Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 35 | 33 | 28 | 30 | 45 | 31 | 32 | 25 |
N.S. |
1 | 0.97 | 0.92 | 0.78 | 0.83 | 1.25 | 0.86 | 0.89 | 0.69 |
time (sec) |
N/A | 0.163 | 0.017 | 0.248 | 0.182 | 0.230 | 0.050 | 0.282 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 81 | 87 | 60 | 90 | 165 | 88 | 62 | 65 |
N.S. |
1 | 0.93 | 1.00 | 0.69 | 1.03 | 1.90 | 1.01 | 0.71 | 0.75 |
time (sec) |
N/A | 0.214 | 0.027 | 0.262 | 0.194 | 0.245 | 0.092 | 0.305 | 0.095 |
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 | 81 | 86 | 70 | 62 | 69 | 116 | 80 | 67 | 77 |
N.S. |
1 | 1.06 | 0.86 | 0.77 | 0.85 | 1.43 | 0.99 | 0.83 | 0.95 |
time (sec) |
N/A | 0.227 | 0.035 | 0.849 | 0.263 | 0.238 | 0.102 | 0.311 | 0.115 |
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 | 104 | 75 | 87 | 60 | 90 | 165 | 90 | 62 | 90 |
N.S. |
1 | 0.72 | 0.84 | 0.58 | 0.87 | 1.59 | 0.87 | 0.60 | 0.87 |
time (sec) |
N/A | 0.218 | 0.025 | 0.253 | 0.179 | 0.246 | 0.076 | 0.299 | 0.242 |
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 | 102 | 101 | 99 | 64 | 94 | 173 | 90 | 66 | 85 |
N.S. |
1 | 0.99 | 0.97 | 0.63 | 0.92 | 1.70 | 0.88 | 0.65 | 0.83 |
time (sec) |
N/A | 0.235 | 0.052 | 0.284 | 0.178 | 0.236 | 0.091 | 0.292 | 0.246 |
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 | 40 | 44 | 40 | 35 | 39 | 39 | 37 | 47 | 37 |
N.S. |
1 | 1.10 | 1.00 | 0.88 | 0.98 | 0.98 | 0.92 | 1.18 | 0.92 |
time (sec) |
N/A | 0.171 | 0.006 | 0.179 | 0.189 | 0.242 | 0.114 | 0.293 | 0.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 102 | 62 | 55 | 83 | 113 | 102 | 58 | 79 |
N.S. |
1 | 1.23 | 0.75 | 0.66 | 1.00 | 1.36 | 1.23 | 0.70 | 0.95 |
time (sec) |
N/A | 0.190 | 0.025 | 0.292 | 0.261 | 0.233 | 0.323 | 0.288 | 0.149 |
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 | 49 | 53 | 43 | 32 | 31 | 37 | 42 | 31 | 31 |
N.S. |
1 | 1.08 | 0.88 | 0.65 | 0.63 | 0.76 | 0.86 | 0.63 | 0.63 |
time (sec) |
N/A | 0.236 | 0.025 | 0.203 | 0.207 | 0.234 | 0.235 | 0.277 | 0.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 55 | 32 | 31 | 31 | 48 | 31 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.58 | 0.56 | 0.56 | 0.87 | 0.56 | 0.56 |
time (sec) |
N/A | 0.545 | 0.193 | 0.216 | 0.195 | 0.241 | 1.214 | 0.312 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 16 | 22 | 19 | 18 | 18 | 19 | 18 | 18 |
N.S. |
1 | 0.73 | 1.00 | 0.86 | 0.82 | 0.82 | 0.86 | 0.82 | 0.82 |
time (sec) |
N/A | 0.153 | 0.016 | 0.092 | 0.192 | 0.236 | 0.052 | 0.279 | 0.134 |
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 | 16 | 18 | 13 | 12 | 11 | 22 | 12 | 11 |
N.S. |
1 | 1.07 | 1.20 | 0.87 | 0.80 | 0.73 | 1.47 | 0.80 | 0.73 |
time (sec) |
N/A | 0.142 | 0.017 | 0.040 | 0.217 | 0.233 | 0.486 | 0.275 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 27 | 24 | 21 | 20 | 19 | 20 | 21 | 19 |
N.S. |
1 | 1.08 | 0.96 | 0.84 | 0.80 | 0.76 | 0.80 | 0.84 | 0.76 |
time (sec) |
N/A | 0.167 | 0.021 | 0.179 | 0.189 | 0.233 | 0.056 | 0.313 | 0.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 23 | 31 | 26 | 25 | 25 | 27 | 26 | 25 |
N.S. |
1 | 0.70 | 0.94 | 0.79 | 0.76 | 0.76 | 0.82 | 0.79 | 0.76 |
time (sec) |
N/A | 0.180 | 0.356 | 0.065 | 0.190 | 0.239 | 0.525 | 0.309 | 0.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 33 | 24 | 17 | 19 | 19 | 134 | 19 | 16 |
N.S. |
1 | 1.14 | 0.83 | 0.59 | 0.66 | 0.66 | 4.62 | 0.66 | 0.55 |
time (sec) |
N/A | 0.149 | 0.033 | 0.201 | 0.184 | 0.232 | 0.678 | 0.276 | 0.575 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 56 | 36 | 30 | 55 | 63 | 3966 | 49 | 43 |
N.S. |
1 | 1.08 | 0.69 | 0.58 | 1.06 | 1.21 | 76.27 | 0.94 | 0.83 |
time (sec) |
N/A | 0.148 | 0.054 | 0.214 | 0.186 | 0.237 | 1.557 | 0.316 | 0.049 |
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 | 118 | 132 | 70 | 59 | 111 | 125 | 0 | 104 | 96 |
N.S. |
1 | 1.12 | 0.59 | 0.50 | 0.94 | 1.06 | 0.00 | 0.88 | 0.81 |
time (sec) |
N/A | 0.202 | 0.094 | 0.310 | 0.190 | 0.240 | 0.000 | 0.299 | 0.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 104 | 118 | 90 | 85 | 105 | 86 | 12993 | 82 | 120 |
N.S. |
1 | 1.13 | 0.87 | 0.82 | 1.01 | 0.83 | 124.93 | 0.79 | 1.15 |
time (sec) |
N/A | 0.197 | 0.242 | 0.642 | 0.291 | 0.254 | 37.158 | 0.314 | 0.244 |
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 | 38 | 57 | 64 | 39 | 43 | 32 | 0 | 29 | 43 |
N.S. |
1 | 1.50 | 1.68 | 1.03 | 1.13 | 0.84 | 0.00 | 0.76 | 1.13 |
time (sec) |
N/A | 0.152 | 0.094 | 0.187 | 0.279 | 0.234 | 0.000 | 0.311 | 0.219 |
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 | 92 | 131 | 99 | 141 | 130 | 73 | 0 | 103 | 140 |
N.S. |
1 | 1.42 | 1.08 | 1.53 | 1.41 | 0.79 | 0.00 | 1.12 | 1.52 |
time (sec) |
N/A | 0.200 | 0.380 | 0.161 | 0.294 | 0.238 | 0.000 | 0.311 | 0.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 47 | 64 | 0 | 65 | 0 | 74 | 95 |
N.S. |
1 | 1.00 | 0.87 | 1.19 | 0.00 | 1.20 | 0.00 | 1.37 | 1.76 |
time (sec) |
N/A | 0.218 | 0.119 | 0.276 | 0.000 | 0.245 | 0.000 | 0.303 | 0.646 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | C | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 304 | 474 | 157 | 0 | 0 | 367 | 0 | 0 | 0 |
N.S. |
1 | 1.56 | 0.52 | 0.00 | 0.00 | 1.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.923 | 11.239 | 0.000 | 0.000 | 0.263 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | C | F | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 292 | 0 | 455 | 0 | 0 | 785 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.56 | 0.00 | 0.00 | 2.69 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 36.725 | 0.000 | 0.000 | 0.289 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 27 | 25 | 22 | 0 | 47 | 0 | 0 | 25 |
N.S. |
1 | 1.08 | 1.00 | 0.88 | 0.00 | 1.88 | 0.00 | 0.00 | 1.00 |
time (sec) |
N/A | 0.188 | 0.022 | 0.229 | 0.000 | 0.234 | 0.000 | 0.000 | 0.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 28 | 25 | 22 | 0 | 69 | 0 | 0 | 25 |
N.S. |
1 | 1.12 | 1.00 | 0.88 | 0.00 | 2.76 | 0.00 | 0.00 | 1.00 |
time (sec) |
N/A | 0.205 | 0.022 | 0.830 | 0.000 | 0.234 | 0.000 | 0.000 | 0.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 70 | 30 | 27 | 0 | 77 | 0 | 0 | 30 |
N.S. |
1 | 1.32 | 0.57 | 0.51 | 0.00 | 1.45 | 0.00 | 0.00 | 0.57 |
time (sec) |
N/A | 0.210 | 0.051 | 1.448 | 0.000 | 0.226 | 0.000 | 0.000 | 0.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 114 | 123 | 370 | 0 | 128 | 0 | 0 | 0 |
N.S. |
1 | 1.70 | 1.84 | 5.52 | 0.00 | 1.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.217 | 0.132 | 0.532 | 0.000 | 0.233 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 94 | 96 | 86 | 0 | 142 | 0 | 83 | 0 |
N.S. |
1 | 0.77 | 0.79 | 0.70 | 0.00 | 1.16 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.487 | 0.120 | 0.762 | 0.000 | 0.250 | 0.000 | 0.344 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 150 | 284 | 229 | 1374 | 0 | 280 | 0 | 0 | 0 |
N.S. |
1 | 1.89 | 1.53 | 9.16 | 0.00 | 1.87 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.323 | 0.550 | 5.166 | 0.000 | 0.244 | 0.000 | 0.000 | 0.000 |
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 | 43 | 43 | 39 | 26 | 51 | 64 | 0 | 23 | 27 |
N.S. |
1 | 1.00 | 0.91 | 0.60 | 1.19 | 1.49 | 0.00 | 0.53 | 0.63 |
time (sec) |
N/A | 0.152 | 0.231 | 0.276 | 0.224 | 0.236 | 0.000 | 0.287 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 37 | 35 | 0 | 62 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.83 | 0.00 | 1.48 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.170 | 0.025 | 0.154 | 0.000 | 0.242 | 0.000 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 106 | 58 | 71 | 0 | 138 | 0 | 75 | 0 |
N.S. |
1 | 0.76 | 0.42 | 0.51 | 0.00 | 0.99 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.202 | 0.064 | 0.165 | 0.000 | 0.242 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 98 | 123 | 446 | 0 | 128 | 0 | 0 | 0 |
N.S. |
1 | 1.31 | 1.64 | 5.95 | 0.00 | 1.71 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.187 | 0.131 | 0.566 | 0.000 | 0.238 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 27 | 23 | 20 | 0 | 22 | 0 | 0 | 24 |
N.S. |
1 | 0.93 | 0.79 | 0.69 | 0.00 | 0.76 | 0.00 | 0.00 | 0.83 |
time (sec) |
N/A | 0.158 | 0.020 | 0.070 | 0.000 | 0.231 | 0.000 | 0.000 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 33 | 29 | 0 | 44 | 0 | 0 | 37 |
N.S. |
1 | 1.00 | 0.36 | 0.32 | 0.00 | 0.48 | 0.00 | 0.00 | 0.40 |
time (sec) |
N/A | 0.191 | 0.051 | 0.083 | 0.000 | 0.255 | 0.000 | 0.000 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 32 | 15 | 16 | 33 | 20 | 36 | 16 |
N.S. |
1 | 1.00 | 1.68 | 0.79 | 0.84 | 1.74 | 1.05 | 1.89 | 0.84 |
time (sec) |
N/A | 0.141 | 0.096 | 0.348 | 0.273 | 0.239 | 0.253 | 0.295 | 0.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 12 | 23 | 5 | 8 | 29 | 3 | 24 | 4 |
N.S. |
1 | 1.50 | 2.88 | 0.62 | 1.00 | 3.62 | 0.38 | 3.00 | 0.50 |
time (sec) |
N/A | 0.135 | 0.082 | 0.293 | 0.279 | 0.268 | 0.245 | 0.275 | 0.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 33 | 12 | 11 | 40 | 12 | 31 | 11 |
N.S. |
1 | 1.00 | 2.75 | 1.00 | 0.92 | 3.33 | 1.00 | 2.58 | 0.92 |
time (sec) |
N/A | 0.132 | 0.093 | 0.256 | 0.263 | 0.247 | 0.256 | 0.283 | 0.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 24 | 0 | 23 | 0 | 51 | 79 |
N.S. |
1 | 1.00 | 1.06 | 0.77 | 0.00 | 0.74 | 0.00 | 1.65 | 2.55 |
time (sec) |
N/A | 0.134 | 0.144 | 0.582 | 0.000 | 0.244 | 0.000 | 0.286 | 0.583 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 40 | 22 | 0 | 54 | 0 | 57 | 61 |
N.S. |
1 | 1.00 | 1.29 | 0.71 | 0.00 | 1.74 | 0.00 | 1.84 | 1.97 |
time (sec) |
N/A | 0.142 | 0.137 | 0.245 | 0.000 | 0.240 | 0.000 | 0.273 | 0.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 21 | 112 | 48 | 37 | 42 | 78 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 4.67 | 2.00 | 1.54 | 1.75 | 3.25 |
time (sec) |
N/A | 0.145 | 0.060 | 0.339 | 0.274 | 0.240 | 2.274 | 0.266 | 0.831 |
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 | 25 | 25 | 25 | 21 | 101 | 32 | 24 | 20 | 83 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 4.04 | 1.28 | 0.96 | 0.80 | 3.32 |
time (sec) |
N/A | 0.146 | 0.039 | 0.458 | 0.287 | 0.244 | 2.288 | 0.288 | 0.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 57 | 37 | 0 | 72 | 0 | 74 | 107 |
N.S. |
1 | 1.00 | 1.33 | 0.86 | 0.00 | 1.67 | 0.00 | 1.72 | 2.49 |
time (sec) |
N/A | 0.164 | 0.164 | 0.598 | 0.000 | 0.249 | 0.000 | 0.312 | 0.115 |
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 | 62 | 62 | 62 | 49 | 54 | 74 | 0 | 109 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.87 | 1.19 | 0.00 | 1.76 | 0.00 |
time (sec) |
N/A | 0.206 | 0.232 | 0.556 | 0.271 | 0.256 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 81 | 90 | 69 | 0 | 151 | 0 | 164 | 0 |
N.S. |
1 | 0.99 | 1.10 | 0.84 | 0.00 | 1.84 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 0.322 | 0.373 | 0.783 | 0.000 | 0.252 | 0.000 | 0.323 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 102 | 53 | 0 | 237 | 0 | 165 | 0 |
N.S. |
1 | 1.00 | 1.62 | 0.84 | 0.00 | 3.76 | 0.00 | 2.62 | 0.00 |
time (sec) |
N/A | 0.235 | 0.198 | 1.438 | 0.000 | 0.254 | 0.000 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 103 | 128 | 0 | 105 | 0 | 152 | 0 |
N.S. |
1 | 1.00 | 1.84 | 2.29 | 0.00 | 1.88 | 0.00 | 2.71 | 0.00 |
time (sec) |
N/A | 0.197 | 0.184 | 1.034 | 0.000 | 0.253 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 123 | 158 | 0 | 229 | 0 | 257 | 0 |
N.S. |
1 | 1.00 | 1.76 | 2.26 | 0.00 | 3.27 | 0.00 | 3.67 | 0.00 |
time (sec) |
N/A | 0.221 | 0.266 | 1.649 | 0.000 | 0.260 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 124 | 192 | 0 | 1339 | 0 | 629 | 0 |
N.S. |
1 | 1.00 | 1.55 | 2.40 | 0.00 | 16.74 | 0.00 | 7.86 | 0.00 |
time (sec) |
N/A | 0.286 | 1.314 | 0.941 | 0.000 | 0.337 | 0.000 | 0.418 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | F | B | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 85 | 82 | 0 | 81 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.24 | 2.16 | 0.00 | 2.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.159 | 0.574 | 0.537 | 0.000 | 0.234 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 75 | 57 | 40 | 48 | 42 | 153 | 36 | 35 |
N.S. |
1 | 1.15 | 0.88 | 0.62 | 0.74 | 0.65 | 2.35 | 0.55 | 0.54 |
time (sec) |
N/A | 0.167 | 0.174 | 0.287 | 0.275 | 0.245 | 4.218 | 0.279 | 0.031 |
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 | 49 | 54 | 28 | 25 | 37 | 31 | 41 | 51 | 25 |
N.S. |
1 | 1.10 | 0.57 | 0.51 | 0.76 | 0.63 | 0.84 | 1.04 | 0.51 |
time (sec) |
N/A | 0.156 | 0.050 | 0.234 | 0.280 | 0.263 | 1.065 | 0.289 | 0.035 |
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 | 49 | 54 | 28 | 25 | 37 | 44 | 139 | 26 | 187 |
N.S. |
1 | 1.10 | 0.57 | 0.51 | 0.76 | 0.90 | 2.84 | 0.53 | 3.82 |
time (sec) |
N/A | 0.144 | 0.058 | 0.218 | 0.186 | 0.241 | 2.934 | 0.298 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 354 | 10 | 62 | 58 | 11 | 154 |
N.S. |
1 | 1.00 | 1.00 | 29.50 | 0.83 | 5.17 | 4.83 | 0.92 | 12.83 |
time (sec) |
N/A | 0.216 | 0.020 | 0.075 | 0.188 | 0.243 | 0.738 | 0.272 | 0.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 26 | 11 | 10 | 37 | 29 | 22 | 24 |
N.S. |
1 | 1.00 | 2.17 | 0.92 | 0.83 | 3.08 | 2.42 | 1.83 | 2.00 |
time (sec) |
N/A | 0.149 | 0.163 | 0.224 | 0.274 | 0.250 | 4.842 | 0.300 | 0.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 48 | 23 | 0 | 67 | 0 | 64 | 77 |
N.S. |
1 | 1.00 | 1.78 | 0.85 | 0.00 | 2.48 | 0.00 | 2.37 | 2.85 |
time (sec) |
N/A | 0.144 | 0.125 | 0.266 | 0.000 | 0.250 | 0.000 | 0.296 | 0.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 55 | 38 | 0 | 83 | 0 | 101 | 117 |
N.S. |
1 | 1.00 | 1.15 | 0.79 | 0.00 | 1.73 | 0.00 | 2.10 | 2.44 |
time (sec) |
N/A | 0.147 | 0.141 | 0.297 | 0.000 | 0.242 | 0.000 | 0.301 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 54 | 57 | 107 | 77 | 0 | 72 | 0 |
N.S. |
1 | 1.00 | 1.32 | 1.39 | 2.61 | 1.88 | 0.00 | 1.76 | 0.00 |
time (sec) |
N/A | 0.160 | 0.191 | 0.454 | 0.271 | 0.234 | 0.000 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 47 | 50 | 0 | 50 | 0 | 123 | 115 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 0.00 | 1.06 | 0.00 | 2.62 | 2.45 |
time (sec) |
N/A | 0.160 | 0.234 | 0.621 | 0.000 | 0.238 | 0.000 | 0.294 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 108 | 82 | 0 | 160 | 0 | 135 | 159 |
N.S. |
1 | 1.00 | 1.23 | 0.93 | 0.00 | 1.82 | 0.00 | 1.53 | 1.81 |
time (sec) |
N/A | 0.400 | 0.333 | 1.450 | 0.000 | 0.248 | 0.000 | 0.319 | 0.474 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 106 | 654 | 0 | 170 | 0 | 176 | 216 |
N.S. |
1 | 1.00 | 0.78 | 4.81 | 0.00 | 1.25 | 0.00 | 1.29 | 1.59 |
time (sec) |
N/A | 1.376 | 0.377 | 0.040 | 0.000 | 0.244 | 0.000 | 0.300 | 0.645 |
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 | 64 | 66 | 68 | 44 | 63 | 51 | 78 | 45 | 56 |
N.S. |
1 | 1.03 | 1.06 | 0.69 | 0.98 | 0.80 | 1.22 | 0.70 | 0.88 |
time (sec) |
N/A | 0.191 | 0.133 | 0.470 | 0.275 | 0.240 | 0.252 | 0.280 | 0.106 |
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 | 89 | 91 | 76 | 57 | 81 | 60 | 92 | 54 | 75 |
N.S. |
1 | 1.02 | 0.85 | 0.64 | 0.91 | 0.67 | 1.03 | 0.61 | 0.84 |
time (sec) |
N/A | 0.216 | 0.141 | 0.306 | 0.269 | 0.246 | 0.252 | 0.315 | 0.340 |
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 | 113 | 118 | 84 | 65 | 101 | 68 | 102 | 63 | 96 |
N.S. |
1 | 1.04 | 0.74 | 0.58 | 0.89 | 0.60 | 0.90 | 0.56 | 0.85 |
time (sec) |
N/A | 0.242 | 0.153 | 0.323 | 0.276 | 0.238 | 0.275 | 0.311 | 0.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 78 | 35 | 54 | 62 | 0 | 71 | 0 |
N.S. |
1 | 1.00 | 1.59 | 0.71 | 1.10 | 1.27 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.186 | 0.185 | 0.468 | 0.277 | 0.252 | 0.000 | 0.321 | 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 | 79 | 79 | 78 | 50 | 66 | 64 | 0 | 147 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.63 | 0.84 | 0.81 | 0.00 | 1.86 | 0.00 |
time (sec) |
N/A | 0.217 | 0.325 | 0.563 | 0.268 | 0.238 | 0.000 | 0.301 | 0.000 |
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 | 12 | 12 | 20 | 10 | 11 | 18 | 14 | 34 | 12 |
N.S. |
1 | 1.00 | 1.67 | 0.83 | 0.92 | 1.50 | 1.17 | 2.83 | 1.00 |
time (sec) |
N/A | 0.138 | 0.071 | 0.408 | 0.275 | 0.240 | 0.201 | 0.298 | 0.265 |
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 | 53 | 58 | 47 | 33 | 48 | 39 | 41 | 39 | 0 |
N.S. |
1 | 1.09 | 0.89 | 0.62 | 0.91 | 0.74 | 0.77 | 0.74 | 0.00 |
time (sec) |
N/A | 0.181 | 0.107 | 0.418 | 0.278 | 0.232 | 0.237 | 0.329 | 0.000 |
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 | 19 | 19 | 19 | 16 | 22 | 34 | 0 | 15 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 1.16 | 1.79 | 0.00 | 0.79 | 0.68 |
time (sec) |
N/A | 0.128 | 0.132 | 0.431 | 0.188 | 0.233 | 0.000 | 0.298 | 0.032 |
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 | 17 | 17 | 17 | 14 | 22 | 28 | 0 | 13 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.29 | 1.65 | 0.00 | 0.76 | 0.88 |
time (sec) |
N/A | 0.130 | 0.129 | 0.428 | 0.189 | 0.234 | 0.000 | 0.308 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 61 | 47 | 33 | 47 | 64 | 0 | 38 | 0 |
N.S. |
1 | 1.09 | 0.84 | 0.59 | 0.84 | 1.14 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.184 | 0.155 | 0.422 | 0.267 | 0.238 | 0.000 | 0.290 | 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 | 65 | 75 | 52 | 38 | 56 | 44 | 46 | 44 | 61 |
N.S. |
1 | 1.15 | 0.80 | 0.58 | 0.86 | 0.68 | 0.71 | 0.68 | 0.94 |
time (sec) |
N/A | 0.193 | 0.096 | 0.419 | 0.271 | 0.234 | 0.232 | 0.310 | 0.133 |
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 | 55 | 60 | 52 | 38 | 56 | 44 | 85 | 44 | 43 |
N.S. |
1 | 1.09 | 0.95 | 0.69 | 1.02 | 0.80 | 1.55 | 0.80 | 0.78 |
time (sec) |
N/A | 0.169 | 0.153 | 0.424 | 0.271 | 0.257 | 0.308 | 0.306 | 0.233 |
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 | 74 | 84 | 62 | 48 | 77 | 54 | 168 | 54 | 56 |
N.S. |
1 | 1.14 | 0.84 | 0.65 | 1.04 | 0.73 | 2.27 | 0.73 | 0.76 |
time (sec) |
N/A | 0.187 | 0.255 | 0.420 | 0.274 | 0.246 | 0.451 | 0.288 | 0.074 |
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 | 38 | 33 | 31 | 37 | 52 | 0 | 67 | 31 |
N.S. |
1 | 1.00 | 0.87 | 0.82 | 0.97 | 1.37 | 0.00 | 1.76 | 0.82 |
time (sec) |
N/A | 0.153 | 0.108 | 0.428 | 0.282 | 0.240 | 0.000 | 0.290 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 60 | 42 | 42 | 50 | 63 | 0 | 84 | 0 |
N.S. |
1 | 1.05 | 0.74 | 0.74 | 0.88 | 1.11 | 0.00 | 1.47 | 0.00 |
time (sec) |
N/A | 0.176 | 0.120 | 0.428 | 0.283 | 0.256 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 65 | 45 | 41 | 58 | 94 | 0 | 80 | 0 |
N.S. |
1 | 1.05 | 0.73 | 0.66 | 0.94 | 1.52 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.189 | 0.189 | 0.437 | 0.270 | 0.251 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 87 | 52 | 46 | 71 | 107 | 0 | 117 | 0 |
N.S. |
1 | 1.10 | 0.66 | 0.58 | 0.90 | 1.35 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.213 | 0.201 | 0.517 | 0.279 | 0.239 | 0.000 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 18 | 22 | 25 | 30 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.82 | 1.00 | 1.14 | 1.36 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.140 | 0.115 | 0.422 | 0.269 | 0.238 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 85 | 69 | 0 | 110 | 0 | 147 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.80 | 0.00 | 1.28 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 0.420 | 0.281 | 0.453 | 0.000 | 0.262 | 0.000 | 0.339 | 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 | 62 | 67 | 71 | 56 | 61 | 92 | 0 | 149 | 0 |
N.S. |
1 | 1.08 | 1.15 | 0.90 | 0.98 | 1.48 | 0.00 | 2.40 | 0.00 |
time (sec) |
N/A | 0.229 | 0.270 | 0.481 | 0.284 | 0.250 | 0.000 | 0.346 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 81 | 84 | 64 | 0 | 174 | 0 | 235 | 0 |
N.S. |
1 | 1.07 | 1.11 | 0.84 | 0.00 | 2.29 | 0.00 | 3.09 | 0.00 |
time (sec) |
N/A | 0.273 | 0.611 | 0.836 | 0.000 | 0.243 | 0.000 | 0.293 | 0.000 |
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 | 36 | 36 | 26 | 21 | 28 | 22 | 0 | 30 | 19 |
N.S. |
1 | 1.00 | 0.72 | 0.58 | 0.78 | 0.61 | 0.00 | 0.83 | 0.53 |
time (sec) |
N/A | 0.247 | 0.127 | 0.374 | 0.279 | 0.243 | 0.000 | 0.291 | 0.307 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 95 | 63 | 0 | 147 | 0 | 148 | 0 |
N.S. |
1 | 1.00 | 1.09 | 0.72 | 0.00 | 1.69 | 0.00 | 1.70 | 0.00 |
time (sec) |
N/A | 0.366 | 0.539 | 1.822 | 0.000 | 0.251 | 0.000 | 0.300 | 0.000 |
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 | 58 | 63 | 39 | 38 | 76 | 98 | 0 | 33 | 69 |
N.S. |
1 | 1.09 | 0.67 | 0.66 | 1.31 | 1.69 | 0.00 | 0.57 | 1.19 |
time (sec) |
N/A | 0.174 | 0.313 | 0.441 | 0.186 | 0.238 | 0.000 | 0.287 | 0.279 |
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 | 47 | 47 | 33 | 30 | 59 | 73 | 0 | 27 | 29 |
N.S. |
1 | 1.00 | 0.70 | 0.64 | 1.26 | 1.55 | 0.00 | 0.57 | 0.62 |
time (sec) |
N/A | 0.155 | 0.217 | 0.325 | 0.177 | 0.246 | 0.000 | 0.293 | 0.057 |
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 | 47 | 47 | 33 | 30 | 59 | 51 | 0 | 39 | 29 |
N.S. |
1 | 1.00 | 0.70 | 0.64 | 1.26 | 1.09 | 0.00 | 0.83 | 0.62 |
time (sec) |
N/A | 0.161 | 0.227 | 0.369 | 0.189 | 0.244 | 0.000 | 0.320 | 0.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 43 | 40 | 0 | 39 | 0 | 60 | 0 |
N.S. |
1 | 1.00 | 1.48 | 1.38 | 0.00 | 1.34 | 0.00 | 2.07 | 0.00 |
time (sec) |
N/A | 0.211 | 0.291 | 0.072 | 0.000 | 0.255 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 59 | 54 | 52 | 0 | 63 | 0 | 66 | 0 |
N.S. |
1 | 1.31 | 1.20 | 1.16 | 0.00 | 1.40 | 0.00 | 1.47 | 0.00 |
time (sec) |
N/A | 0.188 | 0.133 | 0.082 | 0.000 | 0.248 | 0.000 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 64 | 55 | 0 | 54 | 0 | 54 | 71 |
N.S. |
1 | 1.00 | 0.81 | 0.70 | 0.00 | 0.68 | 0.00 | 0.68 | 0.90 |
time (sec) |
N/A | 0.297 | 0.206 | 0.049 | 0.000 | 0.244 | 0.000 | 0.279 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 72 | 80 | 0 | 99 | 0 | 105 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.00 | 0.00 | 1.24 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.460 | 0.241 | 0.438 | 0.000 | 0.255 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 159 | 140 | 0 | 155 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.89 | 0.00 | 0.98 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.624 | 5.512 | 0.023 | 0.000 | 0.253 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 39 | 31 | 30 | 38 | 28 | 131 | 29 | 29 |
N.S. |
1 | 0.95 | 0.76 | 0.73 | 0.93 | 0.68 | 3.20 | 0.71 | 0.71 |
time (sec) |
N/A | 0.145 | 0.047 | 0.273 | 0.277 | 0.240 | 1.881 | 0.287 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 17 | 10 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.31 | 0.77 | 0.85 | 0.85 |
time (sec) |
N/A | 0.130 | 0.033 | 0.023 | 0.192 | 0.246 | 0.231 | 0.298 | 0.480 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 71 | 78 | 85 | 67 | 76 | 80 | 541 | 76 | 90 |
N.S. |
1 | 1.10 | 1.20 | 0.94 | 1.07 | 1.13 | 7.62 | 1.07 | 1.27 |
time (sec) |
N/A | 0.187 | 0.127 | 0.589 | 0.273 | 0.249 | 1.294 | 0.334 | 0.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 23 | 18 | 28 | 29 | 178 | 49 | 23 |
N.S. |
1 | 1.00 | 0.58 | 0.45 | 0.70 | 0.72 | 4.45 | 1.22 | 0.58 |
time (sec) |
N/A | 0.151 | 0.027 | 0.315 | 0.189 | 0.236 | 0.877 | 0.282 | 0.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 59 | 48 | 53 | 52 | 52 | 51 | 53 | 36 |
N.S. |
1 | 1.23 | 1.00 | 1.10 | 1.08 | 1.08 | 1.06 | 1.10 | 0.75 |
time (sec) |
N/A | 0.172 | 0.049 | 0.289 | 0.267 | 0.252 | 1.018 | 2.151 | 0.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 71 | 36 | 20 | 45 | 25 | 3303 | 63 | 45 |
N.S. |
1 | 1.03 | 0.52 | 0.29 | 0.65 | 0.36 | 47.87 | 0.91 | 0.65 |
time (sec) |
N/A | 0.172 | 0.028 | 0.292 | 0.183 | 0.238 | 1.122 | 0.270 | 0.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | C | A | B |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 193 | 171 | 120 | 85 | 157 | 120 | 44 | 142 | 77 |
N.S. |
1 | 0.89 | 0.62 | 0.44 | 0.81 | 0.62 | 0.23 | 0.74 | 0.40 |
time (sec) |
N/A | 0.305 | 0.358 | 0.329 | 0.280 | 0.263 | 2.753 | 0.311 | 1.310 |
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 | 13 | 13 | 13 | 10 | 9 | 9 | 26 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.69 | 0.69 | 2.00 | 0.69 | 0.69 |
time (sec) |
N/A | 0.133 | 0.014 | 0.342 | 0.188 | 0.248 | 0.115 | 0.298 | 0.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 10 | 9 | 9 | 12 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.69 | 0.69 | 0.92 | 0.69 | 0.69 |
time (sec) |
N/A | 0.129 | 0.018 | 0.302 | 0.177 | 0.236 | 0.181 | 0.294 | 0.345 |