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Chapter 2
detailed summary tables of results

 2.1 List of integrals sorted by grade for each CAS
  2.1.1 Rubi
  2.1.2 Mathematica
  2.1.3 Maple
  2.1.4 Maxima
  2.1.5 FriCAS
  2.1.6 Sympy
  2.1.7 Giac
 2.2 Detailed conclusion table per each integral for all CAS systems
 2.3 Detailed conclusion table specific for Rubi results

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 48, 49, 52, 54, 56, 57, 60, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 188 }

B grade: { 39, 62, 139, 187, 189 }

C grade: { 41, 42, 43, 44, 45, 46, 47, 50, 51, 53, 55, 58, 59, 61, 63, 64, 65, 66 }

F grade: { 75, 86}

2.1.3 Maple

A grade: { 4, 5, 6, 7, 8, 13, 14, 15, 19, 20, 21, 22, 25, 26, 27, 28, 32, 35, 36, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 75, 77, 78, 80, 82, 83, 85, 86, 87, 98, 102, 103, 121, 122, 126, 127, 130, 131, 132, 135, 136, 137, 140, 141, 142, 146, 153, 160, 174, 178, 179, 183, 184, 188 }

B grade: { 1, 2, 3, 9, 10, 11, 12, 16, 17, 18, 23, 24, 29, 30, 31, 33, 34, 37, 38, 39, 76, 79, 118, 119, 120, 123, 124, 125, 128, 129, 133, 134, 138, 139, 187, 189 }

C grade: { 84, 104, 105, 106, 107, 108, 109, 110, 143, 144, 145, 150, 151, 152, 157, 158, 159, 173 }

F grade: { 67, 68, 69, 70, 71, 72, 73, 74, 81, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 111, 112, 113, 114, 115, 116, 117, 147, 148, 149, 154, 155, 156, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 175, 176, 177, 180, 181, 182, 185, 186 }

2.1.4 Maxima

A grade: { 4, 12, 19, 23, 24, 25, 32, 75, 77, 78, 80, 82, 83, 85, 86, 88, 98, 102, 103, 125, 136, 137, 144, 145, 146, 150, 151, 152, 153, 160, 164, 165, 166, 174, 179, 183, 184, 188

B grade: { 1, 2, 3, 9, 10, 11, 16, 17, 18, 29, 30, 33, 34, 35, 37, 38, 67, 68, 69, 70, 71, 72, 73, 74, 118, 119, 120, 123, 124, 128, 129, 130, 133, 134, 135, 138, 139, 140, 143, 157, 158, 159, 173, 178 }

C grade: { 5, 6, 7, 8, 13, 14, 15, 20, 21, 22, 26, 27, 28, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 121, 122, 126, 127, 147, 148, 149, 154, 155, 156, 167, 168, 169 }

F grade: { 31, 36, 39, 40, 76, 79, 81, 84, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 131, 132, 141, 142, 161, 162, 163, 170, 171, 172, 175, 176, 177, 180, 181, 182, 185, 186, 187, 189 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 32, 35, 36, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 91, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 130, 131, 132, 135, 136, 137, 140, 141, 142, 146, 153, 160, 173, 174, 178, 179, 183, 188 }

B grade: { 7, 8, 22, 31, 34, 39, 55, 129, 134, 139, 187, 189 }

C grade: { 29, 30, 33, 37, 38, 128, 133, 138, 185, 186 }

F grade: { 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 143, 144, 145, 147, 148, 149, 150, 151, 152, 154, 155, 156, 157, 158, 159, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 175, 176, 177, 180, 181, 182, 184 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 9, 10, 11, 12, 16, 17, 18, 19, 23, 24, 25, 26, 32, 36, 40, 63, 64, 65, 66, 75, 77, 83, 85, 98, 102, 103, 118, 119, 120, 123, 124, 125, 130, 131, 132, 135, 136, 137, 140, 141, 142, 174, 179, 183, 184, 188 }

B grade: { }

C grade: { }

F grade: { 5, 6, 7, 8, 13, 14, 15, 20, 21, 22, 27, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 67, 68, 69, 70, 71, 72, 73, 74, 76, 78, 79, 80, 81, 82, 84, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 121, 122, 126, 127, 128, 129, 133, 134, 138, 139, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 175, 176, 177, 178, 180, 181, 182, 185, 186, 187, 189 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 9, 10, 11, 12, 16, 17, 18, 19, 23, 24, 25, 32, 36, 40, 75, 77, 78, 80, 82, 83, 85, 86, 88, 98, 102, 103, 118, 119, 120, 123, 124, 125, 131, 132, 136, 137, 141, 142, 174, 179, 183, 184, 188 }

B grade: { 35, 130, 135, 140 }

C grade: { 5, 6, 7, 8, 13, 14, 15, 20, 26, 27, 28, 41, 42, 43, 44, 48, 49, 50, 51, 56, 57, 58, 59, 63, 64, 65, 121, 122, 126 }

F grade: { 21, 22, 29, 30, 31, 33, 34, 37, 38, 39, 45, 46, 47, 52, 53, 54, 55, 60, 61, 62, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 79, 81, 84, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 127, 128, 129, 133, 134, 138, 139, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 175, 176, 177, 178, 180, 181, 182, 185, 186, 187, 189 }

2.2 Detailed conclusion table per each integral for all CAS systems

Detailed conclusion table per each integral is given by 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 just an F.

In this table,the column normalized size is defined as \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 76 539 649 347 311 230
normalized size 1 1. 0.84 5.92 7.13 3.81 3.42 2.53
time (sec) N/A 0.093 0.337 0.029 1.116 1.026 2.878 1.134
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 61 302 375 228 202 149
normalized size 1 1. 0.87 4.31 5.36 3.26 2.89 2.13
time (sec) N/A 0.066 0.222 0.029 1.012 1.065 1.313 1.123
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 44 143 184 136 112 86
normalized size 1 1. 0.9 2.92 3.76 2.78 2.29 1.76
time (sec) N/A 0.041 0.167 0.026 1.01 1.129 0.638 1.101
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 26 51 68 69 46 41
normalized size 1 1. 0.96 1.89 2.52 2.56 1.7 1.52
time (sec) N/A 0.016 0.056 0.029 0.96 1.058 0.234 1.1
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 50 72 192 200 0 779
normalized size 1 1. 0.96 1.38 3.69 3.85 0. 14.98
time (sec) N/A 0.098 0.099 0.027 1.218 1.06 0. 1.182
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 65 109 224 302 0 4298
normalized size 1 1. 0.89 1.49 3.07 4.14 0. 58.88
time (sec) N/A 0.11 0.393 0.03 1.315 1.107 0. 1.49
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 89 143 271 471 0 7449
normalized size 1 1. 0.86 1.38 2.61 4.53 0. 71.62
time (sec) N/A 0.138 0.609 0.033 1.601 1.16 0. 1.538
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 127 127 144 179 339 639 0 11310
normalized size 1 1. 1.13 1.41 2.67 5.03 0. 89.06
time (sec) N/A 0.159 0.552 0.032 1.934 1.174 0. 1.886
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 161 161 132 1027 968 593 660 300
normalized size 1 1. 0.82 6.38 6.01 3.68 4.1 1.86
time (sec) N/A 0.102 0.658 0.047 1.189 1.164 5.988 1.101
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 134 134 106 587 578 394 456 207
normalized size 1 1. 0.79 4.38 4.31 2.94 3.4 1.54
time (sec) N/A 0.074 0.451 0.027 1.114 1.158 3.263 1.125
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 95 95 77 289 300 247 264 127
normalized size 1 1. 0.81 3.04 3.16 2.6 2.78 1.34
time (sec) N/A 0.053 0.312 0.026 1.069 1.094 1.424 1.122
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 50 112 122 130 126 65
normalized size 1 1. 0.91 2.04 2.22 2.36 2.29 1.18
time (sec) N/A 0.025 0.16 0.028 1.054 1.026 0.619 1.104
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 65 105 217 236 0 824
normalized size 1 1. 0.83 1.35 2.78 3.03 0. 10.56
time (sec) N/A 0.153 0.131 0.029 1.207 1.162 0. 1.203
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 75 156 231 319 0 3976
normalized size 1 1. 0.9 1.88 2.78 3.84 0. 47.9
time (sec) N/A 0.134 0.64 0.03 1.314 1.157 0. 1.341
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 102 193 278 502 0 6934
normalized size 1 1. 0.91 1.72 2.48 4.48 0. 61.91
time (sec) N/A 0.197 0.925 0.032 1.617 1.424 0. 1.972
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 225 225 385 1023 1249 759 772 474
normalized size 1 1. 1.71 4.55 5.55 3.37 3.43 2.11
time (sec) N/A 0.254 1.03 0.071 1.223 1.546 10.42 1.151
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 175 175 121 560 722 494 495 312
normalized size 1 1. 0.69 3.2 4.13 2.82 2.83 1.78
time (sec) N/A 0.156 0.969 0.029 1.113 1.504 5.387 1.123
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 93 265 360 297 284 185
normalized size 1 1. 0.76 2.15 2.93 2.41 2.31 1.5
time (sec) N/A 0.097 0.603 0.029 1.062 1.47 3.029 1.201
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 52 95 139 153 126 93
normalized size 1 1. 0.69 1.27 1.85 2.04 1.68 1.24
time (sec) N/A 0.042 0.164 0.027 0.997 1.38 1.18 1.2
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 103 166 373 406 0 8201
normalized size 1 1. 0.85 1.37 3.08 3.36 0. 67.78
time (sec) N/A 0.244 0.262 0.03 1.347 1.328 0. 2.088
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 200 242 410 571 0 0
normalized size 1 1. 1.38 1.67 2.83 3.94 0. 0.
time (sec) N/A 0.225 0.698 0.048 1.614 1.436 0. 0.
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 184 184 221 311 458 861 0 0
normalized size 1 1. 1.2 1.69 2.49 4.68 0. 0.
time (sec) N/A 0.345 0.852 0.035 1.962 1.614 0. 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 172 172 100 440 409 271 253 146
normalized size 1 1. 0.58 2.56 2.38 1.58 1.47 0.85
time (sec) N/A 0.154 0.414 0.056 1.056 1.41 9.483 1.113
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 134 134 92 241 254 217 209 113
normalized size 1 1. 0.69 1.8 1.9 1.62 1.56 0.84
time (sec) N/A 0.108 0.176 0.029 1.067 1.31 6.461 1.129
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 53 110 132 161 138 86
normalized size 1 1. 0.66 1.38 1.65 2.01 1.72 1.08
time (sec) N/A 0.047 0.133 0.026 1.017 1.36 3.419 1.136
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A A C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 52 52 123 274 60 578
normalized size 1 1. 0.88 0.88 2.08 4.64 1.02 9.8
time (sec) N/A 0.158 0.102 0.03 1.207 1.472 5.737 1.141
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 79 90 980 312 0 4347
normalized size 1 1. 1.2 1.36 14.85 4.73 0. 65.86
time (sec) N/A 0.151 0.22 0.03 1.35 1.442 0. 1.259
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 90 90 119 124 1073 389 0 5292
normalized size 1 1. 1.32 1.38 11.92 4.32 0. 58.8
time (sec) N/A 0.297 0.303 0.033 1.384 1.448 0. 1.265
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 205 205 196 685 961 2367 0 0
normalized size 1 1. 0.96 3.34 4.69 11.55 0. 0.
time (sec) N/A 0.157 0.188 0.397 2.075 1.813 0. 0.
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 137 137 130 392 535 1534 0 0
normalized size 1 1. 0.95 2.86 3.91 11.2 0. 0.
time (sec) N/A 0.092 0.109 0.366 1.851 1.707 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) B F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 75 75 87 167 0 837 0 0
normalized size 1 1. 1.16 2.23 0. 11.16 0. 0.
time (sec) N/A 0.042 0.006 0.368 0. 1.561 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.022 4.468 0.243 0. 0. 0. 0.
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 114 114 109 316 1426 2010 0 0
normalized size 1 1. 0.96 2.77 12.51 17.63 0. 0.
time (sec) N/A 0.215 0.487 0.432 2.733 1.781 0. 0.
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 75 170 437 1187 0 0
normalized size 1 1. 0.91 2.07 5.33 14.48 0. 0.
time (sec) N/A 0.134 0.243 0.374 2.513 1.734 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 36 37 215 115 0 1970
normalized size 1 1. 1.29 1.32 7.68 4.11 0. 70.36
time (sec) N/A 0.027 0.013 0.026 2.115 1.408 0. 1.595
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.039 5.597 0.332 0. 0. 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 337 337 311 1127 5168 3213 0 0
normalized size 1 1. 0.92 3.34 15.34 9.53 0. 0.
time (sec) N/A 0.269 2.935 0.458 7.551 2.489 0. 0.
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 193 193 184 584 2556 2034 0 0
normalized size 1 1. 0.95 3.03 13.24 10.54 0. 0.
time (sec) N/A 0.143 1.234 0.411 2.997 2.037 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-1) B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 389 267 0 1170 0 0
normalized size 1 1. 3.32 2.28 0. 10. 0. 0.
time (sec) N/A 0.069 3.798 0.197 0. 1.786 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.038 1.448 0.018 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 194 194 124 232 886 466 0 1374
normalized size 1 1. 0.64 1.2 4.57 2.4 0. 7.08
time (sec) N/A 0.423 0.056 0.031 2.246 1.482 0. 1.264
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 169 169 122 189 855 394 0 767
normalized size 1 1. 0.72 1.12 5.06 2.33 0. 4.54
time (sec) N/A 0.236 0.101 0.03 2.23 1.478 0. 1.209
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 124 144 776 328 0 335
normalized size 1 1. 0.87 1.01 5.46 2.31 0. 2.36
time (sec) N/A 0.172 0.092 0.029 2.053 1.415 0. 1.166
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 124 100 714 269 0 224
normalized size 1 1. 1.05 0.85 6.05 2.28 0. 1.9
time (sec) N/A 0.134 0.06 0.031 2.123 1.35 0. 1.145
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 139 139 147 140 632 363 0 0
normalized size 1 1. 1.06 1.01 4.55 2.61 0. 0.
time (sec) N/A 0.186 0.33 0.03 1.568 1.428 0. 0.
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 168 168 190 180 632 510 0 0
normalized size 1 1. 1.13 1.07 3.76 3.04 0. 0.
time (sec) N/A 0.262 0.303 0.03 1.511 1.476 0. 0.
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 193 193 228 220 632 680 0 0
normalized size 1 1. 1.18 1.14 3.27 3.52 0. 0.
time (sec) N/A 0.296 0.388 0.03 1.56 1.587 0. 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 231 231 194 242 937 613 0 1419
normalized size 1 1. 0.84 1.05 4.06 2.65 0. 6.14
time (sec) N/A 0.435 1.897 0.038 2.202 1.853 0. 1.38
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 203 203 175 197 902 479 0 772
normalized size 1 1. 0.86 0.97 4.44 2.36 0. 3.8
time (sec) N/A 0.342 1.532 0.036 2.221 1.922 0. 1.279
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 158 158 146 150 824 369 0 331
normalized size 1 1. 0.92 0.95 5.22 2.34 0. 2.09
time (sec) N/A 0.278 0.545 0.036 2.285 1.883 0. 1.202
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 130 130 145 108 747 279 0 220
normalized size 1 1. 1.12 0.83 5.75 2.15 0. 1.69
time (sec) N/A 0.243 0.247 0.039 2.137 1.704 0. 1.183
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 135 135 133 146 640 333 0 0
normalized size 1 1. 0.99 1.08 4.74 2.47 0. 0.
time (sec) N/A 0.258 0.633 0.037 1.473 1.851 0. 0.
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 170 170 181 189 644 498 0 0
normalized size 1 1. 1.06 1.11 3.79 2.93 0. 0.
time (sec) N/A 0.312 1.418 0.036 1.551 1.979 0. 0.
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 216 216 244 230 644 733 0 0
normalized size 1 1. 1.13 1.06 2.98 3.39 0. 0.
time (sec) N/A 0.324 1.29 0.037 1.652 2.07 0. 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 247 247 237 273 644 927 0 0
normalized size 1 1. 0.96 1.11 2.61 3.75 0. 0.
time (sec) N/A 0.407 0.857 0.036 1.718 2.239 0. 0.
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 410 410 542 474 1863 921 0 2719
normalized size 1 1. 1.32 1.16 4.54 2.25 0. 6.63
time (sec) N/A 1.139 3.232 0.043 2.627 2.131 0. 1.608
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 354 354 390 386 1793 763 0 1515
normalized size 1 1. 1.1 1.09 5.06 2.16 0. 4.28
time (sec) N/A 0.991 1.696 0.043 2.702 2.068 0. 1.442
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 304 304 254 294 1651 645 0 662
normalized size 1 1. 0.84 0.97 5.43 2.12 0. 2.18
time (sec) N/A 0.484 0.443 0.04 2.611 1.992 0. 1.293
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 257 257 236 212 1530 551 0 443
normalized size 1 1. 0.92 0.82 5.95 2.14 0. 1.72
time (sec) N/A 0.417 0.409 0.043 2.577 1.711 0. 1.161
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 271 271 299 286 1260 682 0 0
normalized size 1 1. 1.1 1.06 4.65 2.52 0. 0.
time (sec) N/A 0.564 1.548 0.042 1.892 1.984 0. 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 292 292 268 368 1261 914 0 0
normalized size 1 1. 0.92 1.26 4.32 3.13 0. 0.
time (sec) N/A 0.738 2.059 0.043 1.735 2.329 0. 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A C A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 356 356 1429 450 1261 1229 0 0
normalized size 1 1. 4.01 1.26 3.54 3.45 0. 0.
time (sec) N/A 0.831 6.333 0.042 1.706 2.531 0. 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A A C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 55 34 100 134 83 93
normalized size 1 1. 1.12 0.69 2.04 2.73 1.69 1.9
time (sec) N/A 0.057 0.013 0.027 1.78 1.59 16.241 1.142
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A A C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 48 27 90 105 61 72
normalized size 1 1. 1.33 0.75 2.5 2.92 1.69 2.
time (sec) N/A 0.035 0.006 0.028 1.749 1.629 1.193 1.135
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A A C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 51 19 81 76 37 47
normalized size 1 1. 2.12 0.79 3.38 3.17 1.54 1.96
time (sec) N/A 0.02 0.007 0.026 1.878 1.656 0.996 1.137
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A C A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 63 28 28 111 61 0
normalized size 1 1. 1.8 0.8 0.8 3.17 1.74 0.
time (sec) N/A 0.037 0.042 0.028 2.438 1.665 4.173 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F B A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 183 183 122 0 770 331 0 0
normalized size 1 1. 0.67 0. 4.21 1.81 0. 0.
time (sec) N/A 0.24 0.107 0.191 1.564 1.755 0. 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 152 152 124 0 701 258 0 0
normalized size 1 1. 0.82 0. 4.61 1.7 0. 0.
time (sec) N/A 0.149 0.118 0.178 1.597 1.727 0. 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 152 152 124 0 701 258 0 0
normalized size 1 1. 0.82 0. 4.61 1.7 0. 0.
time (sec) N/A 0.162 0.1 0.174 1.558 1.789 0. 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 135 135 124 0 636 208 0 0
normalized size 1 1. 0.92 0. 4.71 1.54 0. 0.
time (sec) N/A 0.116 0.06 0.177 1.62 1.739 0. 0.
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 135 135 124 0 636 208 0 0
normalized size 1 1. 0.92 0. 4.71 1.54 0. 0.
time (sec) N/A 0.12 0.064 0.165 1.616 1.665 0. 0.
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 151 151 121 0 632 290 0 0
normalized size 1 1. 0.8 0. 4.19 1.92 0. 0.
time (sec) N/A 0.146 0.054 0.181 1.473 1.749 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 153 153 121 0 632 290 0 0
normalized size 1 1. 0.79 0. 4.13 1.9 0. 0.
time (sec) N/A 0.155 0.057 0.183 1.558 1.733 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F B A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 182 182 125 0 632 452 0 0
normalized size 1 1. 0.69 0. 3.47 2.48 0. 0.
time (sec) N/A 0.204 0.054 0.186 1.491 1.866 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A F A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.017 0. 0.464 0. 0. 0. 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 133 0 0 0 0
normalized size 1 1. 1. 8.31 0. 0. 0. 0.
time (sec) N/A 0.009 0.028 1.411 0. 0. 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.029 0.704 0.141 0. 0. 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 60 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.038 2.026 0.122 0. 0. 0. 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 36 179 0 0 0 0
normalized size 1 1. 0.86 4.26 0. 0. 0. 0.
time (sec) N/A 0.02 0.031 2.089 0. 0. 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.028 16.498 0.122 0. 0. 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 40 0 0 0 0 0
normalized size 1 1. 0.95 0. 0. 0. 0. 0.
time (sec) N/A 0.059 0.415 0.275 0. 0. 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 61 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.077 5.124 0.085 0. 0. 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.017 0.299 0.125 0. 0. 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 18 0 0 0 0
normalized size 1 1. 1. 1.12 0. 0. 0. 0.
time (sec) N/A 0.009 0.015 0.03 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.028 0.199 0.132 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A F A A F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 54 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.036 0. 0.123 0. 0. 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 38 101 0 0 0 0
normalized size 1 1. 1. 2.66 0. 0. 0. 0.
time (sec) N/A 0.017 0.054 2.207 0. 0. 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A F A F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.028 15.343 180. 0. 0. 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 33 0 0 0 0 0
normalized size 1 1. 0.87 0. 0. 0. 0. 0.
time (sec) N/A 0.055 0.388 0.22 0. 0. 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 17 0 0 0 0 0
normalized size 1 1. 0.85 0. 0. 0. 0. 0.
time (sec) N/A 0.043 0.086 0.22 0. 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 17 0 0 54 0 0
normalized size 1 1. 0.71 0. 0. 2.25 0. 0.
time (sec) N/A 0.046 0.075 0.213 0. 1.598 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 33 0 0 0 0 0
normalized size 1 1. 0.7 0. 0. 0. 0. 0.
time (sec) N/A 0.061 0.129 0.298 0. 0. 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 29 0 0 0 0 0
normalized size 1 1. 0.91 0. 0. 0. 0. 0.
time (sec) N/A 0.086 0.145 0.226 0. 0. 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 17 0 0 0 0 0
normalized size 1 1. 0.71 0. 0. 0. 0. 0.
time (sec) N/A 0.081 0.09 0.166 0. 0. 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 17 0 0 0 0 0
normalized size 1 1. 0.71 0. 0. 0. 0. 0.
time (sec) N/A 0.079 0.139 0.161 0. 0. 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 45 0 0 0 0 0
normalized size 1 1. 0.96 0. 0. 0. 0. 0.
time (sec) N/A 0.094 0.107 0.167 0. 0. 0. 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 51 0 0 0 0 0
normalized size 1 1. 0.82 0. 0. 0. 0. 0.
time (sec) N/A 0.154 0.105 0.151 0. 0. 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.041 0.726 0.559 0. 0. 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 275 275 253 0 0 470 0 0
normalized size 1 1. 0.92 0. 0. 1.71 0. 0.
time (sec) N/A 0.304 0.182 0.342 0. 1.848 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 162 162 150 0 0 340 0 0
normalized size 1 1. 0.93 0. 0. 2.1 0. 0.
time (sec) N/A 0.213 0.198 0.287 0. 1.733 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 131 131 122 0 0 223 0 0
normalized size 1 1. 0.93 0. 0. 1.7 0. 0.
time (sec) N/A 0.097 0.048 0.211 0. 1.767 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.019 5.456 0.205 0. 0. 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.035 0.826 0.194 0. 0. 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 75 455 0 153 0 0
normalized size 1 1. 1. 6.07 0. 2.04 0. 0.
time (sec) N/A 0.08 0.019 0.09 0. 1.706 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 79 354 0 153 0 0
normalized size 1 1. 1. 4.48 0. 1.94 0. 0.
time (sec) N/A 0.077 0.016 0.078 0. 1.68 0. 0.
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 75 291 0 153 0 0
normalized size 1 1. 1. 3.88 0. 2.04 0. 0.
time (sec) N/A 0.077 0.015 0.077 0. 1.691 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 79 379 0 136 0 0
normalized size 1 1. 1. 4.8 0. 1.72 0. 0.
time (sec) N/A 0.071 0.014 0.073 0. 1.698 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 62 427 0 142 0 0
normalized size 1 1. 0.95 6.57 0. 2.18 0. 0.
time (sec) N/A 0.073 0.023 0.078 0. 1.701 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 75 530 0 153 0 0
normalized size 1 1. 1. 7.07 0. 2.04 0. 0.
time (sec) N/A 0.074 0.015 0.082 0. 1.714 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 75 600 0 153 0 0
normalized size 1 1. 1. 8. 0. 2.04 0. 0.
time (sec) N/A 0.074 0.015 0.086 0. 1.653 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 99 99 92 0 0 235 0 0
normalized size 1 1. 0.93 0. 0. 2.37 0. 0.
time (sec) N/A 0.157 0.112 180. 0. 1.7 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 96 0 0 235 0 0
normalized size 1 1. 0.93 0. 0. 2.28 0. 0.
time (sec) N/A 0.144 0.103 180. 0. 1.679 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 90 0 0 235 0 0
normalized size 1 1. 0.93 0. 0. 2.42 0. 0.
time (sec) N/A 0.137 0.098 180. 0. 2.107 0. 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 90 0 0 203 0 0
normalized size 1 1. 0.87 0. 0. 1.97 0. 0.
time (sec) N/A 0.133 0.119 180. 0. 1.943 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 77 0 0 193 0 0
normalized size 1 1. 0.91 0. 0. 2.27 0. 0.
time (sec) N/A 0.126 0.058 180. 0. 1.955 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 91 0 0 227 0 0
normalized size 1 1. 0.9 0. 0. 2.25 0. 0.
time (sec) N/A 0.138 0.108 180. 0. 2.035 0. 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 95 95 95 0 0 235 0 0
normalized size 1 1. 1. 0. 0. 2.47 0. 0.
time (sec) N/A 0.142 0.092 180. 0. 1.835 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 122 476 616 362 264 211
normalized size 1 1. 1.37 5.35 6.92 4.07 2.97 2.37
time (sec) N/A 0.115 0.557 0.038 1.317 1.69 1.659 1.153
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 80 236 317 228 151 127
normalized size 1 1. 1.19 3.52 4.73 3.4 2.25 1.9
time (sec) N/A 0.085 0.334 0.04 1.213 1.631 0.786 1.175
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 52 89 123 126 68 62
normalized size 1 1. 1.18 2.02 2.8 2.86 1.55 1.41
time (sec) N/A 0.042 0.23 0.033 1.168 1.624 0.316 1.143
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 55 95 232 234 0 934
normalized size 1 1. 0.85 1.46 3.57 3.6 0. 14.37
time (sec) N/A 0.15 0.129 0.036 1.421 1.673 0. 1.171
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 78 143 265 332 0 4419
normalized size 1 1. 0.88 1.61 2.98 3.73 0. 49.65
time (sec) N/A 0.163 0.32 0.036 1.525 1.707 0. 1.274
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 237 237 217 1129 1281 751 779 458
normalized size 1 1. 0.92 4.76 5.41 3.17 3.29 1.93
time (sec) N/A 0.261 1.436 0.04 1.189 1.787 4.306 1.124
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 168 168 193 564 667 448 456 279
normalized size 1 1. 1.15 3.36 3.97 2.67 2.71 1.66
time (sec) N/A 0.179 0.656 0.042 1.2 1.662 1.962 1.153
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 80 218 266 228 219 144
normalized size 1 1. 0.68 1.85 2.25 1.93 1.86 1.22
time (sec) N/A 0.097 0.483 0.037 1.214 1.627 0.821 1.128
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 114 192 455 467 0 9360
normalized size 1 1. 0.79 1.32 3.14 3.22 0. 64.55
time (sec) N/A 0.338 0.232 0.04 1.527 1.661 0. 1.617
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 159 159 206 276 500 683 0 0
normalized size 1 1. 1.3 1.74 3.14 4.3 0. 0.
time (sec) N/A 0.317 0.498 0.046 1.83 1.838 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 134 134 151 364 1264 1019 0 0
normalized size 1 1. 1.13 2.72 9.43 7.6 0. 0.
time (sec) N/A 0.282 0.305 0.453 1.721 1.77 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 125 197 382 564 0 0
normalized size 1 1. 1.24 1.95 3.78 5.58 0. 0.
time (sec) N/A 0.199 0.33 0.381 1.606 1.683 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 70 60 216 149 70 316
normalized size 1 1. 1.43 1.22 4.41 3.04 1.43 6.45
time (sec) N/A 0.064 0.076 0.054 1.201 1.669 0.75 1.145
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.06 2.748 0.293 0. 0. 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.057 2.729 0.335 0. 0. 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 271 271 250 678 4420 1796 0 0
normalized size 1 1. 0.92 2.5 16.31 6.63 0. 0.
time (sec) N/A 0.367 1.018 0.628 4.917 1.911 0. 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 212 212 212 358 1041 956 0 0
normalized size 1 1. 1. 1.69 4.91 4.51 0. 0.
time (sec) N/A 0.256 1.064 0.349 2.651 1.754 0. 0.
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 113 123 1030 298 146 1022
normalized size 1 1. 0.92 1. 8.37 2.42 1.19 8.31
time (sec) N/A 0.095 0.508 0.11 1.27 1.671 1.432 1.503
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.054 12.181 2.144 0. 0. 0. 0.
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.052 13.232 2.551 0. 0. 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 133 133 164 468 1295 1173 0 0
normalized size 1 1. 1.23 3.52 9.74 8.82 0. 0.
time (sec) N/A 0.284 1.238 0.46 2.068 1.777 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 102 102 292 247 425 743 0 0
normalized size 1 1. 2.86 2.42 4.17 7.28 0. 0.
time (sec) N/A 0.203 5.482 0.398 1.959 1.72 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 57 85 216 151 90 309
normalized size 1 1. 1.14 1.7 4.32 3.02 1.8 6.18
time (sec) N/A 0.065 0.263 0.063 1.167 1.63 0.896 1.161
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.062 2.541 0.295 0. 0. 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.058 2.405 0.328 0. 0. 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 53 132 278 0 0 0
normalized size 1 1. 0.48 1.2 2.53 0. 0. 0.
time (sec) N/A 0.134 0.21 0.29 2.869 0. 0. 0.
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 44 105 165 0 0 0
normalized size 1 1. 0.5 1.19 1.88 0. 0. 0.
time (sec) N/A 0.112 0.158 0.231 2.812 0. 0. 0.
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 34 80 82 0 0 0
normalized size 1 1. 0.64 1.51 1.55 0. 0. 0.
time (sec) N/A 0.061 0.128 0.218 2.52 0. 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 29 43 27 84 0 0
normalized size 1 1. 1.12 1.65 1.04 3.23 0. 0.
time (sec) N/A 0.013 0.033 0.496 2.676 1.501 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 55 0 82 0 0 0
normalized size 1 1. 0.65 0. 0.98 0. 0. 0.
time (sec) N/A 0.121 0.091 0.268 2.584 0. 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 75 0 267 0 0 0
normalized size 1 1. 0.68 0. 2.43 0. 0. 0.
time (sec) N/A 0.133 0.162 0.215 2.65 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 151 151 98 0 313 0 0 0
normalized size 1 1. 0.65 0. 2.07 0. 0. 0.
time (sec) N/A 0.162 0.253 0.223 2.519 0. 0. 0.
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 33 87 65 0 0 0
normalized size 1 1. 0.49 1.28 0.96 0. 0. 0.
time (sec) N/A 0.111 0.055 0.214 2.338 0. 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 29 70 49 0 0 0
normalized size 1 1. 0.55 1.32 0.92 0. 0. 0.
time (sec) N/A 0.096 0.044 0.155 2.172 0. 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 22 55 32 0 0 0
normalized size 1 1. 0.69 1.72 1. 0. 0. 0.
time (sec) N/A 0.05 0.021 0.154 2.3 0. 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 18 25 16 57 0 0
normalized size 1 1. 1.2 1.67 1.07 3.8 0. 0.
time (sec) N/A 0.011 0.008 0.373 2.381 1.561 0. 0.
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 23 0 23 0 0 0
normalized size 1 1. 1. 0. 1. 0. 0. 0.
time (sec) N/A 0.087 0.007 0.197 2.535 0. 0. 0.
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 33 0 31 0 0 0
normalized size 1 1. 0.79 0. 0.74 0. 0. 0.
time (sec) N/A 0.091 0.058 0.149 2.186 0. 0. 0.
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F C F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 44 0 26 0 0 0
normalized size 1 1. 0.66 0. 0.39 0. 0. 0.
time (sec) N/A 0.106 0.075 0.152 2.134 0. 0. 0.
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 34 86 174 0 0 0
normalized size 1 1. 0.47 1.19 2.42 0. 0. 0.
time (sec) N/A 0.115 0.051 0.163 1.971 0. 0. 0.
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 30 69 135 0 0 0
normalized size 1 1. 0.54 1.23 2.41 0. 0. 0.
time (sec) N/A 0.098 0.042 0.096 1.987 0. 0. 0.
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 23 54 97 0 0 0
normalized size 1 1. 0.68 1.59 2.85 0. 0. 0.
time (sec) N/A 0.051 0.024 0.095 1.823 0. 0. 0.
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 19 25 31 59 0 0
normalized size 1 1. 1.19 1.56 1.94 3.69 0. 0.
time (sec) N/A 0.011 0.007 0.961 1.946 1.552 0. 0.
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 24 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.088 0.021 0.137 0. 0. 0. 0.
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 34 0 0 0 0 0
normalized size 1 1. 0.77 0. 0. 0. 0. 0.
time (sec) N/A 0.092 0.026 0.096 0. 0. 0. 0.
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 45 0 0 0 0 0
normalized size 1 1. 0.64 0. 0. 0. 0. 0.
time (sec) N/A 0.106 0.057 0.096 0. 0. 0. 0.
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 185 185 67 0 132 0 0 0
normalized size 1 1. 0.36 0. 0.71 0. 0. 0.
time (sec) N/A 0.183 0.298 0.129 2.253 0. 0. 0.
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 54 0 97 0 0 0
normalized size 1 1. 0.37 0. 0.67 0. 0. 0.
time (sec) N/A 0.144 0.241 0.088 1.989 0. 0. 0.
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 45 0 65 0 0 0
normalized size 1 1. 0.51 0. 0.73 0. 0. 0.
time (sec) N/A 0.072 0.066 0.089 2.34 0. 0. 0.
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F C F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 36 0 39 0 0 0
normalized size 1 1. 0.65 0. 0.71 0. 0. 0.
time (sec) N/A 0.128 0.02 0.089 2.429 0. 0. 0.
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F C F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 53 0 50 0 0 0
normalized size 1 1. 0.67 0. 0.63 0. 0. 0.
time (sec) N/A 0.126 0.085 0.089 2.104 0. 0. 0.
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F C F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 66 0 45 0 0 0
normalized size 1 1. 0.61 0. 0.41 0. 0. 0.
time (sec) N/A 0.165 0.055 0.092 2.248 0. 0. 0.
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 374 374 199 0 0 0 0 0
normalized size 1 1. 0.53 0. 0. 0. 0. 0.
time (sec) N/A 0.212 0.127 0.197 0. 0. 0. 0.
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 262 262 146 0 0 0 0 0
normalized size 1 1. 0.56 0. 0. 0. 0. 0.
time (sec) N/A 0.167 0.077 0.184 0. 0. 0. 0.
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 156 156 89 0 0 0 0 0
normalized size 1 1. 0.57 0. 0. 0. 0. 0.
time (sec) N/A 0.086 0.051 0.178 0. 0. 0. 0.
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 40 54 122 347 0 0
normalized size 1 1. 0.87 1.17 2.65 7.54 0. 0.
time (sec) N/A 0.022 0.015 0.243 2.139 1.663 0. 0.
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.069 0.972 0.178 0. 0. 0. 0.
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 235 235 170 0 0 0 0 0
normalized size 1 1. 0.72 0. 0. 0. 0. 0.
time (sec) N/A 0.173 0.098 0.125 0. 0. 0. 0.
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 117 0 0 0 0 0
normalized size 1 1. 0.72 0. 0. 0. 0. 0.
time (sec) N/A 0.141 0.049 0.089 0. 0. 0. 0.
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 83 0 0 0 0 0
normalized size 1 1. 0.86 0. 0. 0. 0. 0.
time (sec) N/A 0.078 0.033 0.093 0. 0. 0. 0.
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 36 25 109 273 0 0
normalized size 1 1. 0.97 0.68 2.95 7.38 0. 0.
time (sec) N/A 0.02 0.015 0.889 2.026 1.632 0. 0.
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.077 3.124 0.087 0. 0. 0. 0.
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 423 423 257 0 0 0 0 0
normalized size 1 1. 0.61 0. 0. 0. 0. 0.
time (sec) N/A 0.26 0.459 0.112 0. 0. 0. 0.
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 257 257 185 0 0 0 0 0
normalized size 1 1. 0.72 0. 0. 0. 0. 0.
time (sec) N/A 0.189 0.118 0.116 0. 0. 0. 0.
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 150 150 165 0 0 0 0 0
normalized size 1 1. 1.1 0. 0. 0. 0. 0.
time (sec) N/A 0.117 0.18 0.105 0. 0. 0. 0.
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.079 11.306 0.112 0. 0. 0. 0.
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.065 1.071 0.164 0. 0. 0. 0.
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 383 383 290 0 0 2719 0 0
normalized size 1 1. 0.76 0. 0. 7.1 0. 0.
time (sec) N/A 0.559 0.899 0.231 0. 2.537 0. 0.
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 329 329 379 0 0 3218 0 0
normalized size 1 1. 1.15 0. 0. 9.78 0. 0.
time (sec) N/A 0.663 0.701 0.44 0. 2.513 0. 0.
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 214 214 756 414 0 2338 0 0
normalized size 1 1. 3.53 1.93 0. 10.93 0. 0.
time (sec) N/A 0.4 0.811 0.418 0. 2.375 0. 0.
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.049 0.819 0.191 0. 0. 0. 0.
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 296 296 933 674 0 3575 0 0
normalized size 1 1. 3.15 2.28 0. 12.08 0. 0.
time (sec) N/A 0.523 9.653 0.795 0. 2.884 0. 0.

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac{\text{number of rules}}{\text{integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [180] had the largest ratio of [ 0.6429 ]

Table 2.1Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\)
1 A 5 2 1. 14 0.143
2 A 4 2 1. 14 0.143
3 A 3 2 1. 14 0.143
4 A 2 2 1. 12 0.167
5 A 3 3 1. 14 0.214
6 A 4 4 1. 14 0.286
7 A 5 4 1. 14 0.286
8 A 6 4 1. 14 0.286
9 A 6 4 1. 16 0.25
10 A 4 3 1. 16 0.188
11 A 4 4 1. 16 0.25
12 A 2 1 1. 14 0.071
13 A 5 4 1. 16 0.25
14 A 5 5 1. 16 0.312
15 A 7 6 1. 16 0.375
16 A 12 4 1. 16 0.25
17 A 8 4 1. 16 0.25
18 A 6 4 1. 16 0.25
19 A 3 3 1. 14 0.214
20 A 8 4 1. 16 0.25
21 A 8 4 1. 16 0.25
22 A 12 5 1. 16 0.312
23 A 8 3 1. 12 0.25
24 A 8 4 1. 12 0.333
25 A 3 2 1. 10 0.2
26 A 8 4 1. 12 0.333
27 A 8 4 1. 12 0.333
28 A 14 5 1. 12 0.417
29 A 9 5 1. 14 0.357
30 A 7 4 1. 14 0.286
31 A 5 3 1. 12 0.25
32 A 0 0 0. 0 0.
33 A 6 6 1. 16 0.375
34 A 5 5 1. 16 0.312
35 A 2 2 1. 14 0.143
36 A 0 0 0. 0 0.
37 A 15 8 1. 16 0.5
38 A 9 6 1. 16 0.375
39 A 6 4 1. 14 0.286
40 A 0 0 0. 0 0.
41 A 8 6 1. 16 0.375
42 A 7 6 1. 16 0.375
43 A 6 6 1. 16 0.375
44 A 5 5 1. 16 0.312
45 A 6 6 1. 16 0.375
46 A 7 6 1. 16 0.375
47 A 8 6 1. 16 0.375
48 A 10 9 1. 18 0.5
49 A 9 8 1. 18 0.444
50 A 8 7 1. 18 0.389
51 A 7 6 1. 18 0.333
52 A 7 7 1. 18 0.389
53 A 9 8 1. 18 0.444
54 A 9 9 1. 18 0.5
55 A 11 8 1. 18 0.444
56 A 23 8 1. 18 0.444
57 A 20 8 1. 18 0.444
58 A 14 7 1. 18 0.389
59 A 12 6 1. 18 0.333
60 A 12 6 1. 18 0.333
61 A 18 7 1. 18 0.389
62 A 19 8 1. 18 0.444
63 A 4 3 1. 8 0.375
64 A 3 3 1. 8 0.375
65 A 2 2 1. 8 0.25
66 A 3 3 1. 8 0.375
67 A 5 3 1. 16 0.188
68 A 4 3 1. 16 0.188
69 A 4 3 1. 16 0.188
70 A 3 2 1. 16 0.125
71 A 3 2 1. 16 0.125
72 A 4 3 1. 16 0.188
73 A 4 3 1. 16 0.188
74 A 5 3 1. 16 0.188
75 A 0 0 0. 0 0.
76 A 1 1 1. 10 0.1
77 A 0 0 0. 0 0.
78 A 0 0 0. 0 0.
79 A 2 2 1. 10 0.2
80 A 0 0 0. 0 0.
81 A 2 1 1. 28 0.036
82 A 0 0 0. 0 0.
83 A 0 0 0. 0 0.
84 A 1 1 1. 10 0.1
85 A 0 0 0. 0 0.
86 A 0 0 0. 0 0.
87 A 2 2 1. 10 0.2
88 A 0 0 0. 0 0.
89 A 2 1 1. 25 0.04
90 A 2 1 1. 17 0.059
91 A 2 1 1. 20 0.05
92 A 3 1 1. 20 0.05
93 A 3 2 1. 21 0.095
94 A 4 2 1. 20 0.1
95 A 4 2 1. 20 0.1
96 A 5 2 1. 20 0.1
97 A 7 5 1. 24 0.208
98 A 0 0 0. 0 0.
99 A 8 3 1. 16 0.188
100 A 5 3 1. 16 0.188
101 A 3 2 1. 14 0.143
102 A 0 0 0. 0 0.
103 A 0 0 0. 0 0.
104 A 3 2 1. 12 0.167
105 A 3 2 1. 12 0.167
106 A 3 2 1. 12 0.167
107 A 3 2 1. 10 0.2
108 A 3 2 1. 12 0.167
109 A 3 2 1. 12 0.167
110 A 3 2 1. 12 0.167
111 A 5 3 1. 14 0.214
112 A 5 3 1. 14 0.214
113 A 5 3 1. 14 0.214
114 A 5 3 1. 12 0.25
115 A 5 3 1. 14 0.214
116 A 5 3 1. 14 0.214
117 A 5 3 1. 14 0.214
118 A 6 3 1. 18 0.167
119 A 5 3 1. 18 0.167
120 A 4 3 1. 16 0.188
121 A 5 4 1. 18 0.222
122 A 6 5 1. 18 0.278
123 A 10 6 1. 20 0.3
124 A 9 7 1. 20 0.35
125 A 6 4 1. 18 0.222
126 A 9 5 1. 20 0.25
127 A 9 5 1. 20 0.25
128 A 7 7 1. 20 0.35
129 A 6 6 1. 20 0.3
130 A 3 3 1. 18 0.167
131 A 0 0 0. 0 0.
132 A 0 0 0. 0 0.
133 A 10 9 1. 20 0.45
134 A 9 9 1. 20 0.45
135 A 4 4 1. 18 0.222
136 A 0 0 0. 0 0.
137 A 0 0 0. 0 0.
138 A 7 7 1. 21 0.333
139 A 6 6 1. 21 0.286
140 A 3 3 1. 19 0.158
141 A 0 0 0. 0 0.
142 A 0 0 0. 0 0.
143 A 5 3 1. 18 0.167
144 A 4 3 1. 18 0.167
145 A 3 3 1. 16 0.188
146 A 1 1 1. 14 0.071
147 A 4 4 1. 18 0.222
148 A 5 5 1. 18 0.278
149 A 6 5 1. 18 0.278
150 A 5 3 1. 14 0.214
151 A 4 3 1. 14 0.214
152 A 3 3 1. 12 0.25
153 A 1 1 1. 10 0.1
154 A 2 2 1. 14 0.143
155 A 3 3 1. 14 0.214
156 A 4 3 1. 14 0.214
157 A 5 3 1. 15 0.2
158 A 4 3 1. 15 0.2
159 A 3 3 1. 13 0.231
160 A 1 1 1. 11 0.091
161 A 2 2 1. 15 0.133
162 A 3 3 1. 15 0.2
163 A 4 3 1. 15 0.2
164 A 9 5 1. 14 0.357
165 A 7 5 1. 14 0.357
166 A 4 4 1. 12 0.333
167 A 5 3 1. 14 0.214
168 A 5 3 1. 14 0.214
169 A 7 4 1. 14 0.286
170 A 10 6 1. 18 0.333
171 A 8 5 1. 18 0.278
172 A 6 4 1. 16 0.25
173 A 2 2 1. 14 0.143
174 A 0 0 0. 0 0.
175 A 10 6 1. 15 0.4
176 A 8 5 1. 15 0.333
177 A 6 4 1. 13 0.308
178 A 2 2 1. 11 0.182
179 A 0 0 0. 0 0.
180 A 16 9 1. 14 0.643
181 A 10 7 1. 14 0.5
182 A 7 5 1. 12 0.417
183 A 0 0 0. 0 0.
184 A 0 0 0. 0 0.
185 A 12 7 1. 12 0.583
186 A 10 6 1. 16 0.375
187 A 8 5 1. 14 0.357
188 A 0 0 0. 0 0.
189 A 11 8 1. 18 0.444

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