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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
  2.1.8 Mupad
 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, 88, 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, 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, 36, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 80, 82, 83, 85, 86, 88, 98, 102, 103, 125, 131, 136, 137, 141, 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, 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, 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, 132, 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, 80, 82, 83, 85, 86, 88, 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, 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, 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, 143, 144, 145, 146, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 174, 178, 179, 183, 184, 188 }

B grade: { 6, 14, 21, 35, 122, 127, 130, 135, 140, 173 }

C grade: { 5, 7, 8, 13, 15, 20, 26, 27, 28, 41, 42, 43, 44, 48, 49, 50, 51, 56, 57, 58, 59, 63, 64, 65, 121, 126, 147, 148, 149 }

F grade: { 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, 128, 129, 133, 134, 138, 139, 170, 171, 172, 175, 176, 177, 180, 181, 182, 185, 186, 187, 189 }

2.1.8 Mupad

A grade: { 32, 36, 40, 75, 77, 78, 80, 82, 83, 85, 86, 88, 98, 102, 103, 131, 132, 136, 137, 141, 142, 174, 179, 183, 184, 188 }

B grade: { 1, 2, 3, 4, 9, 10, 11, 12, 16, 17, 18, 19, 23, 24, 25, 35, 64, 65, 76, 79, 84, 87, 89, 90, 91, 92, 118, 119, 120, 123, 124, 125, 130, 135, 140, 143, 144, 145, 146, 150, 151, 152, 153, 157, 158, 159, 160, 173 }

C grade: { }

F grade: { 5, 6, 7, 8, 13, 14, 15, 20, 21, 22, 26, 27, 28, 29, 30, 31, 33, 34, 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, 63, 66, 67, 68, 69, 70, 71, 72, 73, 74, 81, 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, 147, 148, 149, 154, 155, 156, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 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 Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 76 539 481 169 311 170 219
normalized size 1 1.00 0.84 5.92 5.29 1.86 3.42 1.87 2.41
time (sec) N/A 0.093 0.346 0.024 0.804 0.761 2.547 0.401 0.418
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 61 302 278 109 202 110 147
normalized size 1 1.00 0.87 4.31 3.97 1.56 2.89 1.57 2.10
time (sec) N/A 0.066 0.231 0.031 0.826 0.770 1.190 0.471 0.294
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 44 143 136 62 112 64 84
normalized size 1 1.00 0.90 2.92 2.78 1.27 2.29 1.31 1.71
time (sec) N/A 0.041 0.177 0.024 0.708 0.566 0.540 0.403 0.120
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 26 51 50 28 46 30 34
normalized size 1 1.00 0.96 1.89 1.85 1.04 1.70 1.11 1.26
time (sec) N/A 0.016 0.061 0.022 0.340 0.863 0.204 0.432 0.180
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 50 72 142 78 0 577 -1
normalized size 1 1.00 0.96 1.38 2.73 1.50 0.00 11.10 -0.02
time (sec) N/A 0.098 0.101 0.027 0.823 0.758 0.000 0.636 0.000
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 65 109 166 123 0 523 -1
normalized size 1 1.00 0.89 1.49 2.27 1.68 0.00 7.16 -0.01
time (sec) N/A 0.110 0.402 0.026 0.921 0.949 0.000 0.467 0.000
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C B F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 89 143 201 209 0 5518 -1
normalized size 1 1.00 0.86 1.38 1.93 2.01 0.00 53.06 -0.01
time (sec) N/A 0.138 0.613 0.023 1.106 0.664 0.000 1.115 0.000
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C B F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 127 127 144 179 251 295 0 8378 -1
normalized size 1 1.00 1.13 1.41 1.98 2.32 0.00 65.97 -0.01
time (sec) N/A 0.159 0.567 0.024 1.293 0.860 0.000 1.465 0.000
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 161 132 1027 717 287 660 222 349
normalized size 1 1.00 0.82 6.38 4.45 1.78 4.10 1.38 2.17
time (sec) N/A 0.102 0.680 0.077 0.766 0.780 4.598 0.532 0.614
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 106 587 428 190 456 153 229
normalized size 1 1.00 0.79 4.38 3.19 1.42 3.40 1.14 1.71
time (sec) N/A 0.074 0.445 0.023 0.725 0.920 2.547 0.422 0.458
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 77 289 222 113 264 94 179
normalized size 1 1.00 0.81 3.04 2.34 1.19 2.78 0.99 1.88
time (sec) N/A 0.053 0.306 0.025 0.722 0.604 1.181 0.528 0.207
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 50 112 90 53 126 48 57
normalized size 1 1.00 0.91 2.04 1.64 0.96 2.29 0.87 1.04
time (sec) N/A 0.025 0.163 0.022 0.678 0.823 0.499 0.568 0.096
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 65 105 161 88 0 610 -1
normalized size 1 1.00 0.83 1.35 2.06 1.13 0.00 7.82 -0.01
time (sec) N/A 0.153 0.131 0.026 0.994 0.658 0.000 0.628 0.000
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 75 156 171 127 0 534 -1
normalized size 1 1.00 0.90 1.88 2.06 1.53 0.00 6.43 -0.01
time (sec) N/A 0.134 0.623 0.025 0.933 0.838 0.000 0.842 0.000
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 112 112 102 193 206 218 0 5136 -1
normalized size 1 1.00 0.91 1.72 1.84 1.95 0.00 45.86 -0.01
time (sec) N/A 0.197 0.924 0.025 0.999 0.697 0.000 1.350 0.000
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 225 225 385 1023 925 350 772 351 532
normalized size 1 1.00 1.71 4.55 4.11 1.56 3.43 1.56 2.36
time (sec) N/A 0.254 0.986 0.054 0.695 0.882 7.882 0.531 1.143
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 175 175 121 560 535 227 495 231 364
normalized size 1 1.00 0.69 3.20 3.06 1.30 2.83 1.32 2.08
time (sec) N/A 0.156 0.959 0.031 0.560 0.697 4.187 0.415 0.724
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 93 265 267 128 284 137 173
normalized size 1 1.00 0.76 2.15 2.17 1.04 2.31 1.11 1.41
time (sec) N/A 0.097 0.616 0.034 0.384 0.724 2.224 0.451 0.592
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 52 95 103 60 126 69 77
normalized size 1 1.00 0.69 1.27 1.37 0.80 1.68 0.92 1.03
time (sec) N/A 0.042 0.172 0.030 0.348 0.685 0.916 0.524 0.260
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 103 166 276 153 0 6075 -1
normalized size 1 1.00 0.85 1.37 2.28 1.26 0.00 50.21 -0.01
time (sec) N/A 0.244 0.253 0.032 0.591 0.491 0.000 1.678 0.000
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 200 242 304 227 0 1000 -1
normalized size 1 1.00 1.38 1.67 2.10 1.57 0.00 6.90 -0.01
time (sec) N/A 0.225 0.701 0.028 0.640 0.757 0.000 1.036 0.000
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C B F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 184 184 221 311 339 375 0 0 -1
normalized size 1 1.00 1.20 1.69 1.84 2.04 0.00 0.00 -0.01
time (sec) N/A 0.345 0.826 0.034 1.007 0.751 0.000 0.000 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 172 172 100 440 303 115 253 108 138
normalized size 1 1.00 0.58 2.56 1.76 0.67 1.47 0.63 0.80
time (sec) N/A 0.154 0.419 0.078 0.388 0.616 5.670 0.442 0.796
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 92 241 188 88 209 84 104
normalized size 1 1.00 0.69 1.80 1.40 0.66 1.56 0.63 0.78
time (sec) N/A 0.108 0.178 0.030 0.348 0.658 3.217 0.360 0.543
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 53 110 98 63 138 64 63
normalized size 1 1.00 0.66 1.38 1.22 0.79 1.72 0.80 0.79
time (sec) N/A 0.047 0.125 0.027 0.532 0.859 1.811 0.447 0.339
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A A C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 52 52 91 61 60 428 -1
normalized size 1 1.00 0.88 0.88 1.54 1.03 1.02 7.25 -0.02
time (sec) N/A 0.158 0.100 0.028 0.806 0.671 2.460 0.492 0.000
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 79 90 726 87 0 3220 -1
normalized size 1 1.00 1.20 1.36 11.00 1.32 0.00 48.79 -0.02
time (sec) N/A 0.151 0.220 0.030 0.921 0.695 0.000 0.579 0.000
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 119 124 795 130 0 3920 -1
normalized size 1 1.00 1.32 1.38 8.83 1.44 0.00 43.56 -0.01
time (sec) N/A 0.297 0.304 0.032 0.766 0.687 0.000 0.760 0.000
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 205 205 196 685 712 966 0 0 -1
normalized size 1 1.00 0.96 3.34 3.47 4.71 0.00 0.00 -0.00
time (sec) N/A 0.157 0.191 0.216 1.142 1.025 0.000 0.000 0.000
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 137 137 130 392 396 598 0 0 -1
normalized size 1 1.00 0.95 2.86 2.89 4.36 0.00 0.00 -0.01
time (sec) N/A 0.092 0.098 0.140 0.726 0.897 0.000 0.000 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) B F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 75 75 87 172 0 306 0 0 -1
normalized size 1 1.00 1.16 2.29 0.00 4.08 0.00 0.00 -0.01
time (sec) N/A 0.042 0.005 0.007 0.000 0.939 0.000 0.000 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.022 4.549 0.092 0.000 0.839 0.000 0.000 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 109 316 1056 786 0 0 -1
normalized size 1 1.00 0.96 2.77 9.26 6.89 0.00 0.00 -0.01
time (sec) N/A 0.215 0.507 0.195 1.425 1.224 0.000 0.000 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 75 170 324 450 0 0 -1
normalized size 1 1.00 0.91 2.07 3.95 5.49 0.00 0.00 -0.01
time (sec) N/A 0.134 0.252 0.077 1.484 0.920 0.000 0.000 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 36 37 159 45 0 1459 55
normalized size 1 1.00 1.29 1.32 5.68 1.61 0.00 52.11 1.96
time (sec) N/A 0.027 0.012 0.022 1.013 0.678 0.000 5.834 0.832
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.039 5.623 0.203 0.000 0.780 0.000 0.000 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B C F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 337 337 311 1127 3828 1311 0 0 -1
normalized size 1 1.00 0.92 3.34 11.36 3.89 0.00 0.00 -0.00
time (sec) N/A 0.269 2.992 0.304 5.469 1.014 0.000 0.000 0.000
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B C F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 193 193 184 584 1893 795 0 0 -1
normalized size 1 1.00 0.95 3.03 9.81 4.12 0.00 0.00 -0.01
time (sec) N/A 0.143 0.922 0.170 2.704 1.240 0.000 0.000 0.000
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-1) B F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 389 267 0 435 0 0 -1
normalized size 1 1.00 3.32 2.28 0.00 3.72 0.00 0.00 -0.01
time (sec) N/A 0.069 3.682 0.115 0.000 0.962 0.000 0.000 0.000
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.038 1.422 0.000 0.000 0.777 0.000 0.000 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 194 194 124 232 261 190 0 1239 -1
normalized size 1 1.00 0.64 1.20 1.35 0.98 0.00 6.39 -0.01
time (sec) N/A 0.423 0.059 0.035 0.943 1.072 0.000 0.908 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 169 169 122 189 240 156 0 773 -1
normalized size 1 1.00 0.72 1.12 1.42 0.92 0.00 4.57 -0.01
time (sec) N/A 0.236 0.100 0.028 1.083 1.713 0.000 0.610 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 142 142 124 144 196 126 0 422 -1
normalized size 1 1.00 0.87 1.01 1.38 0.89 0.00 2.97 -0.01
time (sec) N/A 0.172 0.092 0.029 1.071 0.658 0.000 0.513 0.000
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 124 100 159 108 0 166 -1
normalized size 1 1.00 1.05 0.85 1.35 0.92 0.00 1.41 -0.01
time (sec) N/A 0.134 0.058 0.032 0.988 0.469 0.000 0.500 0.000
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 139 139 147 140 129 144 0 0 -1
normalized size 1 1.00 1.06 1.01 0.93 1.04 0.00 0.00 -0.01
time (sec) N/A 0.186 0.319 0.032 1.741 0.616 0.000 0.000 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 168 168 190 180 129 208 0 0 -1
normalized size 1 1.00 1.13 1.07 0.77 1.24 0.00 0.00 -0.01
time (sec) N/A 0.262 0.294 0.030 1.720 0.762 0.000 0.000 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 193 193 228 220 129 296 0 0 -1
normalized size 1 1.00 1.18 1.14 0.67 1.53 0.00 0.00 -0.01
time (sec) N/A 0.296 0.344 0.031 1.796 0.664 0.000 0.000 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F(-1) C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 231 231 194 242 293 258 0 1311 -1
normalized size 1 1.00 0.84 1.05 1.27 1.12 0.00 5.68 -0.00
time (sec) N/A 0.435 2.143 0.054 2.164 0.620 0.000 0.837 0.000
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 203 203 175 197 272 195 0 807 -1
normalized size 1 1.00 0.86 0.97 1.34 0.96 0.00 3.98 -0.00
time (sec) N/A 0.342 1.666 0.044 1.606 0.556 0.000 1.039 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 158 158 146 150 227 148 0 428 -1
normalized size 1 1.00 0.92 0.95 1.44 0.94 0.00 2.71 -0.01
time (sec) N/A 0.278 0.531 0.044 1.385 0.726 0.000 2.030 0.000
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 130 130 145 108 187 114 0 163 -1
normalized size 1 1.00 1.12 0.83 1.44 0.88 0.00 1.25 -0.01
time (sec) N/A 0.243 0.223 0.057 1.444 0.504 0.000 0.486 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 135 135 133 146 135 136 0 0 -1
normalized size 1 1.00 0.99 1.08 1.00 1.01 0.00 0.00 -0.01
time (sec) N/A 0.258 0.663 0.048 1.818 0.548 0.000 0.000 0.000
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 170 170 181 189 135 206 0 0 -1
normalized size 1 1.00 1.06 1.11 0.79 1.21 0.00 0.00 -0.01
time (sec) N/A 0.312 1.389 0.046 2.205 0.676 0.000 0.000 0.000
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 216 216 244 230 135 323 0 0 -1
normalized size 1 1.00 1.13 1.06 0.62 1.50 0.00 0.00 -0.00
time (sec) N/A 0.324 1.268 0.044 1.752 0.819 0.000 0.000 0.000
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 247 247 237 273 135 417 0 0 -1
normalized size 1 1.00 0.96 1.11 0.55 1.69 0.00 0.00 -0.00
time (sec) N/A 0.407 0.863 0.056 1.790 0.711 0.000 0.000 0.000
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F(-1) C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 410 410 542 474 543 368 0 2457 -1
normalized size 1 1.00 1.32 1.16 1.32 0.90 0.00 5.99 -0.00
time (sec) N/A 1.139 3.099 0.057 1.410 0.697 0.000 1.921 0.000
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 354 354 390 386 495 299 0 1533 -1
normalized size 1 1.00 1.10 1.09 1.40 0.84 0.00 4.33 -0.00
time (sec) N/A 0.991 1.600 0.053 1.890 0.566 0.000 2.181 0.000
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 304 304 254 294 422 245 0 838 -1
normalized size 1 1.00 0.84 0.97 1.39 0.81 0.00 2.76 -0.00
time (sec) N/A 0.484 0.424 0.052 1.628 0.471 0.000 3.156 0.000
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 257 257 236 212 375 213 0 328 -1
normalized size 1 1.00 0.92 0.82 1.46 0.83 0.00 1.28 -0.00
time (sec) N/A 0.417 0.356 0.061 1.385 0.641 0.000 0.617 0.000
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 271 271 299 286 252 265 0 0 -1
normalized size 1 1.00 1.10 1.06 0.93 0.98 0.00 0.00 -0.00
time (sec) N/A 0.564 1.563 0.052 1.981 0.658 0.000 0.000 0.000
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 292 292 268 368 253 367 0 0 -1
normalized size 1 1.00 0.92 1.26 0.87 1.26 0.00 0.00 -0.00
time (sec) N/A 0.738 2.007 0.053 2.024 0.751 0.000 0.000 0.000
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A C A F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 356 356 1429 450 253 528 0 0 -1
normalized size 1 1.00 4.01 1.26 0.71 1.48 0.00 0.00 -0.00
time (sec) N/A 0.831 6.309 0.048 2.090 0.676 0.000 0.000 0.000
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A A C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 55 34 74 35 83 69 -1
normalized size 1 1.00 1.12 0.69 1.51 0.71 1.69 1.41 -0.02
time (sec) N/A 0.057 0.011 0.035 1.330 0.894 4.776 0.488 0.000
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A A C B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 48 27 67 26 61 53 26
normalized size 1 1.00 1.33 0.75 1.86 0.72 1.69 1.47 0.72
time (sec) N/A 0.035 0.006 0.032 1.051 0.514 0.853 0.442 0.028
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A A C B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 51 19 60 18 37 35 18
normalized size 1 1.00 2.12 0.79 2.50 0.75 1.54 1.46 0.75
time (sec) N/A 0.020 0.006 0.031 0.750 0.629 0.720 0.340 0.033
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A C A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 63 28 21 31 61 0 -1
normalized size 1 1.00 1.80 0.80 0.60 0.89 1.74 0.00 -0.03
time (sec) N/A 0.037 0.043 0.031 1.395 0.463 1.597 0.000 0.000
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 183 183 122 0 235 132 0 0 -1
normalized size 1 1.00 0.67 0.00 1.28 0.72 0.00 0.00 -0.01
time (sec) N/A 0.240 0.108 0.091 1.335 0.845 0.000 0.000 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 152 152 124 0 186 102 0 0 -1
normalized size 1 1.00 0.82 0.00 1.22 0.67 0.00 0.00 -0.01
time (sec) N/A 0.149 0.112 0.099 1.872 0.862 0.000 0.000 0.000
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 152 152 124 0 186 102 0 0 -1
normalized size 1 1.00 0.82 0.00 1.22 0.67 0.00 0.00 -0.01
time (sec) N/A 0.162 0.094 0.092 1.734 1.138 0.000 0.000 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 135 135 124 0 137 86 0 0 -1
normalized size 1 1.00 0.92 0.00 1.01 0.64 0.00 0.00 -0.01
time (sec) N/A 0.116 0.059 0.085 2.073 0.977 0.000 0.000 0.000
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 135 135 124 0 138 86 0 0 -1
normalized size 1 1.00 0.92 0.00 1.02 0.64 0.00 0.00 -0.01
time (sec) N/A 0.120 0.061 0.085 1.741 0.609 0.000 0.000 0.000
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 151 121 0 138 117 0 0 -1
normalized size 1 1.00 0.80 0.00 0.91 0.77 0.00 0.00 -0.01
time (sec) N/A 0.146 0.056 0.056 1.558 0.948 0.000 0.000 0.000
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 153 153 121 0 138 117 0 0 -1
normalized size 1 1.00 0.79 0.00 0.90 0.76 0.00 0.00 -0.01
time (sec) N/A 0.155 0.053 0.070 1.960 0.905 0.000 0.000 0.000
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 182 182 125 0 137 183 0 0 -1
normalized size 1 1.00 0.69 0.00 0.75 1.01 0.00 0.00 -0.01
time (sec) N/A 0.204 0.052 0.078 1.818 0.909 0.000 0.000 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A F(-1) A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.017 0.000 0.326 0.000 0.000 0.000 0.000 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 133 0 0 0 0 15
normalized size 1 1.00 1.00 8.31 0.00 0.00 0.00 0.00 0.94
time (sec) N/A 0.009 0.014 0.001 0.000 0.623 0.000 0.000 0.183
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.029 0.657 0.055 0.000 0.000 0.000 0.000 0.000
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 61 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.038 1.940 0.043 0.000 0.000 0.000 0.000 0.000
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 36 179 0 0 0 0 35
normalized size 1 1.00 0.86 4.26 0.00 0.00 0.00 0.00 0.83
time (sec) N/A 0.020 0.024 0.183 0.000 0.642 0.000 0.000 0.188
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.028 15.481 0.042 0.000 0.000 0.000 0.000 0.000
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 40 0 0 0 0 0 -1
normalized size 1 1.00 0.95 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.059 0.433 0.211 0.000 0.000 0.000 0.000 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 63 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.077 4.972 0.059 0.000 0.000 0.000 0.000 0.000
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.017 0.297 0.039 0.000 0.000 0.000 0.000 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 18 0 0 0 0 15
normalized size 1 1.00 1.00 1.12 0.00 0.00 0.00 0.00 0.94
time (sec) N/A 0.009 0.016 0.000 0.000 1.006 0.000 0.000 0.200
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.028 0.198 0.052 0.000 0.000 0.000 0.000 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A F(-1) A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 55 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.036 0.000 0.048 0.000 0.000 0.000 0.000 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 38 101 0 0 0 0 42
normalized size 1 1.00 1.00 2.66 0.00 0.00 0.00 0.00 1.11
time (sec) N/A 0.017 0.049 0.000 0.000 0.919 0.000 0.000 0.437
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.028 14.911 0.042 0.000 0.000 0.000 0.000 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 33 0 0 0 0 0 51
normalized size 1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 1.34
time (sec) N/A 0.055 0.398 0.178 0.000 0.000 0.000 0.000 0.657
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 17 0 0 0 0 0 15
normalized size 1 1.00 0.85 0.00 0.00 0.00 0.00 0.00 0.75
time (sec) N/A 0.043 0.087 0.257 0.000 0.000 0.000 0.000 0.332
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 17 0 0 15 0 0 16
normalized size 1 1.00 0.71 0.00 0.00 0.62 0.00 0.00 0.67
time (sec) N/A 0.046 0.080 0.260 0.000 0.909 0.000 0.000 0.139
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F(-1) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 33 0 0 0 0 0 31
normalized size 1 1.00 0.70 0.00 0.00 0.00 0.00 0.00 0.66
time (sec) N/A 0.061 0.140 0.365 0.000 0.000 0.000 0.000 0.527
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 29 0 0 0 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.086 0.150 0.262 0.000 0.000 0.000 0.000 0.000
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 17 0 0 0 0 0 -1
normalized size 1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.081 0.095 0.183 0.000 0.000 0.000 0.000 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 17 0 0 0 0 0 -1
normalized size 1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.079 0.144 0.182 0.000 0.000 0.000 0.000 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 45 0 0 0 0 0 -1
normalized size 1 1.00 0.96 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.094 0.110 0.198 0.000 0.000 0.000 0.000 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 51 0 0 0 0 0 -1
normalized size 1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.154 0.109 0.170 0.000 0.000 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.041 0.823 0.295 0.000 0.658 0.000 0.000 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 275 275 253 0 0 186 0 0 -1
normalized size 1 1.00 0.92 0.00 0.00 0.68 0.00 0.00 -0.00
time (sec) N/A 0.304 0.167 0.295 0.000 0.921 0.000 0.000 0.000
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 162 150 0 0 134 0 0 -1
normalized size 1 1.00 0.93 0.00 0.00 0.83 0.00 0.00 -0.01
time (sec) N/A 0.213 0.196 0.214 0.000 1.771 0.000 0.000 0.000
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 131 131 122 0 0 96 0 0 -1
normalized size 1 1.00 0.93 0.00 0.00 0.73 0.00 0.00 -0.01
time (sec) N/A 0.097 0.045 0.104 0.000 1.037 0.000 0.000 0.000
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.019 5.436 0.091 0.000 1.075 0.000 0.000 0.000
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.035 0.804 0.086 0.000 1.138 0.000 0.000 0.000
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 75 455 0 54 0 0 -1
normalized size 1 1.00 1.00 6.07 0.00 0.72 0.00 0.00 -0.01
time (sec) N/A 0.080 0.020 0.154 0.000 0.532 0.000 0.000 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 79 354 0 54 0 0 -1
normalized size 1 1.00 1.00 4.48 0.00 0.68 0.00 0.00 -0.01
time (sec) N/A 0.077 0.017 0.115 0.000 1.405 0.000 0.000 0.000
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 75 291 0 54 0 0 -1
normalized size 1 1.00 1.00 3.88 0.00 0.72 0.00 0.00 -0.01
time (sec) N/A 0.077 0.016 0.109 0.000 0.442 0.000 0.000 0.000
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 79 379 0 50 0 0 -1
normalized size 1 1.00 1.00 4.80 0.00 0.63 0.00 0.00 -0.01
time (sec) N/A 0.071 0.015 0.102 0.000 0.759 0.000 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 62 427 0 50 0 0 -1
normalized size 1 1.00 0.95 6.57 0.00 0.77 0.00 0.00 -0.02
time (sec) N/A 0.073 0.023 0.108 0.000 0.683 0.000 0.000 0.000
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 75 530 0 54 0 0 -1
normalized size 1 1.00 1.00 7.07 0.00 0.72 0.00 0.00 -0.01
time (sec) N/A 0.074 0.017 0.115 0.000 0.703 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 75 600 0 54 0 0 -1
normalized size 1 1.00 1.00 8.00 0.00 0.72 0.00 0.00 -0.01
time (sec) N/A 0.074 0.016 0.113 0.000 0.492 0.000 0.000 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 92 0 0 77 0 0 -1
normalized size 1 1.00 0.93 0.00 0.00 0.78 0.00 0.00 -0.01
time (sec) N/A 0.157 0.111 0.135 0.000 0.667 0.000 0.000 0.000
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 96 0 0 77 0 0 -1
normalized size 1 1.00 0.93 0.00 0.00 0.75 0.00 0.00 -0.01
time (sec) N/A 0.144 0.105 0.147 0.000 0.628 0.000 0.000 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 90 0 0 77 0 0 -1
normalized size 1 1.00 0.93 0.00 0.00 0.79 0.00 0.00 -0.01
time (sec) N/A 0.137 0.101 0.215 0.000 0.750 0.000 0.000 0.000
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 90 0 0 69 0 0 -1
normalized size 1 1.00 0.87 0.00 0.00 0.67 0.00 0.00 -0.01
time (sec) N/A 0.133 0.115 0.162 0.000 0.495 0.000 0.000 0.000
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 77 0 0 64 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 0.75 0.00 0.00 -0.01
time (sec) N/A 0.126 0.059 0.202 0.000 0.683 0.000 0.000 0.000
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 91 0 0 77 0 0 -1
normalized size 1 1.00 0.90 0.00 0.00 0.76 0.00 0.00 -0.01
time (sec) N/A 0.138 0.104 0.136 0.000 1.046 0.000 0.000 0.000
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 95 0 0 77 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.81 0.00 0.00 -0.01
time (sec) N/A 0.142 0.093 0.151 0.000 0.710 0.000 0.000 0.000
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 122 476 456 168 264 156 189
normalized size 1 1.00 1.37 5.35 5.12 1.89 2.97 1.75 2.12
time (sec) N/A 0.115 0.588 0.047 0.624 0.623 1.382 0.449 0.258
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 80 236 235 102 151 94 112
normalized size 1 1.00 1.19 3.52 3.51 1.52 2.25 1.40 1.67
time (sec) N/A 0.085 0.353 0.033 0.750 0.728 0.613 0.440 0.287
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 52 89 91 51 68 46 52
normalized size 1 1.00 1.18 2.02 2.07 1.16 1.55 1.05 1.18
time (sec) N/A 0.042 0.224 0.033 0.344 0.683 0.254 0.419 0.092
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 55 95 172 92 0 692 -1
normalized size 1 1.00 0.85 1.46 2.65 1.42 0.00 10.65 -0.02
time (sec) N/A 0.150 0.133 0.036 0.928 0.725 0.000 0.488 0.000
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 78 143 196 135 0 578 -1
normalized size 1 1.00 0.88 1.61 2.20 1.52 0.00 6.49 -0.01
time (sec) N/A 0.163 0.331 0.039 1.000 0.858 0.000 0.542 0.000
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 237 237 217 1129 949 369 779 339 452
normalized size 1 1.00 0.92 4.76 4.00 1.56 3.29 1.43 1.91
time (sec) N/A 0.261 1.443 0.052 0.974 0.573 3.453 0.716 0.912
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 168 168 193 564 494 212 456 207 255
normalized size 1 1.00 1.15 3.36 2.94 1.26 2.71 1.23 1.52
time (sec) N/A 0.179 0.647 0.051 1.000 0.583 1.592 0.807 0.592
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 80 218 197 98 219 107 117
normalized size 1 1.00 0.68 1.85 1.67 0.83 1.86 0.91 0.99
time (sec) N/A 0.097 0.496 0.047 0.994 0.595 0.628 0.391 0.203
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 114 192 337 186 0 6933 -1
normalized size 1 1.00 0.79 1.32 2.32 1.28 0.00 47.81 -0.01
time (sec) N/A 0.338 0.227 0.050 1.139 0.583 0.000 2.032 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 159 159 206 276 370 284 0 1133 -1
normalized size 1 1.00 1.30 1.74 2.33 1.79 0.00 7.13 -0.01
time (sec) N/A 0.317 0.500 0.049 1.345 0.689 0.000 1.000 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 151 364 936 418 0 0 -1
normalized size 1 1.00 1.13 2.72 6.99 3.12 0.00 0.00 -0.01
time (sec) N/A 0.282 0.328 0.165 1.164 0.652 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 125 197 286 222 0 0 -1
normalized size 1 1.00 1.24 1.95 2.83 2.20 0.00 0.00 -0.01
time (sec) N/A 0.199 0.336 0.113 1.062 0.659 0.000 0.000 0.000
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 70 60 160 58 70 234 65
normalized size 1 1.00 1.43 1.22 3.27 1.18 1.43 4.78 1.33
time (sec) N/A 0.064 0.080 0.086 0.428 0.740 0.648 0.611 0.661
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.060 2.803 0.171 0.000 0.712 0.000 0.000 0.000
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.057 2.689 0.228 0.000 0.654 0.000 0.000 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B C F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 271 271 250 678 3274 769 0 0 -1
normalized size 1 1.00 0.92 2.50 12.08 2.84 0.00 0.00 -0.00
time (sec) N/A 0.367 1.048 0.459 3.961 0.660 0.000 0.000 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 212 212 212 358 772 390 0 0 -1
normalized size 1 1.00 1.00 1.69 3.64 1.84 0.00 0.00 -0.00
time (sec) N/A 0.256 1.081 0.353 2.470 1.217 0.000 0.000 0.000
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 113 123 763 118 146 757 175
normalized size 1 1.00 0.92 1.00 6.20 0.96 1.19 6.15 1.42
time (sec) N/A 0.095 0.520 0.179 0.989 0.546 1.091 3.029 4.287
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.054 12.171 2.537 0.000 0.623 0.000 0.000 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.052 12.783 3.264 0.000 1.079 0.000 0.000 0.000
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 133 133 164 468 959 467 0 0 -1
normalized size 1 1.00 1.23 3.52 7.21 3.51 0.00 0.00 -0.01
time (sec) N/A 0.284 1.250 0.158 1.340 0.831 0.000 0.000 0.000
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 102 102 292 247 314 283 0 0 -1
normalized size 1 1.00 2.86 2.42 3.08 2.77 0.00 0.00 -0.01
time (sec) N/A 0.203 5.528 0.119 0.677 0.647 0.000 0.000 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 57 85 160 59 90 229 65
normalized size 1 1.00 1.14 1.70 3.20 1.18 1.80 4.58 1.30
time (sec) N/A 0.065 0.246 0.089 0.864 0.570 0.771 0.605 0.522
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.062 2.398 0.154 0.000 0.597 0.000 0.000 0.000
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 24 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.058 2.331 0.209 0.000 0.586 0.000 0.000 0.000
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B F(-2) F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 53 132 206 0 0 98 83
normalized size 1 1.00 0.48 1.20 1.87 0.00 0.00 0.89 0.75
time (sec) N/A 0.134 0.224 0.097 1.713 0.000 0.000 0.472 0.546
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A F(-2) F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 44 105 122 0 0 77 63
normalized size 1 1.00 0.50 1.19 1.39 0.00 0.00 0.88 0.72
time (sec) N/A 0.112 0.161 0.064 1.556 0.000 0.000 0.561 0.431
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A F(-2) F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 34 80 61 0 0 57 46
normalized size 1 1.00 0.64 1.51 1.15 0.00 0.00 1.08 0.87
time (sec) N/A 0.061 0.127 0.061 1.486 0.000 0.000 0.442 0.205
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 29 43 20 32 0 30 33
normalized size 1 1.00 1.12 1.65 0.77 1.23 0.00 1.15 1.27
time (sec) N/A 0.013 0.033 0.073 1.340 0.762 0.000 1.012 0.332
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F C F(-2) F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 55 0 61 0 0 166 -1
normalized size 1 1.00 0.65 0.00 0.73 0.00 0.00 1.98 -0.01
time (sec) N/A 0.121 0.089 0.098 2.239 0.000 0.000 0.537 0.000
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F C F(-2) F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 75 0 198 0 0 560 -1
normalized size 1 1.00 0.68 0.00 1.80 0.00 0.00 5.09 -0.01
time (sec) N/A 0.133 0.157 0.062 0.982 0.000 0.000 1.077 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F C F(-2) F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 151 98 0 232 0 0 662 -1
normalized size 1 1.00 0.65 0.00 1.54 0.00 0.00 4.38 -0.01
time (sec) N/A 0.162 0.266 0.067 1.516 0.000 0.000 1.231 0.000
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A F(-2) F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 33 87 48 0 0 55 91
normalized size 1 1.00 0.49 1.28 0.71 0.00 0.00 0.81 1.34
time (sec) N/A 0.111 0.055 0.096 1.228 0.000 0.000 0.415 0.426
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A F(-2) F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 29 70 36 0 0 43 70
normalized size 1 1.00 0.55 1.32 0.68 0.00 0.00 0.81 1.32
time (sec) N/A 0.096 0.044 0.067 1.287 0.000 0.000 0.419 0.340
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A F(-2) F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 22 55 24 0 0 31 50
normalized size 1 1.00 0.69 1.72 0.75 0.00 0.00 0.97 1.56
time (sec) N/A 0.050 0.021 0.067 1.505 0.000 0.000 0.396 0.307
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 18 25 12 18 0 17 34
normalized size 1 1.00 1.20 1.67 0.80 1.20 0.00 1.13 2.27
time (sec) N/A 0.011 0.007 0.070 1.482 0.676 0.000 1.372 0.288
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F C F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 23 0 17 0 0 16 -1
normalized size 1 1.00 1.00 0.00 0.74 0.00 0.00 0.70 -0.04
time (sec) N/A 0.087 0.006 0.091 1.517 0.000 0.000 0.435 0.000
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F C F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 33 0 23 0 0 34 -1
normalized size 1 1.00 0.79 0.00 0.55 0.00 0.00 0.81 -0.02
time (sec) N/A 0.091 0.059 0.066 0.897 0.000 0.000 0.437 0.000
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F C F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 44 0 19 0 0 48 -1
normalized size 1 1.00 0.66 0.00 0.28 0.00 0.00 0.72 -0.01
time (sec) N/A 0.106 0.074 0.067 1.405 0.000 0.000 0.412 0.000
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B F(-2) F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 34 86 129 0 0 55 92
normalized size 1 1.00 0.47 1.19 1.79 0.00 0.00 0.76 1.28
time (sec) N/A 0.115 0.052 0.070 1.145 0.000 0.000 0.469 0.434
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B F(-2) F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 30 69 100 0 0 51 71
normalized size 1 1.00 0.54 1.23 1.79 0.00 0.00 0.91 1.27
time (sec) N/A 0.098 0.042 0.061 1.382 0.000 0.000 0.373 0.343
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B F(-2) F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 23 54 72 0 0 31 48
normalized size 1 1.00 0.68 1.59 2.12 0.00 0.00 0.91 1.41
time (sec) N/A 0.051 0.023 0.055 1.693 0.000 0.000 0.422 0.316
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 19 25 23 19 0 26 34
normalized size 1 1.00 1.19 1.56 1.44 1.19 0.00 1.62 2.12
time (sec) N/A 0.011 0.007 0.125 1.067 0.582 0.000 0.412 0.292
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 0 0 0 0 16 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.67 -0.04
time (sec) N/A 0.088 0.021 0.083 0.000 0.000 0.000 0.399 0.000
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 34 0 0 0 0 34 -1
normalized size 1 1.00 0.77 0.00 0.00 0.00 0.00 0.77 -0.02
time (sec) N/A 0.092 0.027 0.057 0.000 0.000 0.000 2.646 0.000
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 45 0 0 0 0 48 -1
normalized size 1 1.00 0.64 0.00 0.00 0.00 0.00 0.69 -0.01
time (sec) N/A 0.106 0.057 0.068 0.000 0.000 0.000 0.454 0.000
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 185 185 67 0 98 0 0 113 -1
normalized size 1 1.00 0.36 0.00 0.53 0.00 0.00 0.61 -0.01
time (sec) N/A 0.183 0.297 0.057 0.815 0.000 0.000 0.479 0.000
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 54 0 72 0 0 85 -1
normalized size 1 1.00 0.37 0.00 0.50 0.00 0.00 0.59 -0.01
time (sec) N/A 0.144 0.219 0.055 1.081 0.000 0.000 0.374 0.000
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 45 0 48 0 0 59 -1
normalized size 1 1.00 0.51 0.00 0.54 0.00 0.00 0.66 -0.01
time (sec) N/A 0.072 0.068 0.058 1.067 0.000 0.000 0.480 0.000
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F C F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 36 0 29 0 0 32 -1
normalized size 1 1.00 0.65 0.00 0.53 0.00 0.00 0.58 -0.02
time (sec) N/A 0.128 0.020 0.058 1.176 0.000 0.000 0.425 0.000
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F C F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 53 0 37 0 0 62 -1
normalized size 1 1.00 0.67 0.00 0.47 0.00 0.00 0.78 -0.01
time (sec) N/A 0.126 0.085 0.053 1.333 0.000 0.000 0.424 0.000
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F C F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 66 0 33 0 0 92 -1
normalized size 1 1.00 0.61 0.00 0.30 0.00 0.00 0.84 -0.01
time (sec) N/A 0.165 0.053 0.054 1.087 0.000 0.000 0.518 0.000
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 374 374 199 0 0 0 0 0 -1
normalized size 1 1.00 0.53 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.212 0.126 0.060 0.000 0.557 0.000 0.000 0.000
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 262 262 146 0 0 0 0 0 -1
normalized size 1 1.00 0.56 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.167 0.075 0.061 0.000 0.620 0.000 0.000 0.000
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 156 156 89 0 0 0 0 0 -1
normalized size 1 1.00 0.57 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.086 0.047 0.054 0.000 0.657 0.000 0.000 0.000
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 40 54 90 126 0 93 45
normalized size 1 1.00 0.87 1.17 1.96 2.74 0.00 2.02 0.98
time (sec) N/A 0.022 0.015 0.125 1.625 0.673 0.000 1.860 0.332
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.069 0.893 0.055 0.000 0.558 0.000 0.000 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 235 235 170 0 0 0 0 0 -1
normalized size 1 1.00 0.72 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.173 0.100 0.053 0.000 0.723 0.000 0.000 0.000
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 117 0 0 0 0 0 -1
normalized size 1 1.00 0.72 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.141 0.049 0.056 0.000 0.549 0.000 0.000 0.000
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 83 0 0 0 0 0 -1
normalized size 1 1.00 0.86 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.078 0.033 0.056 0.000 0.804 0.000 0.000 0.000
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 36 25 81 87 0 20 -1
normalized size 1 1.00 0.97 0.68 2.19 2.35 0.00 0.54 -0.03
time (sec) N/A 0.020 0.015 0.183 1.929 0.681 0.000 0.489 0.000
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.077 2.956 0.059 0.000 0.945 0.000 0.000 0.000
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 423 423 257 0 0 0 0 0 -1
normalized size 1 1.00 0.61 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.260 0.411 0.058 0.000 0.732 0.000 0.000 0.000
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 257 257 185 0 0 0 0 0 -1
normalized size 1 1.00 0.72 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.189 0.119 0.056 0.000 0.607 0.000 0.000 0.000
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 165 0 0 0 0 0 -1
normalized size 1 1.00 1.10 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.117 0.177 0.061 0.000 1.605 0.000 0.000 0.000
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.079 11.139 0.056 0.000 0.562 0.000 0.000 0.000
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 21 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.065 1.507 0.089 0.000 0.000 0.000 0.000 0.000
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 383 383 290 0 0 1074 0 0 -1
normalized size 1 1.00 0.76 0.00 0.00 2.80 0.00 0.00 -0.00
time (sec) N/A 0.559 0.917 0.065 0.000 0.749 0.000 0.000 0.000
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-2) C F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 329 329 379 0 0 1267 0 0 -1
normalized size 1 1.00 1.15 0.00 0.00 3.85 0.00 0.00 -0.00
time (sec) N/A 0.663 0.716 0.158 0.000 0.792 0.000 0.000 0.000
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-2) B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 214 214 756 414 0 917 0 0 -1
normalized size 1 1.00 3.53 1.93 0.00 4.29 0.00 0.00 -0.00
time (sec) N/A 0.400 0.829 0.090 0.000 0.958 0.000 0.000 0.000
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.049 0.837 0.048 0.000 0.628 0.000 0.000 0.000
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-2) B F(-1) F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 296 296 933 674 0 1482 0 0 -1
normalized size 1 1.00 3.15 2.28 0.00 5.01 0.00 0.00 -0.00
time (sec) N/A 0.523 9.751 0.696 0.000 1.593 0.000 0.000 0.000

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 [.6429]

Table 2.1:Rubi 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 1.00 14 0.143
2 A 4 2 1.00 14 0.143
3 A 3 2 1.00 14 0.143
4 A 2 2 1.00 12 0.167
5 A 3 3 1.00 14 0.214
6 A 4 4 1.00 14 0.286
7 A 5 4 1.00 14 0.286
8 A 6 4 1.00 14 0.286
9 A 6 4 1.00 16 0.250
10 A 4 3 1.00 16 0.188
11 A 4 4 1.00 16 0.250
12 A 2 1 1.00 14 0.071
13 A 5 4 1.00 16 0.250
14 A 5 5 1.00 16 0.312
15 A 7 6 1.00 16 0.375
16 A 12 4 1.00 16 0.250
17 A 8 4 1.00 16 0.250
18 A 6 4 1.00 16 0.250
19 A 3 3 1.00 14 0.214
20 A 8 4 1.00 16 0.250
21 A 8 4 1.00 16 0.250
22 A 12 5 1.00 16 0.312
23 A 8 3 1.00 12 0.250
24 A 8 4 1.00 12 0.333
25 A 3 2 1.00 10 0.200
26 A 8 4 1.00 12 0.333
27 A 8 4 1.00 12 0.333
28 A 14 5 1.00 12 0.417
29 A 9 5 1.00 14 0.357
30 A 7 4 1.00 14 0.286
31 A 5 3 1.00 12 0.250
32 A 0 0 0.00 0 0.000
33 A 6 6 1.00 16 0.375
34 A 5 5 1.00 16 0.312
35 A 2 2 1.00 14 0.143
36 A 0 0 0.00 0 0.000
37 A 15 8 1.00 16 0.500
38 A 9 6 1.00 16 0.375
39 A 6 4 1.00 14 0.286
40 A 0 0 0.00 0 0.000
41 A 8 6 1.00 16 0.375
42 A 7 6 1.00 16 0.375
43 A 6 6 1.00 16 0.375
44 A 5 5 1.00 16 0.312
45 A 6 6 1.00 16 0.375
46 A 7 6 1.00 16 0.375
47 A 8 6 1.00 16 0.375
48 A 10 9 1.00 18 0.500
49 A 9 8 1.00 18 0.444
50 A 8 7 1.00 18 0.389
51 A 7 6 1.00 18 0.333
52 A 7 7 1.00 18 0.389
53 A 9 8 1.00 18 0.444
54 A 9 9 1.00 18 0.500
55 A 11 8 1.00 18 0.444
56 A 23 8 1.00 18 0.444
57 A 20 8 1.00 18 0.444
58 A 14 7 1.00 18 0.389
59 A 12 6 1.00 18 0.333
60 A 12 6 1.00 18 0.333
61 A 18 7 1.00 18 0.389
62 A 19 8 1.00 18 0.444
63 A 4 3 1.00 8 0.375
64 A 3 3 1.00 8 0.375
65 A 2 2 1.00 8 0.250
66 A 3 3 1.00 8 0.375
67 A 5 3 1.00 16 0.188
68 A 4 3 1.00 16 0.188
69 A 4 3 1.00 16 0.188
70 A 3 2 1.00 16 0.125
71 A 3 2 1.00 16 0.125
72 A 4 3 1.00 16 0.188
73 A 4 3 1.00 16 0.188
74 A 5 3 1.00 16 0.188
75 A 0 0 0.00 0 0.000
76 A 1 1 1.00 10 0.100
77 A 0 0 0.00 0 0.000
78 A 0 0 0.00 0 0.000
79 A 2 2 1.00 10 0.200
80 A 0 0 0.00 0 0.000
81 A 2 1 1.00 28 0.036
82 A 0 0 0.00 0 0.000
83 A 0 0 0.00 0 0.000
84 A 1 1 1.00 10 0.100
85 A 0 0 0.00 0 0.000
86 A 0 0 0.00 0 0.000
87 A 2 2 1.00 10 0.200
88 A 0 0 0.00 0 0.000
89 A 2 1 1.00 25 0.040
90 A 2 1 1.00 17 0.059
91 A 2 1 1.00 20 0.050
92 A 3 1 1.00 20 0.050
93 A 3 2 1.00 21 0.095
94 A 4 2 1.00 20 0.100
95 A 4 2 1.00 20 0.100
96 A 5 2 1.00 20 0.100
97 A 7 5 1.00 24 0.208
98 A 0 0 0.00 0 0.000
99 A 8 3 1.00 16 0.188
100 A 5 3 1.00 16 0.188
101 A 3 2 1.00 14 0.143
102 A 0 0 0.00 0 0.000
103 A 0 0 0.00 0 0.000
104 A 3 2 1.00 12 0.167
105 A 3 2 1.00 12 0.167
106 A 3 2 1.00 12 0.167
107 A 3 2 1.00 10 0.200
108 A 3 2 1.00 12 0.167
109 A 3 2 1.00 12 0.167
110 A 3 2 1.00 12 0.167
111 A 5 3 1.00 14 0.214
112 A 5 3 1.00 14 0.214
113 A 5 3 1.00 14 0.214
114 A 5 3 1.00 12 0.250
115 A 5 3 1.00 14 0.214
116 A 5 3 1.00 14 0.214
117 A 5 3 1.00 14 0.214
118 A 6 3 1.00 18 0.167
119 A 5 3 1.00 18 0.167
120 A 4 3 1.00 16 0.188
121 A 5 4 1.00 18 0.222
122 A 6 5 1.00 18 0.278
123 A 10 6 1.00 20 0.300
124 A 9 7 1.00 20 0.350
125 A 6 4 1.00 18 0.222
126 A 9 5 1.00 20 0.250
127 A 9 5 1.00 20 0.250
128 A 7 7 1.00 20 0.350
129 A 6 6 1.00 20 0.300
130 A 3 3 1.00 18 0.167
131 A 0 0 0.00 0 0.000
132 A 0 0 0.00 0 0.000
133 A 10 9 1.00 20 0.450
134 A 9 9 1.00 20 0.450
135 A 4 4 1.00 18 0.222
136 A 0 0 0.00 0 0.000
137 A 0 0 0.00 0 0.000
138 A 7 7 1.00 21 0.333
139 A 6 6 1.00 21 0.286
140 A 3 3 1.00 19 0.158
141 A 0 0 0.00 0 0.000
142 A 0 0 0.00 0 0.000
143 A 5 3 1.00 18 0.167
144 A 4 3 1.00 18 0.167
145 A 3 3 1.00 16 0.188
146 A 1 1 1.00 14 0.071
147 A 4 4 1.00 18 0.222
148 A 5 5 1.00 18 0.278
149 A 6 5 1.00 18 0.278
150 A 5 3 1.00 14 0.214
151 A 4 3 1.00 14 0.214
152 A 3 3 1.00 12 0.250
153 A 1 1 1.00 10 0.100
154 A 2 2 1.00 14 0.143
155 A 3 3 1.00 14 0.214
156 A 4 3 1.00 14 0.214
157 A 5 3 1.00 15 0.200
158 A 4 3 1.00 15 0.200
159 A 3 3 1.00 13 0.231
160 A 1 1 1.00 11 0.091
161 A 2 2 1.00 15 0.133
162 A 3 3 1.00 15 0.200
163 A 4 3 1.00 15 0.200
164 A 9 5 1.00 14 0.357
165 A 7 5 1.00 14 0.357
166 A 4 4 1.00 12 0.333
167 A 5 3 1.00 14 0.214
168 A 5 3 1.00 14 0.214
169 A 7 4 1.00 14 0.286
170 A 10 6 1.00 18 0.333
171 A 8 5 1.00 18 0.278
172 A 6 4 1.00 16 0.250
173 A 2 2 1.00 14 0.143
174 A 0 0 0.00 0 0.000
175 A 10 6 1.00 15 0.400
176 A 8 5 1.00 15 0.333
177 A 6 4 1.00 13 0.308
178 A 2 2 1.00 11 0.182
179 A 0 0 0.00 0 0.000
180 A 16 9 1.00 14 0.643
181 A 10 7 1.00 14 0.500
182 A 7 5 1.00 12 0.417
183 A 0 0 0.00 0 0.000
184 A 0 0 0.00 0 0.000
185 A 12 7 1.00 12 0.583
186 A 10 6 1.00 16 0.375
187 A 8 5 1.00 14 0.357
188 A 0 0 0.00 0 0.000
189 A 11 8 1.00 18 0.444

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