 | 0.96 | 0.91 |
time (sec) |
N/A | 0.171 | 0.002 | 0.037 | 0.181 | 0.275 | 0.037 | 0.276 | 5.959 |
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 | 24 | 23 | 22 | 25 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.92 | 1.04 | 0.79 | 0.92 | 0.92 |
time (sec) |
N/A | 0.166 | 0.001 | 0.019 | 0.185 | 0.248 | 0.035 | 0.280 | 0.036 |
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 | 28 | 27 | 24 | 24 | 27 | 24 | 24 | 23 |
N.S. |
1 | 1.04 | 1.00 | 0.89 | 0.89 | 1.00 | 0.89 | 0.89 | 0.85 |
time (sec) |
N/A | 0.174 | 0.008 | 0.024 | 0.181 | 0.273 | 0.055 | 0.278 | 5.942 |
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 | 23 | 23 | 22 | 21 | 26 | 22 | 22 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.91 | 1.13 | 0.96 | 0.96 | 1.04 |
time (sec) |
N/A | 0.165 | 0.007 | 0.019 | 0.194 | 0.463 | 0.059 | 0.263 | 0.027 |
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 | 30 | 24 | 23 | 26 | 28 | 24 | 34 | 24 |
N.S. |
1 | 1.25 | 1.00 | 0.96 | 1.08 | 1.17 | 1.00 | 1.42 | 1.00 |
time (sec) |
N/A | 0.173 | 0.001 | 0.021 | 0.190 | 0.267 | 0.077 | 0.267 | 0.048 |
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 | 28 | 28 | 25 | 26 | 26 | 27 | 26 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.93 | 0.93 | 0.96 | 0.93 | 0.89 |
time (sec) |
N/A | 0.172 | 0.001 | 0.019 | 0.196 | 0.240 | 0.080 | 0.275 | 0.040 |
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 | 16 | 16 | 30 | 25 | 14 | 24 | 26 | 24 | 26 |
N.S. |
1 | 1.00 | 1.88 | 1.56 | 0.88 | 1.50 | 1.62 | 1.50 | 1.62 |
time (sec) |
N/A | 0.139 | 0.001 | 0.019 | 0.193 | 0.242 | 0.088 | 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 | 30 | 30 | 30 | 25 | 26 | 26 | 27 | 26 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.87 | 0.87 | 0.90 | 0.87 | 0.87 |
time (sec) |
N/A | 0.175 | 0.001 | 0.019 | 0.184 | 0.269 | 0.093 | 0.270 | 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 | 30 | 34 | 30 | 25 | 26 | 26 | 27 | 26 | 26 |
N.S. |
1 | 1.13 | 1.00 | 0.83 | 0.87 | 0.87 | 0.90 | 0.87 | 0.87 |
time (sec) |
N/A | 0.176 | 0.001 | 0.020 | 0.191 | 0.266 | 0.100 | 0.300 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 25 | 26 | 26 | 27 | 26 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.87 | 0.87 | 0.90 | 0.87 | 0.87 |
time (sec) |
N/A | 0.170 | 0.001 | 0.020 | 0.184 | 0.262 | 0.111 | 0.273 | 0.044 |
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 | 35 | 35 | 35 | 32 | 31 | 31 | 32 | 31 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.89 | 0.89 | 0.91 | 0.89 | 0.89 |
time (sec) |
N/A | 0.177 | 0.002 | 0.021 | 0.185 | 0.255 | 0.020 | 0.287 | 0.047 |
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 | 39 | 34 | 36 | 33 | 37 | 36 | 33 |
N.S. |
1 | 1.10 | 1.00 | 0.87 | 0.92 | 0.85 | 0.95 | 0.92 | 0.85 |
time (sec) |
N/A | 0.183 | 0.007 | 0.027 | 0.183 | 0.276 | 0.044 | 0.288 | 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 | 34 | 34 | 34 | 33 | 32 | 36 | 29 | 32 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 0.94 | 1.06 | 0.85 | 0.94 | 0.94 |
time (sec) |
N/A | 0.180 | 0.005 | 0.022 | 0.193 | 0.258 | 0.040 | 0.293 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 42 | 40 | 35 | 36 | 38 | 37 | 35 | 34 |
N.S. |
1 | 1.05 | 1.00 | 0.88 | 0.90 | 0.95 | 0.92 | 0.88 | 0.85 |
time (sec) |
N/A | 0.186 | 0.009 | 0.042 | 0.193 | 0.257 | 0.058 | 0.267 | 0.041 |
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 | 37 | 37 | 34 | 34 | 36 | 36 | 34 | 36 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.92 | 0.97 | 0.97 | 0.92 | 0.97 |
time (sec) |
N/A | 0.181 | 0.005 | 0.023 | 0.180 | 0.236 | 0.064 | 0.378 | 5.984 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 41 | 40 | 35 | 37 | 39 | 37 | 36 | 37 |
N.S. |
1 | 1.02 | 1.00 | 0.88 | 0.92 | 0.98 | 0.92 | 0.90 | 0.92 |
time (sec) |
N/A | 0.184 | 0.008 | 0.025 | 0.184 | 0.240 | 0.087 | 0.362 | 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 | 34 | 34 | 34 | 33 | 32 | 37 | 34 | 33 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 0.94 | 1.09 | 1.00 | 0.97 | 1.00 |
time (sec) |
N/A | 0.176 | 0.007 | 0.027 | 0.182 | 0.263 | 0.095 | 0.270 | 0.033 |
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 | 39 | 34 | 39 | 39 | 37 | 47 | 36 |
N.S. |
1 | 1.10 | 1.00 | 0.87 | 1.00 | 1.00 | 0.95 | 1.21 | 0.92 |
time (sec) |
N/A | 0.187 | 0.006 | 0.022 | 0.184 | 0.269 | 0.118 | 0.271 | 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 | 39 | 39 | 39 | 36 | 37 | 37 | 39 | 37 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.95 | 0.95 | 1.00 | 0.95 | 0.90 |
time (sec) |
N/A | 0.181 | 0.005 | 0.023 | 0.190 | 0.237 | 0.122 | 0.277 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 43 | 36 | 14 | 35 | 37 | 35 | 37 |
N.S. |
1 | 1.00 | 2.69 | 2.25 | 0.88 | 2.19 | 2.31 | 2.19 | 2.31 |
time (sec) |
N/A | 0.141 | 0.009 | 0.022 | 0.188 | 0.240 | 0.128 | 0.275 | 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 | 43 | 43 | 43 | 36 | 37 | 37 | 39 | 37 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.86 | 0.86 | 0.91 | 0.86 | 0.86 |
time (sec) |
N/A | 0.182 | 0.006 | 0.020 | 0.196 | 0.252 | 0.133 | 0.276 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 44 | 43 | 36 | 37 | 37 | 39 | 37 | 37 |
N.S. |
1 | 1.10 | 1.08 | 0.90 | 0.92 | 0.92 | 0.98 | 0.92 | 0.92 |
time (sec) |
N/A | 0.159 | 0.006 | 0.022 | 0.184 | 0.261 | 0.148 | 0.267 | 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 | 43 | 43 | 43 | 36 | 37 | 37 | 39 | 37 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.86 | 0.86 | 0.91 | 0.86 | 0.86 |
time (sec) |
N/A | 0.181 | 0.009 | 0.023 | 0.190 | 0.275 | 0.147 | 0.272 | 0.035 |
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 | 68 | 68 | 68 | 60 | 60 | 148 | 107 | 65 | 54 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.88 | 2.18 | 1.57 | 0.96 | 0.79 |
time (sec) |
N/A | 0.199 | 0.031 | 0.075 | 0.282 | 0.296 | 0.088 | 0.276 | 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 | 53 | 52 | 53 | 46 | 46 | 45 | 44 | 47 | 45 |
N.S. |
1 | 0.98 | 1.00 | 0.87 | 0.87 | 0.85 | 0.83 | 0.89 | 0.85 |
time (sec) |
N/A | 0.198 | 0.007 | 0.026 | 0.190 | 0.269 | 0.070 | 0.273 | 0.071 |
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 | 55 | 49 | 50 | 126 | 95 | 55 | 43 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.91 | 2.29 | 1.73 | 1.00 | 0.78 |
time (sec) |
N/A | 0.193 | 0.025 | 0.032 | 0.271 | 0.259 | 0.094 | 0.276 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 39 | 40 | 34 | 34 | 33 | 32 | 35 | 33 |
N.S. |
1 | 0.98 | 1.00 | 0.85 | 0.85 | 0.82 | 0.80 | 0.88 | 0.82 |
time (sec) |
N/A | 0.187 | 0.007 | 0.040 | 0.194 | 0.233 | 0.068 | 0.280 | 5.938 |
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 | 42 | 42 | 42 | 38 | 37 | 99 | 80 | 40 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.88 | 2.36 | 1.90 | 0.95 | 0.76 |
time (sec) |
N/A | 0.185 | 0.021 | 0.030 | 0.285 | 0.247 | 0.077 | 0.289 | 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 | 27 | 26 | 27 | 23 | 23 | 22 | 20 | 24 | 22 |
N.S. |
1 | 0.96 | 1.00 | 0.85 | 0.85 | 0.81 | 0.74 | 0.89 | 0.81 |
time (sec) |
N/A | 0.173 | 0.008 | 0.020 | 0.190 | 0.230 | 0.058 | 0.288 | 0.043 |
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 | 31 | 31 | 31 | 27 | 26 | 82 | 56 | 26 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.84 | 2.65 | 1.81 | 0.84 | 0.74 |
time (sec) |
N/A | 0.155 | 0.011 | 0.026 | 0.282 | 0.261 | 0.067 | 0.282 | 5.771 |
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 | 14 | 13 | 13 | 10 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.67 | 0.93 | 0.87 |
time (sec) |
N/A | 0.148 | 0.003 | 0.017 | 0.190 | 0.251 | 0.045 | 0.275 | 0.031 |
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 | 24 | 24 | 16 | 15 | 67 | 53 | 15 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.62 | 2.79 | 2.21 | 0.62 | 0.67 |
time (sec) |
N/A | 0.146 | 0.006 | 0.022 | 0.289 | 0.261 | 0.058 | 0.290 | 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 | 15 | 15 | 22 | 14 | 13 | 18 | 15 | 24 | 18 |
N.S. |
1 | 1.00 | 1.47 | 0.93 | 0.87 | 1.20 | 1.00 | 1.60 | 1.20 |
time (sec) |
N/A | 0.138 | 0.008 | 0.023 | 0.193 | 0.233 | 0.095 | 0.275 | 5.855 |
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 | 34 | 34 | 34 | 30 | 29 | 82 | 65 | 29 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.85 | 2.41 | 1.91 | 0.85 | 0.76 |
time (sec) |
N/A | 0.157 | 0.015 | 0.034 | 0.301 | 0.254 | 0.081 | 0.278 | 0.048 |
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 | 36 | 35 | 32 | 33 | 33 | 31 | 43 | 31 |
N.S. |
1 | 1.03 | 1.00 | 0.91 | 0.94 | 0.94 | 0.89 | 1.23 | 0.89 |
time (sec) |
N/A | 0.179 | 0.009 | 0.026 | 0.228 | 0.251 | 0.127 | 0.265 | 0.076 |
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 | 43 | 51 | 43 | 39 | 40 | 106 | 87 | 40 | 37 |
N.S. |
1 | 1.19 | 1.00 | 0.91 | 0.93 | 2.47 | 2.02 | 0.93 | 0.86 |
time (sec) |
N/A | 0.169 | 0.024 | 0.043 | 0.277 | 0.407 | 0.115 | 0.291 | 5.796 |
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 | 50 | 49 | 44 | 47 | 45 | 42 | 57 | 46 |
N.S. |
1 | 1.02 | 1.00 | 0.90 | 0.96 | 0.92 | 0.86 | 1.16 | 0.94 |
time (sec) |
N/A | 0.197 | 0.013 | 0.027 | 0.215 | 0.273 | 0.150 | 0.281 | 0.084 |
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 | 58 | 68 | 58 | 52 | 52 | 132 | 100 | 52 | 48 |
N.S. |
1 | 1.17 | 1.00 | 0.90 | 0.90 | 2.28 | 1.72 | 0.90 | 0.83 |
time (sec) |
N/A | 0.185 | 0.026 | 0.041 | 0.293 | 0.280 | 0.127 | 0.300 | 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 | 92 | 95 | 82 | 74 | 82 | 212 | 134 | 84 | 77 |
N.S. |
1 | 1.03 | 0.89 | 0.80 | 0.89 | 2.30 | 1.46 | 0.91 | 0.84 |
time (sec) |
N/A | 0.216 | 0.065 | 0.039 | 0.284 | 0.278 | 0.154 | 0.281 | 6.117 |
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 | 70 | 68 | 60 | 63 | 65 | 81 | 66 | 80 | 68 |
N.S. |
1 | 0.97 | 0.86 | 0.90 | 0.93 | 1.16 | 0.94 | 1.14 | 0.97 |
time (sec) |
N/A | 0.222 | 0.023 | 0.034 | 0.187 | 0.275 | 0.126 | 0.278 | 0.071 |
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 | 79 | 82 | 71 | 65 | 71 | 190 | 124 | 73 | 66 |
N.S. |
1 | 1.04 | 0.90 | 0.82 | 0.90 | 2.41 | 1.57 | 0.92 | 0.84 |
time (sec) |
N/A | 0.217 | 0.052 | 0.035 | 0.298 | 0.278 | 0.145 | 0.277 | 6.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 56 | 49 | 54 | 54 | 70 | 53 | 55 | 57 |
N.S. |
1 | 0.98 | 0.86 | 0.95 | 0.95 | 1.23 | 0.93 | 0.96 | 1.00 |
time (sec) |
N/A | 0.204 | 0.017 | 0.062 | 0.234 | 0.257 | 0.121 | 0.269 | 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 | 66 | 69 | 60 | 53 | 59 | 164 | 107 | 61 | 56 |
N.S. |
1 | 1.05 | 0.91 | 0.80 | 0.89 | 2.48 | 1.62 | 0.92 | 0.85 |
time (sec) |
N/A | 0.197 | 0.045 | 0.037 | 0.284 | 0.283 | 0.138 | 0.282 | 0.074 |
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 | 43 | 38 | 41 | 43 | 56 | 39 | 41 | 45 |
N.S. |
1 | 0.98 | 0.86 | 0.93 | 0.98 | 1.27 | 0.89 | 0.93 | 1.02 |
time (sec) |
N/A | 0.189 | 0.021 | 0.029 | 0.200 | 0.251 | 0.107 | 0.276 | 5.920 |
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 | 58 | 51 | 42 | 45 | 136 | 83 | 42 | 43 |
N.S. |
1 | 1.05 | 0.93 | 0.76 | 0.82 | 2.47 | 1.51 | 0.76 | 0.78 |
time (sec) |
N/A | 0.173 | 0.035 | 0.034 | 0.285 | 0.255 | 0.119 | 0.273 | 5.905 |
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 | 31 | 27 | 30 | 32 | 35 | 29 | 32 | 29 |
N.S. |
1 | 0.94 | 0.82 | 0.91 | 0.97 | 1.06 | 0.88 | 0.97 | 0.88 |
time (sec) |
N/A | 0.172 | 0.010 | 0.026 | 0.290 | 0.263 | 0.085 | 0.276 | 0.045 |
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 | 45 | 45 | 45 | 36 | 36 | 120 | 78 | 35 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.80 | 2.67 | 1.73 | 0.78 | 0.73 |
time (sec) |
N/A | 0.157 | 0.024 | 0.031 | 0.381 | 0.253 | 0.096 | 0.268 | 0.042 |
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 | 16 | 16 | 15 | 14 | 15 | 15 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.94 | 0.94 | 0.88 | 0.88 |
time (sec) |
N/A | 0.141 | 0.002 | 0.019 | 0.299 | 0.268 | 0.068 | 0.272 | 0.026 |
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 | 45 | 45 | 45 | 36 | 35 | 120 | 78 | 35 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.78 | 2.67 | 1.73 | 0.78 | 0.73 |
time (sec) |
N/A | 0.158 | 0.027 | 0.031 | 0.379 | 0.302 | 0.097 | 0.267 | 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 | 38 | 39 | 33 | 35 | 37 | 47 | 34 | 47 | 34 |
N.S. |
1 | 1.03 | 0.87 | 0.92 | 0.97 | 1.24 | 0.89 | 1.24 | 0.89 |
time (sec) |
N/A | 0.188 | 0.017 | 0.030 | 0.234 | 0.265 | 0.142 | 0.276 | 0.061 |
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 | 61 | 54 | 45 | 49 | 136 | 92 | 47 | 44 |
N.S. |
1 | 1.07 | 0.95 | 0.79 | 0.86 | 2.39 | 1.61 | 0.82 | 0.77 |
time (sec) |
N/A | 0.176 | 0.040 | 0.039 | 0.293 | 0.271 | 0.141 | 0.273 | 5.942 |
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 | 52 | 41 | 54 | 52 | 73 | 51 | 51 | 51 |
N.S. |
1 | 1.06 | 0.84 | 1.10 | 1.06 | 1.49 | 1.04 | 1.04 | 1.04 |
time (sec) |
N/A | 0.196 | 0.039 | 0.038 | 0.211 | 0.281 | 0.175 | 0.282 | 5.639 |
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 | 68 | 78 | 67 | 55 | 64 | 172 | 114 | 59 | 58 |
N.S. |
1 | 1.15 | 0.99 | 0.81 | 0.94 | 2.53 | 1.68 | 0.87 | 0.85 |
time (sec) |
N/A | 0.191 | 0.043 | 0.045 | 0.297 | 0.262 | 0.177 | 0.269 | 5.551 |
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 | 66 | 68 | 57 | 65 | 70 | 90 | 68 | 86 | 67 |
N.S. |
1 | 1.03 | 0.86 | 0.98 | 1.06 | 1.36 | 1.03 | 1.30 | 1.02 |
time (sec) |
N/A | 0.215 | 0.060 | 0.038 | 0.203 | 0.250 | 0.220 | 0.266 | 0.084 |
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 | 87 | 89 | 71 | 76 | 89 | 115 | 92 | 92 | 90 |
N.S. |
1 | 1.02 | 0.82 | 0.87 | 1.02 | 1.32 | 1.06 | 1.06 | 1.03 |
time (sec) |
N/A | 0.234 | 0.060 | 0.040 | 0.193 | 0.245 | 0.217 | 0.286 | 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 | 98 | 109 | 88 | 74 | 93 | 256 | 144 | 84 | 87 |
N.S. |
1 | 1.11 | 0.90 | 0.76 | 0.95 | 2.61 | 1.47 | 0.86 | 0.89 |
time (sec) |
N/A | 0.234 | 0.053 | 0.047 | 0.271 | 0.282 | 0.226 | 0.271 | 5.657 |
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 | 74 | 76 | 58 | 65 | 77 | 103 | 78 | 69 | 78 |
N.S. |
1 | 1.03 | 0.78 | 0.88 | 1.04 | 1.39 | 1.05 | 0.93 | 1.05 |
time (sec) |
N/A | 0.218 | 0.051 | 0.069 | 0.185 | 0.260 | 0.204 | 0.266 | 5.864 |
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 | 85 | 96 | 77 | 62 | 82 | 230 | 133 | 73 | 77 |
N.S. |
1 | 1.13 | 0.91 | 0.73 | 0.96 | 2.71 | 1.56 | 0.86 | 0.91 |
time (sec) |
N/A | 0.221 | 0.061 | 0.042 | 0.274 | 0.263 | 0.219 | 0.265 | 5.864 |
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 | 65 | 62 | 48 | 54 | 66 | 91 | 68 | 53 | 68 |
N.S. |
1 | 0.95 | 0.74 | 0.83 | 1.02 | 1.40 | 1.05 | 0.82 | 1.05 |
time (sec) |
N/A | 0.205 | 0.060 | 0.030 | 0.182 | 0.262 | 0.182 | 0.272 | 5.884 |
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 | 74 | 85 | 66 | 51 | 68 | 202 | 107 | 54 | 64 |
N.S. |
1 | 1.15 | 0.89 | 0.69 | 0.92 | 2.73 | 1.45 | 0.73 | 0.86 |
time (sec) |
N/A | 0.189 | 0.051 | 0.038 | 0.268 | 0.260 | 0.196 | 0.276 | 6.096 |
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 | 39 | 42 | 55 | 69 | 53 | 42 | 52 |
N.S. |
1 | 1.04 | 0.80 | 0.86 | 1.12 | 1.41 | 1.08 | 0.86 | 1.06 |
time (sec) |
N/A | 0.197 | 0.018 | 0.029 | 0.188 | 0.258 | 0.157 | 0.262 | 6.069 |
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 | 72 | 55 | 47 | 59 | 188 | 110 | 45 | 56 |
N.S. |
1 | 1.12 | 0.86 | 0.73 | 0.92 | 2.94 | 1.72 | 0.70 | 0.88 |
time (sec) |
N/A | 0.180 | 0.050 | 0.035 | 0.281 | 0.268 | 0.158 | 0.277 | 5.730 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 24 | 15 | 14 | 36 | 36 | 22 | 37 |
N.S. |
1 | 1.00 | 1.50 | 0.94 | 0.88 | 2.25 | 2.25 | 1.38 | 2.31 |
time (sec) |
N/A | 0.139 | 0.008 | 0.031 | 0.232 | 0.258 | 0.131 | 0.302 | 5.617 |
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 | 65 | 70 | 58 | 49 | 62 | 190 | 110 | 50 | 55 |
N.S. |
1 | 1.08 | 0.89 | 0.75 | 0.95 | 2.92 | 1.69 | 0.77 | 0.85 |
time (sec) |
N/A | 0.174 | 0.031 | 0.035 | 0.281 | 0.284 | 0.152 | 0.279 | 5.474 |
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 | 16 | 16 | 15 | 26 | 26 | 27 | 14 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.62 | 1.62 | 1.69 | 0.88 | 1.75 |
time (sec) |
N/A | 0.146 | 0.003 | 0.020 | 0.186 | 0.262 | 0.111 | 0.276 | 5.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 70 | 55 | 57 | 58 | 188 | 105 | 45 | 55 |
N.S. |
1 | 1.13 | 0.89 | 0.92 | 0.94 | 3.03 | 1.69 | 0.73 | 0.89 |
time (sec) |
N/A | 0.175 | 0.036 | 0.032 | 0.264 | 0.255 | 0.160 | 0.279 | 0.071 |
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 | 43 | 46 | 60 | 90 | 56 | 59 | 56 |
N.S. |
1 | 1.02 | 0.80 | 0.85 | 1.11 | 1.67 | 1.04 | 1.09 | 1.04 |
time (sec) |
N/A | 0.193 | 0.035 | 0.036 | 0.192 | 0.359 | 0.207 | 0.276 | 5.710 |
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 | 76 | 88 | 68 | 54 | 71 | 202 | 116 | 57 | 66 |
N.S. |
1 | 1.16 | 0.89 | 0.71 | 0.93 | 2.66 | 1.53 | 0.75 | 0.87 |
time (sec) |
N/A | 0.192 | 0.040 | 0.047 | 0.273 | 0.260 | 0.209 | 0.277 | 5.880 |
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 | 67 | 69 | 59 | 66 | 77 | 119 | 80 | 82 | 75 |
N.S. |
1 | 1.03 | 0.88 | 0.99 | 1.15 | 1.78 | 1.19 | 1.22 | 1.12 |
time (sec) |
N/A | 0.210 | 0.061 | 0.045 | 0.188 | 0.257 | 0.263 | 0.292 | 5.717 |
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 | 87 | 105 | 79 | 64 | 86 | 238 | 138 | 71 | 80 |
N.S. |
1 | 1.21 | 0.91 | 0.74 | 0.99 | 2.74 | 1.59 | 0.82 | 0.92 |
time (sec) |
N/A | 0.207 | 0.050 | 0.052 | 0.265 | 0.274 | 0.234 | 0.273 | 5.869 |
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 | 86 | 88 | 74 | 77 | 92 | 134 | 90 | 80 | 88 |
N.S. |
1 | 1.02 | 0.86 | 0.90 | 1.07 | 1.56 | 1.05 | 0.93 | 1.02 |
time (sec) |
N/A | 0.228 | 0.054 | 0.044 | 0.188 | 0.265 | 0.266 | 0.274 | 5.881 |
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 | 71 | 73 | 94 | 78 | 100 | 152 | 92 | 69 | 54 |
N.S. |
1 | 1.03 | 1.32 | 1.10 | 1.41 | 2.14 | 1.30 | 0.97 | 0.76 |
time (sec) |
N/A | 0.190 | 0.295 | 0.049 | 0.263 | 0.316 | 2.039 | 0.286 | 6.033 |
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 | 21 | 21 | 26 | 27 | 17 | 27 | 41 | 27 | 23 |
N.S. |
1 | 1.00 | 1.24 | 1.29 | 0.81 | 1.29 | 1.95 | 1.29 | 1.10 |
time (sec) |
N/A | 0.149 | 0.007 | 0.023 | 0.183 | 0.272 | 0.444 | 0.294 | 5.688 |
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 | 45 | 58 | 62 | 53 | 127 | 41 | 52 | 35 |
N.S. |
1 | 0.96 | 1.23 | 1.32 | 1.13 | 2.70 | 0.87 | 1.11 | 0.74 |
time (sec) |
N/A | 0.170 | 0.077 | 0.028 | 0.277 | 0.337 | 0.995 | 0.292 | 5.730 |
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 | 42 | 42 | 62 | 63 | 53 | 108 | 56 | 69 | 55 |
N.S. |
1 | 1.00 | 1.48 | 1.50 | 1.26 | 2.57 | 1.33 | 1.64 | 1.31 |
time (sec) |
N/A | 0.166 | 0.053 | 0.022 | 0.262 | 0.310 | 0.850 | 0.296 | 5.716 |
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 | 38 | 43 | 62 | 60 | 49 | 109 | 56 | 61 | 30 |
N.S. |
1 | 1.13 | 1.63 | 1.58 | 1.29 | 2.87 | 1.47 | 1.61 | 0.79 |
time (sec) |
N/A | 0.172 | 0.092 | 0.032 | 0.271 | 0.297 | 0.833 | 0.294 | 5.911 |
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 | 50 | 50 | 60 | 72 | 73 | 129 | 42 | 50 | 39 |
N.S. |
1 | 1.00 | 1.20 | 1.44 | 1.46 | 2.58 | 0.84 | 1.00 | 0.78 |
time (sec) |
N/A | 0.170 | 0.097 | 0.031 | 0.268 | 0.289 | 1.018 | 0.316 | 5.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 28 | 42 | 63 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 1.56 | 2.33 | 3.50 | 1.33 |
time (sec) |
N/A | 0.142 | 0.076 | 0.044 | 0.196 | 0.254 | 0.530 | 0.309 | 5.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 77 | 76 | 86 | 114 | 158 | 92 | 78 | 0 |
N.S. |
1 | 1.04 | 1.03 | 1.16 | 1.54 | 2.14 | 1.24 | 1.05 | 0.00 |
time (sec) |
N/A | 0.193 | 0.143 | 0.037 | 0.271 | 0.300 | 2.010 | 0.294 | 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 | 68 | 71 | 69 | 77 | 98 | 157 | 70 | 68 | 52 |
N.S. |
1 | 1.04 | 1.01 | 1.13 | 1.44 | 2.31 | 1.03 | 1.00 | 0.76 |
time (sec) |
N/A | 0.177 | 0.129 | 0.030 | 0.286 | 0.284 | 1.700 | 0.285 | 6.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 64 | 74 | 78 | 68 | 129 | 78 | 89 | 0 |
N.S. |
1 | 1.05 | 1.21 | 1.28 | 1.11 | 2.11 | 1.28 | 1.46 | 0.00 |
time (sec) |
N/A | 0.186 | 0.078 | 0.028 | 0.273 | 0.287 | 1.330 | 0.285 | 0.000 |