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 | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 79 | 51 | 72 | 71 | 50 | 75 | 67 | 0 |
N.S. |
1 | 1.05 | 0.68 | 0.96 | 0.95 | 0.67 | 1.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.210 | 0.026 | 0.091 | 0.301 | 0.277 | 0.343 | 0.269 | 0.000 |
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 | 69 | 83 | 54 | 60 | 61 | 48 | 66 | 57 | 0 |
N.S. |
1 | 1.20 | 0.78 | 0.87 | 0.88 | 0.70 | 0.96 | 0.83 | 0.00 |
time (sec) |
N/A | 0.196 | 0.025 | 0.065 | 0.287 | 0.255 | 0.328 | 0.274 | 0.000 |
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 | 54 | 58 | 42 | 52 | 50 | 41 | 53 | 47 | 0 |
N.S. |
1 | 1.07 | 0.78 | 0.96 | 0.93 | 0.76 | 0.98 | 0.87 | 0.00 |
time (sec) |
N/A | 0.199 | 0.020 | 0.072 | 0.296 | 0.257 | 0.205 | 0.278 | 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 | 45 | 51 | 42 | 40 | 40 | 37 | 42 | 37 | 38 |
N.S. |
1 | 1.13 | 0.93 | 0.89 | 0.89 | 0.82 | 0.93 | 0.82 | 0.84 |
time (sec) |
N/A | 0.167 | 0.013 | 0.069 | 0.290 | 0.256 | 0.169 | 0.274 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 25 | 26 | 26 | 24 | 26 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.00 | 1.00 | 0.92 | 1.00 | 0.92 |
time (sec) |
N/A | 0.148 | 0.006 | 0.073 | 0.289 | 0.249 | 0.076 | 0.269 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 59 | 51 | 68 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 1.00 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.294 | 0.014 | 0.707 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 34 | 26 | 38 | 82 | 34 | 48 | 25 |
N.S. |
1 | 1.00 | 1.26 | 0.96 | 1.41 | 3.04 | 1.26 | 1.78 | 0.93 |
time (sec) |
N/A | 0.180 | 0.010 | 0.079 | 0.299 | 0.261 | 0.983 | 0.279 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 31 | 29 | 28 | 27 | 53 | 68 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.85 | 0.82 | 0.79 | 1.56 | 2.00 | 0.00 |
time (sec) |
N/A | 0.165 | 0.014 | 0.070 | 0.271 | 0.242 | 0.719 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 57 | 67 | 50 | 60 | 110 | 109 | 77 | 0 |
N.S. |
1 | 1.02 | 1.20 | 0.89 | 1.07 | 1.96 | 1.95 | 1.38 | 0.00 |
time (sec) |
N/A | 0.187 | 0.017 | 0.073 | 0.288 | 0.272 | 1.675 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 63 | 41 | 52 | 50 | 37 | 102 | 130 | 0 |
N.S. |
1 | 1.09 | 0.71 | 0.90 | 0.86 | 0.64 | 1.76 | 2.24 | 0.00 |
time (sec) |
N/A | 0.183 | 0.020 | 0.073 | 0.276 | 0.253 | 1.006 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 86 | 72 | 73 | 82 | 122 | 184 | 101 | 0 |
N.S. |
1 | 1.08 | 0.90 | 0.91 | 1.02 | 1.52 | 2.30 | 1.26 | 0.00 |
time (sec) |
N/A | 0.201 | 0.048 | 0.083 | 0.279 | 0.269 | 3.320 | 0.270 | 0.000 |
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 | 120 | 141 | 82 | 76 | 102 | 76 | 121 | 100 | 0 |
N.S. |
1 | 1.18 | 0.68 | 0.63 | 0.85 | 0.63 | 1.01 | 0.83 | 0.00 |
time (sec) |
N/A | 0.494 | 0.043 | 1.075 | 0.304 | 0.261 | 0.516 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 115 | 74 | 91 | 0 | 70 | 97 | 87 | 0 |
N.S. |
1 | 1.17 | 0.76 | 0.93 | 0.00 | 0.71 | 0.99 | 0.89 | 0.00 |
time (sec) |
N/A | 0.464 | 0.027 | 0.908 | 0.000 | 0.258 | 0.335 | 0.297 | 0.000 |
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 | 82 | 95 | 63 | 59 | 72 | 59 | 83 | 68 | 0 |
N.S. |
1 | 1.16 | 0.77 | 0.72 | 0.88 | 0.72 | 1.01 | 0.83 | 0.00 |
time (sec) |
N/A | 0.355 | 0.033 | 1.135 | 0.279 | 0.264 | 0.265 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 66 | 57 | 63 | 0 | 51 | 58 | 55 | 0 |
N.S. |
1 | 1.10 | 0.95 | 1.05 | 0.00 | 0.85 | 0.97 | 0.92 | 0.00 |
time (sec) |
N/A | 0.317 | 0.019 | 0.419 | 0.000 | 0.254 | 0.197 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 42 | 35 | 37 | 33 | 36 | 37 | 33 | 45 |
N.S. |
1 | 1.20 | 1.00 | 1.06 | 0.94 | 1.03 | 1.06 | 0.94 | 1.29 |
time (sec) |
N/A | 0.223 | 0.015 | 0.464 | 0.273 | 0.249 | 0.090 | 0.274 | 0.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 90 | 73 | 101 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.23 | 1.00 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.416 | 0.016 | 0.642 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 75 | 98 | 136 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.32 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.385 | 0.111 | 0.433 | 0.000 | 0.000 | 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 | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 46 | 43 | 47 | 39 | 44 | 0 | 82 | 0 |
N.S. |
1 | 1.07 | 1.00 | 1.09 | 0.91 | 1.02 | 0.00 | 1.91 | 0.00 |
time (sec) |
N/A | 0.266 | 0.021 | 0.488 | 0.282 | 0.261 | 0.000 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 120 | 152 | 166 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 1.23 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.539 | 0.452 | 1.223 | 0.000 | 0.000 | 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 | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 89 | 69 | 82 | 74 | 62 | 0 | 185 | 0 |
N.S. |
1 | 1.02 | 0.79 | 0.94 | 0.85 | 0.71 | 0.00 | 2.13 | 0.00 |
time (sec) |
N/A | 0.370 | 0.031 | 0.517 | 0.281 | 0.253 | 0.000 | 0.348 | 0.000 |
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 | 201 | 303 | 122 | 159 | 171 | 104 | 202 | 175 | 0 |
N.S. |
1 | 1.51 | 0.61 | 0.79 | 0.85 | 0.52 | 1.00 | 0.87 | 0.00 |
time (sec) |
N/A | 1.236 | 0.044 | 2.254 | 0.295 | 0.246 | 0.657 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 167 | 245 | 115 | 151 | 0 | 96 | 167 | 141 | 0 |
N.S. |
1 | 1.47 | 0.69 | 0.90 | 0.00 | 0.57 | 1.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.947 | 0.052 | 1.102 | 0.000 | 0.250 | 0.477 | 0.268 | 0.000 |
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 | 136 | 176 | 95 | 106 | 120 | 78 | 134 | 117 | 0 |
N.S. |
1 | 1.29 | 0.70 | 0.78 | 0.88 | 0.57 | 0.99 | 0.86 | 0.00 |
time (sec) |
N/A | 0.680 | 0.038 | 1.122 | 0.286 | 0.266 | 0.352 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 117 | 85 | 90 | 0 | 69 | 99 | 83 | 0 |
N.S. |
1 | 1.18 | 0.86 | 0.91 | 0.00 | 0.70 | 1.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.478 | 0.030 | 0.636 | 0.000 | 0.250 | 0.274 | 0.275 | 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 | 60 | 69 | 60 | 57 | 59 | 44 | 60 | 56 | 59 |
N.S. |
1 | 1.15 | 1.00 | 0.95 | 0.98 | 0.73 | 1.00 | 0.93 | 0.98 |
time (sec) |
N/A | 0.295 | 0.016 | 0.479 | 0.310 | 0.248 | 0.117 | 0.269 | 0.326 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 123 | 101 | 135 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.22 | 1.00 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.497 | 0.018 | 0.665 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 122 | 127 | 139 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.553 | 0.084 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 107 | 92 | 117 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.90 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.548 | 0.155 | 0.756 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 192 | 194 | 165 | 256 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.86 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.977 | 0.612 | 1.155 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 181 | 151 | 190 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.89 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.910 | 0.245 | 0.792 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 282 | 500 | 167 | 332 | 0 | 153 | 275 | 245 | 0 |
N.S. |
1 | 1.77 | 0.59 | 1.18 | 0.00 | 0.54 | 0.98 | 0.87 | 0.00 |
time (sec) |
N/A | 2.478 | 0.064 | 2.306 | 0.000 | 0.255 | 1.184 | 0.281 | 0.000 |
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 | 250 | 416 | 150 | 197 | 206 | 134 | 248 | 212 | 0 |
N.S. |
1 | 1.66 | 0.60 | 0.79 | 0.82 | 0.54 | 0.99 | 0.85 | 0.00 |
time (sec) |
N/A | 2.120 | 0.051 | 2.456 | 0.304 | 0.260 | 0.923 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 198 | 291 | 135 | 213 | 0 | 121 | 197 | 173 | 0 |
N.S. |
1 | 1.47 | 0.68 | 1.08 | 0.00 | 0.61 | 0.99 | 0.87 | 0.00 |
time (sec) |
N/A | 1.452 | 0.046 | 1.189 | 0.000 | 0.267 | 0.667 | 0.280 | 0.000 |
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 | 166 | 230 | 114 | 130 | 146 | 99 | 165 | 140 | 0 |
N.S. |
1 | 1.39 | 0.69 | 0.78 | 0.88 | 0.60 | 0.99 | 0.84 | 0.00 |
time (sec) |
N/A | 1.178 | 0.062 | 1.222 | 0.291 | 0.264 | 0.473 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 132 | 96 | 113 | 0 | 82 | 110 | 101 | 0 |
N.S. |
1 | 1.18 | 0.86 | 1.01 | 0.00 | 0.73 | 0.98 | 0.90 | 0.00 |
time (sec) |
N/A | 0.710 | 0.030 | 0.698 | 0.000 | 0.247 | 0.354 | 0.293 | 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 | 69 | 85 | 69 | 67 | 74 | 55 | 70 | 65 | 63 |
N.S. |
1 | 1.23 | 1.00 | 0.97 | 1.07 | 0.80 | 1.01 | 0.94 | 0.91 |
time (sec) |
N/A | 0.384 | 0.021 | 0.462 | 0.281 | 0.243 | 0.184 | 0.274 | 0.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 154 | 119 | 168 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.29 | 1.00 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.608 | 0.017 | 0.639 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 176 | 185 | 549 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 3.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.694 | 0.738 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 136 | 115 | 150 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 0.95 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.671 | 0.283 | 0.857 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 304 | 304 | 1475 | 419 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 4.85 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.369 | 12.057 | 1.287 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 48 | 40 | 40 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 0.87 | 0.73 | 0.73 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.276 | 0.068 | 0.776 | 0.000 | 0.000 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 39 | 33 | 33 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.91 | 0.77 | 0.77 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.259 | 0.073 | 0.661 | 0.000 | 0.000 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 37 | 31 | 31 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.90 | 0.76 | 0.76 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.259 | 0.053 | 0.662 | 0.000 | 0.000 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 28 | 24 | 24 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.97 | 0.83 | 0.83 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.247 | 0.056 | 0.656 | 0.000 | 0.000 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 20 | 22 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.96 | 0.74 | 0.81 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.242 | 0.038 | 0.605 | 0.000 | 0.000 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.242 | 0.022 | 0.694 | 0.000 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 11 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.192 | 0.027 | 0.463 | 0.000 | 0.000 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 |
time (sec) |
N/A | 0.161 | 0.182 | 3.198 | 0.329 | 0.233 | 0.310 | 0.289 | 0.256 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.159 | 0.792 | 1.747 | 0.335 | 0.228 | 0.331 | 0.322 | 0.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 75 | 86 | 105 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 0.91 | 1.05 | 1.28 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.250 | 0.138 | 0.875 | 0.000 | 0.000 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 66 | 63 | 78 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 0.94 | 0.90 | 1.11 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.237 | 0.140 | 0.796 | 0.000 | 0.000 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 64 | 61 | 81 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 0.94 | 0.90 | 1.19 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.237 | 0.148 | 0.698 | 0.000 | 0.000 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 55 | 50 | 54 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 0.98 | 0.89 | 0.96 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.224 | 0.127 | 0.653 | 0.000 | 0.000 | 0.000 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 53 | 50 | 57 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 0.98 | 0.93 | 1.06 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.221 | 0.109 | 0.684 | 0.000 | 0.000 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 37 | 30 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.79 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.231 | 0.075 | 0.609 | 0.000 | 0.000 | 0.000 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 32 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.309 | 0.038 | 0.530 | 0.000 | 0.000 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 127 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 12.70 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.157 | 1.140 | 4.814 | 0.536 | 0.239 | 0.395 | 0.307 | 0.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 136 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 13.60 | 1.20 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.155 | 14.827 | 1.755 | 0.647 | 0.238 | 0.441 | 0.362 | 0.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 132 | 103 | 121 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.35 | 1.05 | 1.23 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.651 | 0.100 | 0.739 | 0.000 | 0.000 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 108 | 70 | 82 | 0 | 0 | 0 | 75 | 0 |
N.S. |
1 | 1.30 | 0.84 | 0.99 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.724 | 0.112 | 0.597 | 0.000 | 0.000 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 102 | 65 | 82 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.24 | 0.79 | 1.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.749 | 0.103 | 0.705 | 0.000 | 0.000 | 0.000 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 69 | 63 | 43 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.10 | 1.00 | 0.68 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.653 | 0.037 | 0.612 | 0.000 | 0.000 | 0.000 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 54 | 47 | 43 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.06 | 0.92 | 0.84 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.366 | 0.034 | 0.536 | 0.000 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 124 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 12.40 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.158 | 0.611 | 3.166 | 1.384 | 0.236 | 0.506 | 0.314 | 0.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 143 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 14.30 | 1.20 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.159 | 7.671 | 1.667 | 1.703 | 0.235 | 0.592 | 0.388 | 0.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 208 | 159 | 171 | 0 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.32 | 1.01 | 1.08 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.623 | 0.130 | 0.690 | 0.000 | 0.000 | 0.000 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 178 | 107 | 114 | 0 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.24 | 0.75 | 0.80 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.727 | 0.219 | 0.611 | 0.000 | 0.000 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 174 | 112 | 117 | 0 | 0 | 0 | 121 | 0 |
N.S. |
1 | 1.23 | 0.79 | 0.83 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.934 | 0.130 | 0.640 | 0.000 | 0.000 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 107 | 86 | 60 | 0 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.10 | 0.89 | 0.62 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.616 | 0.086 | 0.613 | 0.000 | 0.000 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 90 | 71 | 63 | 0 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.15 | 0.91 | 0.81 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.512 | 0.041 | 0.438 | 0.000 | 0.000 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 200 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 20.00 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.155 | 3.525 | 3.005 | 4.424 | 0.230 | 0.578 | 0.317 | 0.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 229 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 22.90 | 1.20 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.154 | 17.336 | 1.615 | 5.042 | 0.240 | 0.802 | 0.436 | 0.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 120 | 194 | 143 | 0 | 0 | 0 | 247 | 0 |
N.S. |
1 | 0.99 | 1.60 | 1.18 | 0.00 | 0.00 | 0.00 | 2.04 | 0.00 |
time (sec) |
N/A | 0.463 | 0.084 | 0.943 | 0.000 | 0.000 | 0.000 | 0.339 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 94 | 131 | 91 | 0 | 0 | 0 | 153 | 0 |
N.S. |
1 | 0.99 | 1.38 | 0.96 | 0.00 | 0.00 | 0.00 | 1.61 | 0.00 |
time (sec) |
N/A | 0.429 | 0.057 | 0.859 | 0.000 | 0.000 | 0.000 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 88 | 128 | 96 | 0 | 0 | 0 | 165 | 0 |
N.S. |
1 | 1.02 | 1.49 | 1.12 | 0.00 | 0.00 | 0.00 | 1.92 | 0.00 |
time (sec) |
N/A | 0.418 | 0.070 | 0.835 | 0.000 | 0.000 | 0.000 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 57 | 49 | 43 | 0 | 0 | 0 | 71 | 0 |
N.S. |
1 | 0.97 | 0.83 | 0.73 | 0.00 | 0.00 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.376 | 0.027 | 0.667 | 0.000 | 0.000 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 69 | 49 | 0 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.00 | 1.57 | 1.11 | 0.00 | 0.00 | 0.00 | 1.89 | 0.00 |
time (sec) |
N/A | 0.336 | 0.023 | 0.876 | 0.000 | 0.000 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.160 | 0.204 | 1.050 | 0.000 | 0.000 | 0.401 | 0.454 | 0.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 282 | 337 | 185 | 193 | 0 | 0 | 0 | 355 | 0 |
N.S. |
1 | 1.20 | 0.66 | 0.68 | 0.00 | 0.00 | 0.00 | 1.26 | 0.00 |
time (sec) |
N/A | 1.888 | 0.094 | 0.994 | 0.000 | 0.000 | 0.000 | 0.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 201 | 128 | 118 | 0 | 0 | 0 | 225 | 0 |
N.S. |
1 | 1.28 | 0.82 | 0.75 | 0.00 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 1.440 | 0.054 | 0.918 | 0.000 | 0.000 | 0.000 | 0.334 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 193 | 125 | 130 | 0 | 0 | 0 | 237 | 0 |
N.S. |
1 | 1.31 | 0.85 | 0.88 | 0.00 | 0.00 | 0.00 | 1.61 | 0.00 |
time (sec) |
N/A | 1.003 | 0.076 | 0.867 | 0.000 | 0.000 | 0.000 | 0.341 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 95 | 64 | 64 | 0 | 0 | 0 | 107 | 0 |
N.S. |
1 | 1.07 | 0.72 | 0.72 | 0.00 | 0.00 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.748 | 0.048 | 0.786 | 0.000 | 0.000 | 0.000 | 0.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 76 | 66 | 72 | 0 | 0 | 0 | 119 | 0 |
N.S. |
1 | 1.01 | 0.88 | 0.96 | 0.00 | 0.00 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 0.406 | 0.027 | 0.776 | 0.000 | 0.000 | 0.000 | 0.347 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.155 | 0.204 | 1.045 | 0.000 | 0.000 | 1.526 | 0.533 | 0.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 298 | 402 | 194 | 233 | 0 | 0 | 0 | 463 | 0 |
N.S. |
1 | 1.35 | 0.65 | 0.78 | 0.00 | 0.00 | 0.00 | 1.55 | 0.00 |
time (sec) |
N/A | 2.281 | 0.081 | 1.053 | 0.000 | 0.000 | 0.000 | 0.374 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 205 | 272 | 131 | 154 | 0 | 0 | 0 | 297 | 0 |
N.S. |
1 | 1.33 | 0.64 | 0.75 | 0.00 | 0.00 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 1.613 | 0.055 | 0.954 | 0.000 | 0.000 | 0.000 | 0.351 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 235 | 128 | 156 | 0 | 0 | 0 | 309 | 0 |
N.S. |
1 | 1.32 | 0.72 | 0.88 | 0.00 | 0.00 | 0.00 | 1.74 | 0.00 |
time (sec) |
N/A | 1.333 | 0.065 | 0.944 | 0.000 | 0.000 | 0.000 | 0.362 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 131 | 73 | 79 | 0 | 0 | 0 | 143 | 0 |
N.S. |
1 | 1.10 | 0.61 | 0.66 | 0.00 | 0.00 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.799 | 0.069 | 0.773 | 0.000 | 0.000 | 0.000 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 95 | 69 | 88 | 0 | 0 | 0 | 155 | 0 |
N.S. |
1 | 1.08 | 0.78 | 1.00 | 0.00 | 0.00 | 0.00 | 1.76 | 0.00 |
time (sec) |
N/A | 0.525 | 0.023 | 0.776 | 0.000 | 0.000 | 0.000 | 0.348 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.154 | 0.200 | 1.146 | 0.000 | 0.000 | 19.287 | 0.553 | 0.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 102 | 192 | 72 | 0 | 0 | 0 | 139 | 0 |
N.S. |
1 | 0.96 | 1.81 | 0.68 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.292 | 0.078 | 0.831 | 0.000 | 0.000 | 0.000 | 0.323 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 64 | 130 | 43 | 0 | 0 | 0 | 81 | 0 |
N.S. |
1 | 0.98 | 2.00 | 0.66 | 0.00 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.262 | 0.054 | 0.753 | 0.000 | 0.000 | 0.000 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 70 | 126 | 50 | 0 | 0 | 0 | 93 | 0 |
N.S. |
1 | 0.99 | 1.77 | 0.70 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.268 | 0.065 | 0.818 | 0.000 | 0.000 | 0.000 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 21 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.267 | 0.020 | 0.629 | 0.000 | 0.000 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 68 | 26 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 2.19 | 0.84 | 0.00 | 0.00 | 0.00 | 1.52 | 0.00 |
time (sec) |
N/A | 0.227 | 0.021 | 0.704 | 0.000 | 0.000 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.153 | 0.200 | 0.993 | 0.000 | 0.000 | 0.400 | 0.384 | 0.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 14 | 12 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 1.17 | 1.00 | 1.00 |
time (sec) |
N/A | 0.156 | 1.961 | 1.080 | 0.000 | 0.000 | 0.525 | 0.402 | 0.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 165 | 306 | 182 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.79 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.319 | 0.222 | 1.072 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 126 | 226 | 121 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.78 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.290 | 0.358 | 0.937 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |