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 | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 40 | 21 | 21 | 19 | 19 | 17 | 0 | 19 |
N.S. |
1 | 1.90 | 1.00 | 1.00 | 0.90 | 0.90 | 0.81 | 0.00 | 0.90 |
time (sec) |
N/A | 0.213 | 0.083 | 0.143 | 0.226 | 0.278 | 0.944 | 0.000 | 12.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 23 | 21 | 83 | 30 | 29 | 30 | 30 |
N.S. |
1 | 0.00 | 1.05 | 0.95 | 3.77 | 1.36 | 1.32 | 1.36 | 1.36 |
time (sec) |
N/A | 0.000 | 0.504 | 0.262 | 4.279 | 0.238 | 0.109 | 0.264 | 12.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 44 | 24 | 49 | 53 | 27 | 31 | 292 |
N.S. |
1 | 0.00 | 1.76 | 0.96 | 1.96 | 2.12 | 1.08 | 1.24 | 11.68 |
time (sec) |
N/A | 0.000 | 0.113 | 0.893 | 0.231 | 0.257 | 0.134 | 0.340 | 12.520 |
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 | 34 | 0 | 32 | 30 | 30 | 29 | 29 | 29 | 254 |
N.S. |
1 | 0.00 | 0.94 | 0.88 | 0.88 | 0.85 | 0.85 | 0.85 | 7.47 |
time (sec) |
N/A | 0.000 | 0.126 | 33.842 | 0.338 | 0.256 | 0.237 | 0.349 | 15.848 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 54 | 17 | 16 | 0 | 15 | 12 | 0 | 15 |
N.S. |
1 | 2.57 | 0.81 | 0.76 | 0.00 | 0.71 | 0.57 | 0.00 | 0.71 |
time (sec) |
N/A | 0.233 | 0.231 | 0.128 | 0.000 | 0.259 | 0.091 | 0.000 | 12.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 41 | 26 | 23 | 24 | 24 | 26 | 24 | 22 |
N.S. |
1 | 1.28 | 0.81 | 0.72 | 0.75 | 0.75 | 0.81 | 0.75 | 0.69 |
time (sec) |
N/A | 0.176 | 0.046 | 0.115 | 0.180 | 0.248 | 0.083 | 0.258 | 11.967 |
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 | 17 | 0 | 16 | 18 | 21 | 16 | 15 | 35 | 16 |
N.S. |
1 | 0.00 | 0.94 | 1.06 | 1.24 | 0.94 | 0.88 | 2.06 | 0.94 |
time (sec) |
N/A | 0.000 | 0.092 | 0.135 | 0.256 | 0.244 | 0.146 | 0.446 | 12.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 52 | 22 | 36 | 66 | 36 | 53 | 36 | 33 |
N.S. |
1 | 1.86 | 0.79 | 1.29 | 2.36 | 1.29 | 1.89 | 1.29 | 1.18 |
time (sec) |
N/A | 0.267 | 1.368 | 0.085 | 0.226 | 0.259 | 0.105 | 0.260 | 12.766 |
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 | 32 | 0 | 35 | 36 | 58 | 36 | 32 | 100 | 52 |
N.S. |
1 | 0.00 | 1.09 | 1.12 | 1.81 | 1.12 | 1.00 | 3.12 | 1.62 |
time (sec) |
N/A | 0.000 | 1.306 | 0.323 | 0.442 | 0.241 | 0.233 | 0.277 | 13.424 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 37 | 58 | 36 | 0 | 52 | 36 |
N.S. |
1 | 0.00 | 1.00 | 1.54 | 2.42 | 1.50 | 0.00 | 2.17 | 1.50 |
time (sec) |
N/A | 0.000 | 0.156 | 94.416 | 0.336 | 0.242 | 0.000 | 0.913 | 12.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 27 | 250 | 33 | 32 | 0 | 34 | 33 |
N.S. |
1 | 0.00 | 0.90 | 8.33 | 1.10 | 1.07 | 0.00 | 1.13 | 1.10 |
time (sec) |
N/A | 0.000 | 0.215 | 0.330 | 0.648 | 0.252 | 0.000 | 3.316 | 14.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F(-1) | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 27 | 27 | 0 | 333 | 89 | 102 | 140 | 0 |
N.S. |
1 | 1.04 | 1.04 | 0.00 | 12.81 | 3.42 | 3.92 | 5.38 | 0.00 |
time (sec) |
N/A | 0.962 | 0.068 | 0.000 | 0.346 | 0.261 | 4.223 | 1.618 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 18 | 16 | 15 | 21 | 13 | 10 | 13 | 15 |
N.S. |
1 | 0.67 | 0.59 | 0.56 | 0.78 | 0.48 | 0.37 | 0.48 | 0.56 |
time (sec) |
N/A | 0.185 | 0.161 | 0.119 | 0.226 | 0.243 | 0.054 | 0.277 | 11.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 25 | 27 | 18 | 23 | 17 | 20 | 21 | 20 |
N.S. |
1 | 1.19 | 1.29 | 0.86 | 1.10 | 0.81 | 0.95 | 1.00 | 0.95 |
time (sec) |
N/A | 0.190 | 0.006 | 0.038 | 0.188 | 0.256 | 0.074 | 0.288 | 12.627 |
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 | 15 | 30 | 18 | 35 | 36 | 36 | 37 | 36 | 34 |
N.S. |
1 | 2.00 | 1.20 | 2.33 | 2.40 | 2.40 | 2.47 | 2.40 | 2.27 |
time (sec) |
N/A | 0.161 | 0.009 | 0.043 | 0.183 | 0.244 | 0.031 | 0.265 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 34 | 27 | 21 | 26 | 19 | 26 | 21 |
N.S. |
1 | 1.08 | 1.42 | 1.12 | 0.88 | 1.08 | 0.79 | 1.08 | 0.88 |
time (sec) |
N/A | 0.774 | 2.406 | 0.621 | 0.251 | 0.240 | 0.116 | 0.299 | 11.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 20 | 21 | 20 | 21 | 21 | 17 | 21 | 19 |
N.S. |
1 | 0.91 | 0.95 | 0.91 | 0.95 | 0.95 | 0.77 | 0.95 | 0.86 |
time (sec) |
N/A | 0.151 | 0.000 | 0.060 | 0.173 | 0.226 | 0.025 | 0.275 | 11.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 56 | 34 | 50 | 54 | 56 | 58 | 0 |
N.S. |
1 | 0.00 | 2.07 | 1.26 | 1.85 | 2.00 | 2.07 | 2.15 | 0.00 |
time (sec) |
N/A | 0.000 | 5.393 | 0.403 | 0.229 | 0.268 | 0.156 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 26 | 35 | 35 | 35 | 27 | 37 | 0 |
N.S. |
1 | 0.00 | 0.74 | 1.00 | 1.00 | 1.00 | 0.77 | 1.06 | 0.00 |
time (sec) |
N/A | 0.000 | 0.099 | 0.663 | 0.336 | 0.245 | 0.182 | 0.415 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | F(-1) | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 26 | 27 | 27 | 0 | 27 | 732 |
N.S. |
1 | 0.00 | 0.00 | 0.84 | 0.87 | 0.87 | 0.00 | 0.87 | 23.61 |
time (sec) |
N/A | 0.000 | 0.000 | 0.121 | 0.451 | 0.262 | 0.000 | 27.334 | 12.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 20 | 33 | 51 | 28 | 22 | 44 | 190 |
N.S. |
1 | 0.00 | 0.77 | 1.27 | 1.96 | 1.08 | 0.85 | 1.69 | 7.31 |
time (sec) |
N/A | 0.000 | 0.185 | 3.541 | 0.339 | 0.249 | 0.157 | 0.361 | 11.888 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 46 | 151 | 165 | 168 | 360 | 4600 | 55 |
N.S. |
1 | 0.00 | 1.39 | 4.58 | 5.00 | 5.09 | 10.91 | 139.39 | 1.67 |
time (sec) |
N/A | 0.000 | 0.183 | 1.997 | 0.494 | 0.271 | 1.520 | 0.982 | 12.628 |
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 | 25 | 32 | 49 | 29 | 147 | 58 | 58 | 217 | 222 |
N.S. |
1 | 1.28 | 1.96 | 1.16 | 5.88 | 2.32 | 2.32 | 8.68 | 8.88 |
time (sec) |
N/A | 3.047 | 0.949 | 0.429 | 46.611 | 0.248 | 0.458 | 0.303 | 13.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 23 | 25 | 69 | 46 | 26 | 25 | 24 |
N.S. |
1 | 0.00 | 0.85 | 0.93 | 2.56 | 1.70 | 0.96 | 0.93 | 0.89 |
time (sec) |
N/A | 0.000 | 0.702 | 0.375 | 0.521 | 0.245 | 2.563 | 0.715 | 12.645 |
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 | 20 | 0 | 20 | 33 | 20 | 31 | 27 | 31 | 32 |
N.S. |
1 | 0.00 | 1.00 | 1.65 | 1.00 | 1.55 | 1.35 | 1.55 | 1.60 |
time (sec) |
N/A | 0.000 | 0.145 | 2.142 | 0.321 | 0.244 | 0.068 | 0.310 | 12.888 |
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 | 19 | 17 | 17 | 16 | 15 | 15 | 15 | 16 | 15 |
N.S. |
1 | 0.89 | 0.89 | 0.84 | 0.79 | 0.79 | 0.79 | 0.84 | 0.79 |
time (sec) |
N/A | 0.133 | 0.004 | 0.517 | 0.190 | 0.250 | 0.027 | 0.264 | 0.075 |
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 | 23 | 79 | 79 | 71 | 55 | 55 | 75 | 55 | 70 |
N.S. |
1 | 3.43 | 3.43 | 3.09 | 2.39 | 2.39 | 3.26 | 2.39 | 3.04 |
time (sec) |
N/A | 0.214 | 0.007 | 0.120 | 0.190 | 0.237 | 0.035 | 0.272 | 0.067 |
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 | 21 | 66 | 21 | 23 | 22 | 25 | 20 | 25 | 18 |
N.S. |
1 | 3.14 | 1.00 | 1.10 | 1.05 | 1.19 | 0.95 | 1.19 | 0.86 |
time (sec) |
N/A | 0.250 | 0.053 | 0.283 | 0.248 | 0.263 | 0.076 | 0.286 | 12.225 |
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 | 13 | 13 | 12 | 67 | 11 | 10 | 11 | 11 |
N.S. |
1 | 0.65 | 0.65 | 0.60 | 3.35 | 0.55 | 0.50 | 0.55 | 0.55 |
time (sec) |
N/A | 0.220 | 0.011 | 0.054 | 0.195 | 0.265 | 0.077 | 0.253 | 12.113 |
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 | 17 | 21 | 17 | 13 | 16 | 16 | 15 | 16 | 18 |
N.S. |
1 | 1.24 | 1.00 | 0.76 | 0.94 | 0.94 | 0.88 | 0.94 | 1.06 |
time (sec) |
N/A | 0.141 | 0.001 | 0.025 | 0.189 | 0.259 | 0.029 | 0.270 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 56 | 43 | 38 | 43 | 55 | 42 | 0 | 38 |
N.S. |
1 | 1.81 | 1.39 | 1.23 | 1.39 | 1.77 | 1.35 | 0.00 | 1.23 |
time (sec) |
N/A | 0.294 | 0.067 | 0.059 | 0.193 | 0.264 | 0.172 | 0.000 | 12.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 20 | 22 | 21 | 22 | 22 | 29 | 0 |
N.S. |
1 | 0.00 | 0.91 | 1.00 | 0.95 | 1.00 | 1.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.000 | 0.252 | 24.964 | 0.264 | 0.271 | 10.441 | 0.256 | 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 | 14 | 4 | 4 | 5 | 4 | 4 | 3 | 5 | 4 |
N.S. |
1 | 0.29 | 0.29 | 0.36 | 0.29 | 0.29 | 0.21 | 0.36 | 0.29 |
time (sec) |
N/A | 0.119 | 0.000 | 0.021 | 0.208 | 0.241 | 0.019 | 0.261 | 0.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 30 | 27 | 26 | 26 | 22 | 26 | 26 |
N.S. |
1 | 0.00 | 1.03 | 0.93 | 0.90 | 0.90 | 0.76 | 0.90 | 0.90 |
time (sec) |
N/A | 0.000 | 0.076 | 0.252 | 0.307 | 0.263 | 0.153 | 0.307 | 0.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 21 | 21 | 10 | 9 | 9 | 14 | 9 | 9 |
N.S. |
1 | 1.40 | 1.40 | 0.67 | 0.60 | 0.60 | 0.93 | 0.60 | 0.60 |
time (sec) |
N/A | 0.162 | 0.059 | 0.160 | 0.191 | 0.246 | 0.048 | 0.261 | 0.035 |
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 | 24 | 0 | 31 | 20 | 19 | 45 | 17 | 0 | 20 |
N.S. |
1 | 0.00 | 1.29 | 0.83 | 0.79 | 1.88 | 0.71 | 0.00 | 0.83 |
time (sec) |
N/A | 0.000 | 0.846 | 7.101 | 0.224 | 0.271 | 0.181 | 0.000 | 0.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 19 | 20 | 18 | 17 | 17 | 14 | 18 | 17 |
N.S. |
1 | 0.73 | 0.77 | 0.69 | 0.65 | 0.65 | 0.54 | 0.69 | 0.65 |
time (sec) |
N/A | 0.173 | 0.009 | 0.521 | 0.199 | 0.244 | 0.041 | 0.262 | 12.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 56 | 33 | 44 | 34 | 49 | 46 | 0 |
N.S. |
1 | 0.00 | 1.93 | 1.14 | 1.52 | 1.17 | 1.69 | 1.59 | 0.00 |
time (sec) |
N/A | 0.000 | 2.472 | 0.430 | 0.348 | 0.251 | 0.108 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 77 | 14 | 15 | 44 | 14 | 12 | 14 | 13 |
N.S. |
1 | 5.50 | 1.00 | 1.07 | 3.14 | 1.00 | 0.86 | 1.00 | 0.93 |
time (sec) |
N/A | 0.335 | 0.045 | 0.223 | 0.199 | 0.258 | 0.068 | 0.254 | 0.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 20 | 86 | 26 | 26 | 44 | 27 | 27 | 114 |
N.S. |
1 | 1.25 | 5.38 | 1.62 | 1.62 | 2.75 | 1.69 | 1.69 | 7.12 |
time (sec) |
N/A | 0.342 | 0.071 | 0.125 | 0.205 | 0.245 | 0.803 | 0.267 | 12.875 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 194 | 24 | 34 | 44 | 29 | 27 | 0 | 0 |
N.S. |
1 | 8.08 | 1.00 | 1.42 | 1.83 | 1.21 | 1.12 | 0.00 | 0.00 |
time (sec) |
N/A | 0.728 | 0.211 | 0.051 | 0.390 | 0.265 | 94.968 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 19 | 17 | 20 | 19 | 17 | 21 | 26 |
N.S. |
1 | 0.00 | 0.83 | 0.74 | 0.87 | 0.83 | 0.74 | 0.91 | 1.13 |
time (sec) |
N/A | 0.000 | 0.339 | 0.043 | 0.317 | 0.279 | 0.092 | 0.258 | 12.786 |
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 | 7 | 9 | 7 | 9 | 9 | 7 | 9 | 6 |
N.S. |
1 | 0.29 | 0.38 | 0.29 | 0.38 | 0.38 | 0.29 | 0.38 | 0.25 |
time (sec) |
N/A | 0.120 | 0.000 | 0.004 | 0.194 | 0.248 | 0.017 | 0.251 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 84 | 48 | 52 | 628 | 84 | 36 | 55 | 40 |
N.S. |
1 | 3.82 | 2.18 | 2.36 | 28.55 | 3.82 | 1.64 | 2.50 | 1.82 |
time (sec) |
N/A | 0.837 | 0.121 | 0.137 | 0.261 | 0.300 | 0.137 | 0.255 | 12.864 |
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 | 20 | 16 | 16 | 17 | 16 | 16 | 15 | 17 | 16 |
N.S. |
1 | 0.80 | 0.80 | 0.85 | 0.80 | 0.80 | 0.75 | 0.85 | 0.80 |
time (sec) |
N/A | 0.258 | 0.009 | 0.019 | 0.273 | 0.259 | 0.046 | 0.260 | 12.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 88 | 24 | 52 | 27 | 28 | 41 | 52 | 29 |
N.S. |
1 | 3.26 | 0.89 | 1.93 | 1.00 | 1.04 | 1.52 | 1.93 | 1.07 |
time (sec) |
N/A | 2.374 | 0.428 | 1.070 | 0.320 | 0.266 | 0.238 | 0.347 | 0.625 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 9 | 8 | 9 | 8 | 9 | 7 | 8 | 8 |
N.S. |
1 | 0.41 | 0.36 | 0.41 | 0.36 | 0.41 | 0.32 | 0.36 | 0.36 |
time (sec) |
N/A | 0.125 | 0.000 | 0.021 | 0.198 | 0.240 | 0.015 | 0.271 | 0.002 |
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 | 29 | 57 | 37 | 29 | 36 | 31 | 24 | 31 | 0 |
N.S. |
1 | 1.97 | 1.28 | 1.00 | 1.24 | 1.07 | 0.83 | 1.07 | 0.00 |
time (sec) |
N/A | 2.790 | 0.074 | 0.687 | 0.242 | 0.266 | 0.136 | 0.273 | 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 | 20 | 20 | 17 | 16 | 16 | 12 | 18 | 16 |
N.S. |
1 | 0.67 | 0.67 | 0.57 | 0.53 | 0.53 | 0.40 | 0.60 | 0.53 |
time (sec) |
N/A | 0.185 | 0.009 | 0.060 | 0.279 | 0.259 | 0.048 | 0.303 | 13.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 32 | 22 | 18 | 23 | 17 | 19 | 21 | 18 |
N.S. |
1 | 1.60 | 1.10 | 0.90 | 1.15 | 0.85 | 0.95 | 1.05 | 0.90 |
time (sec) |
N/A | 0.507 | 0.049 | 0.137 | 0.208 | 0.248 | 0.113 | 0.269 | 11.972 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 33 | 33 | 34 | 33 | 33 | 31 | 35 | 33 |
N.S. |
1 | 1.50 | 1.50 | 1.55 | 1.50 | 1.50 | 1.41 | 1.59 | 1.50 |
time (sec) |
N/A | 0.308 | 0.037 | 0.045 | 0.191 | 0.254 | 0.092 | 0.262 | 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 | 15 | 10 | 10 | 9 | 8 | 8 | 7 | 8 | 8 |
N.S. |
1 | 0.67 | 0.67 | 0.60 | 0.53 | 0.53 | 0.47 | 0.53 | 0.53 |
time (sec) |
N/A | 0.167 | 0.010 | 0.049 | 0.235 | 0.253 | 0.061 | 0.254 | 11.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 18 | 31 | 30 | 25 | 31 | 29 | 25 | 25 |
N.S. |
1 | 1.00 | 1.72 | 1.67 | 1.39 | 1.72 | 1.61 | 1.39 | 1.39 |
time (sec) |
N/A | 0.134 | 0.000 | 0.017 | 0.199 | 0.245 | 0.021 | 0.275 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 13 | 21 | 12 | 11 | 11 | 10 | 13 | 11 |
N.S. |
1 | 0.87 | 1.40 | 0.80 | 0.73 | 0.73 | 0.67 | 0.87 | 0.73 |
time (sec) |
N/A | 0.148 | 0.006 | 0.739 | 0.191 | 0.255 | 0.049 | 0.252 | 11.922 |
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 | 19 | 73 | 115 | 39 | 45 | 49 | 42 | 46 | 322 |
N.S. |
1 | 3.84 | 6.05 | 2.05 | 2.37 | 2.58 | 2.21 | 2.42 | 16.95 |
time (sec) |
N/A | 0.416 | 0.057 | 0.114 | 0.191 | 0.256 | 0.509 | 0.278 | 12.845 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | A | A | B | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 207 | 61 | 53 | 55 | 104 | 62 | 0 |
N.S. |
1 | 0.00 | 6.68 | 1.97 | 1.71 | 1.77 | 3.35 | 2.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.365 | 0.434 | 0.367 | 0.260 | 0.578 | 0.384 | 0.000 |
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 | 29 | 29 | 29 | 28 | 22 | 28 | 29 |
N.S. |
1 | 0.00 | 1.04 | 1.04 | 1.04 | 1.00 | 0.79 | 1.00 | 1.04 |
time (sec) |
N/A | 0.000 | 0.124 | 7.572 | 0.498 | 0.238 | 0.249 | 0.576 | 12.554 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 24 | 63 | 94 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 2.42 | 3.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.077 | 5.680 | 0.323 | 0.255 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 63 | 26 | 51 | 48 | 50 | 54 | 66 | 0 |
N.S. |
1 | 2.62 | 1.08 | 2.12 | 2.00 | 2.08 | 2.25 | 2.75 | 0.00 |
time (sec) |
N/A | 0.663 | 0.786 | 2.280 | 0.270 | 0.256 | 4.537 | 0.276 | 0.000 |
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 | 9 | 9 | 9 | 8 | 15 | 7 | 7 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.67 | 0.78 | 0.78 | 0.78 | 0.78 |
time (sec) |
N/A | 0.142 | 0.004 | 0.021 | 0.194 | 0.253 | 0.060 | 0.274 | 12.292 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 61 | 29 | 22 | 0 | 25 | 87 | 25 | 22 |
N.S. |
1 | 2.44 | 1.16 | 0.88 | 0.00 | 1.00 | 3.48 | 1.00 | 0.88 |
time (sec) |
N/A | 0.305 | 0.024 | 0.240 | 0.000 | 0.246 | 0.452 | 0.271 | 0.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 30 | 22 | 27 | 19 | 26 | 22 | 0 | 20 |
N.S. |
1 | 1.20 | 0.88 | 1.08 | 0.76 | 1.04 | 0.88 | 0.00 | 0.80 |
time (sec) |
N/A | 0.950 | 0.474 | 9.831 | 0.361 | 0.264 | 0.167 | 0.000 | 12.409 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 26 | 28 | 37 | 55 | 31 | 64 | 0 |
N.S. |
1 | 0.00 | 1.04 | 1.12 | 1.48 | 2.20 | 1.24 | 2.56 | 0.00 |
time (sec) |
N/A | 0.000 | 0.116 | 154.820 | 0.271 | 0.252 | 0.553 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 46 | 35 | 372 | 369 | 185 | 557 | 0 |
N.S. |
1 | 0.00 | 1.59 | 1.21 | 12.83 | 12.72 | 6.38 | 19.21 | 0.00 |
time (sec) |
N/A | 0.000 | 0.231 | 0.833 | 0.757 | 0.266 | 0.355 | 0.385 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 11 | 11 | 11 | 10 | 10 | 12 | 10 | 10 |
N.S. |
1 | 0.73 | 0.73 | 0.73 | 0.67 | 0.67 | 0.80 | 0.67 | 0.67 |
time (sec) |
N/A | 0.175 | 0.009 | 0.199 | 0.196 | 0.245 | 0.060 | 0.279 | 12.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 0.86 | 0.71 | 0.86 | 0.86 |
time (sec) |
N/A | 0.152 | 0.017 | 0.153 | 0.270 | 0.246 | 0.054 | 0.277 | 12.417 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 38 | 82 | 234 | 64 | 97 | 94 | 74 |
N.S. |
1 | 0.00 | 1.52 | 3.28 | 9.36 | 2.56 | 3.88 | 3.76 | 2.96 |
time (sec) |
N/A | 0.000 | 0.148 | 1.481 | 0.262 | 0.263 | 0.773 | 0.300 | 13.678 |
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 | 31 | 123 | 28 | 27 | 29 | 28 | 29 | 0 | 29 |
N.S. |
1 | 3.97 | 0.90 | 0.87 | 0.94 | 0.90 | 0.94 | 0.00 | 0.94 |
time (sec) |
N/A | 0.698 | 0.117 | 44.097 | 0.343 | 0.252 | 11.688 | 0.000 | 13.386 |
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 | 28 | 0 | 28 | 27 | 51 | 193 | 60 | 0 | 55 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.82 | 6.89 | 2.14 | 0.00 | 1.96 |
time (sec) |
N/A | 0.000 | 0.375 | 9.012 | 0.893 | 0.278 | 1.095 | 0.000 | 12.651 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 32 | 28 | 24 | 35 | 23 | 29 | 0 | 23 |
N.S. |
1 | 1.14 | 1.00 | 0.86 | 1.25 | 0.82 | 1.04 | 0.00 | 0.82 |
time (sec) |
N/A | 0.233 | 0.220 | 0.831 | 0.207 | 0.249 | 3.039 | 0.000 | 12.681 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 24 | 22 | 20 | 23 | 27 | 19 | 23 | 19 |
N.S. |
1 | 0.96 | 0.88 | 0.80 | 0.92 | 1.08 | 0.76 | 0.92 | 0.76 |
time (sec) |
N/A | 0.162 | 0.016 | 0.082 | 0.186 | 0.233 | 0.044 | 0.270 | 0.072 |
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 | 11 | 0 | 10 | 7 | 6 | 6 | 7 | 6 | 6 |
N.S. |
1 | 0.00 | 0.91 | 0.64 | 0.55 | 0.55 | 0.64 | 0.55 | 0.55 |
time (sec) |
N/A | 0.000 | 0.035 | 0.531 | 0.233 | 0.258 | 0.059 | 0.253 | 12.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-1) | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 0 | 14 | 19 | 0 | 18 | 17 | 18 | 13 |
N.S. |
1 | 0.00 | 1.00 | 1.36 | 0.00 | 1.29 | 1.21 | 1.29 | 0.93 |
time (sec) |
N/A | 0.000 | 0.058 | 0.225 | 0.000 | 0.243 | 0.098 | 0.264 | 12.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 37 | 21 | 16 | 37 | 15 | 17 | 21 | 15 |
N.S. |
1 | 1.76 | 1.00 | 0.76 | 1.76 | 0.71 | 0.81 | 1.00 | 0.71 |
time (sec) |
N/A | 0.174 | 0.052 | 0.114 | 0.208 | 0.258 | 0.053 | 0.272 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 21 | 17 | 24 | 16 | 17 | 21 | 14 |
N.S. |
1 | 0.95 | 0.95 | 0.77 | 1.09 | 0.73 | 0.77 | 0.95 | 0.64 |
time (sec) |
N/A | 0.192 | 0.023 | 0.208 | 0.216 | 0.242 | 0.071 | 0.279 | 12.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F(-1) | A | A | A | B | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 0 | 54 | 41 | 29 | 103 | 33 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 1.93 | 1.46 | 1.04 | 3.68 | 1.18 |
time (sec) |
N/A | 0.000 | 0.137 | 0.000 | 0.318 | 0.246 | 0.115 | 0.289 | 13.411 |
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 | 19 | 23 | 19 | 22 | 21 | 21 | 14 | 142 | 18 |
N.S. |
1 | 1.21 | 1.00 | 1.16 | 1.11 | 1.11 | 0.74 | 7.47 | 0.95 |
time (sec) |
N/A | 0.833 | 1.256 | 0.736 | 0.232 | 0.242 | 0.132 | 0.277 | 12.681 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 141 | 29 | 68 | 0 | 83 | 75 | 109 | 33 |
N.S. |
1 | 5.22 | 1.07 | 2.52 | 0.00 | 3.07 | 2.78 | 4.04 | 1.22 |
time (sec) |
N/A | 0.515 | 0.125 | 0.742 | 0.000 | 0.254 | 0.151 | 0.310 | 11.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 138 | 24 | 36 | 269 | 33 | 61 | 44 | 24 |
N.S. |
1 | 6.00 | 1.04 | 1.57 | 11.70 | 1.43 | 2.65 | 1.91 | 1.04 |
time (sec) |
N/A | 0.807 | 1.138 | 0.219 | 0.298 | 0.242 | 0.212 | 0.279 | 0.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 47 | 38 | 49 | 44 | 71 | 54 | 44 | 59 |
N.S. |
1 | 1.96 | 1.58 | 2.04 | 1.83 | 2.96 | 2.25 | 1.83 | 2.46 |
time (sec) |
N/A | 0.210 | 0.051 | 0.202 | 0.210 | 0.247 | 0.172 | 0.279 | 12.959 |
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 | 23 | 15 | 13 | 15 | 14 | 17 | 12 | 15 | 14 |
N.S. |
1 | 0.65 | 0.57 | 0.65 | 0.61 | 0.74 | 0.52 | 0.65 | 0.61 |
time (sec) |
N/A | 0.245 | 0.015 | 0.069 | 0.218 | 0.256 | 0.109 | 0.280 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 14 | 14 | 15 | 14 | 14 | 14 | 16 | 14 |
N.S. |
1 | 0.82 | 0.82 | 0.88 | 0.82 | 0.82 | 0.82 | 0.94 | 0.82 |
time (sec) |
N/A | 0.302 | 0.009 | 0.046 | 0.193 | 0.237 | 0.061 | 0.291 | 12.296 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 29 | 60 | 48 | 58 | 26 | 58 | 0 |
N.S. |
1 | 0.00 | 1.07 | 2.22 | 1.78 | 2.15 | 0.96 | 2.15 | 0.00 |
time (sec) |
N/A | 0.000 | 0.530 | 1.758 | 0.280 | 0.241 | 0.181 | 0.897 | 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 | 14 | 24 | 26 | 19 | 16 | 16 | 20 | 20 | 12 |
N.S. |
1 | 1.71 | 1.86 | 1.36 | 1.14 | 1.14 | 1.43 | 1.43 | 0.86 |
time (sec) |
N/A | 0.181 | 0.011 | 0.097 | 0.193 | 0.245 | 0.073 | 0.290 | 12.512 |
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 | 35 | 32 | 32 | 31 | 29 | 35 | 31 |
N.S. |
1 | 0.00 | 1.25 | 1.14 | 1.14 | 1.11 | 1.04 | 1.25 | 1.11 |
time (sec) |
N/A | 0.000 | 0.366 | 15.544 | 0.351 | 0.247 | 0.287 | 0.307 | 12.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 11 | 11 | 11 | 10 | 10 | 10 | 10 | 10 |
N.S. |
1 | 0.79 | 0.79 | 0.79 | 0.71 | 0.71 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.140 | 0.006 | 0.085 | 0.191 | 0.232 | 0.047 | 0.280 | 12.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 26 | 23 | 23 | 22 | 22 | 20 | 22 | 24 |
N.S. |
1 | 1.13 | 1.00 | 1.00 | 0.96 | 0.96 | 0.87 | 0.96 | 1.04 |
time (sec) |
N/A | 0.430 | 0.863 | 0.459 | 0.284 | 0.248 | 0.121 | 0.276 | 12.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 87 | 33 | 48 | 47 | 43 | 54 | 45 | 33 |
N.S. |
1 | 3.35 | 1.27 | 1.85 | 1.81 | 1.65 | 2.08 | 1.73 | 1.27 |
time (sec) |
N/A | 0.256 | 0.109 | 0.112 | 0.189 | 0.239 | 0.108 | 0.281 | 0.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 25 | 19 | 13 | 41 | 12 | 10 | 12 | 10 |
N.S. |
1 | 1.19 | 0.90 | 0.62 | 1.95 | 0.57 | 0.48 | 0.57 | 0.48 |
time (sec) |
N/A | 0.247 | 0.025 | 0.459 | 0.275 | 0.242 | 0.057 | 0.271 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 4123 | 629 | 33 | 32 | 30 | 32 | 40 | 0 |
N.S. |
1 | 137.43 | 20.97 | 1.10 | 1.07 | 1.00 | 1.07 | 1.33 | 0.00 |
time (sec) |
N/A | 9.586 | 11.883 | 0.325 | 0.330 | 0.253 | 0.100 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 38 | 37 | 34 | 36 | 31 | 0 | 34 |
N.S. |
1 | 0.93 | 1.41 | 1.37 | 1.26 | 1.33 | 1.15 | 0.00 | 1.26 |
time (sec) |
N/A | 1.002 | 0.525 | 0.429 | 0.317 | 0.247 | 0.161 | 0.000 | 11.945 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 21 | 21 | 19 | 18 | 18 | 20 | 18 | 21 |
N.S. |
1 | 1.11 | 1.11 | 1.00 | 0.95 | 0.95 | 1.05 | 0.95 | 1.11 |
time (sec) |
N/A | 0.613 | 0.306 | 0.185 | 0.203 | 0.263 | 0.135 | 0.303 | 11.656 |
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 | 26 | 0 | 26 | 27 | 29 | 29 | 31 | 38 | 29 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 1.12 | 1.12 | 1.19 | 1.46 | 1.12 |
time (sec) |
N/A | 0.000 | 0.432 | 0.559 | 0.221 | 0.251 | 0.067 | 0.313 | 11.878 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F(-1) | B | A | A | F(-1) | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 0 | 45 | 28 | 26 | 0 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 2.05 | 1.27 | 1.18 | 0.00 | 1.27 |
time (sec) |
N/A | 0.604 | 0.105 | 180.000 | 0.390 | 0.248 | 0.208 | 0.000 | 15.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 29 | 25 | 18 | 21 | 36 | 17 | 36 | 17 |
N.S. |
1 | 1.32 | 1.14 | 0.82 | 0.95 | 1.64 | 0.77 | 1.64 | 0.77 |
time (sec) |
N/A | 0.580 | 0.062 | 0.794 | 0.236 | 0.256 | 0.067 | 0.292 | 0.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 13 | 13 | 10 | 9 | 40 | 10 | 0 | 9 |
N.S. |
1 | 0.72 | 0.72 | 0.56 | 0.50 | 2.22 | 0.56 | 0.00 | 0.50 |
time (sec) |
N/A | 0.180 | 0.041 | 0.270 | 0.209 | 0.241 | 0.233 | 0.000 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 15 | 15 | 15 | 14 | 15 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.88 | 0.88 | 0.82 | 0.88 | 0.82 |
time (sec) |
N/A | 0.149 | 0.007 | 0.080 | 0.196 | 0.236 | 0.054 | 0.258 | 0.105 |
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 | 27 | 29 | 34 | 30 | 24 | 86 | 28 |
N.S. |
1 | 0.00 | 1.12 | 1.21 | 1.42 | 1.25 | 1.00 | 3.58 | 1.17 |
time (sec) |
N/A | 0.000 | 0.261 | 8.004 | 0.229 | 0.246 | 0.067 | 0.296 | 12.881 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 21 | 24 | 33 | 19 | 24 | 20 |
N.S. |
1 | 0.00 | 1.00 | 0.91 | 1.04 | 1.43 | 0.83 | 1.04 | 0.87 |
time (sec) |
N/A | 0.000 | 0.151 | 0.241 | 0.247 | 0.249 | 0.102 | 0.283 | 0.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | F | B | B | B | B | B | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 97 | 0 | 90 | 142 | 169 | 90 | 152 | 362 |
N.S. |
1 | 3.88 | 0.00 | 3.60 | 5.68 | 6.76 | 3.60 | 6.08 | 14.48 |
time (sec) |
N/A | 2.318 | 0.000 | 0.570 | 0.575 | 0.262 | 0.912 | 1.375 | 16.726 |