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 | 33 | 33 | 33 | 28 | 27 | 27 | 29 | 29 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.82 | 0.82 | 0.88 | 0.88 | 0.85 |
time (sec) |
N/A | 0.159 | 0.009 | 0.166 | 0.211 | 0.398 | 0.015 | 0.276 | 0.045 |
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 | 37 | 33 | 28 | 27 | 27 | 29 | 29 | 28 |
N.S. |
1 | 1.12 | 1.00 | 0.85 | 0.82 | 0.82 | 0.88 | 0.88 | 0.85 |
time (sec) |
N/A | 0.178 | 0.009 | 0.145 | 0.199 | 0.362 | 0.016 | 0.276 | 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 | 33 | 33 | 33 | 28 | 27 | 27 | 29 | 29 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.82 | 0.82 | 0.88 | 0.88 | 0.85 |
time (sec) |
N/A | 0.185 | 0.006 | 0.133 | 0.214 | 0.348 | 0.017 | 0.269 | 9.028 |
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 | 33 | 34 | 33 | 28 | 27 | 27 | 29 | 29 | 28 |
N.S. |
1 | 1.03 | 1.00 | 0.85 | 0.82 | 0.82 | 0.88 | 0.88 | 0.85 |
time (sec) |
N/A | 0.178 | 0.009 | 0.129 | 0.210 | 0.244 | 0.017 | 0.276 | 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 | 28 | 28 | 28 | 25 | 24 | 24 | 26 | 26 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.86 | 0.86 | 0.93 | 0.93 | 0.89 |
time (sec) |
N/A | 0.168 | 0.006 | 0.203 | 0.209 | 0.246 | 0.017 | 0.272 | 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 | 29 | 32 | 29 | 28 | 28 | 25 | 27 | 30 | 26 |
N.S. |
1 | 1.10 | 1.00 | 0.97 | 0.97 | 0.86 | 0.93 | 1.03 | 0.90 |
time (sec) |
N/A | 0.171 | 0.011 | 0.111 | 0.193 | 0.246 | 0.046 | 0.283 | 9.003 |
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 | 26 | 26 | 24 | 24 | 28 | 20 | 23 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.92 | 1.08 | 0.77 | 0.88 | 0.92 |
time (sec) |
N/A | 0.164 | 0.010 | 0.034 | 0.209 | 0.245 | 0.044 | 0.279 | 9.031 |
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 | 30 | 29 | 26 | 28 | 30 | 26 | 42 | 25 |
N.S. |
1 | 1.03 | 1.00 | 0.90 | 0.97 | 1.03 | 0.90 | 1.45 | 0.86 |
time (sec) |
N/A | 0.168 | 0.014 | 0.036 | 0.226 | 0.252 | 0.093 | 0.295 | 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 | 26 | 26 | 27 | 25 | 26 | 29 | 27 | 28 | 26 |
N.S. |
1 | 1.00 | 1.04 | 0.96 | 1.00 | 1.12 | 1.04 | 1.08 | 1.00 |
time (sec) |
N/A | 0.162 | 0.013 | 0.033 | 0.216 | 0.246 | 0.099 | 0.274 | 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 | 29 | 33 | 31 | 26 | 30 | 31 | 29 | 39 | 29 |
N.S. |
1 | 1.14 | 1.07 | 0.90 | 1.03 | 1.07 | 1.00 | 1.34 | 1.00 |
time (sec) |
N/A | 0.174 | 0.019 | 0.027 | 0.213 | 0.380 | 0.196 | 0.286 | 0.053 |
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 | 31 | 33 | 28 | 29 | 29 | 32 | 31 | 29 |
N.S. |
1 | 1.00 | 1.06 | 0.90 | 0.94 | 0.94 | 1.03 | 1.00 | 0.94 |
time (sec) |
N/A | 0.166 | 0.013 | 0.028 | 0.206 | 0.414 | 0.188 | 0.286 | 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 | 55 | 55 | 55 | 52 | 51 | 51 | 56 | 53 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.93 | 0.93 | 1.02 | 0.96 | 0.93 |
time (sec) |
N/A | 0.216 | 0.012 | 1.787 | 0.207 | 0.405 | 0.024 | 0.278 | 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 | 55 | 59 | 55 | 52 | 51 | 51 | 53 | 53 | 51 |
N.S. |
1 | 1.07 | 1.00 | 0.95 | 0.93 | 0.93 | 0.96 | 0.96 | 0.93 |
time (sec) |
N/A | 0.213 | 0.009 | 1.772 | 0.216 | 0.361 | 0.022 | 0.279 | 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 | 55 | 55 | 55 | 52 | 51 | 51 | 56 | 53 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.93 | 0.93 | 1.02 | 0.96 | 0.93 |
time (sec) |
N/A | 0.198 | 0.012 | 1.797 | 0.204 | 0.258 | 0.025 | 0.272 | 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 | 42 | 46 | 51 | 52 | 51 | 51 | 53 | 53 | 51 |
N.S. |
1 | 1.10 | 1.21 | 1.24 | 1.21 | 1.21 | 1.26 | 1.26 | 1.21 |
time (sec) |
N/A | 0.202 | 0.014 | 1.764 | 0.233 | 0.245 | 0.022 | 0.265 | 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 | 50 | 50 | 50 | 49 | 48 | 48 | 53 | 50 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.96 | 0.96 | 1.06 | 1.00 | 0.96 |
time (sec) |
N/A | 0.194 | 0.010 | 1.793 | 0.260 | 0.251 | 0.022 | 0.457 | 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 | 43 | 50 | 51 | 51 | 52 | 49 | 49 | 53 | 48 |
N.S. |
1 | 1.16 | 1.19 | 1.19 | 1.21 | 1.14 | 1.14 | 1.23 | 1.12 |
time (sec) |
N/A | 0.187 | 0.019 | 1.714 | 0.212 | 0.237 | 0.061 | 0.370 | 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 | 48 | 48 | 48 | 49 | 48 | 53 | 48 | 48 | 48 |
N.S. |
1 | 1.00 | 1.00 | 1.02 | 1.00 | 1.10 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.191 | 0.021 | 1.724 | 0.207 | 0.242 | 0.059 | 0.366 | 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 | 51 | 52 | 49 | 48 | 52 | 54 | 48 | 70 | 48 |
N.S. |
1 | 1.02 | 0.96 | 0.94 | 1.02 | 1.06 | 0.94 | 1.37 | 0.94 |
time (sec) |
N/A | 0.199 | 0.028 | 1.807 | 0.217 | 0.245 | 0.114 | 0.541 | 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 | 48 | 48 | 50 | 46 | 50 | 52 | 51 | 50 | 50 |
N.S. |
1 | 1.00 | 1.04 | 0.96 | 1.04 | 1.08 | 1.06 | 1.04 | 1.04 |
time (sec) |
N/A | 0.191 | 0.022 | 1.726 | 0.231 | 0.254 | 0.123 | 0.277 | 0.050 |
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 | 52 | 50 | 46 | 54 | 55 | 51 | 72 | 51 |
N.S. |
1 | 1.02 | 0.98 | 0.90 | 1.06 | 1.08 | 1.00 | 1.41 | 1.00 |
time (sec) |
N/A | 0.199 | 0.032 | 1.743 | 0.255 | 0.391 | 0.281 | 0.284 | 9.035 |
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 | 48 | 48 | 48 | 45 | 51 | 53 | 54 | 53 | 50 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.06 | 1.10 | 1.12 | 1.10 | 1.04 |
time (sec) |
N/A | 0.189 | 0.023 | 1.713 | 0.202 | 0.478 | 0.313 | 0.289 | 9.035 |
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 | 51 | 55 | 53 | 46 | 55 | 55 | 56 | 66 | 51 |
N.S. |
1 | 1.08 | 1.04 | 0.90 | 1.08 | 1.08 | 1.10 | 1.29 | 1.00 |
time (sec) |
N/A | 0.201 | 0.030 | 1.705 | 0.209 | 0.365 | 0.529 | 0.289 | 9.174 |
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 | 53 | 59 | 48 | 53 | 53 | 58 | 55 | 52 |
N.S. |
1 | 1.00 | 1.11 | 0.91 | 1.00 | 1.00 | 1.09 | 1.04 | 0.98 |
time (sec) |
N/A | 0.197 | 0.020 | 1.729 | 0.207 | 0.311 | 0.570 | 0.291 | 9.001 |
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 | 75 | 75 | 75 | 76 | 73 | 73 | 80 | 77 | 69 |
N.S. |
1 | 1.00 | 1.00 | 1.01 | 0.97 | 0.97 | 1.07 | 1.03 | 0.92 |
time (sec) |
N/A | 0.221 | 0.016 | 1.781 | 0.219 | 0.262 | 0.026 | 0.291 | 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 | 68 | 72 | 69 | 76 | 73 | 73 | 82 | 77 | 69 |
N.S. |
1 | 1.06 | 1.01 | 1.12 | 1.07 | 1.07 | 1.21 | 1.13 | 1.01 |
time (sec) |
N/A | 0.231 | 0.021 | 1.767 | 0.224 | 0.251 | 0.028 | 0.286 | 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 | 75 | 75 | 75 | 76 | 73 | 73 | 82 | 77 | 69 |
N.S. |
1 | 1.00 | 1.00 | 1.01 | 0.97 | 0.97 | 1.09 | 1.03 | 0.92 |
time (sec) |
N/A | 0.211 | 0.013 | 1.792 | 0.215 | 0.260 | 0.028 | 0.282 | 0.032 |
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 | 42 | 46 | 69 | 76 | 73 | 73 | 80 | 77 | 69 |
N.S. |
1 | 1.10 | 1.64 | 1.81 | 1.74 | 1.74 | 1.90 | 1.83 | 1.64 |
time (sec) |
N/A | 0.193 | 0.021 | 1.773 | 0.219 | 0.270 | 0.028 | 0.288 | 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 | 70 | 70 | 70 | 73 | 70 | 70 | 76 | 73 | 65 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.00 | 1.00 | 1.09 | 1.04 | 0.93 |
time (sec) |
N/A | 0.210 | 0.013 | 1.794 | 0.217 | 0.233 | 0.024 | 0.281 | 0.031 |
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 | 63 | 71 | 76 | 74 | 71 | 80 | 78 | 67 |
N.S. |
1 | 1.05 | 1.18 | 1.27 | 1.23 | 1.18 | 1.33 | 1.30 | 1.12 |
time (sec) |
N/A | 0.195 | 0.023 | 1.722 | 0.206 | 0.248 | 0.079 | 0.292 | 0.037 |
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 | 65 | 65 | 71 | 69 | 75 | 68 | 70 | 65 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.06 | 1.15 | 1.05 | 1.08 | 1.00 |
time (sec) |
N/A | 0.205 | 0.026 | 1.730 | 0.209 | 0.245 | 0.077 | 0.286 | 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 | 71 | 73 | 73 | 73 | 74 | 77 | 78 | 97 | 67 |
N.S. |
1 | 1.03 | 1.03 | 1.03 | 1.04 | 1.08 | 1.10 | 1.37 | 0.94 |
time (sec) |
N/A | 0.223 | 0.033 | 1.764 | 0.212 | 0.238 | 0.128 | 0.269 | 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 | 69 | 69 | 71 | 70 | 73 | 75 | 75 | 74 | 68 |
N.S. |
1 | 1.00 | 1.03 | 1.01 | 1.06 | 1.09 | 1.09 | 1.07 | 0.99 |
time (sec) |
N/A | 0.219 | 0.026 | 1.909 | 0.206 | 0.256 | 0.138 | 0.267 | 0.058 |
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 | 72 | 73 | 73 | 68 | 76 | 76 | 75 | 98 | 76 |
N.S. |
1 | 1.01 | 1.01 | 0.94 | 1.06 | 1.06 | 1.04 | 1.36 | 1.06 |
time (sec) |
N/A | 0.221 | 0.034 | 1.879 | 0.238 | 0.243 | 0.306 | 0.276 | 8.875 |
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 | 64 | 73 | 75 | 78 | 75 | 73 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.07 | 1.10 | 1.15 | 1.10 | 1.07 |
time (sec) |
N/A | 0.208 | 0.028 | 1.916 | 0.206 | 0.238 | 0.339 | 0.279 | 0.057 |
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 | 72 | 71 | 64 | 77 | 77 | 78 | 99 | 75 |
N.S. |
1 | 1.01 | 1.00 | 0.90 | 1.08 | 1.08 | 1.10 | 1.39 | 1.06 |
time (sec) |
N/A | 0.221 | 0.040 | 2.157 | 0.233 | 0.236 | 0.667 | 0.284 | 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 | 66 | 66 | 66 | 63 | 73 | 75 | 80 | 77 | 71 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 1.11 | 1.14 | 1.21 | 1.17 | 1.08 |
time (sec) |
N/A | 0.213 | 0.031 | 2.116 | 0.237 | 0.234 | 0.769 | 0.283 | 8.912 |
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 | 77 | 64 | 77 | 77 | 82 | 90 | 75 |
N.S. |
1 | 1.05 | 1.22 | 1.02 | 1.22 | 1.22 | 1.30 | 1.43 | 1.19 |
time (sec) |
N/A | 0.201 | 0.036 | 1.873 | 0.222 | 0.236 | 1.272 | 0.276 | 0.082 |
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 | 73 | 73 | 73 | 66 | 75 | 75 | 83 | 79 | 74 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 1.03 | 1.03 | 1.14 | 1.08 | 1.01 |
time (sec) |
N/A | 0.211 | 0.031 | 1.862 | 0.214 | 0.243 | 2.469 | 0.276 | 8.867 |
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 | 53 | 78 | 66 | 75 | 75 | 83 | 79 | 76 |
N.S. |
1 | 1.08 | 1.59 | 1.35 | 1.53 | 1.53 | 1.69 | 1.61 | 1.55 |
time (sec) |
N/A | 0.173 | 0.021 | 1.856 | 0.198 | 0.235 | 3.521 | 0.291 | 8.907 |
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 | 119 | 93 | 119 | 123 | 124 | 274 | 204 | 133 | 144 |
N.S. |
1 | 0.78 | 1.00 | 1.03 | 1.04 | 2.30 | 1.71 | 1.12 | 1.21 |
time (sec) |
N/A | 0.228 | 0.081 | 1.781 | 0.297 | 0.251 | 0.237 | 0.297 | 0.055 |
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 | 95 | 92 | 92 | 97 | 98 | 94 | 101 | 100 |
N.S. |
1 | 0.99 | 0.96 | 0.96 | 1.01 | 1.02 | 0.98 | 1.05 | 1.04 |
time (sec) |
N/A | 0.266 | 0.045 | 1.772 | 0.231 | 0.250 | 0.190 | 0.292 | 8.933 |
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 | 98 | 80 | 98 | 99 | 100 | 228 | 180 | 108 | 118 |
N.S. |
1 | 0.82 | 1.00 | 1.01 | 1.02 | 2.33 | 1.84 | 1.10 | 1.20 |
time (sec) |
N/A | 0.216 | 0.068 | 1.767 | 0.301 | 0.251 | 0.218 | 0.301 | 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 | 75 | 74 | 71 | 73 | 74 | 75 | 70 | 77 | 76 |
N.S. |
1 | 0.99 | 0.95 | 0.97 | 0.99 | 1.00 | 0.93 | 1.03 | 1.01 |
time (sec) |
N/A | 0.233 | 0.032 | 1.754 | 0.238 | 0.244 | 0.179 | 0.276 | 0.060 |
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 | 77 | 67 | 77 | 75 | 78 | 178 | 153 | 85 | 96 |
N.S. |
1 | 0.87 | 1.00 | 0.97 | 1.01 | 2.31 | 1.99 | 1.10 | 1.25 |
time (sec) |
N/A | 0.207 | 0.055 | 1.821 | 0.309 | 0.246 | 0.196 | 0.271 | 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 | 54 | 53 | 47 | 50 | 50 | 51 | 46 | 52 | 52 |
N.S. |
1 | 0.98 | 0.87 | 0.93 | 0.93 | 0.94 | 0.85 | 0.96 | 0.96 |
time (sec) |
N/A | 0.206 | 0.023 | 1.821 | 0.216 | 0.240 | 0.154 | 0.271 | 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 | 58 | 56 | 57 | 51 | 53 | 129 | 90 | 57 | 70 |
N.S. |
1 | 0.97 | 0.98 | 0.88 | 0.91 | 2.22 | 1.55 | 0.98 | 1.21 |
time (sec) |
N/A | 0.181 | 0.041 | 1.781 | 0.319 | 0.261 | 0.178 | 0.289 | 8.986 |
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 | 34 | 31 | 32 | 31 | 30 | 27 | 32 | 31 |
N.S. |
1 | 0.97 | 0.89 | 0.91 | 0.89 | 0.86 | 0.77 | 0.91 | 0.89 |
time (sec) |
N/A | 0.181 | 0.014 | 1.745 | 0.217 | 0.234 | 0.130 | 0.273 | 0.057 |
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 | 40 | 40 | 40 | 34 | 34 | 99 | 82 | 34 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.85 | 2.48 | 2.05 | 0.85 | 0.78 |
time (sec) |
N/A | 0.158 | 0.023 | 1.849 | 0.325 | 0.255 | 0.144 | 0.274 | 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 | 34 | 37 | 34 | 33 | 35 | 32 | 26 | 34 | 32 |
N.S. |
1 | 1.09 | 1.00 | 0.97 | 1.03 | 0.94 | 0.76 | 1.00 | 0.94 |
time (sec) |
N/A | 0.186 | 0.016 | 2.074 | 0.208 | 0.230 | 0.392 | 0.288 | 8.984 |
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 | 37 | 36 | 105 | 82 | 36 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.86 | 2.50 | 1.95 | 0.86 | 0.83 |
time (sec) |
N/A | 0.186 | 0.029 | 1.800 | 0.304 | 0.238 | 0.169 | 0.280 | 8.966 |
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 | 41 | 41 | 41 | 39 | 51 | 103 | 75 | 38 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 1.24 | 2.51 | 1.83 | 0.93 | 0.80 |
time (sec) |
N/A | 0.188 | 0.028 | 1.789 | 0.298 | 0.240 | 0.183 | 0.286 | 0.112 |
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 | 49 | 46 | 48 | 47 | 41 | 71 | 46 |
N.S. |
1 | 1.04 | 1.00 | 0.94 | 0.98 | 0.96 | 0.84 | 1.45 | 0.94 |
time (sec) |
N/A | 0.203 | 0.025 | 1.729 | 0.226 | 0.268 | 0.401 | 0.272 | 0.108 |
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 | 61 | 58 | 60 | 54 | 56 | 135 | 129 | 57 | 53 |
N.S. |
1 | 0.95 | 0.98 | 0.89 | 0.92 | 2.21 | 2.11 | 0.93 | 0.87 |
time (sec) |
N/A | 0.175 | 0.058 | 1.946 | 0.298 | 0.254 | 0.212 | 0.273 | 8.991 |
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 | 71 | 70 | 64 | 70 | 73 | 61 | 100 | 70 |
N.S. |
1 | 1.01 | 1.00 | 0.91 | 1.00 | 1.04 | 0.87 | 1.43 | 1.00 |
time (sec) |
N/A | 0.221 | 0.033 | 1.962 | 0.217 | 0.237 | 0.454 | 0.293 | 8.940 |
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 | 78 | 75 | 78 | 74 | 79 | 184 | 163 | 81 | 70 |
N.S. |
1 | 0.96 | 1.00 | 0.95 | 1.01 | 2.36 | 2.09 | 1.04 | 0.90 |
time (sec) |
N/A | 0.191 | 0.055 | 1.991 | 0.287 | 0.446 | 0.250 | 0.279 | 8.942 |
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 | 92 | 93 | 96 | 86 | 96 | 98 | 88 | 126 | 92 |
N.S. |
1 | 1.01 | 1.04 | 0.93 | 1.04 | 1.07 | 0.96 | 1.37 | 1.00 |
time (sec) |
N/A | 0.240 | 0.042 | 1.840 | 0.216 | 0.384 | 0.496 | 0.275 | 8.944 |
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 | 133 | 133 | 134 | 123 | 136 | 350 | 238 | 139 | 203 |
N.S. |
1 | 1.00 | 1.01 | 0.92 | 1.02 | 2.63 | 1.79 | 1.05 | 1.53 |
time (sec) |
N/A | 0.416 | 0.113 | 1.802 | 0.342 | 0.548 | 0.419 | 0.280 | 8.881 |
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 | 105 | 102 | 93 | 103 | 107 | 148 | 104 | 135 | 121 |
N.S. |
1 | 0.97 | 0.89 | 0.98 | 1.02 | 1.41 | 0.99 | 1.29 | 1.15 |
time (sec) |
N/A | 0.270 | 0.074 | 1.804 | 0.215 | 0.526 | 0.392 | 0.278 | 0.066 |
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 | 110 | 111 | 111 | 100 | 112 | 298 | 211 | 115 | 141 |
N.S. |
1 | 1.01 | 1.01 | 0.91 | 1.02 | 2.71 | 1.92 | 1.05 | 1.28 |
time (sec) |
N/A | 0.357 | 0.092 | 1.827 | 0.288 | 0.252 | 0.387 | 0.273 | 8.857 |
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 | 83 | 79 | 72 | 76 | 82 | 121 | 78 | 106 | 86 |
N.S. |
1 | 0.95 | 0.87 | 0.92 | 0.99 | 1.46 | 0.94 | 1.28 | 1.04 |
time (sec) |
N/A | 0.238 | 0.061 | 1.881 | 0.201 | 0.245 | 0.366 | 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 | 89 | 89 | 89 | 75 | 85 | 240 | 129 | 88 | 104 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.96 | 2.70 | 1.45 | 0.99 | 1.17 |
time (sec) |
N/A | 0.259 | 0.078 | 1.779 | 0.289 | 0.264 | 0.350 | 0.286 | 8.888 |
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 | 58 | 50 | 59 | 60 | 81 | 56 | 70 | 62 |
N.S. |
1 | 0.95 | 0.82 | 0.97 | 0.98 | 1.33 | 0.92 | 1.15 | 1.02 |
time (sec) |
N/A | 0.212 | 0.043 | 1.763 | 0.201 | 0.279 | 0.311 | 0.288 | 0.075 |
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 | 68 | 57 | 61 | 208 | 114 | 59 | 59 |
N.S. |
1 | 1.04 | 1.00 | 0.84 | 0.90 | 3.06 | 1.68 | 0.87 | 0.87 |
time (sec) |
N/A | 0.195 | 0.056 | 1.843 | 0.294 | 0.247 | 0.274 | 0.277 | 8.893 |
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 | 39 | 41 | 38 | 40 | 44 | 36 | 37 | 37 |
N.S. |
1 | 0.95 | 1.00 | 0.93 | 0.98 | 1.07 | 0.88 | 0.90 | 0.90 |
time (sec) |
N/A | 0.188 | 0.015 | 1.789 | 0.205 | 0.237 | 0.189 | 0.276 | 8.872 |
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 | 63 | 63 | 63 | 57 | 57 | 182 | 112 | 57 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.90 | 2.89 | 1.78 | 0.90 | 0.81 |
time (sec) |
N/A | 0.177 | 0.049 | 1.956 | 0.302 | 0.374 | 0.214 | 0.295 | 8.921 |
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 | 53 | 46 | 48 | 51 | 70 | 46 | 52 | 47 |
N.S. |
1 | 1.04 | 0.90 | 0.94 | 1.00 | 1.37 | 0.90 | 1.02 | 0.92 |
time (sec) |
N/A | 0.202 | 0.035 | 2.024 | 0.200 | 0.371 | 0.227 | 0.271 | 0.126 |
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 | 72 | 70 | 62 | 63 | 210 | 114 | 62 | 63 |
N.S. |
1 | 1.03 | 1.00 | 0.89 | 0.90 | 3.00 | 1.63 | 0.89 | 0.90 |
time (sec) |
N/A | 0.209 | 0.036 | 1.822 | 0.295 | 0.396 | 0.262 | 0.287 | 9.029 |
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 | 73 | 72 | 64 | 76 | 76 | 117 | 70 | 80 | 78 |
N.S. |
1 | 0.99 | 0.88 | 1.04 | 1.04 | 1.60 | 0.96 | 1.10 | 1.07 |
time (sec) |
N/A | 0.233 | 0.058 | 1.754 | 0.215 | 0.504 | 0.532 | 0.303 | 8.937 |
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 | 90 | 100 | 90 | 78 | 93 | 250 | 184 | 85 | 83 |
N.S. |
1 | 1.11 | 1.00 | 0.87 | 1.03 | 2.78 | 2.04 | 0.94 | 0.92 |
time (sec) |
N/A | 0.314 | 0.080 | 1.802 | 0.285 | 0.284 | 0.311 | 0.271 | 8.946 |
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 | 97 | 96 | 85 | 96 | 106 | 154 | 100 | 150 | 100 |
N.S. |
1 | 0.99 | 0.88 | 0.99 | 1.09 | 1.59 | 1.03 | 1.55 | 1.03 |
time (sec) |
N/A | 0.260 | 0.107 | 1.737 | 0.213 | 0.256 | 0.587 | 0.293 | 8.952 |
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 | 111 | 125 | 112 | 99 | 119 | 308 | 218 | 112 | 104 |
N.S. |
1 | 1.13 | 1.01 | 0.89 | 1.07 | 2.77 | 1.96 | 1.01 | 0.94 |
time (sec) |
N/A | 0.462 | 0.090 | 1.833 | 0.289 | 0.270 | 0.357 | 0.280 | 8.992 |
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 | 140 | 150 | 133 | 119 | 147 | 416 | 252 | 138 | 177 |
N.S. |
1 | 1.07 | 0.95 | 0.85 | 1.05 | 2.97 | 1.80 | 0.99 | 1.26 |
time (sec) |
N/A | 0.562 | 0.119 | 1.788 | 0.304 | 0.266 | 0.758 | 0.273 | 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 | 111 | 108 | 94 | 102 | 116 | 179 | 119 | 132 | 118 |
N.S. |
1 | 0.97 | 0.85 | 0.92 | 1.05 | 1.61 | 1.07 | 1.19 | 1.06 |
time (sec) |
N/A | 0.279 | 0.070 | 1.756 | 0.216 | 0.251 | 0.807 | 0.285 | 8.946 |
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 | 118 | 126 | 113 | 95 | 120 | 358 | 214 | 111 | 138 |
N.S. |
1 | 1.07 | 0.96 | 0.81 | 1.02 | 3.03 | 1.81 | 0.94 | 1.17 |
time (sec) |
N/A | 0.404 | 0.096 | 1.817 | 0.290 | 0.263 | 0.683 | 0.281 | 8.973 |
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 | 89 | 86 | 92 | 82 | 94 | 142 | 94 | 93 | 95 |
N.S. |
1 | 0.97 | 1.03 | 0.92 | 1.06 | 1.60 | 1.06 | 1.04 | 1.07 |
time (sec) |
N/A | 0.242 | 0.039 | 1.765 | 0.229 | 0.252 | 0.694 | 0.288 | 0.092 |
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 | 95 | 101 | 92 | 77 | 94 | 328 | 194 | 80 | 92 |
N.S. |
1 | 1.06 | 0.97 | 0.81 | 0.99 | 3.45 | 2.04 | 0.84 | 0.97 |
time (sec) |
N/A | 0.263 | 0.076 | 1.767 | 0.282 | 0.257 | 0.584 | 0.304 | 9.016 |
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 | 65 | 64 | 57 | 72 | 89 | 70 | 55 | 70 |
N.S. |
1 | 0.97 | 0.96 | 0.85 | 1.07 | 1.33 | 1.04 | 0.82 | 1.04 |
time (sec) |
N/A | 0.225 | 0.031 | 1.752 | 0.212 | 0.393 | 0.494 | 0.292 | 8.921 |
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 | 90 | 95 | 83 | 76 | 92 | 301 | 155 | 78 | 82 |
N.S. |
1 | 1.06 | 0.92 | 0.84 | 1.02 | 3.34 | 1.72 | 0.87 | 0.91 |
time (sec) |
N/A | 0.216 | 0.088 | 1.773 | 0.289 | 0.465 | 0.408 | 0.290 | 0.112 |
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 | 32 | 30 | 29 | 42 | 42 | 42 | 28 | 44 |
N.S. |
1 | 1.00 | 0.94 | 0.91 | 1.31 | 1.31 | 1.31 | 0.88 | 1.38 |
time (sec) |
N/A | 0.158 | 0.017 | 1.780 | 0.211 | 0.427 | 0.278 | 0.279 | 8.866 |
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 | 92 | 84 | 77 | 92 | 300 | 150 | 78 | 82 |
N.S. |
1 | 1.00 | 0.91 | 0.84 | 1.00 | 3.26 | 1.63 | 0.85 | 0.89 |
time (sec) |
N/A | 0.196 | 0.064 | 1.836 | 0.286 | 0.401 | 0.302 | 0.286 | 8.967 |
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 | 69 | 59 | 61 | 77 | 119 | 75 | 76 | 71 |
N.S. |
1 | 1.01 | 0.87 | 0.90 | 1.13 | 1.75 | 1.10 | 1.12 | 1.04 |
time (sec) |
N/A | 0.222 | 0.053 | 1.822 | 0.201 | 0.239 | 0.294 | 0.288 | 0.145 |
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 | 96 | 107 | 96 | 82 | 96 | 324 | 194 | 82 | 113 |
N.S. |
1 | 1.11 | 1.00 | 0.85 | 1.00 | 3.38 | 2.02 | 0.85 | 1.18 |
time (sec) |
N/A | 0.268 | 0.066 | 1.836 | 0.294 | 0.267 | 0.358 | 0.282 | 8.984 |
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 | 97 | 96 | 86 | 100 | 109 | 197 | 107 | 105 | 107 |
N.S. |
1 | 0.99 | 0.89 | 1.03 | 1.12 | 2.03 | 1.10 | 1.08 | 1.10 |
time (sec) |
N/A | 0.265 | 0.064 | 1.777 | 0.204 | 0.243 | 0.594 | 0.274 | 8.976 |
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 | 117 | 130 | 119 | 98 | 128 | 368 | 226 | 108 | 114 |
N.S. |
1 | 1.11 | 1.02 | 0.84 | 1.09 | 3.15 | 1.93 | 0.92 | 0.97 |
time (sec) |
N/A | 0.384 | 0.075 | 1.789 | 0.293 | 0.266 | 0.401 | 0.281 | 9.045 |
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 | 121 | 121 | 108 | 123 | 137 | 229 | 136 | 132 | 131 |
N.S. |
1 | 1.00 | 0.89 | 1.02 | 1.13 | 1.89 | 1.12 | 1.09 | 1.08 |
time (sec) |
N/A | 0.292 | 0.084 | 1.789 | 0.207 | 0.249 | 0.668 | 0.280 | 0.132 |
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 | 140 | 159 | 140 | 119 | 154 | 426 | 260 | 135 | 135 |
N.S. |
1 | 1.14 | 1.00 | 0.85 | 1.10 | 3.04 | 1.86 | 0.96 | 0.96 |
time (sec) |
N/A | 0.719 | 0.082 | 1.839 | 0.288 | 0.281 | 0.447 | 0.299 | 9.128 |
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 | 148 | 149 | 135 | 143 | 170 | 267 | 165 | 201 | 155 |
N.S. |
1 | 1.01 | 0.91 | 0.97 | 1.15 | 1.80 | 1.11 | 1.36 | 1.05 |
time (sec) |
N/A | 0.339 | 0.129 | 1.809 | 0.214 | 0.427 | 0.697 | 0.290 | 9.113 |
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 | 218 | 214 | 189 | 178 | 321 | 368 | 345 | 245 | 289 |
N.S. |
1 | 0.98 | 0.87 | 0.82 | 1.47 | 1.69 | 1.58 | 1.12 | 1.33 |
time (sec) |
N/A | 0.391 | 1.399 | 1.873 | 0.223 | 0.533 | 0.768 | 0.297 | 10.298 |
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 | 181 | 180 | 170 | 159 | 273 | 321 | 318 | 211 | 233 |
N.S. |
1 | 0.99 | 0.94 | 0.88 | 1.51 | 1.77 | 1.76 | 1.17 | 1.29 |
time (sec) |
N/A | 0.359 | 1.052 | 1.804 | 0.221 | 0.574 | 0.714 | 0.294 | 9.819 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 128 | 147 | 140 | 225 | 272 | 287 | 177 | 177 |
N.S. |
1 | 1.02 | 1.18 | 1.12 | 1.80 | 2.18 | 2.30 | 1.42 | 1.42 |
time (sec) |
N/A | 0.271 | 0.886 | 1.809 | 0.209 | 0.539 | 0.680 | 0.296 | 9.624 |
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 | 107 | 111 | 126 | 116 | 177 | 223 | 255 | 140 | 140 |
N.S. |
1 | 1.04 | 1.18 | 1.08 | 1.65 | 2.08 | 2.38 | 1.31 | 1.31 |
time (sec) |
N/A | 0.247 | 0.615 | 2.114 | 0.211 | 0.269 | 0.626 | 0.297 | 9.673 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 94 | 97 | 91 | 128 | 172 | 0 | 103 | 117 |
N.S. |
1 | 0.94 | 0.97 | 0.91 | 1.28 | 1.72 | 0.00 | 1.03 | 1.17 |
time (sec) |
N/A | 0.261 | 0.189 | 2.046 | 0.215 | 0.264 | 0.000 | 0.284 | 9.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 89 | 87 | 83 | 105 | 161 | 0 | 87 | 0 |
N.S. |
1 | 0.92 | 0.90 | 0.86 | 1.08 | 1.66 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.265 | 0.263 | 1.845 | 0.211 | 0.282 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 86 | 99 | 86 | 96 | 160 | 0 | 163 | 0 |
N.S. |
1 | 1.08 | 1.24 | 1.08 | 1.20 | 2.00 | 0.00 | 2.04 | 0.00 |
time (sec) |
N/A | 0.260 | 0.164 | 2.038 | 0.215 | 0.277 | 0.000 | 0.442 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 65 | 44 | 47 | 111 | 59 | 0 | 250 | 113 |
N.S. |
1 | 1.07 | 0.72 | 0.77 | 1.82 | 0.97 | 0.00 | 4.10 | 1.85 |
time (sec) |
N/A | 0.228 | 0.164 | 2.007 | 0.216 | 0.268 | 0.000 | 0.696 | 9.256 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 99 | 66 | 66 | 161 | 85 | 0 | 310 | 160 |
N.S. |
1 | 1.03 | 0.69 | 0.69 | 1.68 | 0.89 | 0.00 | 3.23 | 1.67 |
time (sec) |
N/A | 0.262 | 0.191 | 1.807 | 0.215 | 0.294 | 0.000 | 0.891 | 9.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 88 | 84 | 209 | 109 | 0 | 370 | 210 |
N.S. |
1 | 1.00 | 0.66 | 0.63 | 1.57 | 0.82 | 0.00 | 2.78 | 1.58 |
time (sec) |
N/A | 0.293 | 0.245 | 1.795 | 0.213 | 0.289 | 0.000 | 1.404 | 9.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 167 | 110 | 104 | 257 | 133 | 0 | 430 | 260 |
N.S. |
1 | 0.98 | 0.65 | 0.61 | 1.51 | 0.78 | 0.00 | 2.53 | 1.53 |
time (sec) |
N/A | 0.339 | 0.260 | 1.944 | 0.218 | 0.488 | 0.000 | 1.854 | 10.218 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 127 | 82 | 91 | 106 | 106 | 0 | 140 | 103 |
N.S. |
1 | 0.97 | 0.63 | 0.69 | 0.81 | 0.81 | 0.00 | 1.07 | 0.79 |
time (sec) |
N/A | 0.278 | 0.088 | 2.415 | 0.226 | 0.426 | 0.000 | 0.294 | 9.127 |