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 | 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 | 14 | 14 | 16 | 14 | 16 | 18 | 12 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.29 | 0.86 | 1.14 | 1.14 |
time (sec) |
N/A | 0.167 | 0.028 | 0.097 | 0.335 | 0.285 | 27.605 | 1.129 | 5.942 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 24 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.20 | 0.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.188 | 0.035 | 0.007 | 0.597 | 0.265 | 0.000 | 1.003 | 0.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 24 | 35 | 0 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.59 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.202 | 0.040 | 0.007 | 2.603 | 0.281 | 0.000 | 1.290 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | F(-1) | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 0 | 22 | 1281 | 63 | 0 | 24 | 24 |
N.S. |
1 | 1.00 | 0.00 | 1.00 | 58.23 | 2.86 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.193 | 0.000 | 0.303 | 24.077 | 0.297 | 0.000 | 7.348 | 6.423 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 1103 | 52 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 55.15 | 2.60 | 0.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.181 | 16.276 | 0.355 | 2.100 | 0.288 | 0.000 | 5.685 | 6.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 974 | 47 | 0 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 69.57 | 3.36 | 0.00 | 1.14 | 1.14 |
time (sec) |
N/A | 0.165 | 2.048 | 0.180 | 0.567 | 0.294 | 0.000 | 3.644 | 6.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 1103 | 52 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 55.15 | 2.60 | 0.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.178 | 1.349 | 0.010 | 2.106 | 0.270 | 0.000 | 4.931 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | F(-1) | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 0 | 22 | 1281 | 63 | 0 | 24 | 24 |
N.S. |
1 | 1.00 | 0.00 | 1.00 | 58.23 | 2.86 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.191 | 0.000 | 0.007 | 24.281 | 0.293 | 0.000 | 7.523 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 24 | 26 | 0 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.18 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.189 | 1.228 | 0.192 | 0.708 | 0.306 | 0.000 | 0.493 | 6.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 115 | 96 | 94 | 0 | 0 | 80 | 0 | 0 | 0 |
N.S. |
1 | 0.83 | 0.82 | 0.00 | 0.00 | 0.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.507 | 0.121 | 0.000 | 0.000 | 0.092 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 83 | 47 | 151 | 146 | 74 | 129 | 0 | 109 |
N.S. |
1 | 0.86 | 0.49 | 1.57 | 1.52 | 0.77 | 1.34 | 0.00 | 1.14 |
time (sec) |
N/A | 0.618 | 0.271 | 0.401 | 0.345 | 0.284 | 1.780 | 0.000 | 7.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 63 | 40 | 133 | 99 | 64 | 107 | 0 | 88 |
N.S. |
1 | 0.85 | 0.54 | 1.80 | 1.34 | 0.86 | 1.45 | 0.00 | 1.19 |
time (sec) |
N/A | 0.502 | 0.248 | 0.366 | 0.315 | 0.265 | 1.011 | 0.000 | 6.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 44 | 30 | 117 | 60 | 55 | 70 | 0 | 63 |
N.S. |
1 | 0.98 | 0.67 | 2.60 | 1.33 | 1.22 | 1.56 | 0.00 | 1.40 |
time (sec) |
N/A | 0.372 | 0.163 | 0.363 | 0.307 | 0.261 | 0.620 | 0.000 | 6.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 105 | 31 | 43 | 49 | 0 | 49 |
N.S. |
1 | 1.00 | 1.00 | 4.20 | 1.24 | 1.72 | 1.96 | 0.00 | 1.96 |
time (sec) |
N/A | 0.228 | 0.059 | 0.720 | 0.288 | 0.290 | 0.423 | 0.000 | 6.288 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 55 | 36 | 36 | 106 | 42 | 57 | 0 | 0 | 0 |
N.S. |
1 | 0.65 | 0.65 | 1.93 | 0.76 | 1.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.467 | 0.110 | 0.385 | 0.327 | 0.261 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 51 | 51 | 102 | 229 | 70 | 0 | 0 | 0 |
N.S. |
1 | 0.66 | 0.66 | 1.32 | 2.97 | 0.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.535 | 0.198 | 0.380 | 0.345 | 0.258 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 70 | 69 | 123 | 256 | 90 | 0 | 0 | 0 |
N.S. |
1 | 0.60 | 0.59 | 1.06 | 2.21 | 0.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.657 | 0.209 | 0.395 | 0.345 | 0.299 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 153 | 130 | 138 | 0 | 0 | 98 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 0.90 | 0.00 | 0.00 | 0.64 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.494 | 0.333 | 0.000 | 0.000 | 0.097 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 57 | 38 | 135 | 32 | 67 | 85 | 0 | 71 |
N.S. |
1 | 0.98 | 0.66 | 2.33 | 0.55 | 1.16 | 1.47 | 0.00 | 1.22 |
time (sec) |
N/A | 0.471 | 0.066 | 0.453 | 0.309 | 0.273 | 1.707 | 0.000 | 6.793 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 119 | 105 | 240 | 73 | 134 | 0 | 0 | 0 |
N.S. |
1 | 0.77 | 0.68 | 1.55 | 0.47 | 0.86 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.497 | 0.292 | 0.446 | 0.320 | 0.294 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 119 | 16 | 51 | 63 | 0 | 53 |
N.S. |
1 | 1.00 | 1.00 | 3.84 | 0.52 | 1.65 | 2.03 | 0.00 | 1.71 |
time (sec) |
N/A | 0.355 | 0.076 | 0.735 | 0.300 | 0.283 | 0.642 | 0.000 | 6.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 94 | 80 | 157 | 51 | 120 | 0 | 0 | 0 |
N.S. |
1 | 0.80 | 0.68 | 1.34 | 0.44 | 1.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.329 | 0.091 | 0.443 | 0.317 | 0.320 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 73 | 50 | 47 | 128 | 47 | 67 | 0 | 0 | 0 |
N.S. |
1 | 0.68 | 0.64 | 1.75 | 0.64 | 0.92 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.382 | 0.095 | 0.434 | 0.380 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 112 | 105 | 232 | 76 | 134 | 0 | 0 | 0 |
N.S. |
1 | 0.83 | 0.78 | 1.72 | 0.56 | 0.99 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.474 | 0.250 | 0.431 | 0.380 | 0.281 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 64 | 67 | 119 | 52 | 86 | 0 | 0 | 0 |
N.S. |
1 | 0.65 | 0.68 | 1.21 | 0.53 | 0.88 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.626 | 0.252 | 0.457 | 0.383 | 0.267 | 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 | 157 | 134 | 142 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.573 | 0.399 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 143 | 120 | 129 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.493 | 0.258 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 143 | 120 | 129 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.474 | 0.247 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 143 | 120 | 129 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.418 | 0.216 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 135 | 112 | 119 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.83 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.303 | 0.130 | 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 | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 73 | 50 | 47 | 131 | 144 | 70 | 0 | 0 | 0 |
N.S. |
1 | 0.68 | 0.64 | 1.79 | 1.97 | 0.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.412 | 0.158 | 0.829 | 0.465 | 0.340 | 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 | 139 | 116 | 110 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.83 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.425 | 0.200 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 143 | 120 | 114 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.433 | 0.213 | 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 | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 169 | 126 | 142 | 0 | 0 | 112 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 0.84 | 0.00 | 0.00 | 0.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.528 | 0.495 | 0.000 | 0.000 | 0.108 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 121 | 79 | 208 | 286 | 111 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.48 | 1.26 | 1.73 | 0.67 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.521 | 0.300 | 0.390 | 0.333 | 0.275 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 101 | 69 | 190 | 219 | 95 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.50 | 1.37 | 1.58 | 0.68 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.456 | 0.288 | 0.388 | 0.393 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 66 | 55 | 174 | 162 | 82 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 0.70 | 2.20 | 2.05 | 1.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.352 | 0.184 | 0.396 | 0.513 | 0.287 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 48 | 47 | 158 | 116 | 60 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 0.85 | 2.87 | 2.11 | 1.09 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.247 | 0.084 | 0.694 | 0.287 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 99 | 56 | 50 | 121 | 52 | 63 | 0 | 0 | 0 |
N.S. |
1 | 0.57 | 0.51 | 1.22 | 0.53 | 0.64 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.420 | 0.119 | 0.381 | 0.328 | 0.288 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 60 | 65 | 112 | 265 | 80 | 0 | 0 | 0 |
N.S. |
1 | 0.70 | 0.76 | 1.30 | 3.08 | 0.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.579 | 0.152 | 0.431 | 0.330 | 0.318 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 101 | 85 | 137 | 296 | 104 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 0.71 | 1.15 | 2.49 | 0.87 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.545 | 0.215 | 0.393 | 0.339 | 0.293 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 209 | 158 | 189 | 0 | 0 | 130 | 0 | 0 | 0 |
N.S. |
1 | 0.76 | 0.90 | 0.00 | 0.00 | 0.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.509 | 0.770 | 0.000 | 0.000 | 0.107 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 81 | 67 | 200 | 47 | 96 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 0.74 | 2.20 | 0.52 | 1.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.434 | 0.279 | 0.436 | 0.297 | 0.311 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 118 | 113 | 309 | 99 | 149 | 0 | 0 | 0 |
N.S. |
1 | 0.61 | 0.58 | 1.58 | 0.51 | 0.76 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.434 | 0.281 | 0.459 | 0.297 | 0.373 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 61 | 55 | 182 | 28 | 72 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.85 | 2.80 | 0.43 | 1.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.384 | 0.131 | 0.704 | 0.287 | 0.332 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 97 | 93 | 224 | 76 | 119 | 0 | 0 | 0 |
N.S. |
1 | 0.66 | 0.63 | 1.51 | 0.51 | 0.80 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.302 | 0.077 | 0.402 | 0.302 | 0.320 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 115 | 64 | 60 | 145 | 55 | 73 | 0 | 0 | 0 |
N.S. |
1 | 0.56 | 0.52 | 1.26 | 0.48 | 0.63 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.370 | 0.144 | 0.454 | 0.349 | 0.336 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 111 | 107 | 301 | 90 | 133 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 0.81 | 2.28 | 0.68 | 1.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.572 | 0.199 | 0.445 | 0.359 | 0.331 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 84 | 79 | 134 | 64 | 100 | 0 | 0 | 0 |
N.S. |
1 | 0.52 | 0.49 | 0.83 | 0.40 | 0.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.457 | 0.182 | 0.450 | 0.352 | 0.289 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 217 | 166 | 194 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.76 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.617 | 0.734 | 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 | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 188 | 137 | 161 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.530 | 0.501 | 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 | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 188 | 137 | 168 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.517 | 0.507 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 188 | 137 | 160 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.477 | 0.524 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 178 | 127 | 149 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.71 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.339 | 0.221 | 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 | C | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 121 | 70 | 63 | 149 | 153 | 78 | 0 | 0 | 0 |
N.S. |
1 | 0.58 | 0.52 | 1.23 | 1.26 | 0.64 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.394 | 0.187 | 0.757 | 0.471 | 0.325 | 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 | 180 | 129 | 125 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.72 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.494 | 0.326 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 184 | 133 | 129 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.72 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.515 | 0.354 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |