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 | 26 | 33 | 35 | 30 | 28 | 28 | 32 | 28 | 23 |
N.S. |
1 | 1.27 | 1.35 | 1.15 | 1.08 | 1.08 | 1.23 | 1.08 | 0.88 |
time (sec) |
N/A | 0.167 | 0.016 | 0.128 | 0.190 | 0.249 | 0.065 | 0.250 | 7.984 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 39 | 44 | 45 | 45 | 49 | 0 | 46 |
N.S. |
1 | 0.00 | 1.30 | 1.47 | 1.50 | 1.50 | 1.63 | 0.00 | 1.53 |
time (sec) |
N/A | 0.000 | 0.251 | 114.704 | 0.603 | 0.260 | 22.966 | 0.000 | 8.282 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 49 | 68 | 35 | 65 | 34 | 34 | 36 | 20 |
N.S. |
1 | 2.33 | 3.24 | 1.67 | 3.10 | 1.62 | 1.62 | 1.71 | 0.95 |
time (sec) |
N/A | 0.543 | 0.102 | 0.158 | 0.237 | 0.253 | 0.083 | 0.305 | 8.255 |
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 | 18 | 17 | 17 | 17 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.231 | 0.017 | 1.180 | 0.189 | 0.250 | 0.107 | 0.260 | 8.216 |
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 | 20 | 20 | 21 | 20 | 20 | 20 | 21 | 20 |
N.S. |
1 | 0.77 | 0.77 | 0.81 | 0.77 | 0.77 | 0.77 | 0.81 | 0.77 |
time (sec) |
N/A | 0.164 | 0.007 | 0.051 | 0.177 | 0.245 | 0.168 | 0.256 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 7 | 7 | 8 | 7 | 7 | 7 | 8 | 7 |
N.S. |
1 | 0.88 | 0.88 | 1.00 | 0.88 | 0.88 | 0.88 | 1.00 | 0.88 |
time (sec) |
N/A | 0.139 | 0.001 | 0.036 | 0.177 | 0.247 | 0.027 | 0.252 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | F(-1) | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 46 | 46 | 0 | 45 | 0 | 48 | 0 |
N.S. |
1 | 0.00 | 1.53 | 1.53 | 0.00 | 1.50 | 0.00 | 1.60 | 0.00 |
time (sec) |
N/A | 0.000 | 0.289 | 172.434 | 0.000 | 0.251 | 0.000 | 9.235 | 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 | 30 | 23 | 23 | 24 | 24 | 23 | 24 | 26 | 23 |
N.S. |
1 | 0.77 | 0.77 | 0.80 | 0.80 | 0.77 | 0.80 | 0.87 | 0.77 |
time (sec) |
N/A | 0.407 | 0.227 | 2.770 | 0.214 | 0.255 | 0.098 | 0.278 | 7.900 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 15 | 15 | 14 | 15 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.00 | 0.93 | 1.00 | 1.53 |
time (sec) |
N/A | 0.353 | 0.016 | 0.291 | 0.220 | 0.248 | 0.059 | 0.257 | 8.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 30 | 30 | 32 | 32 | 26 | 30 | 29 |
N.S. |
1 | 0.00 | 1.07 | 1.07 | 1.14 | 1.14 | 0.93 | 1.07 | 1.04 |
time (sec) |
N/A | 0.000 | 3.743 | 0.059 | 0.235 | 0.256 | 0.139 | 0.261 | 0.136 |
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 | 31 | 31 | 28 | 27 | 42 | 24 | 27 | 26 |
N.S. |
1 | 0.97 | 0.97 | 0.88 | 0.84 | 1.31 | 0.75 | 0.84 | 0.81 |
time (sec) |
N/A | 0.498 | 0.030 | 0.249 | 0.310 | 0.259 | 0.158 | 0.268 | 0.326 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 503 | 36 | 53 | 52 | 52 | 51 | 89 | 33 |
N.S. |
1 | 18.63 | 1.33 | 1.96 | 1.93 | 1.93 | 1.89 | 3.30 | 1.22 |
time (sec) |
N/A | 2.938 | 0.439 | 0.119 | 0.244 | 0.242 | 0.100 | 0.282 | 8.284 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 21 | 47 | 25 | 25 | 24 | 63 | 19 |
N.S. |
1 | 0.00 | 0.91 | 2.04 | 1.09 | 1.09 | 1.04 | 2.74 | 0.83 |
time (sec) |
N/A | 0.000 | 0.069 | 0.146 | 0.185 | 0.256 | 0.121 | 0.264 | 8.494 |
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 | 22 | 20 | 21 | 23 | 22 | 20 | 23 | 20 |
N.S. |
1 | 0.92 | 0.83 | 0.88 | 0.96 | 0.92 | 0.83 | 0.96 | 0.83 |
time (sec) |
N/A | 0.284 | 0.145 | 0.647 | 0.296 | 0.249 | 0.219 | 0.273 | 26.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 29 | 29 | 58 | 32 | 26 | 32 | 28 |
N.S. |
1 | 0.00 | 0.94 | 0.94 | 1.87 | 1.03 | 0.84 | 1.03 | 0.90 |
time (sec) |
N/A | 0.000 | 0.296 | 0.523 | 0.249 | 0.278 | 4.763 | 0.286 | 9.250 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 19 | 23 | 0 | 16 | 26 | 0 | 16 |
N.S. |
1 | 0.00 | 0.90 | 1.10 | 0.00 | 0.76 | 1.24 | 0.00 | 0.76 |
time (sec) |
N/A | 0.000 | 0.020 | 0.975 | 0.000 | 0.255 | 0.098 | 0.000 | 0.171 |
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 | 22 | 41 | 21 | 20 | 40 | 40 | 46 | 40 | 37 |
N.S. |
1 | 1.86 | 0.95 | 0.91 | 1.82 | 1.82 | 2.09 | 1.82 | 1.68 |
time (sec) |
N/A | 0.176 | 0.010 | 0.115 | 0.185 | 0.262 | 0.021 | 0.256 | 8.832 |
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 | 28 | 90 | 24 | 21 | 46 | 30 | 26 | 0 | 49 |
N.S. |
1 | 3.21 | 0.86 | 0.75 | 1.64 | 1.07 | 0.93 | 0.00 | 1.75 |
time (sec) |
N/A | 0.988 | 0.062 | 8.058 | 0.331 | 0.260 | 0.149 | 0.000 | 0.251 |
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 | 26 | 23 | 24 | 26 | 35 | 22 | 27 | 26 |
N.S. |
1 | 1.08 | 0.96 | 1.00 | 1.08 | 1.46 | 0.92 | 1.12 | 1.08 |
time (sec) |
N/A | 0.396 | 0.017 | 0.109 | 0.184 | 0.248 | 0.431 | 0.266 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 46 | 16 | 18 | 38 | 23 | 12 | 25 | 17 |
N.S. |
1 | 2.71 | 0.94 | 1.06 | 2.24 | 1.35 | 0.71 | 1.47 | 1.00 |
time (sec) |
N/A | 0.472 | 0.140 | 0.163 | 0.242 | 0.250 | 0.044 | 0.262 | 7.887 |
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 | 15 | 12 | 17 | 19 | 15 | 22 | 18 | 19 |
N.S. |
1 | 1.25 | 1.00 | 1.42 | 1.58 | 1.25 | 1.83 | 1.50 | 1.58 |
time (sec) |
N/A | 0.156 | 0.011 | 0.842 | 0.183 | 0.249 | 0.079 | 0.256 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 34 | 34 | 35 | 33 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.03 | 0.97 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.702 | 0.166 | 0.592 | 0.274 | 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 | 28 | 15 | 15 | 14 | 11 | 14 | 14 | 11 | 14 |
N.S. |
1 | 0.54 | 0.54 | 0.50 | 0.39 | 0.50 | 0.50 | 0.39 | 0.50 |
time (sec) |
N/A | 0.142 | 0.004 | 0.036 | 0.170 | 0.255 | 0.036 | 0.267 | 0.039 |
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 | 22 | 34 | 21 | 20 | 62 | 19 | 17 | 21 | 25 |
N.S. |
1 | 1.55 | 0.95 | 0.91 | 2.82 | 0.86 | 0.77 | 0.95 | 1.14 |
time (sec) |
N/A | 0.239 | 0.043 | 0.053 | 0.179 | 0.268 | 0.047 | 0.260 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 29 | 22 | 27 | 19 | 26 | 26 | 19 | 21 |
N.S. |
1 | 1.21 | 0.92 | 1.12 | 0.79 | 1.08 | 1.08 | 0.79 | 0.88 |
time (sec) |
N/A | 0.537 | 0.855 | 0.484 | 0.301 | 0.263 | 0.217 | 0.276 | 8.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 28 | 21 | 22 | 20 | 20 | 19 | 21 | 10 |
N.S. |
1 | 1.40 | 1.05 | 1.10 | 1.00 | 1.00 | 0.95 | 1.05 | 0.50 |
time (sec) |
N/A | 0.159 | 0.007 | 0.030 | 0.182 | 0.245 | 0.045 | 0.253 | 8.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 18 | 18 | 17 | 16 | 16 | 15 | 16 | 16 |
N.S. |
1 | 0.90 | 0.90 | 0.85 | 0.80 | 0.80 | 0.75 | 0.80 | 0.80 |
time (sec) |
N/A | 0.145 | 0.016 | 0.053 | 0.183 | 0.254 | 0.034 | 0.257 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 150 | 35 | 66 | 49 | 36 | 49 | 293 |
N.S. |
1 | 0.00 | 4.55 | 1.06 | 2.00 | 1.48 | 1.09 | 1.48 | 8.88 |
time (sec) |
N/A | 0.000 | 0.335 | 0.491 | 0.683 | 0.266 | 0.134 | 0.540 | 0.628 |
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 | 19 | 19 | 17 | 16 | 16 | 17 | 16 | 16 |
N.S. |
1 | 0.70 | 0.70 | 0.63 | 0.59 | 0.59 | 0.63 | 0.59 | 0.59 |
time (sec) |
N/A | 0.435 | 0.177 | 0.043 | 0.220 | 0.252 | 0.088 | 0.256 | 8.884 |
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 | 25 | 44 | 44 | 44 | 42 | 42 | 97 | 42 | 76 |
N.S. |
1 | 1.76 | 1.76 | 1.76 | 1.68 | 1.68 | 3.88 | 1.68 | 3.04 |
time (sec) |
N/A | 0.167 | 0.007 | 0.090 | 0.176 | 0.251 | 0.030 | 0.261 | 8.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 30 | 29 | 54 | 59 | 26 | 0 | 23 |
N.S. |
1 | 0.00 | 1.15 | 1.12 | 2.08 | 2.27 | 1.00 | 0.00 | 0.88 |
time (sec) |
N/A | 0.000 | 0.164 | 0.686 | 0.237 | 0.263 | 0.095 | 0.000 | 8.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 45 | 42 | 45 | 39 | 36 | 93 | 98 |
N.S. |
1 | 0.00 | 1.36 | 1.27 | 1.36 | 1.18 | 1.09 | 2.82 | 2.97 |
time (sec) |
N/A | 0.000 | 0.151 | 0.594 | 0.468 | 0.260 | 0.267 | 0.446 | 0.309 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 47 | 20 | 18 | 323 | 19 | 22 | 19 | 21 |
N.S. |
1 | 2.76 | 1.18 | 1.06 | 19.00 | 1.12 | 1.29 | 1.12 | 1.24 |
time (sec) |
N/A | 0.209 | 0.035 | 0.133 | 0.326 | 0.260 | 0.061 | 0.259 | 8.435 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 29 | 31 | 42 | 64 | 64 | 56 | 64 | 37 |
N.S. |
1 | 1.32 | 1.41 | 1.91 | 2.91 | 2.91 | 2.55 | 2.91 | 1.68 |
time (sec) |
N/A | 0.169 | 0.015 | 0.076 | 0.172 | 0.249 | 0.024 | 0.256 | 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 | 13 | 13 | 11 | 9 | 8 | 8 | 7 | 8 | 8 |
N.S. |
1 | 1.00 | 0.85 | 0.69 | 0.62 | 0.62 | 0.54 | 0.62 | 0.62 |
time (sec) |
N/A | 0.196 | 0.030 | 0.026 | 0.193 | 0.258 | 0.036 | 0.257 | 8.470 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 28 | 28 | 44 | 44 | 27 | 55 | 95 |
N.S. |
1 | 0.00 | 1.04 | 1.04 | 1.63 | 1.63 | 1.00 | 2.04 | 3.52 |
time (sec) |
N/A | 0.000 | 0.069 | 0.271 | 0.337 | 0.258 | 0.103 | 0.413 | 8.307 |
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 | 19 | 10 | 10 | 11 | 10 | 11 | 7 | 11 | 10 |
N.S. |
1 | 0.53 | 0.53 | 0.58 | 0.53 | 0.58 | 0.37 | 0.58 | 0.53 |
time (sec) |
N/A | 0.140 | 0.002 | 0.021 | 0.179 | 0.260 | 0.027 | 0.254 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 30 | 29 | 25 | 32 | 20 | 32 | 32 |
N.S. |
1 | 0.00 | 1.11 | 1.07 | 0.93 | 1.19 | 0.74 | 1.19 | 1.19 |
time (sec) |
N/A | 0.000 | 3.350 | 0.062 | 0.254 | 0.254 | 0.125 | 0.254 | 8.552 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 18 | 14 | 14 | 13 | 13 | 14 | 13 | 13 |
N.S. |
1 | 0.90 | 0.70 | 0.70 | 0.65 | 0.65 | 0.70 | 0.65 | 0.65 |
time (sec) |
N/A | 0.142 | 0.015 | 1.013 | 0.187 | 0.255 | 0.070 | 0.252 | 8.313 |
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 | 32 | 32 | 23 | 27 | 23 | 22 | 21 | 20 |
N.S. |
1 | 1.07 | 1.07 | 0.77 | 0.90 | 0.77 | 0.73 | 0.70 | 0.67 |
time (sec) |
N/A | 0.298 | 1.128 | 0.135 | 0.178 | 0.255 | 0.089 | 0.266 | 8.639 |
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 | 28 | 28 | 28 | 29 | 28 | 28 | 26 | 31 | 28 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.00 | 1.00 | 0.93 | 1.11 | 1.00 |
time (sec) |
N/A | 0.312 | 0.018 | 0.035 | 0.192 | 0.241 | 0.064 | 0.252 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 26 | 43 | 0 | 47 | 63 | 0 | 27 |
N.S. |
1 | 0.00 | 1.13 | 1.87 | 0.00 | 2.04 | 2.74 | 0.00 | 1.17 |
time (sec) |
N/A | 0.000 | 0.107 | 0.473 | 0.000 | 0.269 | 0.151 | 0.000 | 8.448 |
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 | 21 | 20 | 18 | 18 | 22 | 17 | 26 | 17 |
N.S. |
1 | 0.72 | 0.69 | 0.62 | 0.62 | 0.76 | 0.59 | 0.90 | 0.59 |
time (sec) |
N/A | 0.705 | 0.155 | 0.328 | 0.304 | 0.264 | 0.138 | 0.259 | 7.918 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 25 | 34 | 123 | 24 | 0 | 25 |
N.S. |
1 | 0.00 | 0.93 | 0.89 | 1.21 | 4.39 | 0.86 | 0.00 | 0.89 |
time (sec) |
N/A | 0.000 | 5.316 | 104.234 | 1.038 | 0.282 | 1.542 | 0.000 | 7.956 |
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 | 28 | 62 | 23 | 19 | 20 | 20 | 15 | 0 | 20 |
N.S. |
1 | 2.21 | 0.82 | 0.68 | 0.71 | 0.71 | 0.54 | 0.00 | 0.71 |
time (sec) |
N/A | 0.284 | 0.092 | 0.135 | 0.317 | 0.266 | 0.095 | 0.000 | 7.893 |
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 | 28 | 29 | 27 | 24 | 23 | 23 | 22 | 23 | 26 |
N.S. |
1 | 1.04 | 0.96 | 0.86 | 0.82 | 0.82 | 0.79 | 0.82 | 0.93 |
time (sec) |
N/A | 0.381 | 1.826 | 0.076 | 0.307 | 0.266 | 0.146 | 0.289 | 7.752 |
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 | 12 | 17 | 12 | 12 | 37 | 14 | 12 | 14 | 11 |
N.S. |
1 | 1.42 | 1.00 | 1.00 | 3.08 | 1.17 | 1.00 | 1.17 | 0.92 |
time (sec) |
N/A | 0.230 | 0.039 | 0.021 | 0.174 | 0.247 | 0.036 | 0.261 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 50 | 46 | 47 | 45 | 0 | 51 | 45 |
N.S. |
1 | 0.00 | 1.79 | 1.64 | 1.68 | 1.61 | 0.00 | 1.82 | 1.61 |
time (sec) |
N/A | 0.000 | 0.236 | 90.316 | 0.264 | 0.277 | 0.000 | 0.517 | 8.049 |
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 | 27 | 46 | 23 | 21 | 41 | 27 | 17 | 39 | 20 |
N.S. |
1 | 1.70 | 0.85 | 0.78 | 1.52 | 1.00 | 0.63 | 1.44 | 0.74 |
time (sec) |
N/A | 0.533 | 0.118 | 0.132 | 0.213 | 0.263 | 0.107 | 0.258 | 8.039 |
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 | 17 | 18 | 17 | 18 | 22 | 17 | 17 | 16 | 17 |
N.S. |
1 | 1.06 | 1.00 | 1.06 | 1.29 | 1.00 | 1.00 | 0.94 | 1.00 |
time (sec) |
N/A | 0.443 | 0.016 | 0.198 | 0.191 | 0.253 | 0.135 | 0.258 | 0.165 |
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 | 25 | 19 | 22 | 24 | 22 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.76 | 0.88 | 0.96 | 0.88 | 0.88 |
time (sec) |
N/A | 0.495 | 0.081 | 0.103 | 0.237 | 0.255 | 0.070 | 0.266 | 9.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 17 | 17 | 15 | 14 | 31 | 14 | 14 | 14 |
N.S. |
1 | 0.63 | 0.63 | 0.56 | 0.52 | 1.15 | 0.52 | 0.52 | 0.52 |
time (sec) |
N/A | 0.145 | 0.018 | 0.033 | 0.207 | 0.248 | 0.048 | 0.251 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 26 | 27 | 33 | 38 | 20 | 23 | 47 |
N.S. |
1 | 0.00 | 0.87 | 0.90 | 1.10 | 1.27 | 0.67 | 0.77 | 1.57 |
time (sec) |
N/A | 0.000 | 0.206 | 0.318 | 0.296 | 0.259 | 0.053 | 0.278 | 8.340 |
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 | 20 | 20 | 20 | 17 | 50 | 16 | 17 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 2.50 | 0.80 | 0.85 | 0.80 | 0.80 |
time (sec) |
N/A | 0.272 | 0.042 | 0.100 | 0.296 | 0.258 | 0.104 | 0.260 | 9.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 40 | 19 | 44 | 38 | 26 | 0 | 27 | 28 |
N.S. |
1 | 1.82 | 0.86 | 2.00 | 1.73 | 1.18 | 0.00 | 1.23 | 1.27 |
time (sec) |
N/A | 2.941 | 0.109 | 1.911 | 0.342 | 0.258 | 0.000 | 0.360 | 8.884 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 35 | 49 | 0 | 52 | 49 | 81 | 55 |
N.S. |
1 | 0.00 | 1.09 | 1.53 | 0.00 | 1.62 | 1.53 | 2.53 | 1.72 |
time (sec) |
N/A | 0.000 | 0.291 | 98.865 | 0.000 | 0.263 | 3.654 | 1.247 | 9.844 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 52 | 34 | 45 | 45 | 29 | 48 | 35 |
N.S. |
1 | 0.00 | 2.36 | 1.55 | 2.05 | 2.05 | 1.32 | 2.18 | 1.59 |
time (sec) |
N/A | 0.000 | 4.713 | 0.063 | 0.219 | 0.255 | 0.241 | 0.258 | 8.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 23 | 12 | 23 | 20 | 20 | 22 | 22 | 27 |
N.S. |
1 | 1.92 | 1.00 | 1.92 | 1.67 | 1.67 | 1.83 | 1.83 | 2.25 |
time (sec) |
N/A | 0.251 | 0.029 | 0.055 | 0.189 | 0.289 | 0.052 | 0.252 | 7.516 |
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 | 24 | 40 | 29 | 27 | 52 | 33 | 24 | 30 | 26 |
N.S. |
1 | 1.67 | 1.21 | 1.12 | 2.17 | 1.38 | 1.00 | 1.25 | 1.08 |
time (sec) |
N/A | 0.490 | 0.059 | 0.063 | 0.188 | 0.253 | 0.075 | 0.254 | 7.837 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 35 | 27 | 61 | 51 | 0 | 29 |
N.S. |
1 | 0.00 | 1.00 | 1.17 | 0.90 | 2.03 | 1.70 | 0.00 | 0.97 |
time (sec) |
N/A | 0.000 | 2.222 | 0.479 | 0.628 | 0.278 | 0.283 | 0.000 | 8.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 48 | 67 | 88 | 167 | 80 | 80 | 0 | 191 |
N.S. |
1 | 1.41 | 1.97 | 2.59 | 4.91 | 2.35 | 2.35 | 0.00 | 5.62 |
time (sec) |
N/A | 32.582 | 0.662 | 6.079 | 1.313 | 0.294 | 0.789 | 0.000 | 9.591 |
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 | 22 | 22 | 27 | 20 | 26 | 22 | 20 | 22 |
N.S. |
1 | 0.76 | 0.76 | 0.93 | 0.69 | 0.90 | 0.76 | 0.69 | 0.76 |
time (sec) |
N/A | 0.565 | 1.792 | 0.350 | 0.261 | 0.258 | 1.100 | 0.282 | 8.671 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | C | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 19 | 19 | 18 | 11 | 20 | 14 | 12 | 16 |
N.S. |
1 | 1.73 | 1.73 | 1.64 | 1.00 | 1.82 | 1.27 | 1.09 | 1.45 |
time (sec) |
N/A | 0.166 | 0.007 | 0.059 | 0.194 | 0.244 | 0.046 | 0.263 | 8.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 27 | 32 | 31 | 31 | 0 | 0 | 31 |
N.S. |
1 | 0.00 | 0.90 | 1.07 | 1.03 | 1.03 | 0.00 | 0.00 | 1.03 |
time (sec) |
N/A | 0.000 | 0.600 | 52.116 | 0.258 | 0.267 | 0.000 | 0.000 | 8.195 |
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 | 20 | 6 | 11 | 5 | 6 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.18 | 0.35 | 0.65 | 0.29 | 0.35 | 0.82 |
time (sec) |
N/A | 0.443 | 0.072 | 0.130 | 0.255 | 0.278 | 0.056 | 0.263 | 8.162 |
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 | 28 | 27 | 20 | 21 | 21 | 26 | 21 | 21 |
N.S. |
1 | 1.12 | 1.08 | 0.80 | 0.84 | 0.84 | 1.04 | 0.84 | 0.84 |
time (sec) |
N/A | 0.139 | 0.005 | 0.045 | 0.185 | 0.240 | 0.023 | 0.271 | 7.823 |
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 | 31 | 35 | 26 | 22 | 27 | 29 | 31 | 66 | 21 |
N.S. |
1 | 1.13 | 0.84 | 0.71 | 0.87 | 0.94 | 1.00 | 2.13 | 0.68 |
time (sec) |
N/A | 0.375 | 0.075 | 0.094 | 0.189 | 0.252 | 0.086 | 0.272 | 0.103 |
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 | 31 | 31 | 22 | 21 | 36 | 26 | 21 | 22 |
N.S. |
1 | 1.03 | 1.03 | 0.73 | 0.70 | 1.20 | 0.87 | 0.70 | 0.73 |
time (sec) |
N/A | 0.169 | 0.064 | 0.060 | 0.180 | 0.250 | 0.116 | 0.273 | 7.953 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 38 | 31 | 26 | 126 | 26 | 27 | 42 | 0 |
N.S. |
1 | 1.46 | 1.19 | 1.00 | 4.85 | 1.00 | 1.04 | 1.62 | 0.00 |
time (sec) |
N/A | 1.472 | 0.096 | 0.530 | 0.216 | 0.269 | 0.143 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 265 | 243 | 28 | 54 | 27 | 24 | 27 | 41 |
N.S. |
1 | 13.25 | 12.15 | 1.40 | 2.70 | 1.35 | 1.20 | 1.35 | 2.05 |
time (sec) |
N/A | 0.650 | 0.078 | 1.231 | 0.191 | 0.266 | 0.076 | 0.274 | 8.445 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 45 | 49 | 29 | 30 | 37 | 46 | 45 |
N.S. |
1 | 0.00 | 1.80 | 1.96 | 1.16 | 1.20 | 1.48 | 1.84 | 1.80 |
time (sec) |
N/A | 0.000 | 0.088 | 1.203 | 0.227 | 0.261 | 0.395 | 0.378 | 8.635 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 31 | 27 | 43 | 36 | 27 | 28 | 28 |
N.S. |
1 | 0.00 | 1.15 | 1.00 | 1.59 | 1.33 | 1.00 | 1.04 | 1.04 |
time (sec) |
N/A | 0.000 | 0.674 | 0.309 | 0.306 | 0.253 | 0.070 | 0.271 | 8.496 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 60 | 45 | 42 | 42 | 37 | 42 | 39 | 42 |
N.S. |
1 | 2.31 | 1.73 | 1.62 | 1.62 | 1.42 | 1.62 | 1.50 | 1.62 |
time (sec) |
N/A | 0.231 | 0.021 | 0.063 | 0.187 | 0.268 | 0.101 | 0.267 | 8.233 |
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 | 26 | 30 | 26 | 23 | 22 | 52 | 19 | 22 | 24 |
N.S. |
1 | 1.15 | 1.00 | 0.88 | 0.85 | 2.00 | 0.73 | 0.85 | 0.92 |
time (sec) |
N/A | 0.260 | 0.444 | 0.374 | 0.196 | 0.257 | 0.182 | 0.290 | 8.866 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 38 | 37 | 49 | 39 | 32 | 5401 | 40 |
N.S. |
1 | 0.00 | 1.23 | 1.19 | 1.58 | 1.26 | 1.03 | 174.23 | 1.29 |
time (sec) |
N/A | 0.000 | 0.122 | 7.016 | 0.379 | 0.256 | 0.499 | 2.010 | 10.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 1292 | 207 | 323 | 1726 | 333 | 366 | 351 | 183 |
N.S. |
1 | 53.83 | 8.62 | 13.46 | 71.92 | 13.88 | 15.25 | 14.62 | 7.62 |
time (sec) |
N/A | 14.492 | 0.273 | 0.241 | 0.259 | 0.267 | 1.550 | 0.304 | 9.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 45 | 43 | 45 | 44 | 0 | 50 |
N.S. |
1 | 0.00 | 0.97 | 1.55 | 1.48 | 1.55 | 1.52 | 0.00 | 1.72 |
time (sec) |
N/A | 0.000 | 0.695 | 0.756 | 0.432 | 0.259 | 0.231 | 0.000 | 8.549 |
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 | 50 | 34 | 27 | 26 | 33 | 20 | 26 | 26 |
N.S. |
1 | 1.39 | 0.94 | 0.75 | 0.72 | 0.92 | 0.56 | 0.72 | 0.72 |
time (sec) |
N/A | 0.344 | 0.027 | 0.093 | 0.188 | 0.253 | 0.467 | 0.266 | 0.171 |
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 | 20 | 17 | 14 | 13 | 15 | 12 | 15 | 14 |
N.S. |
1 | 1.18 | 1.00 | 0.82 | 0.76 | 0.88 | 0.71 | 0.88 | 0.82 |
time (sec) |
N/A | 0.152 | 0.018 | 0.043 | 0.189 | 0.269 | 0.041 | 0.250 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 30 | 57 | 28 | 59 | 54 | 0 | 208 |
N.S. |
1 | 0.00 | 0.91 | 1.73 | 0.85 | 1.79 | 1.64 | 0.00 | 6.30 |
time (sec) |
N/A | 0.000 | 0.460 | 73.442 | 0.740 | 0.264 | 1.164 | 0.000 | 9.883 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 29 | 52 | 73 | 65 | 70 | 0 | 80 |
N.S. |
1 | 0.00 | 1.04 | 1.86 | 2.61 | 2.32 | 2.50 | 0.00 | 2.86 |
time (sec) |
N/A | 0.000 | 8.939 | 0.647 | 0.407 | 0.270 | 1.965 | 0.000 | 10.093 |
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 | 28 | 28 | 29 | 28 | 24 | 28 | 26 |
N.S. |
1 | 1.15 | 1.04 | 1.04 | 1.07 | 1.04 | 0.89 | 1.04 | 0.96 |
time (sec) |
N/A | 0.724 | 0.272 | 0.257 | 0.233 | 0.264 | 0.090 | 0.266 | 9.786 |
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 | 27 | 28 | 25 | 25 | 24 | 24 | 24 | 28 |
N.S. |
1 | 1.12 | 1.17 | 1.04 | 1.04 | 1.00 | 1.00 | 1.00 | 1.17 |
time (sec) |
N/A | 2.473 | 5.147 | 0.783 | 0.287 | 0.269 | 0.510 | 0.344 | 9.842 |
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 | 24 | 17 | 15 | 20 | 14 | 19 | 14 | 19 |
N.S. |
1 | 1.41 | 1.00 | 0.88 | 1.18 | 0.82 | 1.12 | 0.82 | 1.12 |
time (sec) |
N/A | 0.175 | 0.028 | 0.039 | 0.201 | 0.251 | 0.047 | 0.265 | 0.090 |
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 | 23 | 22 | 22 | 39 | 43 | 43 | 41 | 38 | 24 |
N.S. |
1 | 0.96 | 0.96 | 1.70 | 1.87 | 1.87 | 1.78 | 1.65 | 1.04 |
time (sec) |
N/A | 0.183 | 0.010 | 0.101 | 0.284 | 0.249 | 0.051 | 0.264 | 9.422 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 31 | 52 | 0 | 51 | 42 | 100 | 84 |
N.S. |
1 | 0.00 | 0.84 | 1.41 | 0.00 | 1.38 | 1.14 | 2.70 | 2.27 |
time (sec) |
N/A | 0.000 | 0.400 | 86.047 | 0.000 | 0.266 | 9.091 | 0.495 | 10.378 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 43 | 40 | 33 | 0 | 45 | 37 | 55 | 30 |
N.S. |
1 | 1.23 | 1.14 | 0.94 | 0.00 | 1.29 | 1.06 | 1.57 | 0.86 |
time (sec) |
N/A | 0.453 | 0.196 | 0.072 | 0.000 | 0.257 | 0.101 | 0.275 | 0.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 29 | 22 | 26 | 0 | 23 | 22 | 0 | 21 |
N.S. |
1 | 1.32 | 1.00 | 1.18 | 0.00 | 1.05 | 1.00 | 0.00 | 0.95 |
time (sec) |
N/A | 0.276 | 0.240 | 0.148 | 0.000 | 0.264 | 0.064 | 0.000 | 0.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 87 | 59 | 60 | 51 | 51 | 58 | 51 | 46 |
N.S. |
1 | 3.48 | 2.36 | 2.40 | 2.04 | 2.04 | 2.32 | 2.04 | 1.84 |
time (sec) |
N/A | 0.562 | 0.660 | 0.096 | 0.185 | 0.263 | 0.062 | 0.273 | 9.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 41 | 26 | 20 | 0 | 23 | 24 | 23 | 19 |
N.S. |
1 | 2.05 | 1.30 | 1.00 | 0.00 | 1.15 | 1.20 | 1.15 | 0.95 |
time (sec) |
N/A | 0.639 | 0.217 | 0.070 | 0.000 | 0.255 | 0.106 | 0.266 | 9.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 42 | 43 | 55 | 42 | 42 | 56 | 37 |
N.S. |
1 | 0.00 | 1.27 | 1.30 | 1.67 | 1.27 | 1.27 | 1.70 | 1.12 |
time (sec) |
N/A | 0.000 | 0.127 | 0.376 | 0.260 | 0.280 | 0.132 | 0.299 | 9.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 109 | 73 | 32 | 48 | 72 | 46 | 90 | 48 |
N.S. |
1 | 4.19 | 2.81 | 1.23 | 1.85 | 2.77 | 1.77 | 3.46 | 1.85 |
time (sec) |
N/A | 0.426 | 0.041 | 0.352 | 0.198 | 0.257 | 3.143 | 0.272 | 0.266 |
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 | 16 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.94 | 0.94 | 0.94 | 0.94 | 0.94 |
time (sec) |
N/A | 1.445 | 0.243 | 1.013 | 0.570 | 0.255 | 0.063 | 0.303 | 9.795 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 17 | 15 | 14 | 13 | 13 | 12 | 14 | 13 |
N.S. |
1 | 0.94 | 0.83 | 0.78 | 0.72 | 0.72 | 0.67 | 0.78 | 0.72 |
time (sec) |
N/A | 0.156 | 0.002 | 0.020 | 0.189 | 0.249 | 0.030 | 0.263 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 101 | 82 | 29 | 74 | 74 | 88 | 74 | 74 |
N.S. |
1 | 3.61 | 2.93 | 1.04 | 2.64 | 2.64 | 3.14 | 2.64 | 2.64 |
time (sec) |
N/A | 0.215 | 0.045 | 0.131 | 0.193 | 0.235 | 0.028 | 0.267 | 9.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 22 | 21 | 23 | 24 | 44 | 23 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.88 | 0.96 | 1.00 | 1.83 | 0.96 |
time (sec) |
N/A | 0.000 | 0.114 | 0.302 | 0.283 | 0.253 | 0.104 | 0.279 | 9.102 |
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 | 15 | 13 | 12 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.18 | 0.68 | 0.59 | 0.55 | 0.55 | 0.55 | 0.55 | 0.55 |
time (sec) |
N/A | 0.158 | 0.010 | 0.036 | 0.193 | 0.254 | 0.039 | 0.262 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 48 | 48 | 35 | 33 | 33 | 37 | 39 | 37 |
N.S. |
1 | 2.18 | 2.18 | 1.59 | 1.50 | 1.50 | 1.68 | 1.77 | 1.68 |
time (sec) |
N/A | 1.009 | 0.042 | 0.275 | 0.327 | 0.256 | 0.162 | 0.321 | 9.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 14 | 14 | 13 | 13 | 10 | 30 | 0 |
N.S. |
1 | 0.00 | 0.88 | 0.88 | 0.81 | 0.81 | 0.62 | 1.88 | 0.00 |
time (sec) |
N/A | 0.000 | 0.079 | 0.198 | 0.260 | 0.254 | 1.179 | 0.280 | 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 | 19 | 18 | 18 | 19 | 18 | 18 | 14 | 19 | 18 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 0.95 | 0.95 | 0.74 | 1.00 | 0.95 |
time (sec) |
N/A | 0.162 | 0.002 | 0.014 | 0.175 | 0.257 | 0.027 | 0.263 | 0.033 |