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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, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201 }

B grade: { }

C grade: { 186 }

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, 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, 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, 133, 134, 140, 142, 143, 144, 151, 152, 153, 154, 155, 156, 157, 159, 161, 163, 164, 165, 167, 169, 171, 173, 175, 178, 179, 182, 183, 184, 186, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201 }

B grade: { 27, 85, 86, 129, 132, 135, 136, 137, 145, 146, 185, 187, 188 }

C grade: { 158, 160, 162, 166, 168, 170, 172, 174, 176, 177, 180, 181 }

F grade: { 130, 131, 138, 139, 141, 147, 148, 149, 150 }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 45, 46, 47, 55, 56, 57, 58, 59, 63, 64, 65, 66, 67, 72, 73, 74, 75, 76, 77, 87, 88, 89, 90, 91, 98, 99, 100, 101, 102, 104, 108, 109, 110, 111, 112, 119, 120, 121, 122, 123, 124, 127, 135, 144, 151, 152, 153, 154, 155, 156, 157, 159, 161, 167, 169, 171, 173, 177, 178, 191, 192, 193, 194, 195, 197, 200 }

B grade: { 9, 11, 12, 13, 14, 19, 28, 29, 30, 31, 35, 36, 37, 38, 48, 49, 50, 51, 52, 53, 54, 60, 61, 62, 68, 69, 70, 71, 92, 93, 95, 96, 97, 103, 105, 106, 107, 113, 114, 115, 116, 117, 118, 164, 196, 198, 199, 201 }

C grade: { 24, 25, 26, 27, 32, 33, 34, 158, 160, 162, 166, 168, 170, 172, 174, 176, 186 }

F grade: { 15, 16, 17, 18, 20, 21, 22, 23, 39, 40, 41, 42, 43, 44, 78, 79, 80, 81, 82, 83, 84, 85, 86, 94, 125, 126, 128, 129, 130, 131, 132, 133, 134, 136, 137, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 149, 150, 163, 165, 175, 179, 180, 181, 182, 183, 184, 185, 187, 188, 189, 190 }

2.1.4 Maxima

A grade: { 1, 2, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 48, 49, 50, 51, 52, 54, 56, 64, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 88, 89, 90, 107, 108, 109, 110, 111, 117, 119, 120, 122, 152, 153, 154, 155, 156, 157, 159, 171, 179, 191, 192 }

B grade: { 3, 4, 5, 6, 7, 8, 24, 25, 45, 46, 47, 53, 55, 57, 58, 59, 61, 63, 87, 103, 104, 105, 106, 112, 113, 115, 124, 151, 167, 186, 187, 188, 194 }

C grade: { }

F grade: { 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 39, 40, 41, 42, 43, 44, 60, 62, 65, 67, 78, 79, 80, 81, 82, 83, 84, 85, 86, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 114, 116, 118, 121, 123, 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, 158, 160, 161, 162, 163, 164, 165, 166, 168, 169, 170, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182, 183, 184, 185, 189, 190, 193, 195, 196, 197, 198, 199, 200, 201 }

2.1.5 FriCAS

A grade: { 1, 27, 28, 29, 30, 31, 34, 52, 53, 54, 64, 70, 71, 72, 73, 76, 77, 90, 91, 99, 100, 107, 108, 110, 118, 119, 120, 154, 155, 156, 157, 159, 161, 165, 167, 169, 173, 175, 177, 179, 181, 191 }

B grade: { 2, 3, 4, 5, 6, 7, 8, 24, 25, 26, 32, 33, 35, 36, 37, 38, 45, 46, 47, 48, 49, 50, 51, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 74, 75, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 92, 93, 95, 96, 97, 98, 101, 102, 103, 104, 105, 106, 109, 111, 112, 113, 114, 115, 116, 117, 121, 122, 123, 124, 125, 126, 127, 128, 133, 134, 135, 136, 142, 143, 144, 151, 152, 153, 163, 171, 186, 187, 188, 189, 190, 192, 193, 194, 195 }

C grade: { }

F grade: { 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 39, 40, 41, 42, 43, 44, 94, 129, 130, 131, 132, 137, 138, 139, 140, 141, 145, 146, 147, 148, 149, 150, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 183, 184, 185, 196, 197, 198, 199, 200, 201 }

2.1.6 Sympy

A grade: { 28, 29, 30, 35, 36, 37, 38, 119 }

B grade: { 108 }

C grade: { }

F 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, 31, 32, 33, 34, 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, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 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, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201 }

2.1.7 Giac

A grade: { 1, 2, 4, 6, 7, 8, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 87, 88, 89, 90, 91, 92, 93, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 114, 116, 118, 119, 120, 121, 122, 123, 151, 152, 153, 154, 155, 156, 157, 187, 188, 191, 192, 194, 195 }

B grade: { 3, 5, 26, 58, 59, 66, 79, 80, 83, 85, 86, 106, 113, 115, 117, 124, 186, 193 }

C grade: { }

F grade: { 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 39, 40, 41, 42, 43, 44, 81, 82, 84, 94, 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, 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, 189, 190, 196, 197, 198, 199, 200, 201 }

2.1.8 Mupad

A grade: { }

B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 28, 35, 45, 46, 47, 48, 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, 87, 88, 89, 90, 91, 92, 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, 127, 135, 144, 151, 152, 153, 159, 167, 171, 179, 186, 187, 188, 191, 192, 193, 194, 195 }

C grade: { }

F grade: { 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 49, 50, 51, 78, 79, 80, 81, 82, 83, 84, 85, 86, 93, 94, 125, 126, 128, 129, 130, 131, 132, 133, 134, 136, 137, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 149, 150, 154, 155, 156, 157, 158, 160, 161, 162, 163, 164, 165, 166, 168, 169, 170, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182, 183, 184, 185, 189, 190, 196, 197, 198, 199, 200, 201 }

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 A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 12 11 19 0 12 23
normalized size 1 1.00 1.00 1.09 1.00 1.73 0.00 1.09 2.09
time (sec) N/A 0.005 0.002 0.016 0.361 0.433 0.000 0.129 0.076
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 10 11 18 41 0 18 18
normalized size 1 1.00 1.00 1.10 1.80 4.10 0.00 1.80 1.80
time (sec) N/A 0.010 0.004 0.228 0.306 0.833 0.000 0.135 0.079
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 34 30 65 267 0 76 81
normalized size 1 1.00 1.00 0.88 1.91 7.85 0.00 2.24 2.38
time (sec) N/A 0.016 0.010 0.243 1.127 1.129 0.000 0.139 0.083
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 26 23 90 164 0 31 31
normalized size 1 1.00 1.00 0.88 3.46 6.31 0.00 1.19 1.19
time (sec) N/A 0.012 0.006 0.246 0.323 1.355 0.000 0.110 0.062
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 47 50 112 812 0 102 189
normalized size 1 1.00 0.85 0.91 2.04 14.76 0.00 1.85 3.44
time (sec) N/A 0.028 0.042 0.288 0.568 1.024 0.000 0.115 1.305
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 41 33 205 344 0 42 42
normalized size 1 1.00 1.00 0.80 5.00 8.39 0.00 1.02 1.02
time (sec) N/A 0.015 0.011 0.252 0.318 2.853 0.000 0.114 1.354
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 19 17 49 116 0 18 30
normalized size 1 1.00 1.00 0.89 2.58 6.11 0.00 0.95 1.58
time (sec) N/A 0.010 0.004 0.234 0.315 0.593 0.000 0.112 0.096
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 35 27 137 280 0 30 30
normalized size 1 1.00 1.00 0.77 3.91 8.00 0.00 0.86 0.86
time (sec) N/A 0.014 0.004 0.276 2.080 0.473 0.000 0.136 1.518
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 51 217 0 0 0 0 -1
normalized size 1 1.00 0.77 3.29 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.032 0.078 0.508 0.000 0.658 0.000 0.000 0.000
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 49 103 0 0 0 0 -1
normalized size 1 1.00 0.79 1.66 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.030 0.046 0.572 0.000 0.562 0.000 0.000 0.000
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 40 135 0 0 0 0 -1
normalized size 1 1.00 1.00 3.38 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.020 0.029 0.400 0.000 0.479 0.000 0.000 0.000
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 40 135 0 0 0 0 -1
normalized size 1 1.00 1.00 3.38 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.020 0.037 0.411 0.000 1.138 0.000 0.000 0.000
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 53 174 0 0 0 0 -1
normalized size 1 1.00 0.80 2.64 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.032 0.047 0.579 0.000 1.719 0.000 0.000 0.000
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 59 188 0 0 0 0 -1
normalized size 1 1.00 0.89 2.85 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.033 0.071 0.524 0.000 0.530 0.000 0.000 0.000
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 68 0 0 0 0 0 -1
normalized size 1 1.00 0.67 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.060 0.203 0.319 0.000 1.112 0.000 0.000 0.000
Problem 16 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 74 74 56 0 0 0 0 0 -1
normalized size 1 1.00 0.76 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.038 0.073 0.281 0.000 0.397 0.000 0.000 0.000
Problem 17 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 70 70 52 0 0 0 0 0 -1
normalized size 1 1.00 0.74 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.038 0.040 0.289 0.000 0.395 0.000 0.000 0.000
Problem 18 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 42 42 42 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.022 0.021 0.380 0.000 0.391 0.000 0.000 0.000
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 42 244 0 0 0 0 -1
normalized size 1 1.00 1.00 5.81 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.022 0.029 0.367 0.000 0.393 0.000 0.000 0.000
Problem 20 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 76 76 63 0 0 0 0 0 -1
normalized size 1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.039 0.068 0.269 0.000 0.440 0.000 0.000 0.000
Problem 21 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 76 76 64 0 0 0 0 0 -1
normalized size 1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.039 0.085 0.297 0.000 0.416 0.000 0.000 0.000
Problem 22 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 104 104 70 0 0 0 0 0 -1
normalized size 1 1.00 0.67 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.058 0.132 0.313 0.000 0.451 0.000 0.000 0.000
Problem 23 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 75 75 60 0 0 0 0 0 -1
normalized size 1 1.00 0.80 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.037 0.061 0.443 0.000 0.430 0.000 0.000 0.000
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B B F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 81 230 156 1604 0 124 -1
normalized size 1 1.00 0.90 2.56 1.73 17.82 0.00 1.38 -0.01
time (sec) N/A 0.030 0.106 0.493 0.477 0.424 0.000 0.118 0.000
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C B B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 55 208 112 812 0 102 -1
normalized size 1 1.00 0.85 3.20 1.72 12.49 0.00 1.57 -0.02
time (sec) N/A 0.022 0.123 0.423 0.421 0.444 0.000 0.139 0.000
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 46 183 65 267 0 76 -1
normalized size 1 1.00 1.15 4.58 1.62 6.68 0.00 1.90 -0.02
time (sec) N/A 0.017 0.042 0.434 0.421 0.392 0.000 0.128 0.000
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 29 130 11 19 0 12 -1
normalized size 1 1.00 2.64 11.82 1.00 1.73 0.00 1.09 -0.09
time (sec) N/A 0.011 0.017 0.433 0.316 0.381 0.000 0.131 0.000
Problem 28 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 22 22 22 97 26 10 29 23 53
normalized size 1 1.00 1.00 4.41 1.18 0.45 1.32 1.05 2.41
time (sec) N/A 0.016 0.026 0.414 0.323 0.381 17.320 0.130 0.155
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 44 201 54 32 54 48 -1
normalized size 1 1.00 0.86 3.94 1.06 0.63 1.06 0.94 -0.02
time (sec) N/A 0.020 0.071 0.436 0.326 0.388 18.847 0.115 0.000
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 47 305 82 66 80 70 -1
normalized size 1 1.00 0.62 4.01 1.08 0.87 1.05 0.92 -0.01
time (sec) N/A 0.027 0.084 0.414 0.326 0.456 38.199 0.120 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 57 409 100 108 0 92 -1
normalized size 1 1.00 0.56 4.05 0.99 1.07 0.00 0.91 -0.01
time (sec) N/A 0.035 0.139 0.418 0.325 0.494 0.000 0.134 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 42 127 72 1082 0 65 -1
normalized size 1 1.00 0.65 1.95 1.11 16.65 0.00 1.00 -0.02
time (sec) N/A 0.034 0.036 0.243 0.484 0.494 0.000 0.125 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 29 106 39 310 0 48 -1
normalized size 1 1.00 0.63 2.30 0.85 6.74 0.00 1.04 -0.02
time (sec) N/A 0.024 0.020 0.206 1.448 0.458 0.000 0.134 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 21 72 8 145 0 8 -1
normalized size 1 1.00 0.84 2.88 0.32 5.80 0.00 0.32 -0.04
time (sec) N/A 0.016 0.006 0.222 0.482 0.442 0.000 0.126 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 58 17 79 15 14 33
normalized size 1 1.00 1.00 4.46 1.31 6.08 1.15 1.08 2.54
time (sec) N/A 0.029 0.006 0.211 0.450 0.436 0.594 0.110 0.120
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 27 130 35 277 37 29 -1
normalized size 1 1.00 0.75 3.61 0.97 7.69 1.03 0.81 -0.03
time (sec) N/A 0.020 0.022 0.189 0.438 0.629 1.252 0.135 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 36 196 53 580 60 41 -1
normalized size 1 1.00 0.65 3.56 0.96 10.55 1.09 0.75 -0.02
time (sec) N/A 0.029 0.039 0.194 0.420 0.580 10.170 0.116 0.000
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 42 262 71 970 80 53 -1
normalized size 1 1.00 0.57 3.54 0.96 13.11 1.08 0.72 -0.01
time (sec) N/A 0.040 0.052 0.195 0.428 0.738 136.543 0.132 0.000
Problem 39 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 121 121 63 0 0 0 0 0 -1
normalized size 1 1.00 0.52 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.060 0.103 0.255 0.000 0.500 0.000 0.000 0.000
Problem 40 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 69 69 47 0 0 0 0 0 -1
normalized size 1 1.00 0.68 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.040 0.039 0.191 0.000 0.715 0.000 0.000 0.000
Problem 41 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 46 46 36 0 0 0 0 0 -1
normalized size 1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.034 0.019 0.215 0.000 1.044 0.000 0.000 0.000
Problem 42 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 48 48 38 0 0 0 0 0 -1
normalized size 1 1.00 0.79 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.031 0.042 0.221 0.000 0.525 0.000 0.000 0.000
Problem 43 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 77 77 47 0 0 0 0 0 -1
normalized size 1 1.00 0.61 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.044 0.094 0.188 0.000 1.589 0.000 0.000 0.000
Problem 44 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 121 121 63 0 0 0 0 0 -1
normalized size 1 1.00 0.52 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.064 0.098 0.188 0.000 0.411 0.000 0.000 0.000
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 54 72 620 2804 0 51 498
normalized size 1 1.00 0.33 0.44 3.80 17.20 0.00 0.31 3.06
time (sec) N/A 0.045 0.171 0.255 0.465 0.532 0.000 0.118 1.453
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 42 60 322 1475 0 39 356
normalized size 1 1.00 0.36 0.51 2.75 12.61 0.00 0.33 3.04
time (sec) N/A 0.035 0.096 0.201 0.435 0.473 0.000 0.132 1.374
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 30 46 120 516 0 27 46
normalized size 1 1.00 0.49 0.75 1.97 8.46 0.00 0.44 0.75
time (sec) N/A 0.023 0.058 0.196 0.437 0.428 0.000 0.114 1.344
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 15 29 13 81 0 13 71
normalized size 1 1.00 1.00 1.93 0.87 5.40 0.00 0.87 4.73
time (sec) N/A 0.017 0.006 0.218 0.436 0.430 0.000 0.108 0.058
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 23 89 30 253 0 28 -1
normalized size 1 1.00 0.64 2.47 0.83 7.03 0.00 0.78 -0.03
time (sec) N/A 0.016 0.023 0.233 0.438 0.441 0.000 0.112 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 38 230 65 1141 0 52 -1
normalized size 1 1.00 0.44 2.67 0.76 13.27 0.00 0.60 -0.01
time (sec) N/A 0.036 0.037 0.207 0.466 0.447 0.000 0.131 0.000
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 55 362 103 2600 0 76 -1
normalized size 1 1.00 0.42 2.74 0.78 19.70 0.00 0.58 -0.01
time (sec) N/A 0.056 0.079 0.213 0.494 0.462 0.000 0.135 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 28 130 54 36 0 42 59
normalized size 1 1.00 0.64 2.95 1.23 0.82 0.00 0.95 1.34
time (sec) N/A 0.139 0.104 0.140 0.317 0.413 0.000 0.112 1.483
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 23 67 46 30 0 37 53
normalized size 1 1.00 1.00 2.91 2.00 1.30 0.00 1.61 2.30
time (sec) N/A 0.122 0.048 0.115 0.316 0.382 0.000 0.130 1.359
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 16 78 42 14 0 28 41
normalized size 1 1.00 0.59 2.89 1.56 0.52 0.00 1.04 1.52
time (sec) N/A 0.101 0.067 0.107 0.313 0.398 0.000 0.110 1.341
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 16 27 35 50 0 32 15
normalized size 1 1.00 0.94 1.59 2.06 2.94 0.00 1.88 0.88
time (sec) N/A 0.073 0.020 0.100 0.317 0.399 0.000 0.133 0.068
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 44 23 48 103 0 52 51
normalized size 1 1.00 1.33 0.70 1.45 3.12 0.00 1.58 1.55
time (sec) N/A 0.098 0.055 0.129 0.318 0.391 0.000 0.128 1.439
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 25 23 90 71 0 31 91
normalized size 1 1.00 1.09 1.00 3.91 3.09 0.00 1.35 3.96
time (sec) N/A 0.139 0.041 0.148 0.314 0.377 0.000 0.112 1.352
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 59 45 99 630 0 90 121
normalized size 1 1.00 1.28 0.98 2.15 13.70 0.00 1.96 2.63
time (sec) N/A 0.195 0.220 0.150 0.316 0.398 0.000 0.114 1.351
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 39 39 292 219 0 59 236
normalized size 1 1.00 1.15 1.15 8.59 6.44 0.00 1.74 6.94
time (sec) N/A 0.146 0.064 0.154 0.317 0.386 0.000 0.114 1.376
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 219 488 0 1812 0 197 275
normalized size 1 1.00 1.66 3.70 0.00 13.73 0.00 1.49 2.08
time (sec) N/A 0.370 0.736 0.124 0.000 0.445 0.000 0.138 2.006
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 66 361 128 490 0 87 123
normalized size 1 1.00 1.08 5.92 2.10 8.03 0.00 1.43 2.02
time (sec) N/A 0.180 0.135 0.119 0.320 0.406 0.000 0.137 1.602
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 76 213 0 536 0 100 173
normalized size 1 1.00 0.93 2.60 0.00 6.54 0.00 1.22 2.11
time (sec) N/A 0.212 0.195 0.118 0.000 0.432 0.000 0.137 1.670
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 19 31 46 78 0 34 20
normalized size 1 1.00 0.95 1.55 2.30 3.90 0.00 1.70 1.00
time (sec) N/A 0.088 0.011 0.102 0.314 0.399 0.000 0.117 1.350
Problem 64 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 53 53 37 48 59 58 0 65 148
normalized size 1 1.00 0.70 0.91 1.11 1.09 0.00 1.23 2.79
time (sec) N/A 0.118 0.074 0.135 0.318 0.408 0.000 0.115 1.744
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 75 77 0 452 0 64 151
normalized size 1 1.00 1.14 1.17 0.00 6.85 0.00 0.97 2.29
time (sec) N/A 0.133 0.261 0.156 0.000 0.420 0.000 0.120 1.561
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 86 82 148 828 0 174 255
normalized size 1 1.00 1.01 0.96 1.74 9.74 0.00 2.05 3.00
time (sec) N/A 0.238 0.347 0.180 0.336 0.449 0.000 0.140 1.831
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 156 154 0 2340 0 149 295
normalized size 1 1.00 1.41 1.39 0.00 21.08 0.00 1.34 2.66
time (sec) N/A 0.304 0.598 0.161 0.000 0.452 0.000 0.143 1.747
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 63 139 80 139 0 86 88
normalized size 1 1.00 0.94 2.07 1.19 2.07 0.00 1.28 1.31
time (sec) N/A 0.096 0.089 0.142 0.320 0.394 0.000 0.111 1.447
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 53 111 66 100 0 70 70
normalized size 1 1.00 0.98 2.06 1.22 1.85 0.00 1.30 1.30
time (sec) N/A 0.086 0.077 0.148 0.319 0.385 0.000 0.114 1.358
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 41 41 45 87 56 70 0 51 52
normalized size 1 1.00 1.10 2.12 1.37 1.71 0.00 1.24 1.27
time (sec) N/A 0.080 0.051 0.138 0.317 0.382 0.000 0.111 1.360
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 32 59 41 47 0 35 34
normalized size 1 1.00 1.23 2.27 1.58 1.81 0.00 1.35 1.31
time (sec) N/A 0.057 0.063 0.133 0.309 0.384 0.000 0.113 1.312
Problem 72 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 11 11 10 9 12 14 0 11 11
normalized size 1 1.00 0.91 0.82 1.09 1.27 0.00 1.00 1.00
time (sec) N/A 0.024 0.008 0.073 0.329 0.368 0.000 0.136 1.311
Problem 73 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 20 20 22 21 23 29 0 20 31
normalized size 1 1.00 1.10 1.05 1.15 1.45 0.00 1.00 1.55
time (sec) N/A 0.066 0.029 0.082 0.448 0.387 0.000 0.133 1.305
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 45 39 45 127 0 36 58
normalized size 1 1.00 1.73 1.50 1.73 4.88 0.00 1.38 2.23
time (sec) N/A 0.101 0.086 0.090 0.416 0.376 0.000 0.135 1.318
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 51 61 73 325 0 48 73
normalized size 1 1.00 1.13 1.36 1.62 7.22 0.00 1.07 1.62
time (sec) N/A 0.085 0.087 0.112 0.413 0.384 0.000 0.118 1.345
Problem 76 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 29 29 58 58 33 48 0 29 24
normalized size 1 1.00 2.00 2.00 1.14 1.66 0.00 1.00 0.83
time (sec) N/A 0.015 0.143 0.227 0.312 0.381 0.000 0.117 1.299
Problem 77 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 30 30 59 60 35 50 0 29 24
normalized size 1 1.00 1.97 2.00 1.17 1.67 0.00 0.97 0.80
time (sec) N/A 0.015 0.146 0.227 0.315 0.379 0.000 0.135 1.263
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 99 0 0 924 0 151 -1
normalized size 1 1.00 1.01 0.00 0.00 9.43 0.00 1.54 -0.01
time (sec) N/A 0.120 0.338 0.512 0.000 0.440 0.000 0.322 0.000
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 75 0 0 697 0 118 -1
normalized size 1 1.00 1.14 0.00 0.00 10.56 0.00 1.79 -0.02
time (sec) N/A 0.042 0.200 0.470 0.000 0.412 0.000 0.251 0.000
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 60 0 0 637 0 83 -1
normalized size 1 1.00 1.62 0.00 0.00 17.22 0.00 2.24 -0.03
time (sec) N/A 0.019 0.092 0.605 0.000 0.407 0.000 0.215 0.000
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 118 0 0 868 0 0 -1
normalized size 1 1.00 1.39 0.00 0.00 10.21 0.00 0.00 -0.01
time (sec) N/A 0.074 1.206 0.473 0.000 0.444 0.000 0.000 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 177 0 0 1190 0 0 -1
normalized size 1 1.00 1.55 0.00 0.00 10.44 0.00 0.00 -0.01
time (sec) N/A 0.128 4.774 0.442 0.000 0.443 0.000 0.000 0.000
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 70 0 0 642 0 101 -1
normalized size 1 1.00 1.84 0.00 0.00 16.89 0.00 2.66 -0.03
time (sec) N/A 0.023 2.383 0.582 0.000 0.402 0.000 0.212 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 118 0 0 871 0 0 -1
normalized size 1 1.00 1.36 0.00 0.00 10.01 0.00 0.00 -0.01
time (sec) N/A 0.079 2.232 0.464 0.000 0.421 0.000 0.000 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 39 0 0 233 0 52 -1
normalized size 1 1.00 2.05 0.00 0.00 12.26 0.00 2.74 -0.05
time (sec) N/A 0.017 0.042 0.327 0.000 0.382 0.000 0.144 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 51 0 0 235 0 69 -1
normalized size 1 1.00 2.43 0.00 0.00 11.19 0.00 3.29 -0.05
time (sec) N/A 0.019 0.565 0.316 0.000 0.389 0.000 0.131 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 78 121 211 1028 0 141 233
normalized size 1 1.00 0.73 1.13 1.97 9.61 0.00 1.32 2.18
time (sec) N/A 0.124 0.253 0.430 0.924 0.413 0.000 0.127 1.409
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 55 80 114 521 0 92 165
normalized size 1 1.00 0.75 1.10 1.56 7.14 0.00 1.26 2.26
time (sec) N/A 0.052 0.135 0.339 0.503 0.403 0.000 0.118 1.398
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 32 42 41 157 0 43 70
normalized size 1 1.00 0.97 1.27 1.24 4.76 0.00 1.30 2.12
time (sec) N/A 0.028 0.066 0.281 0.307 0.416 0.000 0.138 0.106
Problem 90 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 16 17 16 26 0 17 38
normalized size 1 1.00 1.00 1.06 1.00 1.62 0.00 1.06 2.38
time (sec) N/A 0.009 0.002 0.017 1.185 0.400 0.000 0.112 1.299
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 60 88 0 270 0 56 131
normalized size 1 1.00 1.02 1.49 0.00 4.58 0.00 0.95 2.22
time (sec) N/A 0.055 0.111 0.209 0.000 0.413 0.000 0.120 0.399
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 203 221 0 1207 0 134 296
normalized size 1 1.00 1.86 2.03 0.00 11.07 0.00 1.23 2.72
time (sec) N/A 0.159 0.411 0.199 0.000 0.425 0.000 0.121 1.849
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 173 173 205 660 0 4125 0 261 -1
normalized size 1 1.00 1.18 3.82 0.00 23.84 0.00 1.51 -0.01
time (sec) N/A 0.308 0.735 0.270 0.000 0.502 0.000 0.137 0.000
Problem 94 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 106 106 168 0 0 0 0 0 -1
normalized size 1 1.00 1.58 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.029 2.468 0.596 0.000 2.252 0.000 0.000 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 146 146 126 406 0 2402 0 182 251
normalized size 1 1.00 0.86 2.78 0.00 16.45 0.00 1.25 1.72
time (sec) N/A 0.657 0.283 0.157 0.000 0.475 0.000 0.122 1.851
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 112 112 99 264 0 1562 0 133 209
normalized size 1 1.00 0.88 2.36 0.00 13.95 0.00 1.19 1.87
time (sec) N/A 0.423 0.167 0.148 0.000 0.458 0.000 0.140 1.713
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 78 174 0 860 0 92 167
normalized size 1 1.00 0.92 2.05 0.00 10.12 0.00 1.08 1.96
time (sec) N/A 0.265 0.129 0.150 0.000 0.437 0.000 0.137 1.579
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 57 94 0 430 0 62 139
normalized size 1 1.00 0.92 1.52 0.00 6.94 0.00 1.00 2.24
time (sec) N/A 0.092 0.118 0.138 0.000 0.430 0.000 0.113 1.481
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 41 36 0 165 0 32 43
normalized size 1 1.00 0.98 0.86 0.00 3.93 0.00 0.76 1.02
time (sec) N/A 0.055 0.026 0.078 0.000 0.408 0.000 0.129 0.116
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 51 0 219 0 45 286
normalized size 1 1.00 1.00 0.94 0.00 4.06 0.00 0.83 5.30
time (sec) N/A 0.100 0.053 0.090 0.000 0.442 0.000 0.119 4.006
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 63 73 0 504 0 61 294
normalized size 1 1.00 0.98 1.14 0.00 7.88 0.00 0.95 4.59
time (sec) N/A 0.140 0.109 0.095 0.000 0.449 0.000 0.120 3.881
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 82 146 0 1444 0 89 476
normalized size 1 1.00 0.94 1.68 0.00 16.60 0.00 1.02 5.47
time (sec) N/A 0.242 0.226 0.095 0.000 0.527 0.000 0.117 5.079
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 60 117 93 686 0 69 143
normalized size 1 1.00 1.25 2.44 1.94 14.29 0.00 1.44 2.98
time (sec) N/A 0.097 0.121 0.156 0.541 0.427 0.000 0.119 1.461
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 38 34 74 437 0 61 96
normalized size 1 1.00 1.06 0.94 2.06 12.14 0.00 1.69 2.67
time (sec) N/A 0.059 0.074 0.129 0.469 0.404 0.000 0.118 1.429
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 41 75 51 210 0 42 67
normalized size 1 1.00 1.32 2.42 1.65 6.77 0.00 1.35 2.16
time (sec) N/A 0.070 0.059 0.141 0.513 0.398 0.000 0.115 1.438
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 10 54 33 85 0 35 33
normalized size 1 1.00 0.71 3.86 2.36 6.07 0.00 2.50 2.36
time (sec) N/A 0.048 0.036 0.129 0.706 0.402 0.000 0.124 1.357
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 15 35 16 14 0 14 25
normalized size 1 1.00 1.07 2.50 1.14 1.00 0.00 1.00 1.79
time (sec) N/A 0.046 0.030 0.102 0.532 0.386 0.000 0.129 1.321
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 12 19 18 16 19 17 14
normalized size 1 1.00 1.33 2.11 2.00 1.78 2.11 1.89 1.56
time (sec) N/A 0.027 0.007 0.104 0.342 0.421 0.176 0.115 1.305
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 44 47 52 136 0 56 65
normalized size 1 1.00 1.10 1.18 1.30 3.40 0.00 1.40 1.62
time (sec) N/A 0.058 0.053 0.158 0.487 0.393 0.000 0.116 1.368
Problem 110 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 38 38 33 56 47 46 0 40 94
normalized size 1 1.00 0.87 1.47 1.24 1.21 0.00 1.05 2.47
time (sec) N/A 0.089 0.077 0.159 0.364 0.397 0.000 0.130 1.352
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 66 69 108 773 0 94 160
normalized size 1 1.00 0.97 1.01 1.59 11.37 0.00 1.38 2.35
time (sec) N/A 0.086 0.186 0.161 0.478 0.407 0.000 0.132 1.429
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 69 78 105 151 0 64 264
normalized size 1 1.00 1.25 1.42 1.91 2.75 0.00 1.16 4.80
time (sec) N/A 0.120 0.105 0.166 0.352 0.384 0.000 0.135 1.535
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 132 415 332 4077 0 267 316
normalized size 1 1.00 1.09 3.43 2.74 33.69 0.00 2.21 2.61
time (sec) N/A 0.149 0.336 0.154 0.584 0.512 0.000 0.138 1.988
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 187 187 185 575 0 4914 0 250 1001
normalized size 1 1.00 0.99 3.07 0.00 26.28 0.00 1.34 5.35
time (sec) N/A 0.293 0.616 0.153 0.000 0.746 0.000 0.142 8.505
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 85 233 164 1280 0 152 155
normalized size 1 1.00 1.18 3.24 2.28 17.78 0.00 2.11 2.15
time (sec) N/A 0.097 0.185 0.147 0.486 0.445 0.000 0.136 1.797
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 113 248 0 1254 0 111 700
normalized size 1 1.00 1.20 2.64 0.00 13.34 0.00 1.18 7.45
time (sec) N/A 0.319 0.419 0.141 0.000 0.513 0.000 0.141 7.263
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 37 107 67 200 0 73 260
normalized size 1 1.00 1.06 3.06 1.91 5.71 0.00 2.09 7.43
time (sec) N/A 0.075 0.087 0.127 0.438 0.407 0.000 0.115 1.598
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 62 113 0 193 0 52 273
normalized size 1 1.00 1.00 1.82 0.00 3.11 0.00 0.84 4.40
time (sec) N/A 0.171 0.086 0.117 0.000 0.446 0.000 0.146 3.921
Problem 119 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 19 19 11 21 26 27 41 19 23
normalized size 1 1.00 0.58 1.11 1.37 1.42 2.16 1.00 1.21
time (sec) N/A 0.032 0.019 0.100 0.311 0.429 0.458 0.130 0.109
Problem 120 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 66 66 44 78 67 81 0 67 271
normalized size 1 1.00 0.67 1.18 1.02 1.23 0.00 1.02 4.11
time (sec) N/A 0.106 0.090 0.155 0.471 0.428 0.000 0.120 1.721
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 81 104 0 646 0 82 383
normalized size 1 1.00 0.71 0.91 0.00 5.67 0.00 0.72 3.36
time (sec) N/A 0.205 0.349 0.175 0.000 0.421 0.000 0.132 1.667
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 112 119 164 1222 0 193 339
normalized size 1 1.00 0.99 1.05 1.45 10.81 0.00 1.71 3.00
time (sec) N/A 0.190 0.323 0.164 0.489 0.466 0.000 0.129 2.218
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 207 207 166 179 0 3530 0 190 713
normalized size 1 1.00 0.80 0.86 0.00 17.05 0.00 0.92 3.44
time (sec) N/A 0.329 0.778 0.175 0.000 0.487 0.000 0.142 1.833
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 178 178 167 215 366 5181 0 380 623
normalized size 1 1.00 0.94 1.21 2.06 29.11 0.00 2.13 3.50
time (sec) N/A 0.320 1.033 0.174 0.366 0.609 0.000 0.143 2.746
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 169 169 160 0 0 4363 0 0 -1
normalized size 1 1.00 0.95 0.00 0.00 25.82 0.00 0.00 -0.01
time (sec) N/A 0.194 5.125 0.644 0.000 1.104 0.000 0.000 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 108 0 0 1589 0 0 -1
normalized size 1 1.00 1.08 0.00 0.00 15.89 0.00 0.00 -0.01
time (sec) N/A 0.122 0.989 0.523 0.000 1.070 0.000 0.000 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 90 43 0 605 0 0 47
normalized size 1 1.00 1.76 0.84 0.00 11.86 0.00 0.00 0.92
time (sec) N/A 0.054 0.152 0.108 0.000 1.036 0.000 0.000 1.692
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 195 0 0 8620 0 0 -1
normalized size 1 1.00 1.84 0.00 0.00 81.32 0.00 0.00 -0.01
time (sec) N/A 0.175 1.828 0.565 0.000 0.974 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 217 217 518 0 0 0 0 0 -1
normalized size 1 1.00 2.39 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.327 20.686 0.609 0.000 0.000 0.000 0.000 0.000
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F(-1) F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 344 344 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.392 180.002 0.494 0.000 0.631 0.000 0.000 0.000
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 125 125 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.026 7.855 0.520 0.000 2.245 0.000 0.000 0.000
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 246 246 539 0 0 0 0 0 -1
normalized size 1 1.00 2.19 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.215 18.227 0.549 0.000 1.269 0.000 0.000 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 148 148 167 0 0 2813 0 0 -1
normalized size 1 1.00 1.13 0.00 0.00 19.01 0.00 0.00 -0.01
time (sec) N/A 0.165 4.412 0.684 0.000 1.085 0.000 0.000 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 111 0 0 925 0 0 -1
normalized size 1 1.00 1.41 0.00 0.00 11.71 0.00 0.00 -0.01
time (sec) N/A 0.108 0.637 0.653 0.000 1.041 0.000 0.000 0.000
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 73 26 0 558 0 0 27
normalized size 1 1.00 2.35 0.84 0.00 18.00 0.00 0.00 0.87
time (sec) N/A 0.047 0.140 0.094 0.000 1.023 0.000 0.000 1.635
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 226 0 0 8908 0 0 -1
normalized size 1 1.00 2.13 0.00 0.00 84.04 0.00 0.00 -0.01
time (sec) N/A 0.148 3.680 0.580 0.000 1.305 0.000 0.000 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 262 262 902 0 0 0 0 0 -1
normalized size 1 1.00 3.44 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.297 7.396 0.654 0.000 0.000 0.000 0.000 0.000
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F(-1) F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 610 610 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.791 180.001 0.638 0.000 0.667 0.000 0.000 0.000
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F(-1) F F F(-1) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 310 310 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.258 180.001 0.491 0.000 0.000 0.000 0.000 0.000
Problem 140 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 106 106 168 0 0 0 0 0 -1
normalized size 1 1.00 1.58 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.021 0.634 0.013 0.000 3.433 0.000 0.000 0.000
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F(-1) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 362 362 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.436 91.352 0.589 0.000 0.000 0.000 0.000 0.000
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 148 148 155 0 0 3745 0 0 -1
normalized size 1 1.00 1.05 0.00 0.00 25.30 0.00 0.00 -0.01
time (sec) N/A 0.191 3.170 0.660 0.000 2.682 0.000 0.000 0.000
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 103 0 0 1107 0 0 -1
normalized size 1 1.00 1.17 0.00 0.00 12.58 0.00 0.00 -0.01
time (sec) N/A 0.141 0.673 0.560 0.000 1.239 0.000 0.000 0.000
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 79 46 0 917 0 0 50
normalized size 1 1.00 1.46 0.85 0.00 16.98 0.00 0.00 0.93
time (sec) N/A 0.062 0.246 0.093 0.000 1.057 0.000 0.000 1.770
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 142 142 904 0 0 0 0 0 -1
normalized size 1 1.00 6.37 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.217 7.367 0.569 0.000 0.000 0.000 0.000 0.000
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 316 316 996 0 0 0 0 0 -1
normalized size 1 1.00 3.15 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.427 7.612 0.696 0.000 0.000 0.000 0.000 0.000
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F(-1) F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 907 907 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.366 180.001 0.612 0.000 7.754 0.000 0.000 0.000
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F(-1) F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 344 344 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.420 180.001 0.471 0.000 9.076 0.000 0.000 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F(-1) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 347 347 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.337 86.669 0.461 0.000 0.000 0.000 0.000 0.000
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F(-1) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 665 665 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.983 110.553 0.565 0.000 0.000 0.000 0.000 0.000
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 191 191 84 91 386 589 0 64 405
normalized size 1 1.00 0.44 0.48 2.02 3.08 0.00 0.34 2.12
time (sec) N/A 0.282 0.091 0.750 0.320 0.774 0.000 0.135 0.167
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 141 141 72 80 209 315 0 51 91
normalized size 1 1.00 0.51 0.57 1.48 2.23 0.00 0.36 0.65
time (sec) N/A 0.167 0.069 0.683 0.320 0.504 0.000 0.134 1.429
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 44 69 84 120 0 38 78
normalized size 1 1.00 0.79 1.23 1.50 2.14 0.00 0.68 1.39
time (sec) N/A 0.113 0.059 0.677 0.321 0.609 0.000 0.133 0.138
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 42 66 21 42 0 20 -1
normalized size 1 1.00 0.95 1.50 0.48 0.95 0.00 0.45 -0.02
time (sec) N/A 0.087 0.040 0.719 0.407 0.420 0.000 0.131 0.000
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 48 106 29 66 0 33 -1
normalized size 1 1.00 0.65 1.43 0.39 0.89 0.00 0.45 -0.01
time (sec) N/A 0.113 0.053 0.830 0.320 0.402 0.000 0.135 0.000
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 162 78 216 74 126 0 82 -1
normalized size 1 1.00 0.48 1.33 0.46 0.78 0.00 0.51 -0.01
time (sec) N/A 0.155 0.067 0.842 0.317 0.411 0.000 0.113 0.000
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 250 250 106 326 112 218 0 110 -1
normalized size 1 1.00 0.42 1.30 0.45 0.87 0.00 0.44 -0.00
time (sec) N/A 0.196 0.106 0.747 0.321 0.434 0.000 0.121 0.000
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 108 108 77 130 0 0 0 0 -1
normalized size 1 1.00 0.71 1.20 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.087 0.178 0.240 0.000 0.415 0.000 0.000 0.000
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 44 39 30 48 0 0 42
normalized size 1 1.00 1.57 1.39 1.07 1.71 0.00 0.00 1.50
time (sec) N/A 0.042 0.047 0.205 0.447 0.410 0.000 0.000 1.471
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 203 203 65 134 0 0 0 0 -1
normalized size 1 1.00 0.32 0.66 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.130 0.115 0.232 0.000 0.427 0.000 0.000 0.000
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 77 97 0 90 0 0 -1
normalized size 1 1.00 1.15 1.45 0.00 1.34 0.00 0.00 -0.01
time (sec) N/A 0.055 0.146 0.263 0.000 0.405 0.000 0.000 0.000
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 58 114 0 0 0 0 -1
normalized size 1 1.00 0.67 1.31 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.060 0.104 0.209 0.000 0.406 0.000 0.000 0.000
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 77 0 0 100 0 0 -1
normalized size 1 1.00 1.31 0.00 0.00 1.69 0.00 0.00 -0.02
time (sec) N/A 0.033 0.096 0.196 0.000 0.405 0.000 0.000 0.000
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 36 167 0 0 0 0 -1
normalized size 1 1.00 1.00 4.64 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.029 0.058 0.488 0.000 0.412 0.000 0.000 0.000
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 55 0 0 57 0 0 -1
normalized size 1 1.00 1.38 0.00 0.00 1.42 0.00 0.00 -0.02
time (sec) N/A 0.045 0.122 0.202 0.000 0.427 0.000 0.000 0.000
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 137 137 59 134 0 0 0 0 -1
normalized size 1 1.00 0.43 0.98 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.099 0.122 0.200 0.000 0.414 0.000 0.000 0.000
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 33 38 42 37 0 0 58
normalized size 1 1.00 1.43 1.65 1.83 1.61 0.00 0.00 2.52
time (sec) N/A 0.040 0.040 0.191 0.406 0.433 0.000 0.000 1.352
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 65 117 0 0 0 0 -1
normalized size 1 1.00 0.81 1.46 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.070 0.101 0.200 0.000 0.430 0.000 0.000 0.000
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 122 122 98 121 0 109 0 0 -1
normalized size 1 1.00 0.80 0.99 0.00 0.89 0.00 0.00 -0.01
time (sec) N/A 0.075 0.194 0.245 0.000 0.441 0.000 0.000 0.000
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 141 141 77 138 0 0 0 0 -1
normalized size 1 1.00 0.55 0.98 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.098 0.184 0.200 0.000 0.442 0.000 0.000 0.000
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 44 47 30 56 0 0 42
normalized size 1 1.00 1.57 1.68 1.07 2.00 0.00 0.00 1.50
time (sec) N/A 0.043 0.053 0.203 0.454 0.420 0.000 0.000 1.453
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 251 251 65 147 0 0 0 0 -1
normalized size 1 1.00 0.26 0.59 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.149 0.119 0.211 0.000 0.432 0.000 0.000 0.000
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 90 113 0 101 0 0 -1
normalized size 1 1.00 0.98 1.23 0.00 1.10 0.00 0.00 -0.01
time (sec) N/A 0.066 0.172 0.282 0.000 0.437 0.000 0.000 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 61 129 0 0 0 0 -1
normalized size 1 1.00 0.55 1.16 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.083 0.112 0.215 0.000 0.429 0.000 0.000 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 88 0 0 109 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 1.24 0.00 0.00 -0.01
time (sec) N/A 0.067 0.168 0.194 0.000 0.418 0.000 0.000 0.000
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 214 214 65 159 0 0 0 0 -1
normalized size 1 1.00 0.30 0.74 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.116 0.115 0.208 0.000 0.482 0.000 0.000 0.000
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 64 131 0 106 0 0 -1
normalized size 1 1.00 0.70 1.42 0.00 1.15 0.00 0.00 -0.01
time (sec) N/A 0.039 0.090 0.238 0.000 0.427 0.000 0.000 0.000
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 45 127 0 0 0 0 -1
normalized size 1 1.00 0.80 2.27 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.036 0.108 0.617 0.000 0.432 0.000 0.000 0.000
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F A A F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 32 0 39 28 0 0 28
normalized size 1 1.00 1.28 0.00 1.56 1.12 0.00 0.00 1.12
time (sec) N/A 0.040 0.035 0.170 0.401 0.415 0.000 0.000 1.334
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 65 0 0 0 0 0 -1
normalized size 1 1.00 0.71 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.077 0.112 0.165 0.000 0.440 0.000 0.000 0.000
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 51 0 0 93 0 0 -1
normalized size 1 1.00 0.77 0.00 0.00 1.41 0.00 0.00 -0.02
time (sec) N/A 0.057 0.111 0.181 0.000 0.436 0.000 0.000 0.000
Problem 182 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 63 63 64 0 0 0 0 0 -1
normalized size 1 1.00 1.02 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.059 0.151 0.163 0.000 0.424 0.000 0.000 0.000
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 69 69 126 0 0 0 0 0 -1
normalized size 1 1.00 1.83 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.070 5.553 1.692 0.000 0.407 0.000 0.000 0.000
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 70 70 101 0 0 0 0 0 -1
normalized size 1 1.00 1.44 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.071 0.903 1.999 0.000 0.425 0.000 0.000 0.000
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 69 69 192 0 0 0 0 0 -1
normalized size 1 1.00 2.78 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.073 13.701 1.827 0.000 0.439 0.000 0.000 0.000
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A C A C B B F B B
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 40 139 29 509 96 189 0 215 66
normalized size 1 3.48 0.72 12.72 2.40 4.72 0.00 5.38 1.65
time (sec) N/A 0.135 0.319 1.065 0.612 0.430 0.000 1.219 1.400
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 62 0 74 48 0 38 49
normalized size 1 1.00 2.48 0.00 2.96 1.92 0.00 1.52 1.96
time (sec) N/A 0.039 0.129 0.495 0.338 0.412 0.000 0.131 1.531
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 64 0 49 49 0 37 36
normalized size 1 1.00 2.56 0.00 1.96 1.96 0.00 1.48 1.44
time (sec) N/A 0.046 0.108 0.696 0.344 0.401 0.000 0.130 1.449
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 57 0 0 474 0 0 -1
normalized size 1 1.00 0.64 0.00 0.00 5.33 0.00 0.00 -0.01
time (sec) N/A 0.089 0.772 0.627 0.000 0.445 0.000 0.000 0.000
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 62 0 0 538 0 0 -1
normalized size 1 1.00 0.95 0.00 0.00 8.28 0.00 0.00 -0.02
time (sec) N/A 0.076 0.877 0.615 0.000 0.446 0.000 0.000 0.000
Problem 191 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 19 19 19 20 19 34 0 27 41
normalized size 1 1.00 1.00 1.05 1.00 1.79 0.00 1.42 2.16
time (sec) N/A 0.016 0.049 0.023 0.313 0.423 0.000 0.118 1.407
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 19 28 70 0 28 24
normalized size 1 1.00 1.00 1.06 1.56 3.89 0.00 1.56 1.33
time (sec) N/A 0.028 0.060 0.291 0.344 0.415 0.000 0.145 1.328
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 55 51 0 452 0 115 139
normalized size 1 1.00 1.00 0.93 0.00 8.22 0.00 2.09 2.53
time (sec) N/A 0.040 0.059 0.301 0.000 0.428 0.000 0.155 1.403
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 42 36 91 272 0 47 55
normalized size 1 1.00 1.00 0.86 2.17 6.48 0.00 1.12 1.31
time (sec) N/A 0.034 0.049 0.293 0.349 0.435 0.000 0.150 1.341
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 75 84 0 1326 0 152 314
normalized size 1 1.00 0.84 0.94 0.00 14.90 0.00 1.71 3.53
time (sec) N/A 0.057 0.094 0.321 0.000 0.448 0.000 0.166 1.348
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 74 295 0 0 0 0 -1
normalized size 1 1.00 0.76 3.04 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.061 0.167 0.727 0.000 0.429 0.000 0.000 0.000
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 93 93 72 141 0 0 0 0 -1
normalized size 1 1.00 0.77 1.52 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.072 0.093 0.641 0.000 0.441 0.000 0.000 0.000
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 58 183 0 0 0 0 -1
normalized size 1 1.00 1.00 3.16 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.069 0.069 0.542 0.000 0.431 0.000 0.000 0.000
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 58 183 0 0 0 0 -1
normalized size 1 1.00 1.00 3.16 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.056 0.076 0.512 0.000 0.420 0.000 0.000 0.000
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 76 237 0 0 0 0 -1
normalized size 1 1.00 0.78 2.44 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.073 0.114 0.675 0.000 0.428 0.000 0.000 0.000
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 87 256 0 0 0 0 -1
normalized size 1 1.00 0.90 2.64 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.070 0.130 0.674 0.000 0.435 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 [177] had the largest ratio of [.6364]

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 1 1 1.00 6 0.167
2 A 2 2 1.00 8 0.250
3 A 2 2 1.00 8 0.250
4 A 2 1 1.00 8 0.125
5 A 3 2 1.00 8 0.250
6 A 2 1 1.00 8 0.125
7 A 2 1 1.00 6 0.167
8 A 2 1 1.00 6 0.167
9 A 3 3 1.00 10 0.300
10 A 3 3 1.00 10 0.300
11 A 2 2 1.00 10 0.200
12 A 2 2 1.00 10 0.200
13 A 3 3 1.00 10 0.300
14 A 3 3 1.00 10 0.300
15 A 4 3 1.00 12 0.250
16 A 3 3 1.00 12 0.250
17 A 3 3 1.00 12 0.250
18 A 2 2 1.00 12 0.167
19 A 2 2 1.00 12 0.167
20 A 3 3 1.00 12 0.250
21 A 3 3 1.00 12 0.250
22 A 4 3 1.00 12 0.250
23 A 2 2 1.00 10 0.200
24 A 5 3 1.00 12 0.250
25 A 4 3 1.00 12 0.250
26 A 3 3 1.00 12 0.250
27 A 2 2 1.00 12 0.167
28 A 2 2 1.00 12 0.167
29 A 3 3 1.00 12 0.250
30 A 4 3 1.00 12 0.250
31 A 5 3 1.00 12 0.250
32 A 5 4 1.00 10 0.400
33 A 4 4 1.00 10 0.400
34 A 3 3 1.00 10 0.300
35 A 2 2 1.00 10 0.200
36 A 3 3 1.00 10 0.300
37 A 4 3 1.00 10 0.300
38 A 5 3 1.00 10 0.300
39 A 7 4 1.00 10 0.400
40 A 5 4 1.00 10 0.400
41 A 4 4 1.00 10 0.400
42 A 4 4 1.00 10 0.400
43 A 5 4 1.00 10 0.400
44 A 7 4 1.00 10 0.400
45 A 3 2 1.00 10 0.200
46 A 3 2 1.00 10 0.200
47 A 3 2 1.00 10 0.200
48 A 3 3 1.00 10 0.300
49 A 3 3 1.00 10 0.300
50 A 5 3 1.00 10 0.300
51 A 7 3 1.00 10 0.300
52 A 7 7 1.00 13 0.538
53 A 6 5 1.00 13 0.385
54 A 5 5 1.00 13 0.385
55 A 5 4 1.00 11 0.364
56 A 6 6 1.00 11 0.546
57 A 6 5 1.00 13 0.385
58 A 7 7 1.00 13 0.538
59 A 7 6 1.00 13 0.462
60 A 6 5 1.00 13 0.385
61 A 5 4 1.00 13 0.308
62 A 5 5 1.00 13 0.385
63 A 5 4 1.00 11 0.364
64 A 4 3 1.00 11 0.273
65 A 5 5 1.00 13 0.385
66 A 6 5 1.00 13 0.385
67 A 6 5 1.00 13 0.385
68 A 7 5 1.00 13 0.385
69 A 6 5 1.00 13 0.385
70 A 5 5 1.00 13 0.385
71 A 4 4 1.00 11 0.364
72 A 1 1 1.00 11 0.091
73 A 3 3 1.00 13 0.231
74 A 4 4 1.00 13 0.308
75 A 6 6 1.00 13 0.462
76 A 2 2 1.00 12 0.167
77 A 2 2 1.00 13 0.154
78 A 5 5 1.00 14 0.357
79 A 4 4 1.00 14 0.286
80 A 2 2 1.00 14 0.143
81 A 5 4 1.00 14 0.286
82 A 6 5 1.00 14 0.357
83 A 2 2 1.00 15 0.133
84 A 5 4 1.00 15 0.267
85 A 2 2 1.00 10 0.200
86 A 2 2 1.00 10 0.200
87 A 6 5 1.00 12 0.417
88 A 5 4 1.00 12 0.333
89 A 4 4 1.00 12 0.333
90 A 2 1 1.00 10 0.100
91 A 3 3 1.00 12 0.250
92 A 5 5 1.00 12 0.417
93 A 6 6 1.00 12 0.500
94 A 1 1 1.00 14 0.071
95 A 8 6 1.00 13 0.462
96 A 7 6 1.00 13 0.462
97 A 6 6 1.00 13 0.462
98 A 5 5 1.00 11 0.454
99 A 3 3 1.00 11 0.273
100 A 5 5 1.00 13 0.385
101 A 6 6 1.00 13 0.462
102 A 7 7 1.00 13 0.538
103 A 5 3 1.00 13 0.231
104 A 3 2 1.00 13 0.154
105 A 4 3 1.00 13 0.231
106 A 3 2 1.00 13 0.154
107 A 3 2 1.00 13 0.154
108 A 2 2 1.00 11 0.182
109 A 3 2 1.00 11 0.182
110 A 4 3 1.00 13 0.231
111 A 3 2 1.00 13 0.154
112 A 5 3 1.00 13 0.231
113 A 3 2 1.00 13 0.154
114 A 15 8 1.00 13 0.615
115 A 3 2 1.00 13 0.154
116 A 6 6 1.00 13 0.462
117 A 3 2 1.00 13 0.154
118 A 7 7 1.00 13 0.538
119 A 4 4 1.00 11 0.364
120 A 3 2 1.00 11 0.182
121 A 9 8 1.00 13 0.615
122 A 3 2 1.00 13 0.154
123 A 15 8 1.00 13 0.615
124 A 3 2 1.00 13 0.154
125 A 5 4 1.00 23 0.174
126 A 5 4 1.00 23 0.174
127 A 4 4 1.00 21 0.190
128 A 7 5 1.00 21 0.238
129 A 13 9 1.00 23 0.391
130 A 7 7 1.00 23 0.304
131 A 1 1 1.00 14 0.071
132 A 5 4 1.00 23 0.174
133 A 5 4 1.00 23 0.174
134 A 5 4 1.00 23 0.174
135 A 3 3 1.00 21 0.143
136 A 7 5 1.00 21 0.238
137 A 11 6 1.00 23 0.261
138 A 11 8 1.00 23 0.348
139 A 6 6 1.00 23 0.261
140 A 1 1 1.00 14 0.071
141 A 9 8 1.00 23 0.348
142 A 5 4 1.00 23 0.174
143 A 5 4 1.00 23 0.174
144 A 4 4 1.00 21 0.190
145 A 7 4 1.00 21 0.190
146 A 11 5 1.00 23 0.217
147 A 17 11 1.00 23 0.478
148 A 7 7 1.00 23 0.304
149 A 6 6 1.00 14 0.429
150 A 14 11 1.00 23 0.478
151 A 6 5 1.00 25 0.200
152 A 6 5 1.00 25 0.200
153 A 4 4 1.00 25 0.160
154 A 4 4 1.00 25 0.160
155 A 5 4 1.00 25 0.160
156 A 6 5 1.00 25 0.200
157 A 6 5 1.00 25 0.200
158 A 6 6 1.00 15 0.400
159 A 3 3 1.00 15 0.200
160 A 8 8 1.00 15 0.533
161 A 6 6 1.00 15 0.400
162 A 5 5 1.00 13 0.385
163 A 6 6 1.00 11 0.546
164 A 3 2 1.00 15 0.133
165 A 5 5 1.00 15 0.333
166 A 6 6 1.00 15 0.400
167 A 3 3 1.00 15 0.200
168 A 5 5 1.00 15 0.333
169 A 8 7 1.00 15 0.467
170 A 7 6 1.00 15 0.400
171 A 3 3 1.00 15 0.200
172 A 9 8 1.00 15 0.533
173 A 7 6 1.00 15 0.400
174 A 6 5 1.00 15 0.333
175 A 7 6 1.00 15 0.400
176 A 8 7 1.00 13 0.538
177 A 7 7 1.00 11 0.636
178 A 4 3 1.00 15 0.200
179 A 3 3 1.00 15 0.200
180 A 5 5 1.00 15 0.333
181 A 6 6 1.00 15 0.400
182 A 4 4 1.00 11 0.364
183 A 4 4 1.00 13 0.308
184 A 4 4 1.00 13 0.308
185 A 4 4 1.00 13 0.308
186 C 9 4 3.48 44 0.091
187 A 3 3 1.00 15 0.200
188 A 4 4 1.00 15 0.267
189 A 3 3 1.00 20 0.150
190 A 3 3 1.00 21 0.143
191 A 2 1 1.00 15 0.067
192 A 3 2 1.00 17 0.118
193 A 3 2 1.00 17 0.118
194 A 3 1 1.00 17 0.059
195 A 4 2 1.00 17 0.118
196 A 4 3 1.00 19 0.158
197 A 4 3 1.00 19 0.158
198 A 3 2 1.00 19 0.105
199 A 3 2 1.00 19 0.105
200 A 4 3 1.00 19 0.158
201 A 4 3 1.00 19 0.158

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