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 | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 93 | 89 | 96 | 283 | 75 | 0 | 119 | 47 | 0 |
N.S. |
1 | 0.46 | 0.44 | 0.48 | 1.42 | 0.38 | 0.00 | 0.60 | 0.24 | 0.00 |
time (sec) |
N/A | 0.427 | 1.048 | 1.036 | 0.034 | 0.068 | 0.000 | 0.204 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 93 | 85 | 95 | 351 | 74 | 0 | 117 | 47 | 0 |
N.S. |
1 | 0.46 | 0.42 | 0.48 | 1.76 | 0.37 | 0.00 | 0.58 | 0.24 | 0.00 |
time (sec) |
N/A | 0.427 | 1.051 | 1.008 | 0.037 | 0.069 | 0.000 | 0.243 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 92 | 88 | 96 | 443 | 75 | 0 | 118 | 48 | 0 |
N.S. |
1 | 0.46 | 0.44 | 0.48 | 2.23 | 0.38 | 0.00 | 0.59 | 0.24 | 0.00 |
time (sec) |
N/A | 0.425 | 1.047 | 1.112 | 0.038 | 0.073 | 0.000 | 0.278 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 86 | 278 | 94 | 379 | 75 | 0 | 121 | 48 | 0 |
N.S. |
1 | 0.46 | 1.49 | 0.50 | 2.03 | 0.40 | 0.00 | 0.65 | 0.26 | 0.00 |
time (sec) |
N/A | 0.396 | 1.047 | 1.097 | 0.036 | 0.071 | 0.000 | 0.241 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 77 | 43 | 90 | 315 | 73 | 0 | 149 | 46 | 196 |
N.S. |
1 | 1.03 | 0.57 | 1.20 | 4.20 | 0.97 | 0.00 | 1.99 | 0.61 | 2.61 |
time (sec) |
N/A | 0.366 | 0.863 | 1.217 | 0.045 | 0.074 | 0.000 | 0.263 | 0.281 | 10.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 103 | 87 | 90 | 375 | 73 | 0 | 149 | 46 | 195 |
N.S. |
1 | 0.90 | 0.76 | 0.78 | 3.26 | 0.63 | 0.00 | 1.30 | 0.40 | 1.70 |
time (sec) |
N/A | 0.429 | 0.886 | 1.190 | 0.038 | 0.067 | 0.000 | 0.268 | 0.291 | 10.855 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 103 | 87 | 90 | 435 | 73 | 0 | 149 | 46 | 196 |
N.S. |
1 | 0.66 | 0.55 | 0.57 | 2.77 | 0.46 | 0.00 | 0.95 | 0.29 | 1.25 |
time (sec) |
N/A | 0.433 | 1.006 | 1.276 | 0.042 | 0.066 | 0.000 | 0.238 | 0.275 | 10.844 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 103 | 87 | 90 | 495 | 73 | 0 | 149 | 46 | 196 |
N.S. |
1 | 0.49 | 0.41 | 0.43 | 2.36 | 0.35 | 0.00 | 0.71 | 0.22 | 0.93 |
time (sec) |
N/A | 0.429 | 1.012 | 1.448 | 0.041 | 0.070 | 0.000 | 0.251 | 0.299 | 10.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 103 | 87 | 90 | 555 | 73 | 0 | 149 | 46 | 196 |
N.S. |
1 | 0.49 | 0.41 | 0.43 | 2.64 | 0.35 | 0.00 | 0.71 | 0.22 | 0.93 |
time (sec) |
N/A | 0.435 | 1.037 | 1.563 | 0.048 | 0.067 | 0.000 | 0.202 | 0.283 | 10.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 103 | 87 | 90 | 615 | 73 | 0 | 149 | 46 | 196 |
N.S. |
1 | 0.49 | 0.41 | 0.43 | 2.93 | 0.35 | 0.00 | 0.71 | 0.22 | 0.93 |
time (sec) |
N/A | 0.422 | 1.041 | 1.614 | 0.044 | 0.067 | 0.000 | 0.270 | 0.261 | 10.800 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 103 | 87 | 90 | 675 | 73 | 0 | 149 | 46 | 196 |
N.S. |
1 | 0.49 | 0.41 | 0.43 | 3.21 | 0.35 | 0.00 | 0.71 | 0.22 | 0.93 |
time (sec) |
N/A | 0.426 | 1.034 | 1.869 | 0.047 | 0.067 | 0.000 | 0.277 | 0.280 | 10.849 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 142 | 125 | 140 | 481 | 118 | 40368 | 220 | 68 | 0 |
N.S. |
1 | 0.47 | 0.41 | 0.46 | 1.59 | 0.39 | 133.23 | 0.73 | 0.22 | 0.00 |
time (sec) |
N/A | 0.573 | 1.054 | 1.184 | 0.046 | 0.065 | 1.252 | 0.186 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 145 | 125 | 140 | 421 | 119 | 24941 | 220 | 68 | 0 |
N.S. |
1 | 0.47 | 0.41 | 0.46 | 1.38 | 0.39 | 81.51 | 0.72 | 0.22 | 0.00 |
time (sec) |
N/A | 0.540 | 1.053 | 1.277 | 0.046 | 0.066 | 1.273 | 0.241 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 145 | 125 | 140 | 361 | 119 | 15400 | 222 | 68 | 0 |
N.S. |
1 | 0.47 | 0.41 | 0.46 | 1.18 | 0.39 | 50.33 | 0.73 | 0.22 | 0.00 |
time (sec) |
N/A | 0.527 | 1.053 | 1.086 | 0.040 | 0.066 | 1.144 | 0.275 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 140 | 125 | 140 | 301 | 119 | 9493 | 221 | 68 | 0 |
N.S. |
1 | 0.66 | 0.59 | 0.66 | 1.42 | 0.56 | 44.78 | 1.04 | 0.32 | 0.00 |
time (sec) |
N/A | 0.529 | 1.052 | 1.117 | 0.035 | 0.068 | 0.985 | 0.249 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 115 | 125 | 140 | 241 | 118 | 5836 | 220 | 68 | 0 |
N.S. |
1 | 0.69 | 0.75 | 0.84 | 1.44 | 0.71 | 34.95 | 1.32 | 0.41 | 0.00 |
time (sec) |
N/A | 0.494 | 1.055 | 1.050 | 0.033 | 0.069 | 0.905 | 0.254 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 89 | 125 | 140 | 183 | 119 | 3563 | 221 | 68 | 0 |
N.S. |
1 | 0.74 | 1.03 | 1.16 | 1.51 | 0.98 | 29.45 | 1.83 | 0.56 | 0.00 |
time (sec) |
N/A | 0.424 | 1.055 | 1.056 | 0.039 | 0.067 | 1.121 | 0.235 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 121 | 138 | 125 | 115 | 2147 | 217 | 65 | 0 |
N.S. |
1 | 1.00 | 1.70 | 1.94 | 1.76 | 1.62 | 30.24 | 3.06 | 0.92 | 0.00 |
time (sec) |
N/A | 0.327 | 1.052 | 1.010 | 0.038 | 0.069 | 0.857 | 0.277 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 105 | 122 | 139 | 236 | 114 | 0 | 190 | 64 | 0 |
N.S. |
1 | 0.40 | 0.47 | 0.53 | 0.90 | 0.44 | 0.00 | 0.73 | 0.24 | 0.00 |
time (sec) |
N/A | 0.453 | 1.069 | 0.993 | 0.039 | 0.072 | 0.000 | 0.205 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 294 | 133 | 128 | 144 | 386 | 121 | 0 | 191 | 70 | 0 |
N.S. |
1 | 0.45 | 0.44 | 0.49 | 1.31 | 0.41 | 0.00 | 0.65 | 0.24 | 0.00 |
time (sec) |
N/A | 0.516 | 1.055 | 1.031 | 0.042 | 0.072 | 0.000 | 0.231 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 136 | 126 | 144 | 461 | 121 | 0 | 191 | 69 | 0 |
N.S. |
1 | 0.46 | 0.42 | 0.48 | 1.55 | 0.41 | 0.00 | 0.64 | 0.23 | 0.00 |
time (sec) |
N/A | 0.502 | 1.073 | 1.017 | 0.053 | 0.071 | 0.000 | 0.260 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 136 | 127 | 144 | 557 | 121 | 0 | 190 | 69 | 0 |
N.S. |
1 | 0.46 | 0.43 | 0.48 | 1.88 | 0.41 | 0.00 | 0.64 | 0.23 | 0.00 |
time (sec) |
N/A | 0.519 | 1.067 | 1.118 | 0.044 | 0.076 | 0.000 | 0.264 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 135 | 126 | 144 | 615 | 121 | 0 | 188 | 70 | 0 |
N.S. |
1 | 0.46 | 0.43 | 0.49 | 2.08 | 0.41 | 0.00 | 0.64 | 0.24 | 0.00 |
time (sec) |
N/A | 0.506 | 1.061 | 1.164 | 0.047 | 0.069 | 0.000 | 0.233 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 132 | 127 | 144 | 673 | 121 | 0 | 188 | 70 | 0 |
N.S. |
1 | 0.45 | 0.43 | 0.49 | 2.30 | 0.41 | 0.00 | 0.64 | 0.24 | 0.00 |
time (sec) |
N/A | 0.508 | 1.065 | 1.279 | 0.058 | 0.066 | 0.000 | 0.254 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 110 | 354 | 142 | 554 | 121 | 0 | 191 | 70 | 0 |
N.S. |
1 | 0.41 | 1.33 | 0.53 | 2.07 | 0.45 | 0.00 | 0.72 | 0.26 | 0.00 |
time (sec) |
N/A | 0.437 | 1.340 | 1.228 | 0.052 | 0.067 | 0.000 | 0.226 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 77 | 122 | 136 | 435 | 119 | 0 | 221 | 68 | 284 |
N.S. |
1 | 1.03 | 1.63 | 1.81 | 5.80 | 1.59 | 0.00 | 2.95 | 0.91 | 3.79 |
time (sec) |
N/A | 0.377 | 1.050 | 1.374 | 0.043 | 0.068 | 0.000 | 0.220 | 0.288 | 10.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 98 | 125 | 136 | 495 | 119 | 0 | 221 | 68 | 284 |
N.S. |
1 | 0.85 | 1.09 | 1.18 | 4.30 | 1.03 | 0.00 | 1.92 | 0.59 | 2.47 |
time (sec) |
N/A | 0.371 | 1.049 | 1.381 | 0.045 | 0.067 | 0.000 | 0.229 | 0.267 | 10.794 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 143 | 125 | 136 | 555 | 119 | 0 | 221 | 68 | 284 |
N.S. |
1 | 0.91 | 0.80 | 0.87 | 3.54 | 0.76 | 0.00 | 1.41 | 0.43 | 1.81 |
time (sec) |
N/A | 0.501 | 1.049 | 1.628 | 0.052 | 0.070 | 0.000 | 0.226 | 0.311 | 10.942 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 145 | 125 | 136 | 615 | 119 | 0 | 221 | 68 | 283 |
N.S. |
1 | 0.73 | 0.63 | 0.68 | 3.09 | 0.60 | 0.00 | 1.11 | 0.34 | 1.42 |
time (sec) |
N/A | 0.507 | 1.056 | 1.831 | 0.056 | 0.069 | 0.000 | 0.243 | 0.275 | 11.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 145 | 125 | 136 | 675 | 119 | 0 | 221 | 68 | 284 |
N.S. |
1 | 0.60 | 0.52 | 0.56 | 2.80 | 0.49 | 0.00 | 0.92 | 0.28 | 1.18 |
time (sec) |
N/A | 0.510 | 1.064 | 2.049 | 0.058 | 0.066 | 0.000 | 0.251 | 0.273 | 10.916 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 145 | 125 | 136 | 735 | 119 | 0 | 221 | 68 | 284 |
N.S. |
1 | 0.47 | 0.41 | 0.44 | 2.40 | 0.39 | 0.00 | 0.72 | 0.22 | 0.93 |
time (sec) |
N/A | 0.501 | 1.056 | 2.115 | 0.058 | 0.066 | 0.000 | 0.227 | 0.280 | 11.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 143 | 125 | 136 | 795 | 119 | 0 | 221 | 68 | 284 |
N.S. |
1 | 0.47 | 0.41 | 0.45 | 2.62 | 0.39 | 0.00 | 0.73 | 0.22 | 0.93 |
time (sec) |
N/A | 0.506 | 1.052 | 2.488 | 0.060 | 0.071 | 0.000 | 0.248 | 0.266 | 10.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 134 | 116 | 138 | 272 | 117 | 726 | 185 | 5 | 0 |
N.S. |
1 | 0.52 | 0.45 | 0.53 | 1.05 | 0.45 | 2.81 | 0.72 | 0.02 | 0.00 |
time (sec) |
N/A | 0.542 | 1.072 | 0.938 | 0.035 | 0.068 | 1.592 | 0.213 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 113 | 96 | 114 | 212 | 94 | 488 | 148 | 5 | 0 |
N.S. |
1 | 0.53 | 0.45 | 0.54 | 1.00 | 0.44 | 2.30 | 0.70 | 0.02 | 0.00 |
time (sec) |
N/A | 0.494 | 1.055 | 0.898 | 0.034 | 0.070 | 1.489 | 0.253 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 92 | 77 | 90 | 125 | 71 | 330 | 113 | 5 | 0 |
N.S. |
1 | 0.55 | 0.46 | 0.54 | 0.75 | 0.43 | 1.99 | 0.68 | 0.03 | 0.00 |
time (sec) |
N/A | 0.440 | 1.054 | 0.797 | 0.032 | 0.071 | 1.209 | 0.243 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 71 | 57 | 66 | 72 | 47 | 219 | 75 | 5 | 0 |
N.S. |
1 | 0.59 | 0.48 | 0.55 | 0.60 | 0.39 | 1.82 | 0.62 | 0.04 | 0.00 |
time (sec) |
N/A | 0.396 | 1.031 | 0.780 | 0.032 | 0.068 | 1.048 | 0.215 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 177 | 43 | 52 | 25 | 134 | 45 | 1 | 79 |
N.S. |
1 | 1.00 | 2.57 | 0.62 | 0.75 | 0.36 | 1.94 | 0.65 | 0.01 | 1.14 |
time (sec) |
N/A | 0.330 | 0.704 | 0.829 | 0.028 | 0.070 | 0.820 | 0.243 | 0.283 | 10.997 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 56 | 111 | 49 | 53 | 28 | 0 | 49 | 2 | 68 |
N.S. |
1 | 0.70 | 1.39 | 0.61 | 0.66 | 0.35 | 0.00 | 0.61 | 0.02 | 0.85 |
time (sec) |
N/A | 0.362 | 0.510 | 0.766 | 0.030 | 0.074 | 0.000 | 0.250 | 0.292 | 10.965 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 86 | 147 | 61 | 106 | 41 | 0 | 81 | 5 | 117 |
N.S. |
1 | 1.10 | 1.88 | 0.78 | 1.36 | 0.53 | 0.00 | 1.04 | 0.06 | 1.50 |
time (sec) |
N/A | 0.385 | 0.524 | 0.792 | 0.033 | 0.072 | 0.000 | 0.234 | 0.296 | 11.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 88 | 180 | 92 | 164 | 69 | 0 | 117 | 5 | 0 |
N.S. |
1 | 0.54 | 1.11 | 0.57 | 1.01 | 0.43 | 0.00 | 0.72 | 0.03 | 0.00 |
time (sec) |
N/A | 0.431 | 0.579 | 0.855 | 0.031 | 0.069 | 0.000 | 0.206 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 112 | 230 | 119 | 224 | 94 | 0 | 153 | 5 | 0 |
N.S. |
1 | 0.53 | 1.09 | 0.56 | 1.06 | 0.45 | 0.00 | 0.73 | 0.02 | 0.00 |
time (sec) |
N/A | 0.475 | 0.716 | 0.869 | 0.036 | 0.081 | 0.000 | 0.234 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 132 | 263 | 143 | 284 | 117 | 0 | 188 | 5 | 0 |
N.S. |
1 | 0.52 | 1.03 | 0.56 | 1.11 | 0.46 | 0.00 | 0.73 | 0.02 | 0.00 |
time (sec) |
N/A | 0.520 | 0.852 | 1.000 | 0.033 | 0.086 | 0.000 | 0.259 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 142 | 140 | 155 | 303 | 197 | 0 | 149 | 71 | 0 |
N.S. |
1 | 0.57 | 0.56 | 0.62 | 1.22 | 0.79 | 0.00 | 0.60 | 0.29 | 0.00 |
time (sec) |
N/A | 0.585 | 1.080 | 1.197 | 0.036 | 0.074 | 0.000 | 0.265 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 120 | 117 | 129 | 242 | 171 | 0 | 134 | 60 | 0 |
N.S. |
1 | 0.59 | 0.58 | 0.64 | 1.20 | 0.85 | 0.00 | 0.66 | 0.30 | 0.00 |
time (sec) |
N/A | 0.519 | 1.065 | 1.197 | 0.033 | 0.077 | 0.000 | 0.266 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 97 | 233 | 110 | 154 | 134 | 0 | 96 | 46 | 0 |
N.S. |
1 | 0.63 | 1.51 | 0.71 | 1.00 | 0.87 | 0.00 | 0.62 | 0.30 | 0.00 |
time (sec) |
N/A | 0.464 | 1.449 | 1.145 | 0.028 | 0.074 | 0.000 | 0.249 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 81 | 187 | 75 | 89 | 81 | 0 | 70 | 33 | 0 |
N.S. |
1 | 0.72 | 1.65 | 0.66 | 0.79 | 0.72 | 0.00 | 0.62 | 0.29 | 0.00 |
time (sec) |
N/A | 0.416 | 1.253 | 1.098 | 0.033 | 0.072 | 0.000 | 0.271 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 176 | 32 | 56 | 38 | 0 | 32 | 12 | 42 |
N.S. |
1 | 1.00 | 2.55 | 0.46 | 0.81 | 0.55 | 0.00 | 0.46 | 0.17 | 0.61 |
time (sec) |
N/A | 0.325 | 0.861 | 1.144 | 0.034 | 0.076 | 0.000 | 0.223 | 0.273 | 10.684 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 83 | 80 | 97 | 96 | 109 | 0 | 83 | 44 | 0 |
N.S. |
1 | 0.59 | 0.57 | 0.69 | 0.69 | 0.78 | 0.00 | 0.59 | 0.31 | 0.00 |
time (sec) |
N/A | 0.417 | 1.044 | 1.070 | 0.026 | 0.075 | 0.000 | 0.249 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 114 | 110 | 132 | 191 | 187 | 0 | 123 | 70 | 0 |
N.S. |
1 | 0.58 | 0.56 | 0.67 | 0.97 | 0.95 | 0.00 | 0.63 | 0.36 | 0.00 |
time (sec) |
N/A | 0.509 | 1.085 | 1.348 | 0.032 | 0.078 | 0.000 | 0.269 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 136 | 133 | 153 | 250 | 225 | 0 | 148 | 86 | 0 |
N.S. |
1 | 0.56 | 0.55 | 0.63 | 1.03 | 0.93 | 0.00 | 0.61 | 0.35 | 0.00 |
time (sec) |
N/A | 0.562 | 1.094 | 3.126 | 0.033 | 0.077 | 0.000 | 0.256 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 148 | 127 | 150 | 211 | 252 | 0 | 144 | 120 | 0 |
N.S. |
1 | 0.60 | 0.52 | 0.61 | 0.86 | 1.03 | 0.00 | 0.59 | 0.49 | 0.00 |
time (sec) |
N/A | 0.603 | 1.077 | 1.311 | 0.059 | 0.074 | 0.000 | 0.222 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 118 | 103 | 115 | 201 | 175 | 0 | 116 | 108 | 0 |
N.S. |
1 | 0.63 | 0.55 | 0.61 | 1.07 | 0.93 | 0.00 | 0.62 | 0.57 | 0.00 |
time (sec) |
N/A | 0.461 | 1.064 | 1.237 | 0.043 | 0.074 | 0.000 | 0.218 | 0.321 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 77 | 73 | 75 | 156 | 105 | 0 | 77 | 37 | 201 |
N.S. |
1 | 1.03 | 0.97 | 1.00 | 2.08 | 1.40 | 0.00 | 1.03 | 0.49 | 2.68 |
time (sec) |
N/A | 0.385 | 1.042 | 1.365 | 0.036 | 0.076 | 0.000 | 0.230 | 0.269 | 10.821 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 87 | 319 | 52 | 90 | 80 | 0 | 52 | 42 | 62 |
N.S. |
1 | 0.72 | 2.64 | 0.43 | 0.74 | 0.66 | 0.00 | 0.43 | 0.35 | 0.51 |
time (sec) |
N/A | 0.421 | 1.307 | 1.220 | 0.032 | 0.068 | 0.000 | 0.208 | 0.281 | 10.799 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 39 | 33 | 56 | 61 | 0 | 33 | 34 | 43 |
N.S. |
1 | 1.00 | 0.55 | 0.46 | 0.79 | 0.86 | 0.00 | 0.46 | 0.48 | 0.61 |
time (sec) |
N/A | 0.324 | 1.025 | 1.106 | 0.026 | 0.066 | 0.000 | 0.243 | 0.270 | 10.780 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 113 | 104 | 121 | 138 | 203 | 0 | 107 | 145 | 0 |
N.S. |
1 | 0.54 | 0.50 | 0.58 | 0.66 | 0.97 | 0.00 | 0.51 | 0.69 | 0.00 |
time (sec) |
N/A | 0.500 | 1.065 | 1.171 | 0.041 | 0.073 | 0.000 | 0.255 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 160 | 148 | 172 | 276 | 347 | 0 | 169 | 171 | 0 |
N.S. |
1 | 0.57 | 0.52 | 0.61 | 0.98 | 1.23 | 0.00 | 0.60 | 0.61 | 0.00 |
time (sec) |
N/A | 0.617 | 1.114 | 1.167 | 0.033 | 0.078 | 0.000 | 0.245 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 52 | 52 | 51 | 56 | 80 | 53 | 37 | 51 |
N.S. |
1 | 1.00 | 0.83 | 0.83 | 0.81 | 0.89 | 1.27 | 0.84 | 0.59 | 0.81 |
time (sec) |
N/A | 0.342 | 0.055 | 0.481 | 0.033 | 0.068 | 0.495 | 0.243 | 0.251 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 52 | 52 | 51 | 56 | 80 | 53 | 37 | 51 |
N.S. |
1 | 1.00 | 0.83 | 0.83 | 0.81 | 0.89 | 1.27 | 0.84 | 0.59 | 0.81 |
time (sec) |
N/A | 0.345 | 0.052 | 0.486 | 0.027 | 0.070 | 0.316 | 0.253 | 0.287 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 52 | 52 | 51 | 56 | 80 | 53 | 37 | 51 |
N.S. |
1 | 1.00 | 0.83 | 0.83 | 0.81 | 0.89 | 1.27 | 0.84 | 0.59 | 0.81 |
time (sec) |
N/A | 0.336 | 0.049 | 0.488 | 0.034 | 0.070 | 0.195 | 0.223 | 0.279 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 52 | 52 | 51 | 54 | 66 | 53 | 35 | 51 |
N.S. |
1 | 1.00 | 0.83 | 0.83 | 0.81 | 0.86 | 1.05 | 0.84 | 0.56 | 0.81 |
time (sec) |
N/A | 0.337 | 0.056 | 0.463 | 0.029 | 0.068 | 0.667 | 0.258 | 0.263 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 51 | 51 | 51 | 51 | 78 | 53 | 34 | 51 |
N.S. |
1 | 1.00 | 0.84 | 0.84 | 0.84 | 0.84 | 1.28 | 0.87 | 0.56 | 0.84 |
time (sec) |
N/A | 0.337 | 0.050 | 0.316 | 0.027 | 0.067 | 0.142 | 0.263 | 0.265 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 49 | 52 | 51 | 51 | 75 | 53 | 35 | 51 |
N.S. |
1 | 1.00 | 0.83 | 0.88 | 0.86 | 0.86 | 1.27 | 0.90 | 0.59 | 0.86 |
time (sec) |
N/A | 0.328 | 0.060 | 0.113 | 0.032 | 0.069 | 0.245 | 0.271 | 0.264 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 47 | 51 | 51 | 50 | 73 | 51 | 38 | 51 |
N.S. |
1 | 1.00 | 0.80 | 0.86 | 0.86 | 0.85 | 1.24 | 0.86 | 0.64 | 0.86 |
time (sec) |
N/A | 0.340 | 0.066 | 0.125 | 0.034 | 0.075 | 0.218 | 0.282 | 0.265 | 10.538 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 47 | 48 | 52 | 51 | 75 | 52 | 39 | 52 |
N.S. |
1 | 1.00 | 0.80 | 0.81 | 0.88 | 0.86 | 1.27 | 0.88 | 0.66 | 0.88 |
time (sec) |
N/A | 0.333 | 0.063 | 0.124 | 0.030 | 0.071 | 0.270 | 0.238 | 0.264 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 50 | 48 | 51 | 51 | 80 | 51 | 39 | 51 |
N.S. |
1 | 1.00 | 0.82 | 0.79 | 0.84 | 0.84 | 1.31 | 0.84 | 0.64 | 0.84 |
time (sec) |
N/A | 0.339 | 0.060 | 0.121 | 0.032 | 0.073 | 0.394 | 0.261 | 0.271 | 10.633 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 90 | 100 | 99 | 104 | 148 | 101 | 59 | 91 |
N.S. |
1 | 1.00 | 0.81 | 0.90 | 0.89 | 0.94 | 1.33 | 0.91 | 0.53 | 0.82 |
time (sec) |
N/A | 0.433 | 0.087 | 0.920 | 0.039 | 0.070 | 0.712 | 0.221 | 0.286 | 10.756 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 90 | 100 | 99 | 104 | 148 | 101 | 59 | 91 |
N.S. |
1 | 1.00 | 0.81 | 0.90 | 0.89 | 0.94 | 1.33 | 0.91 | 0.53 | 0.82 |
time (sec) |
N/A | 0.439 | 0.077 | 0.895 | 0.026 | 0.070 | 0.489 | 0.235 | 0.266 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 90 | 100 | 99 | 104 | 148 | 101 | 59 | 91 |
N.S. |
1 | 1.00 | 0.81 | 0.90 | 0.89 | 0.94 | 1.33 | 0.91 | 0.53 | 0.82 |
time (sec) |
N/A | 0.425 | 0.077 | 0.961 | 0.036 | 0.069 | 0.319 | 0.255 | 0.284 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 90 | 100 | 99 | 102 | 124 | 101 | 57 | 91 |
N.S. |
1 | 1.00 | 0.81 | 0.90 | 0.89 | 0.92 | 1.12 | 0.91 | 0.51 | 0.82 |
time (sec) |
N/A | 0.405 | 0.076 | 0.882 | 0.026 | 0.073 | 0.985 | 0.252 | 0.279 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 89 | 99 | 99 | 99 | 146 | 101 | 56 | 91 |
N.S. |
1 | 1.00 | 0.82 | 0.91 | 0.91 | 0.91 | 1.34 | 0.93 | 0.51 | 0.83 |
time (sec) |
N/A | 0.409 | 0.076 | 0.898 | 0.033 | 0.067 | 0.211 | 0.241 | 0.271 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 87 | 100 | 99 | 99 | 141 | 101 | 58 | 91 |
N.S. |
1 | 1.00 | 0.81 | 0.93 | 0.93 | 0.93 | 1.32 | 0.94 | 0.54 | 0.85 |
time (sec) |
N/A | 0.413 | 0.089 | 0.922 | 0.040 | 0.071 | 0.292 | 0.243 | 0.262 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 86 | 99 | 99 | 99 | 139 | 99 | 61 | 92 |
N.S. |
1 | 1.00 | 0.80 | 0.93 | 0.93 | 0.93 | 1.30 | 0.93 | 0.57 | 0.86 |
time (sec) |
N/A | 0.408 | 0.110 | 0.878 | 0.058 | 0.074 | 0.324 | 0.229 | 0.282 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 85 | 95 | 100 | 99 | 141 | 100 | 61 | 95 |
N.S. |
1 | 1.00 | 0.79 | 0.89 | 0.93 | 0.93 | 1.32 | 0.93 | 0.57 | 0.89 |
time (sec) |
N/A | 0.408 | 0.083 | 0.928 | 0.051 | 0.070 | 0.390 | 0.261 | 0.290 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 85 | 91 | 100 | 99 | 139 | 100 | 61 | 98 |
N.S. |
1 | 1.00 | 0.79 | 0.85 | 0.93 | 0.93 | 1.30 | 0.93 | 0.57 | 0.92 |
time (sec) |
N/A | 0.426 | 0.105 | 0.878 | 0.043 | 0.069 | 0.452 | 0.237 | 0.268 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 152 | 148 | 147 | 152 | 214 | 149 | 81 | 131 |
N.S. |
1 | 1.00 | 0.96 | 0.93 | 0.92 | 0.96 | 1.35 | 0.94 | 0.51 | 0.82 |
time (sec) |
N/A | 0.514 | 0.122 | 0.981 | 0.033 | 0.074 | 1.044 | 0.235 | 0.281 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 128 | 148 | 147 | 152 | 214 | 149 | 81 | 131 |
N.S. |
1 | 1.00 | 0.81 | 0.93 | 0.92 | 0.96 | 1.35 | 0.94 | 0.51 | 0.82 |
time (sec) |
N/A | 0.501 | 0.140 | 0.962 | 0.035 | 0.069 | 0.793 | 0.241 | 0.255 | 10.786 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 152 | 148 | 147 | 152 | 214 | 149 | 81 | 131 |
N.S. |
1 | 1.00 | 0.96 | 0.93 | 0.92 | 0.96 | 1.35 | 0.94 | 0.51 | 0.82 |
time (sec) |
N/A | 0.520 | 0.118 | 0.987 | 0.028 | 0.082 | 0.494 | 0.256 | 0.252 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 128 | 148 | 147 | 150 | 182 | 149 | 79 | 131 |
N.S. |
1 | 1.00 | 0.81 | 0.93 | 0.92 | 0.94 | 1.14 | 0.94 | 0.50 | 0.82 |
time (sec) |
N/A | 0.504 | 0.121 | 0.875 | 0.034 | 0.066 | 1.033 | 0.244 | 0.269 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 127 | 147 | 147 | 147 | 211 | 149 | 78 | 131 |
N.S. |
1 | 1.00 | 0.81 | 0.94 | 0.94 | 0.94 | 1.34 | 0.95 | 0.50 | 0.83 |
time (sec) |
N/A | 0.485 | 0.103 | 0.968 | 0.052 | 0.067 | 0.332 | 0.252 | 0.279 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 151 | 125 | 148 | 147 | 147 | 204 | 149 | 80 | 131 |
N.S. |
1 | 1.00 | 0.83 | 0.98 | 0.97 | 0.97 | 1.35 | 0.99 | 0.53 | 0.87 |
time (sec) |
N/A | 0.485 | 0.118 | 0.894 | 0.036 | 0.076 | 0.408 | 0.263 | 0.309 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 124 | 147 | 147 | 147 | 204 | 147 | 83 | 132 |
N.S. |
1 | 1.00 | 0.81 | 0.96 | 0.96 | 0.96 | 1.33 | 0.96 | 0.54 | 0.86 |
time (sec) |
N/A | 0.493 | 0.122 | 1.000 | 0.084 | 0.072 | 0.570 | 0.215 | 0.270 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 124 | 143 | 148 | 147 | 204 | 148 | 83 | 135 |
N.S. |
1 | 1.00 | 0.80 | 0.92 | 0.95 | 0.95 | 1.32 | 0.95 | 0.54 | 0.87 |
time (sec) |
N/A | 0.513 | 0.116 | 0.878 | 0.042 | 0.071 | 0.550 | 0.257 | 0.281 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 151 | 123 | 139 | 148 | 147 | 202 | 148 | 83 | 138 |
N.S. |
1 | 1.00 | 0.81 | 0.92 | 0.98 | 0.97 | 1.34 | 0.98 | 0.55 | 0.91 |
time (sec) |
N/A | 0.496 | 0.108 | 0.902 | 0.090 | 0.069 | 0.687 | 0.222 | 0.276 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 123 | 135 | 148 | 147 | 204 | 148 | 83 | 141 |
N.S. |
1 | 1.00 | 0.79 | 0.87 | 0.95 | 0.95 | 1.32 | 0.95 | 0.54 | 0.91 |
time (sec) |
N/A | 0.489 | 0.137 | 0.876 | 0.051 | 0.070 | 0.799 | 0.218 | 0.277 | 10.681 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 144 | 128 | 124 | 139 | 341 | 986 | 146 | 68 | 209 |
N.S. |
1 | 1.02 | 0.91 | 0.88 | 0.99 | 2.42 | 6.99 | 1.04 | 0.48 | 1.48 |
time (sec) |
N/A | 0.431 | 0.260 | 1.072 | 0.120 | 0.087 | 105.121 | 0.282 | 0.275 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 125 | 110 | 99 | 115 | 290 | 877 | 122 | 55 | 146 |
N.S. |
1 | 1.07 | 0.94 | 0.85 | 0.98 | 2.48 | 7.50 | 1.04 | 0.47 | 1.25 |
time (sec) |
N/A | 0.407 | 0.222 | 1.119 | 0.162 | 0.086 | 28.786 | 0.261 | 0.277 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 106 | 88 | 77 | 88 | 231 | 762 | 95 | 39 | 107 |
N.S. |
1 | 1.12 | 0.93 | 0.81 | 0.93 | 2.43 | 8.02 | 1.00 | 0.41 | 1.13 |
time (sec) |
N/A | 0.374 | 0.182 | 1.069 | 0.186 | 0.082 | 6.067 | 0.265 | 0.282 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 86 | 67 | 62 | 65 | 198 | 634 | 65 | 29 | 62 |
N.S. |
1 | 1.18 | 0.92 | 0.85 | 0.89 | 2.71 | 8.68 | 0.89 | 0.40 | 0.85 |
time (sec) |
N/A | 0.354 | 0.129 | 1.165 | 0.176 | 0.081 | 2.126 | 0.240 | 0.271 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 64 | 57 | 58 | 177 | 615 | 60 | 25 | 51 |
N.S. |
1 | 1.00 | 1.02 | 0.90 | 0.92 | 2.81 | 9.76 | 0.95 | 0.40 | 0.81 |
time (sec) |
N/A | 0.324 | 0.130 | 1.030 | 0.152 | 0.079 | 2.643 | 0.259 | 0.275 | 10.795 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 87 | 67 | 64 | 65 | 215 | 794 | 60 | 33 | 65 |
N.S. |
1 | 1.16 | 0.89 | 0.85 | 0.87 | 2.87 | 10.59 | 0.80 | 0.44 | 0.87 |
time (sec) |
N/A | 0.354 | 0.125 | 1.198 | 0.188 | 0.084 | 7.032 | 0.254 | 0.259 | 10.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 106 | 90 | 77 | 93 | 257 | 882 | 85 | 46 | 81 |
N.S. |
1 | 1.12 | 0.95 | 0.81 | 0.98 | 2.71 | 9.28 | 0.89 | 0.48 | 0.85 |
time (sec) |
N/A | 0.379 | 0.180 | 1.171 | 0.160 | 0.088 | 27.553 | 0.260 | 0.261 | 10.794 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 125 | 112 | 101 | 118 | 316 | 1017 | 110 | 61 | 103 |
N.S. |
1 | 1.03 | 0.93 | 0.83 | 0.98 | 2.61 | 8.40 | 0.91 | 0.50 | 0.85 |
time (sec) |
N/A | 0.396 | 0.229 | 1.105 | 0.165 | 0.086 | 113.336 | 0.265 | 0.268 | 10.791 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 144 | 131 | 121 | 143 | 367 | 0 | 136 | 72 | 121 |
N.S. |
1 | 1.01 | 0.92 | 0.85 | 1.00 | 2.57 | 0.00 | 0.95 | 0.50 | 0.85 |
time (sec) |
N/A | 0.419 | 0.254 | 1.221 | 0.163 | 0.082 | 0.000 | 0.234 | 0.263 | 10.867 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 160 | 128 | 118 | 161 | 467 | 0 | 143 | 136 | 176 |
N.S. |
1 | 1.03 | 0.82 | 0.76 | 1.03 | 2.99 | 0.00 | 0.92 | 0.87 | 1.13 |
time (sec) |
N/A | 0.420 | 0.364 | 1.309 | 0.154 | 0.094 | 0.000 | 0.272 | 0.257 | 10.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 141 | 110 | 104 | 136 | 437 | 2271 | 111 | 120 | 131 |
N.S. |
1 | 1.05 | 0.82 | 0.78 | 1.01 | 3.26 | 16.95 | 0.83 | 0.90 | 0.98 |
time (sec) |
N/A | 0.427 | 0.311 | 1.270 | 0.131 | 0.086 | 87.834 | 0.214 | 0.274 | 10.780 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 122 | 105 | 96 | 130 | 411 | 2261 | 107 | 113 | 112 |
N.S. |
1 | 0.98 | 0.85 | 0.77 | 1.05 | 3.31 | 18.23 | 0.86 | 0.91 | 0.90 |
time (sec) |
N/A | 0.392 | 0.292 | 1.107 | 0.180 | 0.088 | 44.966 | 0.258 | 0.273 | 11.396 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 120 | 105 | 92 | 128 | 399 | 2302 | 106 | 110 | 107 |
N.S. |
1 | 0.96 | 0.84 | 0.74 | 1.02 | 3.19 | 18.42 | 0.85 | 0.88 | 0.86 |
time (sec) |
N/A | 0.384 | 0.285 | 1.053 | 0.175 | 0.103 | 22.530 | 0.255 | 0.277 | 11.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 121 | 105 | 97 | 129 | 409 | 2300 | 107 | 113 | 112 |
N.S. |
1 | 0.93 | 0.81 | 0.75 | 0.99 | 3.15 | 17.69 | 0.82 | 0.87 | 0.86 |
time (sec) |
N/A | 0.388 | 0.256 | 1.050 | 0.138 | 0.093 | 32.980 | 0.272 | 0.267 | 10.861 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 112 | 105 | 132 | 445 | 2660 | 110 | 124 | 147 |
N.S. |
1 | 1.04 | 0.83 | 0.78 | 0.98 | 3.30 | 19.70 | 0.81 | 0.92 | 1.09 |
time (sec) |
N/A | 0.416 | 0.295 | 1.152 | 0.160 | 0.095 | 75.858 | 0.274 | 0.300 | 10.708 |