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 | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 70 | 81 | 78 | 60 | 74 | 0 | 79 | 56 |
N.S. |
1 | 0.80 | 0.93 | 0.90 | 0.69 | 0.85 | 0.00 | 0.91 | 0.64 |
time (sec) |
N/A | 0.302 | 0.259 | 4.590 | 0.214 | 0.291 | 0.000 | 0.289 | 15.170 |
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 | 98 | 94 | 137 | 108 | 126 | 114 | 0 | 121 | 102 |
N.S. |
1 | 0.96 | 1.40 | 1.10 | 1.29 | 1.16 | 0.00 | 1.23 | 1.04 |
time (sec) |
N/A | 0.449 | 0.022 | 0.490 | 0.231 | 0.304 | 0.000 | 0.295 | 0.238 |
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 | 65 | 58 | 61 | 58 | 43 | 56 | 0 | 57 | 42 |
N.S. |
1 | 0.89 | 0.94 | 0.89 | 0.66 | 0.86 | 0.00 | 0.88 | 0.65 |
time (sec) |
N/A | 0.306 | 0.161 | 0.245 | 0.278 | 0.268 | 0.000 | 0.306 | 14.966 |
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 | 70 | 68 | 93 | 85 | 97 | 95 | 0 | 98 | 77 |
N.S. |
1 | 0.97 | 1.33 | 1.21 | 1.39 | 1.36 | 0.00 | 1.40 | 1.10 |
time (sec) |
N/A | 0.357 | 0.009 | 0.312 | 0.227 | 0.291 | 0.000 | 0.306 | 15.548 |
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 | 43 | 43 | 36 | 35 | 34 | 37 | 0 | 34 | 28 |
N.S. |
1 | 1.00 | 0.84 | 0.81 | 0.79 | 0.86 | 0.00 | 0.79 | 0.65 |
time (sec) |
N/A | 0.274 | 0.068 | 0.191 | 0.205 | 0.289 | 0.000 | 0.300 | 15.745 |
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 | 40 | 40 | 48 | 55 | 58 | 72 | 0 | 60 | 41 |
N.S. |
1 | 1.00 | 1.20 | 1.38 | 1.45 | 1.80 | 0.00 | 1.50 | 1.02 |
time (sec) |
N/A | 0.254 | 0.009 | 0.118 | 0.208 | 0.267 | 0.000 | 0.299 | 16.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 15 | 31 | 0 | 15 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 2.07 | 0.00 | 1.00 | 1.13 |
time (sec) |
N/A | 0.149 | 0.002 | 0.045 | 0.192 | 0.246 | 0.000 | 0.268 | 16.025 |
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 | 24 | 24 | 35 | 30 | 38 | 40 | 0 | 40 | 22 |
N.S. |
1 | 1.00 | 1.46 | 1.25 | 1.58 | 1.67 | 0.00 | 1.67 | 0.92 |
time (sec) |
N/A | 0.242 | 0.013 | 0.099 | 0.200 | 0.252 | 0.000 | 0.270 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | 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 | 24 | 37 | 28 | 51 | 37 | 25 |
N.S. |
1 | 1.00 | 1.06 | 0.77 | 1.19 | 0.90 | 1.65 | 1.19 | 0.81 |
time (sec) |
N/A | 0.203 | 0.027 | 0.080 | 0.286 | 0.248 | 2.523 | 0.274 | 15.911 |
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 | 30 | 30 | 50 | 31 | 27 | 28 | 0 | 34 | 28 |
N.S. |
1 | 1.00 | 1.67 | 1.03 | 0.90 | 0.93 | 0.00 | 1.13 | 0.93 |
time (sec) |
N/A | 0.270 | 0.009 | 0.154 | 0.197 | 0.254 | 0.000 | 0.273 | 0.046 |
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 | 61 | 59 | 45 | 44 | 73 | 49 | 0 | 73 | 67 |
N.S. |
1 | 0.97 | 0.74 | 0.72 | 1.20 | 0.80 | 0.00 | 1.20 | 1.10 |
time (sec) |
N/A | 0.272 | 0.075 | 0.219 | 0.290 | 0.272 | 0.000 | 0.279 | 16.433 |
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 | 50 | 47 | 71 | 49 | 43 | 45 | 0 | 57 | 43 |
N.S. |
1 | 0.94 | 1.42 | 0.98 | 0.86 | 0.90 | 0.00 | 1.14 | 0.86 |
time (sec) |
N/A | 0.296 | 0.008 | 0.228 | 0.197 | 0.265 | 0.000 | 0.276 | 15.990 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 85 | 68 | 61 | 103 | 68 | 0 | 96 | 91 |
N.S. |
1 | 0.96 | 0.76 | 0.69 | 1.16 | 0.76 | 0.00 | 1.08 | 1.02 |
time (sec) |
N/A | 0.341 | 0.079 | 0.256 | 0.279 | 0.252 | 0.000 | 0.280 | 16.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 113 | 46 | 304 | 33 | 0 | 0 | 42 |
N.S. |
1 | 1.00 | 4.35 | 1.77 | 11.69 | 1.27 | 0.00 | 0.00 | 1.62 |
time (sec) |
N/A | 0.213 | 0.442 | 0.724 | 0.429 | 0.273 | 0.000 | 0.000 | 15.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 111 | 44 | 296 | 33 | 0 | 0 | 41 |
N.S. |
1 | 1.00 | 4.44 | 1.76 | 11.84 | 1.32 | 0.00 | 0.00 | 1.64 |
time (sec) |
N/A | 0.218 | 0.299 | 0.340 | 0.428 | 0.257 | 0.000 | 0.000 | 15.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 108 | 84 | 291 | 0 | 142 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.76 | 2.65 | 0.00 | 1.29 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.468 | 1.113 | 22.693 | 0.000 | 0.099 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 104 | 184 | 798 | 0 | 143 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 1.67 | 7.25 | 0.00 | 1.30 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.464 | 1.201 | 5.330 | 0.000 | 0.098 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 58 | 220 | 0 | 111 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.81 | 3.06 | 0.00 | 1.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.360 | 0.458 | 2.141 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 126 | 763 | 0 | 99 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.85 | 11.22 | 0.00 | 1.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.355 | 0.795 | 3.781 | 0.000 | 0.088 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 66 | 218 | 0 | 100 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 2.91 | 0.00 | 1.33 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.361 | 0.443 | 2.913 | 0.000 | 0.095 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 133 | 798 | 0 | 108 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.73 | 10.36 | 0.00 | 1.40 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.362 | 1.218 | 5.274 | 0.000 | 0.091 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 113 | 79 | 291 | 0 | 119 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.71 | 2.60 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.484 | 0.925 | 4.658 | 0.000 | 0.092 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 113 | 143 | 866 | 0 | 129 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.28 | 7.73 | 0.00 | 1.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.488 | 1.325 | 7.760 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 41 | 0 | 19 | 0 | 46 | 21 |
N.S. |
1 | 1.00 | 1.00 | 1.95 | 0.00 | 0.90 | 0.00 | 2.19 | 1.00 |
time (sec) |
N/A | 0.193 | 0.217 | 1.561 | 0.000 | 0.247 | 0.000 | 0.323 | 0.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 107 | 40 | 283 | 29 | 0 | 0 | 37 |
N.S. |
1 | 1.00 | 5.10 | 1.90 | 13.48 | 1.38 | 0.00 | 0.00 | 1.76 |
time (sec) |
N/A | 0.204 | 0.386 | 1.148 | 0.428 | 0.249 | 0.000 | 0.000 | 15.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 41 | 42 | 19 | 0 | 22 | 42 |
N.S. |
1 | 1.00 | 1.00 | 2.16 | 2.21 | 1.00 | 0.00 | 1.16 | 2.21 |
time (sec) |
N/A | 0.190 | 0.031 | 0.319 | 0.195 | 0.235 | 0.000 | 0.312 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 41 | 30 | 19 | 0 | 30 | 19 |
N.S. |
1 | 1.00 | 1.00 | 2.16 | 1.58 | 1.00 | 0.00 | 1.58 | 1.00 |
time (sec) |
N/A | 0.192 | 0.035 | 0.240 | 0.203 | 0.251 | 0.000 | 0.296 | 15.172 |
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 | 19 | 19 | 19 | 36 | 33 | 19 | 0 | 23 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.89 | 1.74 | 1.00 | 0.00 | 1.21 | 1.21 |
time (sec) |
N/A | 0.186 | 0.028 | 0.194 | 0.199 | 0.245 | 0.000 | 0.299 | 0.059 |
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 | 19 | 19 | 19 | 32 | 20 | 19 | 0 | 20 | 21 |
N.S. |
1 | 1.00 | 1.00 | 1.68 | 1.05 | 1.00 | 0.00 | 1.05 | 1.11 |
time (sec) |
N/A | 0.189 | 0.032 | 0.138 | 0.202 | 0.241 | 0.000 | 0.285 | 15.139 |
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 | 17 | 17 | 17 | 18 | 22 | 19 | 0 | 24 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.29 | 1.12 | 0.00 | 1.41 | 1.29 |
time (sec) |
N/A | 0.182 | 0.015 | 0.109 | 0.194 | 0.232 | 0.000 | 0.290 | 15.104 |
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 | 11 | 11 | 11 | 12 | 11 | 19 | 0 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.73 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.170 | 0.002 | 0.062 | 0.197 | 0.236 | 0.000 | 0.269 | 15.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 23 | 12 | 11 | 11 | 14 | 11 | 11 |
N.S. |
1 | 1.00 | 2.09 | 1.09 | 1.00 | 1.00 | 1.27 | 1.00 | 1.00 |
time (sec) |
N/A | 0.154 | 0.014 | 0.078 | 0.199 | 0.251 | 0.059 | 0.266 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 33 | 15 | 23 | 17 | 49 | 14 | 14 |
N.S. |
1 | 1.00 | 1.94 | 0.88 | 1.35 | 1.00 | 2.88 | 0.82 | 0.82 |
time (sec) |
N/A | 0.188 | 0.008 | 0.122 | 0.207 | 0.249 | 3.627 | 0.269 | 15.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 46 | 26 | 21 | 19 | 0 | 21 | 22 |
N.S. |
1 | 1.00 | 2.42 | 1.37 | 1.11 | 1.00 | 0.00 | 1.11 | 1.16 |
time (sec) |
N/A | 0.191 | 0.035 | 0.150 | 0.232 | 0.250 | 0.000 | 0.276 | 0.046 |
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 | 19 | 19 | 31 | 29 | 33 | 19 | 0 | 23 | 19 |
N.S. |
1 | 1.00 | 1.63 | 1.53 | 1.74 | 1.00 | 0.00 | 1.21 | 1.00 |
time (sec) |
N/A | 0.189 | 0.086 | 0.165 | 0.191 | 0.261 | 0.000 | 0.282 | 15.435 |
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 | 19 | 19 | 38 | 37 | 30 | 19 | 0 | 30 | 23 |
N.S. |
1 | 1.00 | 2.00 | 1.95 | 1.58 | 1.00 | 0.00 | 1.58 | 1.21 |
time (sec) |
N/A | 0.196 | 0.030 | 0.204 | 0.207 | 0.251 | 0.000 | 0.287 | 15.531 |
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 | 85 | 90 | 59 | 73 | 95 | 99 | 0 | 164 | 153 |
N.S. |
1 | 1.06 | 0.69 | 0.86 | 1.12 | 1.16 | 0.00 | 1.93 | 1.80 |
time (sec) |
N/A | 0.487 | 0.175 | 0.345 | 0.201 | 0.268 | 0.000 | 0.314 | 18.027 |
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 | 63 | 64 | 60 | 60 | 70 | 88 | 0 | 122 | 109 |
N.S. |
1 | 1.02 | 0.95 | 0.95 | 1.11 | 1.40 | 0.00 | 1.94 | 1.73 |
time (sec) |
N/A | 0.404 | 0.121 | 0.256 | 0.208 | 0.275 | 0.000 | 0.298 | 17.120 |
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 | 47 | 48 | 47 | 47 | 58 | 74 | 0 | 107 | 85 |
N.S. |
1 | 1.02 | 1.00 | 1.00 | 1.23 | 1.57 | 0.00 | 2.28 | 1.81 |
time (sec) |
N/A | 0.360 | 0.009 | 0.182 | 0.198 | 0.270 | 0.000 | 0.326 | 15.824 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 30 | 31 | 60 | 0 | 57 | 47 |
N.S. |
1 | 1.00 | 1.00 | 1.25 | 1.29 | 2.50 | 0.00 | 2.38 | 1.96 |
time (sec) |
N/A | 0.153 | 0.007 | 0.100 | 0.194 | 0.264 | 0.000 | 0.278 | 15.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 29 | 37 | 36 | 0 | 43 | 57 |
N.S. |
1 | 1.00 | 1.00 | 1.81 | 2.31 | 2.25 | 0.00 | 2.69 | 3.56 |
time (sec) |
N/A | 0.235 | 0.002 | 0.115 | 0.196 | 0.260 | 0.000 | 0.284 | 15.211 |
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 | 15 | 15 | 26 | 16 | 20 | 17 | 0 | 39 | 17 |
N.S. |
1 | 1.00 | 1.73 | 1.07 | 1.33 | 1.13 | 0.00 | 2.60 | 1.13 |
time (sec) |
N/A | 0.228 | 0.004 | 0.121 | 0.195 | 0.260 | 0.000 | 0.285 | 15.416 |
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 | 38 | 39 | 35 | 32 | 34 | 29 | 0 | 82 | 31 |
N.S. |
1 | 1.03 | 0.92 | 0.84 | 0.89 | 0.76 | 0.00 | 2.16 | 0.82 |
time (sec) |
N/A | 0.281 | 0.049 | 0.150 | 0.197 | 0.250 | 0.000 | 0.290 | 15.318 |
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 | 54 | 55 | 57 | 44 | 46 | 42 | 0 | 98 | 55 |
N.S. |
1 | 1.02 | 1.06 | 0.81 | 0.85 | 0.78 | 0.00 | 1.81 | 1.02 |
time (sec) |
N/A | 0.310 | 0.046 | 0.184 | 0.214 | 0.256 | 0.000 | 0.292 | 15.615 |
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 | 76 | 81 | 73 | 57 | 57 | 53 | 0 | 140 | 75 |
N.S. |
1 | 1.07 | 0.96 | 0.75 | 0.75 | 0.70 | 0.00 | 1.84 | 0.99 |
time (sec) |
N/A | 0.381 | 0.087 | 0.227 | 0.205 | 0.259 | 0.000 | 0.293 | 15.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 93 | 89 | 69 | 69 | 64 | 0 | 154 | 113 |
N.S. |
1 | 1.01 | 0.97 | 0.75 | 0.75 | 0.70 | 0.00 | 1.67 | 1.23 |
time (sec) |
N/A | 0.391 | 0.076 | 0.275 | 0.216 | 0.255 | 0.000 | 0.287 | 19.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 181 | 102 | 555 | 0 | 207 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.60 | 3.28 | 0.00 | 1.22 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.756 | 0.821 | 1.923 | 0.000 | 0.099 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 147 | 90 | 534 | 0 | 183 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.67 | 3.96 | 0.00 | 1.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.593 | 0.527 | 2.878 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 114 | 73 | 460 | 0 | 143 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.67 | 4.22 | 0.00 | 1.31 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.541 | 0.792 | 1.839 | 0.000 | 0.096 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 57 | 414 | 0 | 122 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.67 | 4.87 | 0.00 | 1.44 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.435 | 0.350 | 2.864 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 120 | 81 | 536 | 0 | 150 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.70 | 4.62 | 0.00 | 1.29 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.550 | 0.511 | 1.727 | 0.000 | 0.100 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 155 | 91 | 566 | 0 | 164 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.62 | 3.85 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.606 | 1.237 | 2.811 | 0.000 | 0.105 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 176 | 191 | 104 | 582 | 0 | 175 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.59 | 3.31 | 0.00 | 0.99 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.775 | 1.324 | 1.725 | 0.000 | 0.108 | 0.000 | 0.000 | 0.000 |
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 | 122 | 120 | 80 | 104 | 127 | 122 | 0 | 246 | 197 |
N.S. |
1 | 0.98 | 0.66 | 0.85 | 1.04 | 1.00 | 0.00 | 2.02 | 1.61 |
time (sec) |
N/A | 0.671 | 0.485 | 0.474 | 0.215 | 0.271 | 0.000 | 0.309 | 17.674 |
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 | 97 | 95 | 71 | 106 | 139 | 117 | 0 | 230 | 160 |
N.S. |
1 | 0.98 | 0.73 | 1.09 | 1.43 | 1.21 | 0.00 | 2.37 | 1.65 |
time (sec) |
N/A | 0.564 | 0.198 | 0.394 | 0.219 | 0.279 | 0.000 | 0.306 | 17.938 |
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 | 78 | 79 | 51 | 68 | 79 | 94 | 0 | 162 | 123 |
N.S. |
1 | 1.01 | 0.65 | 0.87 | 1.01 | 1.21 | 0.00 | 2.08 | 1.58 |
time (sec) |
N/A | 0.538 | 0.165 | 0.261 | 0.205 | 0.265 | 0.000 | 0.299 | 17.097 |
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 | 51 | 51 | 59 | 63 | 75 | 82 | 0 | 115 | 89 |
N.S. |
1 | 1.00 | 1.16 | 1.24 | 1.47 | 1.61 | 0.00 | 2.25 | 1.75 |
time (sec) |
N/A | 0.394 | 0.005 | 0.206 | 0.206 | 0.268 | 0.000 | 0.314 | 15.737 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 35 | 34 | 71 | 0 | 60 | 161 |
N.S. |
1 | 1.00 | 1.00 | 1.30 | 1.26 | 2.63 | 0.00 | 2.22 | 5.96 |
time (sec) |
N/A | 0.161 | 0.001 | 0.026 | 0.205 | 0.264 | 0.000 | 0.294 | 14.946 |
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 | 27 | 27 | 38 | 37 | 46 | 45 | 0 | 70 | 68 |
N.S. |
1 | 1.00 | 1.41 | 1.37 | 1.70 | 1.67 | 0.00 | 2.59 | 2.52 |
time (sec) |
N/A | 0.329 | 0.014 | 0.157 | 0.209 | 0.270 | 0.000 | 0.306 | 14.916 |
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 | 42 | 42 | 55 | 35 | 42 | 33 | 0 | 86 | 34 |
N.S. |
1 | 1.00 | 1.31 | 0.83 | 1.00 | 0.79 | 0.00 | 2.05 | 0.81 |
time (sec) |
N/A | 0.326 | 0.037 | 0.151 | 0.195 | 0.246 | 0.000 | 0.288 | 14.848 |
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 | 56 | 58 | 53 | 49 | 55 | 45 | 0 | 138 | 66 |
N.S. |
1 | 1.04 | 0.95 | 0.88 | 0.98 | 0.80 | 0.00 | 2.46 | 1.18 |
time (sec) |
N/A | 0.430 | 0.077 | 0.184 | 0.199 | 0.272 | 0.000 | 0.297 | 14.711 |
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 | 88 | 86 | 70 | 63 | 77 | 65 | 0 | 200 | 81 |
N.S. |
1 | 0.98 | 0.80 | 0.72 | 0.88 | 0.74 | 0.00 | 2.27 | 0.92 |
time (sec) |
N/A | 0.441 | 0.124 | 0.239 | 0.206 | 0.254 | 0.000 | 0.286 | 15.058 |
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 | 98 | 101 | 87 | 79 | 89 | 73 | 0 | 222 | 104 |
N.S. |
1 | 1.03 | 0.89 | 0.81 | 0.91 | 0.74 | 0.00 | 2.27 | 1.06 |
time (sec) |
N/A | 0.571 | 0.128 | 0.282 | 0.196 | 0.272 | 0.000 | 0.308 | 14.919 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 124 | 102 | 95 | 115 | 93 | 0 | 284 | 126 |
N.S. |
1 | 0.94 | 0.77 | 0.72 | 0.87 | 0.70 | 0.00 | 2.15 | 0.95 |
time (sec) |
N/A | 0.533 | 0.217 | 0.342 | 0.219 | 0.279 | 0.000 | 0.297 | 15.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 179 | 308 | 949 | 0 | 225 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.73 | 5.33 | 0.00 | 1.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.974 | 5.708 | 2.950 | 0.000 | 0.105 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 143 | 302 | 611 | 0 | 193 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 2.22 | 4.49 | 0.00 | 1.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.822 | 2.201 | 1.528 | 0.000 | 0.093 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 156 | 847 | 0 | 153 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.42 | 7.70 | 0.00 | 1.39 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.676 | 1.394 | 2.734 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 143 | 608 | 0 | 160 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.22 | 5.20 | 0.00 | 1.37 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.682 | 1.721 | 1.594 | 0.000 | 0.098 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 150 | 154 | 169 | 956 | 0 | 176 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.13 | 6.37 | 0.00 | 1.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.839 | 2.198 | 2.692 | 0.000 | 0.102 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 190 | 177 | 726 | 0 | 193 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.96 | 3.92 | 0.00 | 1.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.972 | 2.600 | 1.543 | 0.000 | 0.106 | 0.000 | 0.000 | 0.000 |