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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, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 58, 59, 60, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 96, 97, 98, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 132, 133, 134, 135, 136, 138, 139, 140, 141, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 160, 161, 162, 163, 164, 165, 167, 168, 169, 174, 175, 176, 177, 178, 179, 180, 181, 183, 184, 185, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 201, 202, 203, 205, 206, 207, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218 }

B grade: { 22, 28, 57, 131, 137, 166 }

C grade: { }

F grade: { 9, 33, 37, 49, 50, 61, 62, 63, 64, 73, 77, 91, 95, 99, 118, 142, 146, 158, 159, 170, 171, 172, 173, 182, 186, 200, 204, 208 }

2.1.3 Maple

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, 32, 34, 36, 38, 39, 40, 41, 42, 44, 45, 46, 48, 51, 52, 53, 57, 65, 66, 67, 68, 69, 70, 72, 74, 76, 78, 79, 80, 81, 82, 84, 85, 86, 88, 89, 90, 92, 94, 96, 98, 100, 102, 103, 104, 106, 107, 108, 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, 141, 143, 145, 147, 148, 149, 150, 151, 153, 154, 155, 157, 160, 161, 162, 166, 174, 175, 176, 177, 178, 179, 181, 183, 185, 187, 188, 189, 190, 191, 193, 194, 195, 197, 198, 199, 201, 203, 205, 207, 209, 211, 212, 213, 215, 216, 217 }

B grade: { }

C grade: { }

F grade: { 31, 33, 35, 37, 43, 47, 49, 50, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 71, 73, 75, 77, 83, 87, 91, 93, 95, 97, 99, 101, 105, 109, 140, 142, 144, 146, 152, 156, 158, 159, 163, 164, 165, 167, 168, 169, 170, 171, 172, 173, 180, 182, 184, 186, 192, 196, 200, 202, 204, 206, 208, 210, 214, 218 }

2.1.4 Maxima

A grade: { 23, 24, 29, 30, 39, 40, 41, 42, 44, 45, 46, 48, 52, 53, 80, 81, 82, 84, 85, 86, 88, 89, 90, 100, 102, 103, 104, 106, 107, 108, 132, 133, 138, 139, 148, 149, 150, 151, 153, 154, 155, 157, 161, 162, 189, 190, 191, 193, 194, 195, 197, 198, 199, 209, 211, 212, 213, 215, 216, 217 }

B grade: { }

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, 25, 26, 27, 28, 31, 32, 33, 34, 35, 36, 37, 38, 43, 47, 49, 50, 51, 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, 83, 87, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 105, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 137, 140, 141, 142, 143, 144, 145, 146, 147, 152, 156, 158, 159, 160, 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, 192, 196, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 214, 218 }

2.1.5 FriCAS

A grade: { 23, 24, 29, 30, 39, 40, 41, 42, 44, 45, 46, 48, 52, 53, 80, 81, 82, 84, 85, 86, 88, 89, 90, 100, 102, 103, 104, 106, 107, 108, 132, 133, 138, 139, 148, 149, 150, 151, 153, 154, 155, 157, 161, 162, 189, 190, 191, 193, 194, 195, 197, 198, 199, 209, 211, 212, 213, 215, 216, 217 }

B grade: { }

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, 25, 26, 27, 28, 31, 32, 33, 34, 35, 36, 37, 38, 43, 47, 49, 50, 51, 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, 83, 87, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 105, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 137, 140, 141, 142, 143, 144, 145, 146, 147, 152, 156, 158, 159, 160, 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, 192, 196, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 214, 218 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 14, 15, 16, 17, 18, 23, 24, 29, 30, 39, 40, 41, 42, 44, 45, 46, 48, 52, 53, 65, 66, 67, 68, 69, 70, 75, 79, 80, 81, 82, 84, 85, 86, 88, 89, 90, 93, 97, 100, 102, 103, 104, 106, 107, 108, 110, 111, 112, 113, 114, 115, 116, 120, 121, 122, 123, 124, 125, 126, 127, 132, 133, 138, 139, 148, 149, 150, 151, 153, 154, 155, 157, 161, 162, 174, 175, 176, 177, 178, 179, 184, 188, 189, 190, 191, 193, 194, 195, 197, 198, 199, 202, 206, 209, 211, 212, 213, 215, 216, 217 }

B grade: { 8, 10, 117, 119 }

C grade: { }

F grade: { 9, 19, 20, 21, 22, 25, 26, 27, 28, 31, 32, 33, 34, 35, 36, 37, 38, 43, 47, 49, 50, 51, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 71, 72, 73, 74, 76, 77, 78, 83, 87, 91, 92, 94, 95, 96, 98, 99, 101, 105, 109, 118, 128, 129, 130, 131, 134, 135, 136, 137, 140, 141, 142, 143, 144, 145, 146, 147, 152, 156, 158, 159, 160, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 180, 181, 182, 183, 185, 186, 187, 192, 196, 200, 201, 203, 204, 205, 207, 208, 210, 214, 218 }

2.1.7 Giac

A grade: { 23, 24, 29, 30, 39, 40, 41, 42, 44, 45, 46, 48, 52, 53, 80, 81, 82, 84, 85, 86, 88, 89, 90, 100, 102, 103, 104, 106, 107, 108, 132, 133, 138, 139, 148, 149, 150, 151, 153, 154, 155, 157, 161, 162, 189, 190, 191, 193, 194, 195, 197, 198, 199, 209, 211, 212, 213, 215, 216, 217 }

B grade: { }

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, 25, 26, 27, 28, 31, 32, 33, 34, 35, 36, 37, 38, 43, 47, 49, 50, 51, 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, 83, 87, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 105, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 137, 140, 141, 142, 143, 144, 145, 146, 147, 152, 156, 158, 159, 160, 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, 192, 196, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 214, 218 }

2.1.8 Mupad

A grade: { 23, 24, 29, 30, 39, 40, 41, 42, 44, 45, 46, 48, 52, 53, 80, 81, 82, 84, 85, 86, 88, 89, 90, 100, 102, 103, 104, 106, 107, 108, 132, 133, 138, 139, 148, 149, 150, 151, 153, 154, 155, 157, 161, 162, 189, 190, 191, 193, 194, 195, 197, 198, 199, 209, 211, 212, 213, 215, 216, 217 }

B grade: { }

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, 25, 26, 27, 28, 31, 32, 33, 34, 35, 36, 37, 38, 43, 47, 49, 50, 51, 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, 83, 87, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 105, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 137, 140, 141, 142, 143, 144, 145, 146, 147, 152, 156, 158, 159, 160, 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, 192, 196, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 214, 218 }

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 F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 88 123 0 0 184 0 -1
normalized size 1 1.00 0.71 0.99 0.00 0.00 1.48 0.00 -0.01
time (sec) N/A 0.088 0.080 0.030 0.000 0.537 1.977 0.000 0.000
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 83 107 0 0 156 0 -1
normalized size 1 1.00 0.76 0.98 0.00 0.00 1.43 0.00 -0.01
time (sec) N/A 0.111 0.066 0.019 0.000 0.383 1.500 0.000 0.000
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 79 96 0 0 53 0 -1
normalized size 1 1.00 0.80 0.97 0.00 0.00 0.54 0.00 -0.01
time (sec) N/A 0.064 0.095 0.020 0.000 0.419 0.853 0.000 0.000
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 71 80 0 0 121 0 -1
normalized size 1 1.00 0.85 0.95 0.00 0.00 1.44 0.00 -0.01
time (sec) N/A 0.080 0.047 0.019 0.000 0.394 1.460 0.000 0.000
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 74 70 0 0 112 0 -1
normalized size 1 1.00 1.00 0.95 0.00 0.00 1.51 0.00 -0.01
time (sec) N/A 0.047 0.024 0.023 0.000 0.393 0.852 0.000 0.000
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 59 54 0 0 80 0 -1
normalized size 1 1.00 1.00 0.92 0.00 0.00 1.36 0.00 -0.02
time (sec) N/A 0.053 0.015 0.019 0.000 0.410 0.802 0.000 0.000
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 49 44 0 0 53 0 -1
normalized size 1 1.00 1.00 0.90 0.00 0.00 1.08 0.00 -0.02
time (sec) N/A 0.024 0.013 0.022 0.000 0.405 0.517 0.000 0.000
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 26 27 0 0 48 0 -1
normalized size 1 1.00 1.00 1.04 0.00 0.00 1.85 0.00 -0.04
time (sec) N/A 0.005 0.004 0.017 0.000 0.415 0.740 0.000 0.000
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F A F F F(-2) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 73 73 0 29 0 0 0 0 -1
normalized size 1 1.00 0.00 0.40 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.047 0.019 0.055 0.000 0.441 0.000 0.000 0.000
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 28 0 0 42 0 -1
normalized size 1 1.00 1.00 1.04 0.00 0.00 1.56 0.00 -0.04
time (sec) N/A 0.022 0.015 0.021 0.000 0.527 0.635 0.000 0.000
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 44 43 0 0 51 0 -1
normalized size 1 1.00 1.00 0.98 0.00 0.00 1.16 0.00 -0.02
time (sec) N/A 0.029 0.019 0.022 0.000 0.555 0.572 0.000 0.000
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 52 49 0 0 56 0 -1
normalized size 1 1.00 1.00 0.94 0.00 0.00 1.08 0.00 -0.02
time (sec) N/A 0.064 0.020 0.019 0.000 0.480 1.014 0.000 0.000
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 69 65 0 0 110 0 -1
normalized size 1 1.00 1.00 0.94 0.00 0.00 1.59 0.00 -0.01
time (sec) N/A 0.043 0.018 0.020 0.000 0.447 0.965 0.000 0.000
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 77 71 0 0 46 0 -1
normalized size 1 1.00 1.00 0.92 0.00 0.00 0.60 0.00 -0.01
time (sec) N/A 0.089 0.036 0.022 0.000 0.401 0.910 0.000 0.000
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 76 86 0 0 56 0 -1
normalized size 1 1.00 0.81 0.91 0.00 0.00 0.60 0.00 -0.01
time (sec) N/A 0.059 0.064 0.020 0.000 0.444 1.145 0.000 0.000
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 85 93 0 0 68 0 -1
normalized size 1 1.00 0.83 0.91 0.00 0.00 0.67 0.00 -0.01
time (sec) N/A 0.122 0.080 0.025 0.000 0.440 2.053 0.000 0.000
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 84 109 0 0 185 0 -1
normalized size 1 1.00 0.71 0.92 0.00 0.00 1.55 0.00 -0.01
time (sec) N/A 0.081 0.075 0.021 0.000 0.388 2.541 0.000 0.000
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 127 127 96 115 0 0 48 0 -1
normalized size 1 1.00 0.76 0.91 0.00 0.00 0.38 0.00 -0.01
time (sec) N/A 0.153 0.208 0.022 0.000 0.392 2.756 0.000 0.000
Problem 19 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 296 296 424 400 0 0 0 0 -1
normalized size 1 1.00 1.43 1.35 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.401 1.018 0.030 0.000 0.454 0.000 0.000 0.000
Problem 20 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 193 193 236 251 0 0 0 0 -1
normalized size 1 1.00 1.22 1.30 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.226 0.552 0.025 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 A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 61 108 0 0 0 0 -1
normalized size 1 1.00 0.50 0.89 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.114 0.278 0.023 0.000 0.387 0.000 0.000 0.000
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 89 33 0 0 0 0 -1
normalized size 1 1.00 2.47 0.92 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.006 0.044 0.011 0.000 0.560 0.000 0.000 0.000
Problem 23 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 0.015 0.033 0.101 0.000 0.446 0.000 0.000 0.000
Problem 24 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 0.014 5.783 0.092 0.000 0.452 0.000 0.000 0.000
Problem 25 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 229 229 166 189 0 0 0 0 -1
normalized size 1 1.00 0.72 0.83 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.184 0.372 0.024 0.000 0.380 0.000 0.000 0.000
Problem 26 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 147 147 115 121 0 0 0 0 -1
normalized size 1 1.00 0.78 0.82 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.129 0.296 0.023 0.000 0.379 0.000 0.000 0.000
Problem 27 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 96 96 51 80 0 0 0 0 -1
normalized size 1 1.00 0.53 0.83 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.067 0.187 0.024 0.000 0.486 0.000 0.000 0.000
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 89 33 0 0 0 0 -1
normalized size 1 1.00 2.47 0.92 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.007 0.037 0.000 0.000 0.509 0.000 0.000 0.000
Problem 29 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 13 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 -0.08
time (sec) N/A 0.011 0.016 0.028 0.000 0.413 0.000 0.000 0.000
Problem 30 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 13 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 -0.08
time (sec) N/A 0.011 3.674 0.060 0.000 0.382 0.000 0.000 0.000
Problem 31 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 253 253 253 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.428 0.016 0.020 0.000 0.378 0.000 0.000 0.000
Problem 32 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 239 239 171 324 0 0 0 0 -1
normalized size 1 1.00 0.72 1.36 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.318 0.328 0.094 0.000 0.391 0.000 0.000 0.000
Problem 33 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 265 265 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 0.300 0.258 0.021 0.000 0.469 0.000 0.000 0.000
Problem 34 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 177 177 137 208 0 0 0 0 -1
normalized size 1 1.00 0.77 1.18 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.188 0.172 0.061 0.000 0.493 0.000 0.000 0.000
Problem 35 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 140 140 140 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.151 0.006 0.019 0.000 0.543 0.000 0.000 0.000
Problem 36 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 124 124 100 122 0 0 0 0 -1
normalized size 1 1.00 0.81 0.98 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.111 0.132 0.054 0.000 0.402 0.000 0.000 0.000
Problem 37 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 143 143 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 0.086 0.195 0.020 0.000 0.555 0.000 0.000 0.000
Problem 38 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 55 55 55 49 0 0 0 0 -1
normalized size 1 1.00 1.00 0.89 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.038 0.016 0.028 0.000 0.493 0.000 0.000 0.000
Problem 39 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 13 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 -0.08
time (sec) N/A 0.017 0.021 0.023 0.000 0.485 0.000 0.000 0.000
Problem 40 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 38 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 -0.03
time (sec) N/A 0.037 0.030 0.019 0.000 0.457 0.000 0.000 0.000
Problem 41 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 39 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 -0.03
time (sec) N/A 0.038 0.022 0.021 0.000 0.517 0.000 0.000 0.000
Problem 42 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 120 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 -0.01
time (sec) N/A 0.087 0.032 0.020 0.000 0.455 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 127 127 127 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.143 0.007 0.023 0.000 0.469 0.000 0.000 0.000
Problem 44 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 171 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 -0.01
time (sec) N/A 0.154 0.035 0.023 0.000 0.464 0.000 0.000 0.000
Problem 45 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 166 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 -0.01
time (sec) N/A 0.222 0.027 0.022 0.000 0.495 0.000 0.000 0.000
Problem 46 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 259 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 -0.00
time (sec) N/A 0.245 0.035 0.021 0.000 0.413 0.000 0.000 0.000
Problem 47 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 242 242 242 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.393 0.017 0.029 0.000 0.512 0.000 0.000 0.000
Problem 48 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 286 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 -0.00
time (sec) N/A 0.358 0.028 0.021 0.000 0.430 0.000 0.000 0.000
Problem 49 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 497 497 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 0.410 0.881 0.092 0.000 0.455 0.000 0.000 0.000
Problem 50 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 279 279 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 0.196 0.619 0.020 0.000 0.402 0.000 0.000 0.000
Problem 51 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 70 70 67 60 0 0 0 0 -1
normalized size 1 1.00 0.96 0.86 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.168 0.011 0.011 0.000 0.458 0.000 0.000 0.000
Problem 52 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 0.023 0.043 0.091 0.000 0.529 0.000 0.000 0.000
Problem 53 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 0.023 0.094 0.087 0.000 1.055 0.000 0.000 0.000
Problem 54 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 231 231 319 0 0 0 0 0 -1
normalized size 1 1.00 1.38 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.571 8.302 0.161 0.000 0.561 0.000 0.000 0.000
Problem 55 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 227 227 319 0 0 0 0 0 -1
normalized size 1 1.00 1.41 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.435 7.912 0.121 0.000 0.532 0.000 0.000 0.000
Problem 56 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 214 214 316 0 0 0 0 0 -1
normalized size 1 1.00 1.48 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.326 7.720 0.112 0.000 0.403 0.000 0.000 0.000
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 164 80 0 0 0 0 -1
normalized size 1 1.00 2.52 1.23 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.041 0.126 0.040 0.000 0.429 0.000 0.000 0.000
Problem 58 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 217 217 195 0 0 0 0 0 -1
normalized size 1 1.00 0.90 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.511 4.424 0.122 0.000 0.474 0.000 0.000 0.000
Problem 59 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 228 228 200 0 0 0 0 0 -1
normalized size 1 1.00 0.88 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.523 4.513 0.129 0.000 0.485 0.000 0.000 0.000
Problem 60 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 280 280 244 0 0 0 0 0 -1
normalized size 1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.702 6.225 0.086 0.000 0.494 0.000 0.000 0.000
Problem 61 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 64 64 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.069 0.033 0.043 0.000 0.471 0.000 0.000 0.000
Problem 62 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 64 64 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.068 0.047 0.040 0.000 0.473 0.000 0.000 0.000
Problem 63 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 101 101 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 0.057 0.063 0.049 0.000 0.547 0.000 0.000 0.000
Problem 64 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 101 101 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 0.050 0.054 0.054 0.000 0.416 0.000 0.000 0.000
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 12 0 0 10 0 -1
normalized size 1 1.00 1.00 0.92 0.00 0.00 0.77 0.00 -0.08
time (sec) N/A 0.015 0.004 0.007 0.000 0.428 1.040 0.000 0.000
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 12 0 0 10 0 -1
normalized size 1 1.00 1.00 0.92 0.00 0.00 0.77 0.00 -0.08
time (sec) N/A 0.011 0.003 0.005 0.000 0.462 0.366 0.000 0.000
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 10 0 0 8 0 -1
normalized size 1 1.00 1.00 1.11 0.00 0.00 0.89 0.00 -0.11
time (sec) N/A 0.015 0.010 0.082 0.000 0.427 0.217 0.000 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 12 0 0 10 0 -1
normalized size 1 1.00 1.00 1.09 0.00 0.00 0.91 0.00 -0.09
time (sec) N/A 0.015 0.003 0.006 0.000 0.481 0.655 0.000 0.000
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 12 0 0 14 0 -1
normalized size 1 1.00 1.00 0.92 0.00 0.00 1.08 0.00 -0.08
time (sec) N/A 0.015 0.003 0.007 0.000 0.558 1.531 0.000 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 18 0 0 31 0 -1
normalized size 1 1.00 1.00 1.06 0.00 0.00 1.82 0.00 -0.06
time (sec) N/A 0.018 0.008 0.006 0.000 0.420 2.979 0.000 0.000
Problem 71 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 232 232 232 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.384 0.014 0.019 0.000 0.398 0.000 0.000 0.000
Problem 72 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 216 216 153 318 0 0 0 0 -1
normalized size 1 1.00 0.71 1.47 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.265 0.286 0.011 0.000 1.022 0.000 0.000 0.000
Problem 73 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 248 248 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 0.255 0.529 0.017 0.000 0.390 0.000 0.000 0.000
Problem 74 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 158 158 120 202 0 0 0 0 -1
normalized size 1 1.00 0.76 1.28 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.156 0.177 0.008 0.000 0.396 0.000 0.000 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 120 120 120 0 0 0 151 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 1.26 0.00 -0.01
time (sec) N/A 0.118 0.007 0.016 0.000 0.390 17.565 0.000 0.000
Problem 76 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 105 105 83 115 0 0 0 0 -1
normalized size 1 1.00 0.79 1.10 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.081 0.112 0.006 0.000 0.408 0.000 0.000 0.000
Problem 77 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 137 137 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 0.061 0.241 0.014 0.000 0.405 0.000 0.000 0.000
Problem 78 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 49 49 44 46 0 0 0 0 -1
normalized size 1 1.00 0.90 0.94 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.022 0.033 0.007 0.000 0.583 0.000 0.000 0.000
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 12 0 0 10 0 -1
normalized size 1 1.00 1.00 0.92 0.00 0.00 0.77 0.00 -0.08
time (sec) N/A 0.011 0.002 0.000 0.000 0.482 0.340 0.000 0.000
Problem 80 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 0.018 0.035 0.016 0.000 0.395 0.000 0.000 0.000
Problem 81 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 0.018 0.042 0.015 0.000 0.544 0.000 0.000 0.000
Problem 82 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 102 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 -0.01
time (sec) N/A 0.058 0.044 0.014 0.000 0.471 0.000 0.000 0.000
Problem 83 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 109 109 109 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.116 0.013 0.016 0.000 0.446 0.000 0.000 0.000
Problem 84 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 153 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 -0.01
time (sec) N/A 0.121 0.033 0.016 0.000 0.406 0.000 0.000 0.000
Problem 85 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 148 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 -0.01
time (sec) N/A 0.193 0.036 0.016 0.000 0.389 0.000 0.000 0.000
Problem 86 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 241 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 -0.00
time (sec) N/A 0.207 0.031 0.019 0.000 0.425 0.000 0.000 0.000
Problem 87 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 224 224 224 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.353 0.017 0.016 0.000 0.552 0.000 0.000 0.000
Problem 88 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 268 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 -0.00
time (sec) N/A 0.306 0.036 0.015 0.000 0.483 0.000 0.000 0.000
Problem 89 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 263 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 -0.00
time (sec) N/A 0.477 0.042 0.020 0.000 0.414 0.000 0.000 0.000
Problem 90 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 22 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 0.015 0.088 0.040 0.000 0.432 0.000 0.000 0.000
Problem 91 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 307 307 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 0.442 0.058 0.039 0.000 0.574 0.000 0.000 0.000
Problem 92 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 217 217 163 321 0 0 0 0 -1
normalized size 1 1.00 0.75 1.48 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.271 0.212 0.069 0.000 0.479 0.000 0.000 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 184 184 184 0 0 0 264 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 1.43 0.00 -0.01
time (sec) N/A 0.253 0.013 0.032 0.000 0.479 75.440 0.000 0.000
Problem 94 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 166 166 126 212 0 0 0 0 -1
normalized size 1 1.00 0.76 1.28 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.169 0.197 0.053 0.000 0.424 0.000 0.000 0.000
Problem 95 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 195 195 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 0.157 0.046 0.032 0.000 0.492 0.000 0.000 0.000
Problem 96 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 108 108 90 119 0 0 0 0 -1
normalized size 1 1.00 0.83 1.10 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.090 0.088 0.051 0.000 0.420 0.000 0.000 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 73 0 0 0 114 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 1.56 0.00 -0.01
time (sec) N/A 0.055 0.007 0.040 0.000 0.436 2.891 0.000 0.000
Problem 98 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 59 59 48 52 0 0 0 0 -1
normalized size 1 1.00 0.81 0.88 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.032 0.039 0.030 0.000 1.454 0.000 0.000 0.000
Problem 99 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 80 80 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 0.017 0.016 0.025 0.000 0.441 0.000 0.000 0.000
Problem 100 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 0.018 0.038 0.033 0.000 0.403 0.000 0.000 0.000
Problem 101 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 48 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 0.041 0.008 0.034 0.000 0.399 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 94 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 -0.01
time (sec) N/A 0.059 0.044 0.033 0.000 0.532 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 89 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 -0.01
time (sec) N/A 0.088 0.046 0.037 0.000 0.543 0.000 0.000 0.000
Problem 104 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 156 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 -0.01
time (sec) N/A 0.126 0.038 0.033 0.000 0.444 0.000 0.000 0.000
Problem 105 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 163 163 163 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.214 0.009 0.030 0.000 0.422 0.000 0.000 0.000
Problem 106 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 231 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 -0.00
time (sec) N/A 0.205 0.039 0.030 0.000 0.515 0.000 0.000 0.000
Problem 107 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 202 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 -0.00
time (sec) N/A 0.319 0.036 0.034 0.000 0.467 0.000 0.000 0.000
Problem 108 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 271 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 -0.00
time (sec) N/A 0.310 0.036 0.033 0.000 0.416 0.000 0.000 0.000
Problem 109 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 278 278 278 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.516 0.022 0.032 0.000 0.398 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 89 123 0 0 184 0 -1
normalized size 1 1.00 0.72 0.99 0.00 0.00 1.48 0.00 -0.01
time (sec) N/A 0.082 0.078 0.006 0.000 0.494 2.310 0.000 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 83 107 0 0 153 0 -1
normalized size 1 1.00 0.76 0.98 0.00 0.00 1.40 0.00 -0.01
time (sec) N/A 0.114 0.082 0.005 0.000 0.539 2.228 0.000 0.000
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 80 97 0 0 49 0 -1
normalized size 1 1.00 0.81 0.98 0.00 0.00 0.49 0.00 -0.01
time (sec) N/A 0.062 0.063 0.005 0.000 0.467 0.974 0.000 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 71 81 0 0 116 0 -1
normalized size 1 1.00 0.85 0.96 0.00 0.00 1.38 0.00 -0.01
time (sec) N/A 0.077 0.058 0.005 0.000 0.495 1.204 0.000 0.000
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 74 70 0 0 112 0 -1
normalized size 1 1.00 1.00 0.95 0.00 0.00 1.51 0.00 -0.01
time (sec) N/A 0.043 0.022 0.007 0.000 0.384 1.008 0.000 0.000
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 59 54 0 0 80 0 -1
normalized size 1 1.00 1.00 0.92 0.00 0.00 1.36 0.00 -0.02
time (sec) N/A 0.054 0.015 0.006 0.000 0.461 1.110 0.000 0.000
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 49 44 0 0 49 0 -1
normalized size 1 1.00 1.00 0.90 0.00 0.00 1.00 0.00 -0.02
time (sec) N/A 0.026 0.013 0.006 0.000 0.474 0.601 0.000 0.000
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 28 0 0 44 0 -1
normalized size 1 1.00 1.00 1.04 0.00 0.00 1.63 0.00 -0.04
time (sec) N/A 0.005 0.003 0.006 0.000 0.445 0.704 0.000 0.000
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F A F F F(-2) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 69 69 0 23 0 0 0 0 -1
normalized size 1 1.00 0.00 0.33 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.044 0.018 0.042 0.000 0.478 0.000 0.000 0.000
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 28 0 0 53 0 -1
normalized size 1 1.00 1.00 1.04 0.00 0.00 1.96 0.00 -0.04
time (sec) N/A 0.021 0.016 0.007 0.000 0.472 1.056 0.000 0.000
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 44 43 0 0 51 0 -1
normalized size 1 1.00 1.00 0.98 0.00 0.00 1.16 0.00 -0.02
time (sec) N/A 0.029 0.024 0.006 0.000 0.399 0.697 0.000 0.000
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 52 49 0 0 42 0 -1
normalized size 1 1.00 1.00 0.94 0.00 0.00 0.81 0.00 -0.02
time (sec) N/A 0.064 0.019 0.005 0.000 0.451 0.808 0.000 0.000
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 69 64 0 0 110 0 -1
normalized size 1 1.00 1.00 0.93 0.00 0.00 1.59 0.00 -0.01
time (sec) N/A 0.041 0.021 0.005 0.000 0.498 1.348 0.000 0.000
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 77 71 0 0 65 0 -1
normalized size 1 1.00 1.00 0.92 0.00 0.00 0.84 0.00 -0.01
time (sec) N/A 0.089 0.019 0.008 0.000 0.487 1.759 0.000 0.000
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 74 87 0 0 56 0 -1
normalized size 1 1.00 0.79 0.93 0.00 0.00 0.60 0.00 -0.01
time (sec) N/A 0.059 0.123 0.005 0.000 0.427 1.422 0.000 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 84 93 0 0 44 0 -1
normalized size 1 1.00 0.82 0.91 0.00 0.00 0.43 0.00 -0.01
time (sec) N/A 0.118 0.147 0.005 0.000 0.382 1.904 0.000 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 85 108 0 0 185 0 -1
normalized size 1 1.00 0.71 0.91 0.00 0.00 1.55 0.00 -0.01
time (sec) N/A 0.078 0.072 0.004 0.000 0.464 2.908 0.000 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 127 127 96 115 0 0 76 0 -1
normalized size 1 1.00 0.76 0.91 0.00 0.00 0.60 0.00 -0.01
time (sec) N/A 0.144 0.108 0.006 0.000 0.415 3.818 0.000 0.000
Problem 128 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 298 298 424 397 0 0 0 0 -1
normalized size 1 1.00 1.42 1.33 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.373 0.953 0.024 0.000 0.433 0.000 0.000 0.000
Problem 129 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 194 194 237 249 0 0 0 0 -1
normalized size 1 1.00 1.22 1.28 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.205 0.541 0.021 0.000 0.511 0.000 0.000 0.000
Problem 130 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 122 122 74 107 0 0 0 0 -1
normalized size 1 1.00 0.61 0.88 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.113 0.284 0.021 0.000 0.664 0.000 0.000 0.000
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 90 34 0 0 0 0 -1
normalized size 1 1.00 2.43 0.92 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.006 0.039 0.004 0.000 0.513 0.000 0.000 0.000
Problem 132 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 0.014 0.032 0.089 0.000 0.642 0.000 0.000 0.000
Problem 133 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 0.014 2.536 0.092 0.000 0.564 0.000 0.000 0.000
Problem 134 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 227 227 166 187 0 0 0 0 -1
normalized size 1 1.00 0.73 0.82 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.187 0.373 0.020 0.000 0.527 0.000 0.000 0.000
Problem 135 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 148 148 116 122 0 0 0 0 -1
normalized size 1 1.00 0.78 0.82 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.123 0.334 0.020 0.000 0.464 0.000 0.000 0.000
Problem 136 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 95 95 59 79 0 0 0 0 -1
normalized size 1 1.00 0.62 0.83 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.071 0.179 0.020 0.000 0.557 0.000 0.000 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 90 34 0 0 0 0 -1
normalized size 1 1.00 2.43 0.92 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.007 0.037 0.000 0.000 0.576 0.000 0.000 0.000
Problem 138 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 13 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 -0.08
time (sec) N/A 0.010 0.025 0.030 0.000 0.397 0.000 0.000 0.000
Problem 139 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 13 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 -0.08
time (sec) N/A 0.011 1.567 0.060 0.000 0.467 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 253 253 253 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.422 0.027 0.023 0.000 0.393 0.000 0.000 0.000
Problem 141 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 239 239 170 324 0 0 0 0 -1
normalized size 1 1.00 0.71 1.36 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.298 0.273 0.062 0.000 0.414 0.000 0.000 0.000
Problem 142 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 265 265 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 0.288 0.239 0.010 0.000 0.399 0.000 0.000 0.000
Problem 143 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 177 177 137 209 0 0 0 0 -1
normalized size 1 1.00 0.77 1.18 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.188 0.156 0.054 0.000 0.381 0.000 0.000 0.000
Problem 144 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 140 140 140 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.156 0.009 0.012 0.000 0.469 0.000 0.000 0.000
Problem 145 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 124 124 100 122 0 0 0 0 -1
normalized size 1 1.00 0.81 0.98 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.105 0.094 0.052 0.000 0.476 0.000 0.000 0.000
Problem 146 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 144 144 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 0.084 0.198 0.012 0.000 0.423 0.000 0.000 0.000
Problem 147 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 54 54 54 49 0 0 0 0 -1
normalized size 1 1.00 1.00 0.91 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.036 0.013 0.004 0.000 0.469 0.000 0.000 0.000
Problem 148 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 13 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 -0.08
time (sec) N/A 0.016 0.023 0.010 0.000 0.439 0.000 0.000 0.000
Problem 149 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 38 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 -0.03
time (sec) N/A 0.037 0.028 0.012 0.000 0.520 0.000 0.000 0.000
Problem 150 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 39 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 -0.03
time (sec) N/A 0.037 0.020 0.010 0.000 0.471 0.000 0.000 0.000
Problem 151 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 120 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 -0.01
time (sec) N/A 0.083 0.028 0.012 0.000 0.425 0.000 0.000 0.000
Problem 152 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 127 127 127 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.138 0.010 0.013 0.000 0.481 0.000 0.000 0.000
Problem 153 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 171 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 -0.01
time (sec) N/A 0.145 0.032 0.010 0.000 0.441 0.000 0.000 0.000
Problem 154 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 166 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 -0.01
time (sec) N/A 0.220 0.033 0.012 0.000 0.479 0.000 0.000 0.000
Problem 155 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 259 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 -0.00
time (sec) N/A 0.240 0.032 0.012 0.000 0.531 0.000 0.000 0.000
Problem 156 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 242 242 242 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.388 0.024 0.010 0.000 0.407 0.000 0.000 0.000
Problem 157 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 286 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 -0.00
time (sec) N/A 0.342 0.034 0.012 0.000 0.412 0.000 0.000 0.000
Problem 158 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 495 495 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 0.396 0.817 0.089 0.000 0.436 0.000 0.000 0.000
Problem 159 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 279 279 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 0.185 0.681 0.010 0.000 0.540 0.000 0.000 0.000
Problem 160 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 69 69 66 60 0 0 0 0 -1
normalized size 1 1.00 0.96 0.87 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.151 0.018 0.002 0.000 0.448 0.000 0.000 0.000
Problem 161 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 0.023 0.039 0.095 0.000 0.498 0.000 0.000 0.000
Problem 162 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 0.023 0.090 0.094 0.000 0.493 0.000 0.000 0.000
Problem 163 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 231 231 318 0 0 0 0 0 -1
normalized size 1 1.00 1.38 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.522 7.681 0.138 0.000 0.420 0.000 0.000 0.000
Problem 164 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 227 227 318 0 0 0 0 0 -1
normalized size 1 1.00 1.40 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.408 7.542 0.132 0.000 0.430 0.000 0.000 0.000
Problem 165 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 214 214 315 0 0 0 0 0 -1
normalized size 1 1.00 1.47 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.263 7.464 0.125 0.000 0.428 0.000 0.000 0.000
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 165 81 0 0 0 0 -1
normalized size 1 1.00 2.50 1.23 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.040 0.104 0.017 0.000 0.403 0.000 0.000 0.000
Problem 167 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 217 217 194 0 0 0 0 0 -1
normalized size 1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.493 4.617 0.148 0.000 0.408 0.000 0.000 0.000
Problem 168 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 228 228 199 0 0 0 0 0 -1
normalized size 1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.493 4.575 0.135 0.000 0.509 0.000 0.000 0.000
Problem 169 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 280 280 244 0 0 0 0 0 -1
normalized size 1 1.00 0.87 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.607 6.045 0.062 0.000 0.471 0.000 0.000 0.000
Problem 170 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 64 64 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.069 0.046 0.030 0.000 0.542 0.000 0.000 0.000
Problem 171 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 64 64 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.066 0.038 0.018 0.000 0.977 0.000 0.000 0.000
Problem 172 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 101 101 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 0.051 0.044 0.033 0.000 0.544 0.000 0.000 0.000
Problem 173 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 101 101 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 0.048 0.048 0.036 0.000 0.512 0.000 0.000 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 12 0 0 10 0 -1
normalized size 1 1.00 1.00 0.92 0.00 0.00 0.77 0.00 -0.08
time (sec) N/A 0.015 0.010 0.017 0.000 0.487 1.178 0.000 0.000
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 12 0 0 10 0 -1
normalized size 1 1.00 1.00 0.92 0.00 0.00 0.77 0.00 -0.08
time (sec) N/A 0.012 0.008 0.018 0.000 0.420 0.390 0.000 0.000
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 9 9 9 10 0 0 10 0 -1
normalized size 1 1.00 1.00 1.11 0.00 0.00 1.11 0.00 -0.11
time (sec) N/A 0.016 0.013 0.085 0.000 0.395 0.241 0.000 0.000
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 11 11 11 12 0 0 12 0 -1
normalized size 1 1.00 1.00 1.09 0.00 0.00 1.09 0.00 -0.09
time (sec) N/A 0.015 0.009 0.017 0.000 0.509 0.751 0.000 0.000
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 12 0 0 15 0 -1
normalized size 1 1.00 1.00 0.92 0.00 0.00 1.15 0.00 -0.08
time (sec) N/A 0.016 0.009 0.018 0.000 0.418 1.660 0.000 0.000
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 18 0 0 34 0 -1
normalized size 1 1.00 1.00 1.06 0.00 0.00 2.00 0.00 -0.06
time (sec) N/A 0.019 0.015 0.017 0.000 0.485 3.589 0.000 0.000
Problem 180 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 231 231 231 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.383 0.014 0.028 0.000 0.514 0.000 0.000 0.000
Problem 181 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 215 215 154 317 0 0 0 0 -1
normalized size 1 1.00 0.72 1.47 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.259 0.272 0.018 0.000 0.416 0.000 0.000 0.000
Problem 182 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 247 247 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 0.253 0.442 0.025 0.000 0.489 0.000 0.000 0.000
Problem 183 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 157 157 120 202 0 0 0 0 -1
normalized size 1 1.00 0.76 1.29 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.151 0.140 0.024 0.000 0.424 0.000 0.000 0.000
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 120 120 120 0 0 0 151 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 1.26 0.00 -0.01
time (sec) N/A 0.118 0.012 0.026 0.000 0.525 18.870 0.000 0.000
Problem 185 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 104 104 83 114 0 0 0 0 -1
normalized size 1 1.00 0.80 1.10 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.078 0.095 0.018 0.000 0.507 0.000 0.000 0.000
Problem 186 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 136 136 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 0.060 0.239 0.027 0.000 0.446 0.000 0.000 0.000
Problem 187 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 48 48 44 45 0 0 0 0 -1
normalized size 1 1.00 0.92 0.94 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.021 0.031 0.017 0.000 0.508 0.000 0.000 0.000
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 12 0 0 10 0 -1
normalized size 1 1.00 1.00 0.92 0.00 0.00 0.77 0.00 -0.08
time (sec) N/A 0.011 0.003 0.000 0.000 0.401 0.377 0.000 0.000
Problem 189 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 0.017 0.035 0.026 0.000 0.402 0.000 0.000 0.000
Problem 190 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 0.019 0.037 0.026 0.000 0.412 0.000 0.000 0.000
Problem 191 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 102 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 -0.01
time (sec) N/A 0.056 0.032 0.025 0.000 0.403 0.000 0.000 0.000
Problem 192 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 109 109 109 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.115 0.010 0.025 0.000 0.436 0.000 0.000 0.000
Problem 193 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 153 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 -0.01
time (sec) N/A 0.115 0.042 0.026 0.000 0.407 0.000 0.000 0.000
Problem 194 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 148 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 -0.01
time (sec) N/A 0.192 0.052 0.023 0.000 0.443 0.000 0.000 0.000
Problem 195 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 241 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 -0.00
time (sec) N/A 0.204 0.030 0.027 0.000 0.591 0.000 0.000 0.000
Problem 196 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 224 224 224 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.352 0.015 0.029 0.000 0.459 0.000 0.000 0.000
Problem 197 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 268 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 -0.00
time (sec) N/A 0.304 0.041 0.028 0.000 0.484 0.000 0.000 0.000
Problem 198 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 263 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 -0.00
time (sec) N/A 0.495 0.045 0.026 0.000 0.439 0.000 0.000 0.000
Problem 199 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 22 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 0.013 0.081 0.026 0.000 0.492 0.000 0.000 0.000
Problem 200 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 308 308 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 0.431 0.053 0.017 0.000 0.576 0.000 0.000 0.000
Problem 201 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 218 218 163 322 0 0 0 0 -1
normalized size 1 1.00 0.75 1.48 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.271 0.181 0.063 0.000 0.497 0.000 0.000 0.000
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 185 185 185 0 0 0 264 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 1.43 0.00 -0.01
time (sec) N/A 0.254 0.012 0.015 0.000 0.480 77.907 0.000 0.000
Problem 203 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 167 167 126 212 0 0 0 0 -1
normalized size 1 1.00 0.75 1.27 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.174 0.195 0.054 0.000 0.464 0.000 0.000 0.000
Problem 204 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 196 196 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 0.157 0.046 0.020 0.000 0.596 0.000 0.000 0.000
Problem 205 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 109 109 90 120 0 0 0 0 -1
normalized size 1 1.00 0.83 1.10 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.089 0.096 0.049 0.000 0.428 0.000 0.000 0.000
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 74 0 0 0 114 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 1.54 0.00 -0.01
time (sec) N/A 0.057 0.005 0.017 0.000 0.447 3.021 0.000 0.000
Problem 207 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 60 60 48 52 0 0 0 0 -1
normalized size 1 1.00 0.80 0.87 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.032 0.026 0.023 0.000 0.505 0.000 0.000 0.000
Problem 208 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 80 80 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 0.016 0.017 0.013 0.000 0.551 0.000 0.000 0.000
Problem 209 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 0.017 0.037 0.014 0.000 0.409 0.000 0.000 0.000
Problem 210 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 48 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 0.043 0.008 0.017 0.000 0.468 0.000 0.000 0.000
Problem 211 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 94 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 -0.01
time (sec) N/A 0.056 0.045 0.018 0.000 0.407 0.000 0.000 0.000
Problem 212 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 89 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 -0.01
time (sec) N/A 0.089 0.039 0.019 0.000 0.479 0.000 0.000 0.000
Problem 213 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 156 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 -0.01
time (sec) N/A 0.119 0.041 0.023 0.000 0.412 0.000 0.000 0.000
Problem 214 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 163 163 163 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.218 0.012 0.017 0.000 0.535 0.000 0.000 0.000
Problem 215 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 231 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 -0.00
time (sec) N/A 0.200 0.037 0.016 0.000 0.419 0.000 0.000 0.000
Problem 216 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 202 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 -0.00
time (sec) N/A 0.314 0.033 0.014 0.000 0.399 0.000 0.000 0.000
Problem 217 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 271 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 -0.00
time (sec) N/A 0.306 0.044 0.016 0.000 0.578 0.000 0.000 0.000
Problem 218 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 278 278 278 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.520 0.027 0.017 0.000 0.470 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 [140] had the largest ratio of [1.100]

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 6 4 1.00 8 0.500
2 A 6 4 1.00 8 0.500
3 A 5 4 1.00 8 0.500
4 A 5 4 1.00 8 0.500
5 A 4 4 1.00 8 0.500
6 A 4 4 1.00 8 0.500
7 A 3 3 1.00 6 0.500
8 A 1 1 1.00 4 0.250
9 A 3 3 1.00 8 0.375
10 A 2 2 1.00 8 0.250
11 A 3 3 1.00 8 0.375
12 A 4 4 1.00 8 0.500
13 A 4 4 1.00 8 0.500
14 A 5 4 1.00 8 0.500
15 A 5 4 1.00 8 0.500
16 A 6 4 1.00 8 0.500
17 A 6 4 1.00 8 0.500
18 A 7 4 1.00 8 0.500
19 A 14 10 1.00 14 0.714
20 A 11 9 1.00 14 0.643
21 A 8 7 1.00 12 0.583
22 A 1 1 1.00 6 0.167
23 A 0 0 0.00 0 0.000
24 A 0 0 0.00 0 0.000
25 A 14 10 1.00 10 1.000
26 A 11 9 1.00 10 0.900
27 A 8 7 1.00 8 0.875
28 A 1 1 1.00 6 0.167
29 A 0 0 0.00 0 0.000
30 A 0 0 0.00 0 0.000
31 A 23 10 1.00 10 1.000
32 A 19 10 1.00 10 1.000
33 A 16 9 1.00 10 0.900
34 A 12 9 1.00 10 0.900
35 A 10 9 1.00 10 0.900
36 A 8 6 1.00 10 0.600
37 A 5 5 1.00 8 0.625
38 A 4 4 1.00 6 0.667
39 A 0 0 0.00 0 0.000
40 A 0 0 0.00 0 0.000
41 A 0 0 0.00 0 0.000
42 A 0 0 0.00 0 0.000
43 A 9 9 1.00 10 0.900
44 A 0 0 0.00 0 0.000
45 A 0 0 0.00 0 0.000
46 A 0 0 0.00 0 0.000
47 A 20 10 1.00 10 1.000
48 A 0 0 0.00 0 0.000
49 A 18 13 1.00 16 0.812
50 A 10 9 1.00 14 0.643
51 A 4 3 1.00 8 0.375
52 A 0 0 0.00 0 0.000
53 A 0 0 0.00 0 0.000
54 A 14 9 1.00 17 0.529
55 A 14 9 1.00 15 0.600
56 A 14 9 1.00 13 0.692
57 A 3 1 1.00 17 0.059
58 A 14 9 1.00 17 0.529
59 A 14 9 1.00 17 0.529
60 A 16 10 1.00 19 0.526
61 A 4 4 1.00 22 0.182
62 A 4 4 1.00 22 0.182
63 A 4 4 1.00 19 0.210
64 A 4 4 1.00 19 0.210
65 A 2 2 1.00 19 0.105
66 A 2 2 1.00 17 0.118
67 A 2 2 1.00 19 0.105
68 A 2 2 1.00 19 0.105
69 A 2 2 1.00 19 0.105
70 A 2 2 1.00 19 0.105
71 A 22 9 1.00 20 0.450
72 A 18 9 1.00 20 0.450
73 A 15 8 1.00 20 0.400
74 A 11 8 1.00 20 0.400
75 A 9 8 1.00 20 0.400
76 A 7 5 1.00 20 0.250
77 A 4 4 1.00 20 0.200
78 A 2 2 1.00 18 0.111
79 A 2 2 1.00 17 0.118
80 A 0 0 0.00 0 0.000
81 A 0 0 0.00 0 0.000
82 A 0 0 0.00 0 0.000
83 A 8 8 1.00 20 0.400
84 A 0 0 0.00 0 0.000
85 A 0 0 0.00 0 0.000
86 A 0 0 0.00 0 0.000
87 A 19 9 1.00 20 0.450
88 A 0 0 0.00 0 0.000
89 A 0 0 0.00 0 0.000
90 A 0 0 0.00 0 0.000
91 A 23 8 1.00 20 0.400
92 A 18 8 1.00 20 0.400
93 A 16 9 1.00 20 0.450
94 A 13 9 1.00 20 0.450
95 A 10 8 1.00 20 0.400
96 A 7 6 1.00 20 0.300
97 A 5 5 1.00 20 0.250
98 A 4 3 1.00 18 0.167
99 A 1 1 1.00 17 0.059
100 A 0 0 0.00 0 0.000
101 A 4 4 1.00 20 0.200
102 A 0 0 0.00 0 0.000
103 A 0 0 0.00 0 0.000
104 A 0 0 0.00 0 0.000
105 A 13 9 1.00 20 0.450
106 A 0 0 0.00 0 0.000
107 A 0 0 0.00 0 0.000
108 A 0 0 0.00 0 0.000
109 A 26 9 1.00 20 0.450
110 A 6 4 1.00 8 0.500
111 A 6 4 1.00 8 0.500
112 A 5 4 1.00 8 0.500
113 A 5 4 1.00 8 0.500
114 A 4 4 1.00 8 0.500
115 A 4 4 1.00 8 0.500
116 A 3 3 1.00 6 0.500
117 A 1 1 1.00 4 0.250
118 A 3 3 1.00 8 0.375
119 A 2 2 1.00 8 0.250
120 A 3 3 1.00 8 0.375
121 A 4 4 1.00 8 0.500
122 A 4 4 1.00 8 0.500
123 A 5 4 1.00 8 0.500
124 A 5 4 1.00 8 0.500
125 A 6 4 1.00 8 0.500
126 A 6 4 1.00 8 0.500
127 A 7 4 1.00 8 0.500
128 A 14 10 1.00 14 0.714
129 A 11 9 1.00 14 0.643
130 A 8 7 1.00 12 0.583
131 A 1 1 1.00 6 0.167
132 A 0 0 0.00 0 0.000
133 A 0 0 0.00 0 0.000
134 A 14 10 1.00 10 1.000
135 A 11 9 1.00 10 0.900
136 A 8 7 1.00 8 0.875
137 A 1 1 1.00 6 0.167
138 A 0 0 0.00 0 0.000
139 A 0 0 0.00 0 0.000
140 A 23 11 1.00 10 1.100
141 A 19 10 1.00 10 1.000
142 A 16 10 1.00 10 1.000
143 A 12 9 1.00 10 0.900
144 A 10 10 1.00 10 1.000
145 A 8 6 1.00 10 0.600
146 A 5 5 1.00 8 0.625
147 A 4 4 1.00 6 0.667
148 A 0 0 0.00 0 0.000
149 A 0 0 0.00 0 0.000
150 A 0 0 0.00 0 0.000
151 A 0 0 0.00 0 0.000
152 A 9 9 1.00 10 0.900
153 A 0 0 0.00 0 0.000
154 A 0 0 0.00 0 0.000
155 A 0 0 0.00 0 0.000
156 A 20 10 1.00 10 1.000
157 A 0 0 0.00 0 0.000
158 A 18 13 1.00 16 0.812
159 A 10 9 1.00 14 0.643
160 A 4 3 1.00 8 0.375
161 A 0 0 0.00 0 0.000
162 A 0 0 0.00 0 0.000
163 A 14 9 1.00 17 0.529
164 A 14 9 1.00 15 0.600
165 A 14 9 1.00 13 0.692
166 A 3 1 1.00 17 0.059
167 A 14 9 1.00 17 0.529
168 A 14 9 1.00 17 0.529
169 A 16 10 1.00 19 0.526
170 A 4 4 1.00 22 0.182
171 A 4 4 1.00 22 0.182
172 A 4 4 1.00 19 0.210
173 A 4 4 1.00 19 0.210
174 A 2 2 1.00 19 0.105
175 A 2 2 1.00 17 0.118
176 A 2 2 1.00 19 0.105
177 A 2 2 1.00 19 0.105
178 A 2 2 1.00 19 0.105
179 A 2 2 1.00 19 0.105
180 A 22 10 1.00 20 0.500
181 A 18 9 1.00 20 0.450
182 A 15 9 1.00 20 0.450
183 A 11 8 1.00 20 0.400
184 A 9 9 1.00 20 0.450
185 A 7 5 1.00 20 0.250
186 A 4 4 1.00 20 0.200
187 A 2 2 1.00 18 0.111
188 A 2 2 1.00 17 0.118
189 A 0 0 0.00 0 0.000
190 A 0 0 0.00 0 0.000
191 A 0 0 0.00 0 0.000
192 A 8 8 1.00 20 0.400
193 A 0 0 0.00 0 0.000
194 A 0 0 0.00 0 0.000
195 A 0 0 0.00 0 0.000
196 A 19 9 1.00 20 0.450
197 A 0 0 0.00 0 0.000
198 A 0 0 0.00 0 0.000
199 A 0 0 0.00 0 0.000
200 A 23 9 1.00 20 0.450
201 A 18 8 1.00 20 0.400
202 A 16 10 1.00 20 0.500
203 A 13 9 1.00 20 0.450
204 A 10 9 1.00 20 0.450
205 A 7 6 1.00 20 0.300
206 A 5 5 1.00 20 0.250
207 A 4 3 1.00 18 0.167
208 A 1 1 1.00 17 0.059
209 A 0 0 0.00 0 0.000
210 A 4 4 1.00 20 0.200
211 A 0 0 0.00 0 0.000
212 A 0 0 0.00 0 0.000
213 A 0 0 0.00 0 0.000
214 A 13 9 1.00 20 0.450
215 A 0 0 0.00 0 0.000
216 A 0 0 0.00 0 0.000
217 A 0 0 0.00 0 0.000
218 A 26 9 1.00 20 0.450

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