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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, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 30, 32, 33, 35, 38, 40, 41, 43, 46, 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, 74, 76, 77, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 96, 97, 99, 100, 102, 103, 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, 134, 135, 136, 137, 138, 139, 141, 143, 145, 147, 148, 149, 151, 152, 153, 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, 203, 204, 205, 206, 207, 208, 210, 212, 214, 216, 218, 219, 221, 222, 223, 225, 226, 227, 228, 229, 231, 233, 234, 235, 237, 240, 248, 255, 256, 257, 258, 259, 260, 261, 262, 263 }

B grade: { 104, 144, 146, 202, 213, 241 }

C grade: { 26, 28, 29, 31, 34, 36, 37, 39, 42, 44, 45, 47, 73, 75, 78, 80, 93, 95, 98, 101, 133, 140, 142, 150, 154, 209, 211, 215, 217, 220, 224, 230, 232, 236, 238, 239, 242, 243, 244, 245, 246, 247, 249, 250, 251, 252, 253, 254 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 15, 16, 17, 19, 21, 23, 24, 29, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 71, 72, 74, 76, 77, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 139, 140, 141, 142, 143, 149, 150, 151, 152, 153, 154, 155, 161, 162, 163, 164, 165, 166, 167, 170, 171, 172, 173, 174, 180, 182, 184, 202, 203, 204, 205, 206, 207, 257, 258, 260, 261 }

B grade: { 10, 12, 18, 20, 22, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 62, 70, 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, 144, 145, 146, 147, 148, 156, 157, 158, 159, 160, 168, 169, 175, 176, 177, 178, 179, 181, 183, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 208, 209, 210, 211, 212, 213, 219, 220, 221, 222, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 238, 239, 240, 241, 242, 243, 246, 247, 248, 249, 250, 251, 252, 255, 256 }

C grade: { 73, 75, 78, 80, 259, 262, 263 }

F grade: { 214, 215, 216, 217, 218, 223, 224, 235, 236, 237, 244, 245, 253, 254 }

2.1.4 Maxima

A grade: { 5, 6, 30, 49, 50, 51, 52, 53, 54, 66, 68, 74, 76, 77, 79, 81, 86, 94, 102, 110, 112, 121, 138, 139, 140, 150, 172, 174, 175, 176, 178, 202, 204, 206 }

B grade: { 1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 32, 33, 35, 38, 40, 41, 43, 46, 48, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 69, 70, 71, 72, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 95, 96, 97, 98, 99, 100, 101, 103, 104, 105, 107, 114, 116, 119, 123, 125, 128, 130, 132, 134, 135, 136, 137, 141, 142, 143, 144, 145, 146, 147, 148, 149, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 173, 177, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 207, 257, 258 }

C grade: { 203, 205 }

F grade: { 26, 28, 29, 31, 34, 36, 37, 39, 42, 44, 45, 47, 73, 75, 78, 80, 106, 108, 109, 111, 113, 115, 117, 118, 120, 122, 124, 126, 127, 129, 131, 133, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 259, 260, 261, 262, 263 }

2.1.5 FriCAS

A grade: { 1, 3, 4, 81, 82, 83, 89, 138, 203, 205, 206, 207 }

B grade: { 2, 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, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 78, 84, 85, 86, 87, 88, 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, 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, 202, 204, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 222, 223, 224, 225, 227, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 247, 248, 249, 250, 251, 252, 254, 255, 257, 258, 260, 261, 262 }

C grade: { 75, 80, 226, 228, 256 }

F grade: { 41, 42, 47, 48, 65, 73, 74, 76, 77, 79, 200, 201, 220, 246, 253, 259, 263 }

2.1.6 Sympy

A grade: { 77, 79, 134, 135, 136, 137, 138, 144, 145, 146, 147, 148, 156, 157, 158, 159, 160, 168, 169, 170, 171, 172, 173, 174, 175, 191, 193, 195, 206, 208, 210, 212, 233, 242, 251, 257 }

B grade: { 140, 219, 221, 258 }

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, 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, 78, 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, 139, 141, 142, 143, 149, 150, 151, 152, 153, 154, 155, 161, 162, 163, 164, 165, 166, 167, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 192, 194, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 207, 209, 211, 213, 214, 215, 216, 217, 218, 220, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 235, 236, 237, 238, 239, 240, 241, 243, 244, 245, 246, 247, 248, 249, 250, 252, 253, 254, 255, 256, 259, 260, 261, 262, 263 }

2.1.7 Giac

A grade: { 5, 6, 8, 14, 23, 30, 49, 50, 51, 52, 53, 54, 58, 60, 61, 63, 66, 68, 73, 74, 75, 76, 77, 78, 79, 80, 81, 85, 93, 110, 112, 137, 138, 139, 140, 141, 150, 153, 171, 173, 174, 175, 176, 177, 178, 189, 202, 203, 205, 206, 207, 257, 258 }

B grade: { 1, 2, 3, 4, 7, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 55, 56, 57, 59, 62, 64, 65, 67, 69, 70, 71, 72, 82, 83, 84, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 142, 143, 144, 145, 146, 147, 148, 149, 151, 152, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 204, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 227, 234, 255 }

C grade: { 226, 228, 256 }

F grade: { 229, 230, 231, 232, 233, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 259, 260, 261, 262, 263 }

2.1.8 Mupad

A grade: { 76, 77, 79 }

B 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, 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, 75, 78, 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, 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, 190, 191, 192, 193, 194, 195, 196, 201, 202, 203, 204, 205, 206, 207, 208, 210, 212, 219, 221, 225, 226, 227, 229, 231, 233, 234, 238, 240, 242, 247, 249, 251, 255, 256, 257, 258 }

C grade: { }

F grade: { 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 74, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 186, 187, 188, 189, 197, 198, 199, 200, 209, 211, 213, 214, 215, 216, 217, 218, 220, 222, 223, 224, 228, 230, 232, 235, 236, 237, 239, 241, 243, 244, 245, 246, 248, 250, 252, 253, 254, 259, 260, 261, 262, 263 }

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 B A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 56 96 154 120 0 145 101
normalized size 1 1.00 0.77 1.32 2.11 1.64 0.00 1.99 1.38
time (sec) N/A 0.076 0.369 0.267 1.130 0.512 0.000 0.202 0.245
Problem 2 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 47 47 73 75 136 91 0 120 99
normalized size 1 1.00 1.55 1.60 2.89 1.94 0.00 2.55 2.11
time (sec) N/A 0.055 0.054 0.263 0.391 0.785 0.000 0.168 1.174
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 41 66 101 71 0 109 64
normalized size 1 1.00 0.93 1.50 2.30 1.61 0.00 2.48 1.45
time (sec) N/A 0.051 0.210 0.176 1.384 0.651 0.000 0.176 0.145
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 45 44 67 42 0 79 27
normalized size 1 1.00 1.80 1.76 2.68 1.68 0.00 3.16 1.08
time (sec) N/A 0.032 0.056 0.171 0.367 0.563 0.000 0.150 0.118
Problem 5 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 52 27 40 167 0 52 64
normalized size 1 1.00 2.00 1.04 1.54 6.42 0.00 2.00 2.46
time (sec) N/A 0.033 0.029 0.249 0.348 0.745 0.000 0.155 0.118
Problem 6 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 24 24 24 23 39 88 0 45 43
normalized size 1 1.00 1.00 0.96 1.62 3.67 0.00 1.88 1.79
time (sec) N/A 0.033 0.023 0.333 0.340 0.471 0.000 0.162 1.050
Problem 7 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 51 51 87 50 152 924 0 113 156
normalized size 1 1.00 1.71 0.98 2.98 18.12 0.00 2.22 3.06
time (sec) N/A 0.059 0.048 0.345 0.384 0.660 0.000 0.148 1.133
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 44 44 61 55 113 244 0 80 173
normalized size 1 1.00 1.39 1.25 2.57 5.55 0.00 1.82 3.93
time (sec) N/A 0.043 0.072 0.371 0.358 0.723 0.000 0.151 1.097
Problem 9 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 118 118 94 166 295 394 0 295 293
normalized size 1 1.00 0.80 1.41 2.50 3.34 0.00 2.50 2.48
time (sec) N/A 0.133 1.449 0.293 0.358 0.610 0.000 0.458 0.309
Problem 10 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 77 77 71 148 265 259 0 290 215
normalized size 1 1.00 0.92 1.92 3.44 3.36 0.00 3.77 2.79
time (sec) N/A 0.098 0.538 0.293 0.365 0.524 0.000 0.420 0.287
Problem 11 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 79 79 70 118 217 291 0 215 248
normalized size 1 1.00 0.89 1.49 2.75 3.68 0.00 2.72 3.14
time (sec) N/A 0.111 0.902 0.210 0.347 0.476 0.000 0.326 1.177
Problem 12 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 49 49 46 98 171 167 0 162 154
normalized size 1 1.00 0.94 2.00 3.49 3.41 0.00 3.31 3.14
time (sec) N/A 0.053 0.341 0.210 0.354 0.545 0.000 0.216 0.191
Problem 13 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 51 51 50 63 196 890 0 126 160
normalized size 1 1.00 0.98 1.24 3.84 17.45 0.00 2.47 3.14
time (sec) N/A 0.065 0.169 0.243 0.349 0.897 0.000 0.232 0.154
Problem 14 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 46 46 43 68 136 264 0 86 209
normalized size 1 1.00 0.93 1.48 2.96 5.74 0.00 1.87 4.54
time (sec) N/A 0.057 0.492 0.431 0.339 0.516 0.000 0.265 1.157
Problem 15 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 82 82 96 67 181 2462 0 168 261
normalized size 1 1.00 1.17 0.82 2.21 30.02 0.00 2.05 3.18
time (sec) N/A 0.119 1.591 0.382 0.316 0.514 0.000 0.266 0.162
Problem 16 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 72 72 59 81 210 393 0 143 143
normalized size 1 1.00 0.82 1.12 2.92 5.46 0.00 1.99 1.99
time (sec) N/A 0.079 0.520 0.455 0.319 0.714 0.000 0.259 1.080
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 182 182 125 246 480 879 0 507 730
normalized size 1 1.00 0.69 1.35 2.64 4.83 0.00 2.79 4.01
time (sec) N/A 0.222 3.925 0.357 0.340 0.551 0.000 0.793 1.390
Problem 18 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 105 105 91 239 439 540 0 442 361
normalized size 1 1.00 0.87 2.28 4.18 5.14 0.00 4.21 3.44
time (sec) N/A 0.123 0.303 0.319 0.350 0.588 0.000 0.660 0.412
Problem 19 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 122 139 95 180 377 725 0 395 668
normalized size 1 1.14 0.78 1.48 3.09 5.94 0.00 3.24 5.48
time (sec) N/A 0.185 2.198 0.234 0.329 0.875 0.000 0.643 0.315
Problem 20 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 70 70 63 170 321 383 0 322 308
normalized size 1 1.00 0.90 2.43 4.59 5.47 0.00 4.60 4.40
time (sec) N/A 0.068 0.880 0.230 0.326 0.636 0.000 0.391 1.245
Problem 21 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 84 84 79 118 560 2277 0 262 317
normalized size 1 1.00 0.94 1.40 6.67 27.11 0.00 3.12 3.77
time (sec) N/A 0.084 0.326 0.245 0.325 0.793 0.000 0.365 0.246
Problem 22 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 64 64 70 141 348 572 0 202 590
normalized size 1 1.00 1.09 2.20 5.44 8.94 0.00 3.16 9.22
time (sec) N/A 0.064 0.714 0.510 0.326 0.487 0.000 0.443 1.235
Problem 23 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 152 152 127 103 403 5037 0 281 412
normalized size 1 1.00 0.84 0.68 2.65 33.14 0.00 1.85 2.71
time (sec) N/A 0.225 6.197 0.391 0.332 0.967 0.000 0.495 1.256
Problem 24 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 98 98 87 136 493 925 0 257 622
normalized size 1 1.00 0.89 1.39 5.03 9.44 0.00 2.62 6.35
time (sec) N/A 0.097 1.255 0.529 0.344 0.594 0.000 0.462 0.279
Problem 25 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 118 118 93 865 514 2024 0 301 250
normalized size 1 1.00 0.79 7.33 4.36 17.15 0.00 2.55 2.12
time (sec) N/A 0.172 0.273 0.344 0.510 0.802 0.000 1.093 1.678
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 135 202 0 1367 0 810 955
normalized size 1 1.00 1.80 2.69 0.00 18.23 0.00 10.80 12.73
time (sec) N/A 0.128 0.577 0.301 0.000 0.650 0.000 0.495 2.655
Problem 27 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 78 78 67 605 316 916 0 176 198
normalized size 1 1.00 0.86 7.76 4.05 11.74 0.00 2.26 2.54
time (sec) N/A 0.104 0.153 0.316 0.461 0.566 0.000 0.590 1.512
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 107 104 0 666 0 1065 520
normalized size 1 1.00 2.02 1.96 0.00 12.57 0.00 20.09 9.81
time (sec) N/A 0.063 0.273 0.217 0.000 0.915 0.000 0.250 2.002
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 123 69 0 587 0 958 284
normalized size 1 1.00 2.24 1.25 0.00 10.67 0.00 17.42 5.16
time (sec) N/A 0.078 0.211 0.394 0.000 0.551 0.000 0.215 1.921
Problem 30 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 48 48 48 413 62 618 0 69 136
normalized size 1 1.00 1.00 8.60 1.29 12.88 0.00 1.44 2.83
time (sec) N/A 0.063 0.128 0.356 0.433 0.538 0.000 0.348 1.311
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 170 181 0 1790 0 475 787
normalized size 1 1.00 2.00 2.13 0.00 21.06 0.00 5.59 9.26
time (sec) N/A 0.119 0.697 0.391 0.000 1.272 0.000 0.377 1.802
Problem 32 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 70 70 71 750 134 1628 0 132 254
normalized size 1 1.00 1.01 10.71 1.91 23.26 0.00 1.89 3.63
time (sec) N/A 0.088 0.319 0.372 0.463 0.625 0.000 0.360 1.439
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 192 192 132 1246 1690 7366 0 525 -1
normalized size 1 1.00 0.69 6.49 8.80 38.36 0.00 2.73 -0.01
time (sec) N/A 0.252 1.039 0.350 0.718 1.078 0.000 1.906 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 160 267 0 5025 0 1929 -1
normalized size 1 1.00 1.29 2.15 0.00 40.52 0.00 15.56 -0.01
time (sec) N/A 0.218 1.371 0.321 0.000 0.755 0.000 0.943 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 105 1128 840 3918 0 400 -1
normalized size 1 1.00 0.80 8.55 6.36 29.68 0.00 3.03 -0.01
time (sec) N/A 0.165 0.737 0.335 0.586 0.812 0.000 1.132 0.000
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 133 167 0 2252 0 924 -1
normalized size 1 1.00 1.45 1.82 0.00 24.48 0.00 10.04 -0.01
time (sec) N/A 0.075 0.775 0.318 0.000 0.613 0.000 0.408 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 175 331 0 2614 0 1405 -1
normalized size 1 1.00 1.70 3.21 0.00 25.38 0.00 13.64 -0.01
time (sec) N/A 0.144 0.746 0.472 0.000 1.094 0.000 0.373 0.000
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 86 552 212 2562 0 227 -1
normalized size 1 1.00 1.05 6.73 2.59 31.24 0.00 2.77 -0.01
time (sec) N/A 0.076 0.502 0.459 0.505 0.633 0.000 0.621 0.000
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 141 141 203 367 0 6335 0 1074 -1
normalized size 1 1.00 1.44 2.60 0.00 44.93 0.00 7.62 -0.01
time (sec) N/A 0.209 4.346 0.463 0.000 0.733 0.000 0.713 0.000
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 113 113 114 1012 282 5062 0 221 -1
normalized size 1 1.00 1.01 8.96 2.50 44.80 0.00 1.96 -0.01
time (sec) N/A 0.154 0.929 0.467 0.550 0.859 0.000 0.563 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B F(-1) F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 240 240 184 2366 3392 0 0 923 -1
normalized size 1 1.00 0.77 9.86 14.13 0.00 0.00 3.85 -0.00
time (sec) N/A 0.345 0.858 0.394 1.120 0.000 0.000 3.004 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) F(-1) F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 166 166 227 341 0 0 0 1748 -1
normalized size 1 1.00 1.37 2.05 0.00 0.00 0.00 10.53 -0.01
time (sec) N/A 0.286 2.004 0.336 0.000 0.000 0.000 1.639 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 185 185 158 2110 1806 12965 0 584 -1
normalized size 1 1.00 0.85 11.41 9.76 70.08 0.00 3.16 -0.01
time (sec) N/A 0.251 1.340 0.355 0.817 1.712 0.000 1.940 0.000
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 126 126 157 252 0 7119 0 1718 -1
normalized size 1 1.00 1.25 2.00 0.00 56.50 0.00 13.63 -0.01
time (sec) N/A 0.097 1.828 0.305 0.000 1.381 0.000 0.615 0.000
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 156 156 236 1132 0 10716 0 2033 -1
normalized size 1 1.00 1.51 7.26 0.00 68.69 0.00 13.03 -0.01
time (sec) N/A 0.254 1.513 0.447 0.000 1.775 0.000 0.502 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 112 112 109 816 478 8312 0 351 -1
normalized size 1 1.00 0.97 7.29 4.27 74.21 0.00 3.13 -0.01
time (sec) N/A 0.087 1.060 0.439 0.619 0.675 0.000 0.802 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 196 196 269 1083 0 0 0 1877 -1
normalized size 1 1.00 1.37 5.53 0.00 0.00 0.00 9.58 -0.01
time (sec) N/A 0.334 4.447 0.476 0.000 0.000 0.000 1.026 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B F(-1) F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 151 149 1416 615 0 0 407 -1
normalized size 1 1.00 0.99 9.38 4.07 0.00 0.00 2.70 -0.01
time (sec) N/A 0.201 1.401 0.480 0.700 0.000 0.000 0.847 0.000
Problem 49 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 132 132 92 122 194 1530 0 206 156
normalized size 1 1.00 0.70 0.92 1.47 11.59 0.00 1.56 1.18
time (sec) N/A 0.172 0.200 0.299 0.418 0.571 0.000 0.251 0.269
Problem 50 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 98 98 104 129 174 1070 0 142 171
normalized size 1 1.00 1.06 1.32 1.78 10.92 0.00 1.45 1.74
time (sec) N/A 0.120 0.276 0.353 0.412 0.740 0.000 0.192 0.228
Problem 51 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 100 100 69 79 141 924 0 142 115
normalized size 1 1.00 0.69 0.79 1.41 9.24 0.00 1.42 1.15
time (sec) N/A 0.117 0.115 0.205 0.410 0.590 0.000 0.177 1.147
Problem 52 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 63 63 72 85 105 528 0 95 128
normalized size 1 1.00 1.14 1.35 1.67 8.38 0.00 1.51 2.03
time (sec) N/A 0.076 0.126 0.280 0.414 0.948 0.000 0.172 0.139
Problem 53 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 49 49 75 65 83 522 0 74 233
normalized size 1 1.00 1.53 1.33 1.69 10.65 0.00 1.51 4.76
time (sec) N/A 0.074 0.032 0.367 0.408 0.958 0.000 0.159 2.471
Problem 54 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 29 29 29 26 44 141 0 45 79
normalized size 1 1.00 1.00 0.90 1.52 4.86 0.00 1.55 2.72
time (sec) N/A 0.034 0.027 0.356 0.302 1.299 0.000 0.189 0.165
Problem 55 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 71 71 95 62 156 1188 0 143 173
normalized size 1 1.00 1.34 0.87 2.20 16.73 0.00 2.01 2.44
time (sec) N/A 0.090 0.028 0.452 0.421 1.683 0.000 0.165 2.481
Problem 56 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 56 56 74 60 184 1739 0 149 162
normalized size 1 1.00 1.32 1.07 3.29 31.05 0.00 2.66 2.89
time (sec) N/A 0.058 0.223 0.385 0.401 0.739 0.000 0.178 1.235
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 170 206 156 243 379 5034 0 376 359
normalized size 1 1.21 0.92 1.43 2.23 29.61 0.00 2.21 2.11
time (sec) N/A 0.297 2.829 0.320 0.408 0.749 0.000 0.711 0.444
Problem 58 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 182 182 121 250 348 3341 0 300 397
normalized size 1 1.00 0.66 1.37 1.91 18.36 0.00 1.65 2.18
time (sec) N/A 0.225 0.780 0.378 0.407 0.660 0.000 0.485 1.436
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 129 159 137 173 301 3649 0 298 306
normalized size 1 1.23 1.06 1.34 2.33 28.29 0.00 2.31 2.37
time (sec) N/A 0.205 1.602 0.252 0.411 0.742 0.000 0.444 1.360
Problem 60 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 123 123 90 179 253 2230 0 214 338
normalized size 1 1.00 0.73 1.46 2.06 18.13 0.00 1.74 2.75
time (sec) N/A 0.147 0.438 0.320 0.409 0.720 0.000 0.313 1.290
Problem 61 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 98 98 106 134 447 2498 0 178 522
normalized size 1 1.00 1.08 1.37 4.56 25.49 0.00 1.82 5.33
time (sec) N/A 0.136 0.171 0.392 0.407 0.775 0.000 0.285 3.283
Problem 62 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 47 47 94 98 256 518 0 122 483
normalized size 1 1.00 2.00 2.09 5.45 11.02 0.00 2.60 10.28
time (sec) N/A 0.058 0.252 0.457 0.315 0.566 0.000 0.322 1.264
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 107 107 138 108 378 4642 0 192 561
normalized size 1 1.00 1.29 1.01 3.53 43.38 0.00 1.79 5.24
time (sec) N/A 0.160 0.164 0.529 0.411 1.007 0.000 0.312 2.896
Problem 64 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 97 97 147 146 468 4125 0 249 344
normalized size 1 1.00 1.52 1.51 4.82 42.53 0.00 2.57 3.55
time (sec) N/A 0.098 0.218 0.493 0.410 0.617 0.000 0.331 0.261
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 275 306 294 385 647 0 0 708 682
normalized size 1 1.11 1.07 1.40 2.35 0.00 0.00 2.57 2.48
time (sec) N/A 0.494 6.271 0.409 0.432 0.000 0.000 1.633 1.703
Problem 66 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 351 351 291 506 604 8462 0 601 757
normalized size 1 1.00 0.83 1.44 1.72 24.11 0.00 1.71 2.16
time (sec) N/A 0.350 6.614 0.486 0.429 0.603 0.000 1.248 1.598
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 220 241 244 289 544 9862 0 592 617
normalized size 1 1.10 1.11 1.31 2.47 44.83 0.00 2.69 2.80
time (sec) N/A 0.315 6.253 0.293 0.425 0.637 0.000 1.276 0.556
Problem 68 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 269 269 233 410 484 6410 0 485 707
normalized size 1 1.00 0.87 1.52 1.80 23.83 0.00 1.80 2.63
time (sec) N/A 0.249 6.329 0.428 0.424 0.525 0.000 0.678 1.487
Problem 69 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 219 219 154 339 654 7127 0 422 671
normalized size 1 1.00 0.70 1.55 2.99 32.54 0.00 1.93 3.06
time (sec) N/A 0.264 3.206 0.524 0.433 0.550 0.000 0.598 6.399
Problem 70 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 71 71 113 171 679 1192 0 311 1515
normalized size 1 1.00 1.59 2.41 9.56 16.79 0.00 4.38 21.34
time (sec) N/A 0.065 0.770 0.505 0.336 0.404 0.000 0.765 1.378
Problem 71 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 232 232 243 286 586 10985 0 434 731
normalized size 1 1.00 1.05 1.23 2.53 47.35 0.00 1.87 3.15
time (sec) N/A 0.316 6.365 0.614 0.427 0.606 0.000 0.841 8.048
Problem 72 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 138 138 213 219 997 9459 0 437 646
normalized size 1 1.00 1.54 1.59 7.22 68.54 0.00 3.17 4.68
time (sec) N/A 0.115 0.197 0.556 0.426 0.582 0.000 0.825 0.540
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F F(-1) F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 491 491 645 603 0 0 0 362 3313
normalized size 1 1.00 1.31 1.23 0.00 0.00 0.00 0.74 6.75
time (sec) N/A 0.892 4.831 0.509 0.000 0.000 0.000 0.759 4.355
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-1) F(-1) A F(-1)
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 33 0 826 346 0 0 0 344 -1
normalized size 1 0.00 25.03 10.48 0.00 0.00 0.00 10.42 -0.03
time (sec) N/A 0.046 0.535 0.467 0.000 0.000 0.000 3.164 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F C F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 384 384 423 356 0 10695 0 223 2100
normalized size 1 1.00 1.10 0.93 0.00 27.85 0.00 0.58 5.47
time (sec) N/A 0.629 3.813 0.459 0.000 1.413 0.000 0.365 2.815
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-1) F(-1) A A
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 31 0 409 164 0 0 0 189 4474
normalized size 1 0.00 13.19 5.29 0.00 0.00 0.00 6.10 144.32
time (sec) N/A 0.028 0.269 0.528 0.000 0.000 0.000 1.841 87.988
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-1) A A A
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 31 0 319 98 0 0 0 147 3679
normalized size 1 0.00 10.29 3.16 0.00 0.00 0.00 4.74 118.68
time (sec) N/A 0.041 0.179 0.619 0.000 0.000 0.000 1.398 16.503
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 157 157 190 121 0 640 0 21 669
normalized size 1 1.00 1.21 0.77 0.00 4.08 0.00 0.13 4.26
time (sec) N/A 0.140 0.148 0.570 0.000 0.720 0.000 0.252 8.707
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A F(-1) A A A
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 33 0 201 144 0 0 0 68 3643
normalized size 1 0.00 6.09 4.36 0.00 0.00 0.00 2.06 110.39
time (sec) N/A 0.047 0.386 0.595 0.000 0.000 0.000 0.788 26.921
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C C F C F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 215 215 322 187 0 1954 0 180 4563
normalized size 1 1.00 1.50 0.87 0.00 9.09 0.00 0.84 21.22
time (sec) N/A 0.239 3.618 0.600 0.000 1.869 0.000 0.285 3.218
Problem 81 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 63 63 44 82 104 63 0 107 74
normalized size 1 1.00 0.70 1.30 1.65 1.00 0.00 1.70 1.17
time (sec) N/A 0.050 0.169 0.325 0.349 0.412 0.000 0.177 0.212
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 44 37 83 45 0 94 74
normalized size 1 1.00 1.47 1.23 2.77 1.50 0.00 3.13 2.47
time (sec) N/A 0.036 0.018 0.318 0.344 0.392 0.000 0.159 0.210
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 32 54 69 30 0 81 27
normalized size 1 1.00 0.97 1.64 2.09 0.91 0.00 2.45 0.82
time (sec) N/A 0.039 0.060 0.208 0.322 0.394 0.000 0.140 0.146
Problem 84 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 27 27 47 37 55 102 0 56 66
normalized size 1 1.00 1.74 1.37 2.04 3.78 0.00 2.07 2.44
time (sec) N/A 0.032 0.037 0.197 0.440 0.408 0.000 0.143 0.139
Problem 85 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 40 40 48 65 80 323 0 63 125
normalized size 1 1.00 1.20 1.62 2.00 8.08 0.00 1.58 3.12
time (sec) N/A 0.031 0.027 0.270 0.426 0.393 0.000 0.145 0.132
Problem 86 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 28 28 28 53 34 159 0 59 59
normalized size 1 1.00 1.00 1.89 1.21 5.68 0.00 2.11 2.11
time (sec) N/A 0.029 0.013 0.368 0.344 0.382 0.000 0.156 1.218
Problem 87 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 66 66 93 103 181 1046 0 132 280
normalized size 1 1.00 1.41 1.56 2.74 15.85 0.00 2.00 4.24
time (sec) N/A 0.046 0.034 0.386 0.438 0.401 0.000 0.154 1.251
Problem 88 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 48 48 86 75 371 345 0 95 304
normalized size 1 1.00 1.79 1.56 7.73 7.19 0.00 1.98 6.33
time (sec) N/A 0.040 0.053 0.361 0.347 0.393 0.000 0.159 0.165
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 63 124 171 95 0 189 102
normalized size 1 1.00 0.74 1.46 2.01 1.12 0.00 2.22 1.20
time (sec) N/A 0.087 0.327 0.380 0.361 0.412 0.000 0.388 0.266
Problem 90 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 54 54 71 98 161 519 0 164 130
normalized size 1 1.00 1.31 1.81 2.98 9.61 0.00 3.04 2.41
time (sec) N/A 0.060 0.458 0.274 0.502 0.419 0.000 0.364 0.257
Problem 91 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 51 51 54 96 140 105 0 170 77
normalized size 1 1.00 1.06 1.88 2.75 2.06 0.00 3.33 1.51
time (sec) N/A 0.076 0.411 0.213 0.340 0.427 0.000 0.276 1.289
Problem 92 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 60 60 54 122 152 774 0 137 182
normalized size 1 1.00 0.90 2.03 2.53 12.90 0.00 2.28 3.03
time (sec) N/A 0.082 0.178 0.306 0.446 0.428 0.000 0.248 0.237
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B B F A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 91 91 427 173 199 1373 0 157 303
normalized size 1 1.00 4.69 1.90 2.19 15.09 0.00 1.73 3.33
time (sec) N/A 0.085 7.277 0.370 0.461 0.418 0.000 0.203 0.162
Problem 94 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 49 49 49 126 53 391 0 169 482
normalized size 1 1.00 1.00 2.57 1.08 7.98 0.00 3.45 9.84
time (sec) N/A 0.053 0.213 0.458 0.329 0.402 0.000 0.229 1.240
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B B F B B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 125 125 792 236 345 2824 0 291 572
normalized size 1 1.00 6.34 1.89 2.76 22.59 0.00 2.33 4.58
time (sec) N/A 0.152 8.761 0.506 0.426 0.470 0.000 0.215 0.181
Problem 96 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 76 76 83 158 928 677 0 238 732
normalized size 1 1.00 1.09 2.08 12.21 8.91 0.00 3.13 9.63
time (sec) N/A 0.070 0.577 0.466 0.342 0.403 0.000 0.244 1.220
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 81 184 267 227 0 285 133
normalized size 1 1.00 0.89 2.02 2.93 2.49 0.00 3.13 1.46
time (sec) N/A 0.130 0.703 0.380 0.329 0.423 0.000 0.755 1.407
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B B F B B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 87 87 494 206 284 1840 0 279 232
normalized size 1 1.00 5.68 2.37 3.26 21.15 0.00 3.21 2.67
time (sec) N/A 0.105 6.885 0.380 0.431 0.451 0.000 0.656 0.355
Problem 99 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 78 78 69 148 256 369 0 267 243
normalized size 1 1.00 0.88 1.90 3.28 4.73 0.00 3.42 3.12
time (sec) N/A 0.090 0.969 0.240 0.410 0.411 0.000 0.599 0.289
Problem 100 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 99 99 89 257 295 2411 0 257 355
normalized size 1 1.00 0.90 2.60 2.98 24.35 0.00 2.60 3.59
time (sec) N/A 0.116 0.422 0.397 0.698 0.452 0.000 0.384 0.309
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B B B F B B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 149 149 1341 334 362 3465 0 321 535
normalized size 1 1.00 9.00 2.24 2.43 23.26 0.00 2.15 3.59
time (sec) N/A 0.154 16.676 0.421 0.432 0.446 0.000 0.309 1.394
Problem 102 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 67 67 67 227 71 786 0 347 1050
normalized size 1 1.00 1.00 3.39 1.06 11.73 0.00 5.18 15.67
time (sec) N/A 0.061 0.179 0.547 0.325 0.396 0.000 0.392 1.333
Problem 103 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 198 198 158 421 553 6114 0 517 951
normalized size 1 1.00 0.80 2.13 2.79 30.88 0.00 2.61 4.80
time (sec) N/A 0.239 11.837 0.589 0.693 1.184 0.000 0.410 1.364
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 218 269 1847 1185 0 447 1424
normalized size 1 1.00 2.14 2.64 18.11 11.62 0.00 4.38 13.96
time (sec) N/A 0.089 0.910 0.563 0.350 0.401 0.000 0.412 1.333
Problem 105 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 120 120 115 857 514 2180 0 326 967
normalized size 1 1.00 0.96 7.14 4.28 18.17 0.00 2.72 8.06
time (sec) N/A 0.168 0.303 0.465 0.509 0.482 0.000 1.068 1.930
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 79 468 0 1850 0 829 2194
normalized size 1 1.00 0.99 5.85 0.00 23.12 0.00 10.36 27.42
time (sec) N/A 0.109 0.430 0.444 0.000 0.493 0.000 0.487 2.877
Problem 107 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 77 77 77 608 316 948 0 172 880
normalized size 1 1.00 1.00 7.90 4.10 12.31 0.00 2.23 11.43
time (sec) N/A 0.103 0.161 0.432 0.616 0.447 0.000 0.564 1.933
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 53 315 0 766 0 1117 154
normalized size 1 1.00 1.00 5.94 0.00 14.45 0.00 21.08 2.91
time (sec) N/A 0.070 0.107 0.376 0.000 0.451 0.000 0.268 1.676
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 36 235 0 511 0 480 147
normalized size 1 1.00 1.00 6.53 0.00 14.19 0.00 13.33 4.08
time (sec) N/A 0.044 0.047 0.317 0.000 0.423 0.000 0.182 0.335
Problem 110 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 32 32 32 363 36 455 0 44 81
normalized size 1 1.00 1.00 11.34 1.12 14.22 0.00 1.38 2.53
time (sec) N/A 0.056 0.058 0.356 0.525 0.455 0.000 0.329 1.459
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 55 494 0 540 0 563 449
normalized size 1 1.00 1.00 8.98 0.00 9.82 0.00 10.24 8.16
time (sec) N/A 0.073 0.208 0.344 0.000 0.448 0.000 0.397 1.705
Problem 112 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 50 50 50 648 63 649 0 84 176
normalized size 1 1.00 1.00 12.96 1.26 12.98 0.00 1.68 3.52
time (sec) N/A 0.070 0.146 0.303 0.449 0.440 0.000 0.342 1.615
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 79 836 0 1584 0 428 1012
normalized size 1 1.00 0.92 9.72 0.00 18.42 0.00 4.98 11.77
time (sec) N/A 0.120 0.601 0.329 0.000 0.471 0.000 0.402 2.096
Problem 114 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 75 75 71 1077 140 2032 0 153 252
normalized size 1 1.00 0.95 14.36 1.87 27.09 0.00 2.04 3.36
time (sec) N/A 0.092 0.401 0.349 0.456 0.482 0.000 0.361 1.654
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 128 128 111 875 0 6934 0 2074 -1
normalized size 1 1.00 0.87 6.84 0.00 54.17 0.00 16.20 -0.01
time (sec) N/A 0.182 1.186 0.523 0.000 0.563 0.000 0.937 0.000
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 140 140 110 1146 840 4324 0 449 -1
normalized size 1 1.00 0.79 8.19 6.00 30.89 0.00 3.21 -0.01
time (sec) N/A 0.194 0.836 0.472 0.704 0.526 0.000 1.096 0.000
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 84 729 0 3502 0 1838 -1
normalized size 1 1.00 0.83 7.22 0.00 34.67 0.00 18.20 -0.01
time (sec) N/A 0.139 0.762 0.415 0.000 0.543 0.000 0.453 0.000
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 78 666 0 2041 0 1309 -1
normalized size 1 1.00 0.94 8.02 0.00 24.59 0.00 15.77 -0.01
time (sec) N/A 0.071 0.306 0.386 0.000 0.463 0.000 0.324 0.000
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 63 498 125 1515 0 138 -1
normalized size 1 1.00 0.95 7.55 1.89 22.95 0.00 2.09 -0.02
time (sec) N/A 0.066 0.268 0.400 0.518 0.435 0.000 0.558 0.000
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 69 375 0 1555 0 978 -1
normalized size 1 1.00 0.96 5.21 0.00 21.60 0.00 13.58 -0.01
time (sec) N/A 0.077 0.140 0.390 0.000 0.438 0.000 0.599 0.000
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 83 746 127 1443 0 156 -1
normalized size 1 1.00 1.08 9.69 1.65 18.74 0.00 2.03 -0.01
time (sec) N/A 0.079 0.327 0.367 0.538 0.444 0.000 0.554 0.000
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 203 1007 0 2140 0 1035 -1
normalized size 1 1.00 1.99 9.87 0.00 20.98 0.00 10.15 -0.01
time (sec) N/A 0.127 0.555 0.364 0.000 0.516 0.000 0.675 0.000
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 102 1283 209 2869 0 248 -1
normalized size 1 1.00 1.05 13.23 2.15 29.58 0.00 2.56 -0.01
time (sec) N/A 0.129 0.654 0.365 0.604 0.502 0.000 0.596 0.000
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 155 155 265 1477 0 6396 0 870 -1
normalized size 1 1.00 1.71 9.53 0.00 41.26 0.00 5.61 -0.01
time (sec) N/A 0.249 1.414 0.402 0.000 0.573 0.000 0.687 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 198 198 164 2132 1806 13887 0 595 -1
normalized size 1 1.00 0.83 10.77 9.12 70.14 0.00 3.01 -0.01
time (sec) N/A 0.310 1.424 0.514 1.048 0.714 0.000 1.913 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 136 1570 0 11392 0 2145 -1
normalized size 1 1.00 0.88 10.19 0.00 73.97 0.00 13.93 -0.01
time (sec) N/A 0.223 2.137 0.492 0.000 0.652 0.000 0.684 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 134 1676 0 7909 0 1137 -1
normalized size 1 1.00 0.93 11.64 0.00 54.92 0.00 7.90 -0.01
time (sec) N/A 0.141 1.184 0.451 0.000 0.565 0.000 0.445 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 96 96 77 764 366 5840 0 320 -1
normalized size 1 1.00 0.80 7.96 3.81 60.83 0.00 3.33 -0.01
time (sec) N/A 0.075 0.828 0.483 0.632 0.544 0.000 0.750 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 129 129 123 1226 0 6614 0 1495 -1
normalized size 1 1.00 0.95 9.50 0.00 51.27 0.00 11.59 -0.01
time (sec) N/A 0.120 0.724 0.486 0.000 0.567 0.000 0.991 0.000
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 115 1270 360 5659 0 332 -1
normalized size 1 1.00 1.00 11.04 3.13 49.21 0.00 2.89 -0.01
time (sec) N/A 0.097 1.051 0.401 0.697 0.534 0.000 0.731 0.000
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 88 634 0 5077 0 690 -1
normalized size 1 1.00 0.85 6.10 0.00 48.82 0.00 6.63 -0.01
time (sec) N/A 0.091 0.311 0.401 0.000 0.516 0.000 0.823 0.000
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 131 131 128 1776 332 5233 0 338 -1
normalized size 1 1.00 0.98 13.56 2.53 39.95 0.00 2.58 -0.01
time (sec) N/A 0.124 0.995 0.418 0.677 0.546 0.000 0.752 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 156 156 317 1907 0 8070 0 1040 -1
normalized size 1 1.00 2.03 12.22 0.00 51.73 0.00 6.67 -0.01
time (sec) N/A 0.228 3.382 0.402 0.000 0.598 0.000 0.929 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 97 128 199 339 82 134 50
normalized size 1 1.00 1.80 2.37 3.69 6.28 1.52 2.48 0.93
time (sec) N/A 0.052 0.039 0.015 0.328 0.412 0.553 0.210 1.218
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 43 104 168 1205 88 92 53
normalized size 1 1.00 0.88 2.12 3.43 24.59 1.80 1.88 1.08
time (sec) N/A 0.059 0.249 0.014 0.405 0.444 0.419 0.182 0.118
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 65 100 105 160 54 86 34
normalized size 1 1.00 1.81 2.78 2.92 4.44 1.50 2.39 0.94
time (sec) N/A 0.040 0.028 0.016 0.326 0.411 0.292 0.175 1.170
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 41 76 76 399 60 57 37
normalized size 1 1.00 1.32 2.45 2.45 12.87 1.94 1.84 1.19
time (sec) N/A 0.032 0.024 0.016 0.406 0.443 0.205 0.162 1.168
Problem 138 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 19 19 28 47 31 37 20 29 18
normalized size 1 1.00 1.47 2.47 1.63 1.95 1.05 1.53 0.95
time (sec) N/A 0.013 0.007 0.016 0.301 0.403 0.155 0.134 0.073
Problem 139 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 25 25 33 26 35 70 0 46 228
normalized size 1 1.00 1.32 1.04 1.40 2.80 0.00 1.84 9.12
time (sec) N/A 0.041 0.042 0.267 0.312 0.421 0.000 0.159 1.312
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 32 28 31 38 49 30 25
normalized size 1 1.00 1.78 1.56 1.72 2.11 2.72 1.67 1.39
time (sec) N/A 0.029 0.027 0.211 0.323 0.404 7.559 0.170 1.267
Problem 141 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 31 31 39 40 106 407 0 58 76
normalized size 1 1.00 1.26 1.29 3.42 13.13 0.00 1.87 2.45
time (sec) N/A 0.042 0.122 0.268 0.320 0.426 0.000 0.196 1.264
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 61 46 105 156 0 86 162
normalized size 1 1.00 1.69 1.28 2.92 4.33 0.00 2.39 4.50
time (sec) N/A 0.039 0.040 0.235 0.329 0.425 0.000 0.188 1.168
Problem 143 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 49 49 51 68 206 1216 0 93 177
normalized size 1 1.00 1.04 1.39 4.20 24.82 0.00 1.90 3.61
time (sec) N/A 0.062 0.335 0.252 0.337 0.432 0.000 0.236 1.246
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 190 236 369 796 165 300 91
normalized size 1 1.00 2.29 2.84 4.45 9.59 1.99 3.61 1.10
time (sec) N/A 0.079 0.082 0.016 0.344 0.416 1.110 0.318 0.180
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 66 196 333 3441 170 191 100
normalized size 1 1.00 0.87 2.58 4.38 45.28 2.24 2.51 1.32
time (sec) N/A 0.110 0.426 0.016 0.429 0.475 0.886 0.287 1.315
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 137 189 231 483 117 218 67
normalized size 1 1.00 2.17 3.00 3.67 7.67 1.86 3.46 1.06
time (sec) N/A 0.076 0.053 0.017 0.338 0.429 0.643 0.256 1.300
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 50 149 186 1638 122 116 76
normalized size 1 1.00 0.88 2.61 3.26 28.74 2.14 2.04 1.33
time (sec) N/A 0.073 0.323 0.016 0.420 0.431 0.474 0.222 1.206
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 65 144 114 201 68 103 47
normalized size 1 1.00 1.51 3.35 2.65 4.67 1.58 2.40 1.09
time (sec) N/A 0.031 0.750 0.019 0.327 0.396 0.322 0.144 1.243
Problem 149 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 49 49 48 60 104 668 0 141 210
normalized size 1 1.00 0.98 1.22 2.12 13.63 0.00 2.88 4.29
time (sec) N/A 0.077 0.135 0.264 0.422 0.417 0.000 0.208 1.319
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 64 49 64 97 0 71 59
normalized size 1 1.00 1.78 1.36 1.78 2.69 0.00 1.97 1.64
time (sec) N/A 0.067 0.107 0.209 0.347 0.391 0.000 0.253 1.244
Problem 151 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 52 52 50 60 134 677 0 141 211
normalized size 1 1.00 0.96 1.15 2.58 13.02 0.00 2.71 4.06
time (sec) N/A 0.095 0.171 0.267 0.330 0.434 0.000 0.270 1.415
Problem 152 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 43 43 65 59 114 197 0 103 175
normalized size 1 1.00 1.51 1.37 2.65 4.58 0.00 2.40 4.07
time (sec) N/A 0.071 0.619 0.228 0.332 0.404 0.000 0.279 0.175
Problem 153 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 72 72 58 91 236 1649 0 118 197
normalized size 1 1.00 0.81 1.26 3.28 22.90 0.00 1.64 2.74
time (sec) N/A 0.099 0.429 0.288 0.335 0.465 0.000 0.335 1.272
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A B B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 98 87 231 473 0 218 529
normalized size 1 1.00 1.56 1.38 3.67 7.51 0.00 3.46 8.40
time (sec) N/A 0.077 0.094 0.238 0.351 0.410 0.000 0.360 0.204
Problem 155 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 92 92 74 138 390 3454 0 192 362
normalized size 1 1.00 0.80 1.50 4.24 37.54 0.00 2.09 3.93
time (sec) N/A 0.113 0.517 0.257 0.354 0.472 0.000 0.431 0.274
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 123 365 583 1563 260 534 138
normalized size 1 1.00 1.08 3.20 5.11 13.71 2.28 4.68 1.21
time (sec) N/A 0.101 1.519 0.017 0.368 0.449 2.091 0.539 0.260
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 98 307 540 7502 279 309 155
normalized size 1 1.00 0.92 2.87 5.05 70.11 2.61 2.89 1.45
time (sec) N/A 0.152 0.313 0.017 0.454 0.558 1.683 0.466 1.241
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 108 299 400 1036 192 418 106
normalized size 1 1.00 1.15 3.18 4.26 11.02 2.04 4.45 1.13
time (sec) N/A 0.093 1.724 0.017 0.347 0.431 1.200 0.394 1.218
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 76 241 351 4298 211 216 123
normalized size 1 1.00 0.92 2.90 4.23 51.78 2.54 2.60 1.48
time (sec) N/A 0.101 0.249 0.019 0.441 0.488 0.969 0.352 1.253
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 95 235 239 567 126 241 86
normalized size 1 1.00 1.28 3.18 3.23 7.66 1.70 3.26 1.16
time (sec) N/A 0.046 0.615 0.017 0.348 0.410 0.685 0.177 1.282
Problem 161 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 72 72 67 111 214 2381 0 267 380
normalized size 1 1.00 0.93 1.54 2.97 33.07 0.00 3.71 5.28
time (sec) N/A 0.098 0.547 0.286 0.437 0.468 0.000 0.331 0.401
Problem 162 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 59 59 81 80 147 341 0 135 218
normalized size 1 1.00 1.37 1.36 2.49 5.78 0.00 2.29 3.69
time (sec) N/A 0.080 2.312 0.246 0.341 0.428 0.000 0.413 1.308
Problem 163 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 72 72 63 94 203 1686 0 274 327
normalized size 1 1.00 0.88 1.31 2.82 23.42 0.00 3.81 4.54
time (sec) N/A 0.108 0.462 0.275 0.438 0.445 0.000 0.443 2.476
Problem 164 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 59 59 82 80 147 341 0 135 219
normalized size 1 1.00 1.39 1.36 2.49 5.78 0.00 2.29 3.71
time (sec) N/A 0.081 1.284 0.246 0.340 0.437 0.000 0.523 1.287
Problem 165 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 83 83 67 111 264 2393 0 267 381
normalized size 1 1.00 0.81 1.34 3.18 28.83 0.00 3.22 4.59
time (sec) N/A 0.117 0.583 0.270 0.350 0.461 0.000 0.577 0.395
Problem 166 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 74 74 100 100 239 557 0 241 568
normalized size 1 1.00 1.35 1.35 3.23 7.53 0.00 3.26 7.68
time (sec) N/A 0.089 1.781 0.283 0.349 0.441 0.000 0.557 1.299
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 76 161 420 4305 0 217 380
normalized size 1 1.00 0.74 1.56 4.08 41.80 0.00 2.11 3.69
time (sec) N/A 0.129 0.254 0.273 0.355 0.493 0.000 0.782 0.318
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 128 344 410 1176 209 447 133
normalized size 1 1.00 1.16 3.13 3.73 10.69 1.90 4.06 1.21
time (sec) N/A 0.070 1.793 0.018 0.353 0.427 1.276 0.216 0.200
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 160 160 170 472 624 2133 308 721 188
normalized size 1 1.00 1.06 2.95 3.90 13.33 1.92 4.51 1.18
time (sec) N/A 0.094 2.338 0.020 0.357 0.437 2.316 0.308 1.321
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 60 93 133 742 425 132 72
normalized size 1 1.00 0.91 1.41 2.02 11.24 6.44 2.00 1.09
time (sec) N/A 0.115 0.180 0.089 0.428 0.519 13.457 0.260 0.269
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 66 95 509 777 495 87 56
normalized size 1 1.00 1.12 1.61 8.63 13.17 8.39 1.47 0.95
time (sec) N/A 0.108 0.199 0.097 0.603 0.465 11.281 0.226 1.230
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 42 75 82 118 316 96 46
normalized size 1 1.00 0.91 1.63 1.78 2.57 6.87 2.09 1.00
time (sec) N/A 0.104 0.039 0.107 0.409 0.462 9.647 0.229 1.236
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 47 77 215 486 294 65 38
normalized size 1 1.00 1.02 1.67 4.67 10.57 6.39 1.41 0.83
time (sec) N/A 0.083 0.031 0.072 0.451 0.489 8.966 0.184 0.106
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 35 71 58 82 156 61 43
normalized size 1 1.00 0.83 1.69 1.38 1.95 3.71 1.45 1.02
time (sec) N/A 0.061 0.037 0.087 0.327 0.415 8.830 0.174 1.170
Problem 175 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 45 45 65 76 57 484 280 63 37
normalized size 1 1.00 1.44 1.69 1.27 10.76 6.22 1.40 0.82
time (sec) N/A 0.074 0.084 0.144 0.422 0.458 8.957 0.149 0.091
Problem 176 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 60 60 54 121 101 118 0 97 194
normalized size 1 1.00 0.90 2.02 1.68 1.97 0.00 1.62 3.23
time (sec) N/A 0.101 0.076 0.403 0.329 0.453 0.000 0.175 1.468
Problem 177 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 60 60 67 494 329 784 0 89 402
normalized size 1 1.00 1.12 8.23 5.48 13.07 0.00 1.48 6.70
time (sec) N/A 0.106 0.191 0.398 0.475 0.453 0.000 0.205 1.616
Problem 178 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 85 85 60 180 159 747 0 133 313
normalized size 1 1.00 0.71 2.12 1.87 8.79 0.00 1.56 3.68
time (sec) N/A 0.137 0.182 0.422 0.331 0.519 0.000 0.251 1.539
Problem 179 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 82 82 91 580 1038 2368 0 147 519
normalized size 1 1.00 1.11 7.07 12.66 28.88 0.00 1.79 6.33
time (sec) N/A 0.177 0.710 0.484 0.613 0.462 0.000 0.252 1.614
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 69 156 217 1141 0 194 170
normalized size 1 1.00 0.83 1.88 2.61 13.75 0.00 2.34 2.05
time (sec) N/A 0.150 0.560 0.101 0.438 0.549 0.000 0.446 1.609
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 90 172 1010 1950 0 195 1655
normalized size 1 1.00 1.01 1.93 11.35 21.91 0.00 2.19 18.60
time (sec) N/A 0.117 0.599 0.098 0.792 0.477 0.000 0.336 1.692
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 57 118 170 629 0 149 210
normalized size 1 1.00 0.79 1.64 2.36 8.74 0.00 2.07 2.92
time (sec) N/A 0.118 0.530 0.098 0.341 0.466 0.000 0.318 0.427
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 86 162 614 2025 0 177 106
normalized size 1 1.00 1.01 1.91 7.22 23.82 0.00 2.08 1.25
time (sec) N/A 0.108 0.472 0.096 0.605 0.461 0.000 0.307 0.660
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 55 113 170 623 0 149 129
normalized size 1 1.00 0.81 1.66 2.50 9.16 0.00 2.19 1.90
time (sec) N/A 0.086 0.466 0.120 0.342 0.443 0.000 0.266 1.466
Problem 185 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 89 89 97 172 206 1942 0 195 110
normalized size 1 1.00 1.09 1.93 2.31 21.82 0.00 2.19 1.24
time (sec) N/A 0.088 0.578 0.153 0.461 0.473 0.000 0.184 1.541
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 83 325 235 1148 0 195 -1
normalized size 1 1.00 0.87 3.42 2.47 12.08 0.00 2.05 -0.01
time (sec) N/A 0.149 2.164 0.464 0.335 0.563 0.000 0.314 0.000
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 111 1061 976 3725 0 336 -1
normalized size 1 1.00 0.93 8.92 8.20 31.30 0.00 2.82 -0.01
time (sec) N/A 0.194 1.863 0.422 0.637 0.502 0.000 0.361 0.000
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 93 383 402 3468 0 323 -1
normalized size 1 1.00 0.75 3.09 3.24 27.97 0.00 2.60 -0.01
time (sec) N/A 0.189 0.920 0.482 0.346 0.671 0.000 0.378 0.000
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 159 159 139 1137 2345 8482 0 281 -1
normalized size 1 1.00 0.87 7.15 14.75 53.35 0.00 1.77 -0.01
time (sec) N/A 0.283 1.565 0.469 1.084 0.593 0.000 0.442 0.000
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 144 352 3354 7528 0 408 2669
normalized size 1 1.00 1.00 2.44 23.29 52.28 0.00 2.83 18.53
time (sec) N/A 0.208 1.293 0.102 1.891 0.581 0.000 0.602 0.922
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 91 234 376 2584 3937 245 416
normalized size 1 1.00 0.83 2.15 3.45 23.71 36.12 2.25 3.82
time (sec) N/A 0.170 1.098 0.107 0.363 0.482 157.941 0.514 0.825
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 137 137 135 340 2432 7757 0 384 2574
normalized size 1 1.00 0.99 2.48 17.75 56.62 0.00 2.80 18.79
time (sec) N/A 0.195 1.150 0.121 1.345 0.578 0.000 0.488 1.856
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 80 196 384 2611 3434 245 397
normalized size 1 1.00 0.82 2.00 3.92 26.64 35.04 2.50 4.05
time (sec) N/A 0.138 0.505 0.104 0.367 0.480 157.413 0.477 1.805
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 137 137 137 340 1472 7791 0 388 255
normalized size 1 1.00 1.00 2.48 10.74 56.87 0.00 2.83 1.86
time (sec) N/A 0.157 1.166 0.108 0.901 0.577 0.000 0.441 3.471
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 77 193 378 2554 3442 245 235
normalized size 1 1.00 0.82 2.05 4.02 27.17 36.62 2.61 2.50
time (sec) N/A 0.105 0.592 0.120 0.370 0.467 157.269 0.394 2.255
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 142 142 147 352 507 7496 0 409 260
normalized size 1 1.00 1.04 2.48 3.57 52.79 0.00 2.88 1.83
time (sec) N/A 0.163 0.321 0.153 0.566 0.560 0.000 0.211 0.897
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 138 138 117 952 498 4800 0 295 -1
normalized size 1 1.00 0.85 6.90 3.61 34.78 0.00 2.14 -0.01
time (sec) N/A 0.205 1.756 0.499 0.397 0.873 0.000 0.491 0.000
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 178 178 166 2045 1944 11865 0 437 -1
normalized size 1 1.00 0.93 11.49 10.92 66.66 0.00 2.46 -0.01
time (sec) N/A 0.291 6.311 0.481 0.942 0.680 0.000 0.549 0.000
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 171 171 138 1020 770 10720 0 474 -1
normalized size 1 1.00 0.81 5.96 4.50 62.69 0.00 2.77 -0.01
time (sec) N/A 0.262 1.906 0.496 0.421 1.293 0.000 1.062 0.000
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B F(-1) F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 228 228 194 2139 4285 0 0 493 -1
normalized size 1 1.00 0.85 9.38 18.79 0.00 0.00 2.16 -0.00
time (sec) N/A 0.368 3.866 0.496 2.671 0.000 0.000 1.017 0.000
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B F(-1) F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 201 201 203 608 925 0 0 1356 3685
normalized size 1 1.00 1.01 3.02 4.60 0.00 0.00 6.75 18.33
time (sec) N/A 0.277 0.680 0.162 0.743 0.000 0.000 0.530 1.380
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 3 3 19 4 5 8 0 5 3
normalized size 1 1.00 6.33 1.33 1.67 2.67 0.00 1.67 1.00
time (sec) N/A 0.017 0.009 0.082 0.475 0.744 0.000 0.133 0.045
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 21 15 5 1 0 1 14
normalized size 1 1.00 1.31 0.94 0.31 0.06 0.00 0.06 0.88
time (sec) N/A 0.021 0.008 0.112 0.493 2.082 0.000 0.126 0.248
Problem 204 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 22 22 29 21 28 140 0 45 20
normalized size 1 1.00 1.32 0.95 1.27 6.36 0.00 2.05 0.91
time (sec) N/A 0.020 0.021 0.066 0.478 0.451 0.000 0.125 0.100
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 28 28 32 1 0 41 27
normalized size 1 1.00 0.80 0.80 0.91 0.03 0.00 1.17 0.77
time (sec) N/A 0.024 0.023 0.119 0.461 0.613 0.000 0.118 1.173
Problem 206 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 11 11 11 14 11 2 12 11 2
normalized size 1 1.00 1.00 1.27 1.00 0.18 1.09 1.00 0.18
time (sec) N/A 0.021 0.008 0.051 0.417 0.552 0.405 0.141 0.145
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 12 25 1 0 21 14
normalized size 1 1.00 1.00 0.92 1.92 0.08 0.00 1.62 1.08
time (sec) N/A 0.021 0.007 0.089 0.421 0.461 0.000 0.130 0.095
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 85 288 0 4529 97 980 119
normalized size 1 1.00 0.98 3.31 0.00 52.06 1.11 11.26 1.37
time (sec) N/A 0.161 0.521 0.134 0.000 0.867 6.393 2.950 9.603
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 580 337 0 9360 0 938 -1
normalized size 1 1.00 4.79 2.79 0.00 77.36 0.00 7.75 -0.01
time (sec) N/A 0.200 6.217 0.104 0.000 0.951 0.000 3.036 0.000
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 60 253 0 2329 71 630 66
normalized size 1 1.00 0.95 4.02 0.00 36.97 1.13 10.00 1.05
time (sec) N/A 0.119 0.176 0.091 0.000 0.584 4.277 2.177 3.465
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 193 276 0 4825 0 554 -1
normalized size 1 1.00 2.27 3.25 0.00 56.76 0.00 6.52 -0.01
time (sec) N/A 0.125 3.437 0.089 0.000 0.685 0.000 1.744 0.000
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 44 238 0 1543 51 349 51
normalized size 1 1.00 1.00 5.41 0.00 35.07 1.16 7.93 1.16
time (sec) N/A 0.077 0.028 0.096 0.000 0.505 2.257 0.989 1.694
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 137 238 0 3443 0 253 -1
normalized size 1 1.00 2.28 3.97 0.00 57.38 0.00 4.22 -0.02
time (sec) N/A 0.047 0.235 0.106 0.000 0.571 0.000 0.690 0.000
Problem 214 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 56 56 56 0 0 3467 0 255 -1
normalized size 1 1.00 1.00 0.00 0.00 61.91 0.00 4.55 -0.02
time (sec) N/A 0.112 0.031 0.384 0.000 0.602 0.000 0.765 0.000
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 42 0 0 1539 0 348 -1
normalized size 1 1.00 0.88 0.00 0.00 32.06 0.00 7.25 -0.02
time (sec) N/A 0.093 0.135 0.338 0.000 0.506 0.000 1.072 0.000
Problem 216 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 83 83 83 0 0 4891 0 557 -1
normalized size 1 1.00 1.00 0.00 0.00 58.93 0.00 6.71 -0.01
time (sec) N/A 0.155 0.223 0.353 0.000 0.794 0.000 1.757 0.000
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F B F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 78 78 161 0 0 2355 0 629 -1
normalized size 1 1.00 2.06 0.00 0.00 30.19 0.00 8.06 -0.01
time (sec) N/A 0.146 6.218 0.348 0.000 0.599 0.000 2.215 0.000
Problem 218 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 121 121 111 0 0 9642 0 947 -1
normalized size 1 1.00 0.92 0.00 0.00 79.69 0.00 7.83 -0.01
time (sec) N/A 0.213 0.630 0.358 0.000 0.961 0.000 3.118 0.000
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 86 593 0 4941 175 1063 112
normalized size 1 1.00 1.05 7.23 0.00 60.26 2.13 12.96 1.37
time (sec) N/A 0.152 0.444 0.075 0.000 0.832 29.540 4.081 10.989
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 584 633 0 0 0 949 -1
normalized size 1 1.00 4.75 5.15 0.00 0.00 0.00 7.72 -0.01
time (sec) N/A 0.244 6.270 0.073 0.000 0.000 0.000 3.671 0.000
Problem 221 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 59 578 0 2385 128 662 64
normalized size 1 1.00 0.94 9.17 0.00 37.86 2.03 10.51 1.02
time (sec) N/A 0.101 0.175 0.059 0.000 2.124 17.584 2.591 3.711
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 161 578 0 4841 0 584 -1
normalized size 1 1.00 1.83 6.57 0.00 55.01 0.00 6.64 -0.01
time (sec) N/A 0.085 0.367 0.089 0.000 3.055 0.000 1.997 0.000
Problem 223 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 71 71 71 0 0 4039 0 433 -1
normalized size 1 1.00 1.00 0.00 0.00 56.89 0.00 6.10 -0.01
time (sec) N/A 0.136 0.069 0.313 0.000 0.645 0.000 2.776 0.000
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 197 0 0 3913 0 430 -1
normalized size 1 1.00 2.56 0.00 0.00 50.82 0.00 5.58 -0.01
time (sec) N/A 0.127 3.005 0.300 0.000 0.641 0.000 2.795 0.000
Problem 225 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 51 97 0 679 0 104 68
normalized size 1 1.00 1.65 3.13 0.00 21.90 0.00 3.35 2.19
time (sec) N/A 0.027 0.063 0.135 0.000 0.458 0.000 0.154 0.235
Problem 226 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F C F C B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 53 142 0 228 0 104 43
normalized size 1 1.00 1.18 3.16 0.00 5.07 0.00 2.31 0.96
time (sec) N/A 0.035 0.037 0.123 0.000 0.427 0.000 0.166 1.343
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 74 158 0 1027 0 202 78
normalized size 1 1.00 1.48 3.16 0.00 20.54 0.00 4.04 1.56
time (sec) N/A 0.039 0.148 0.100 0.000 0.429 0.000 0.139 0.287
Problem 228 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F C F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 76 211 0 361 0 204 -1
normalized size 1 1.00 1.13 3.15 0.00 5.39 0.00 3.04 -0.01
time (sec) N/A 0.047 0.075 0.106 0.000 0.405 0.000 0.172 0.000
Problem 229 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 68 164 0 2827 0 0 65
normalized size 1 1.00 0.97 2.34 0.00 40.39 0.00 0.00 0.93
time (sec) N/A 0.136 0.537 0.114 0.000 0.673 0.000 0.000 2.166
Problem 230 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 208 178 0 5494 0 0 -1
normalized size 1 1.00 2.36 2.02 0.00 62.43 0.00 0.00 -0.01
time (sec) N/A 0.123 4.900 0.128 0.000 0.769 0.000 0.000 0.000
Problem 231 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 47 129 0 1625 0 0 39
normalized size 1 1.00 1.00 2.74 0.00 34.57 0.00 0.00 0.83
time (sec) N/A 0.106 0.108 0.101 0.000 0.511 0.000 0.000 1.688
Problem 232 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 101 137 0 3361 0 0 -1
normalized size 1 1.00 1.68 2.28 0.00 56.02 0.00 0.00 -0.02
time (sec) N/A 0.093 0.512 0.102 0.000 0.668 0.000 0.000 0.000
Problem 233 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 29 114 0 1361 31 0 23
normalized size 1 1.00 1.00 3.93 0.00 46.93 1.07 0.00 0.79
time (sec) N/A 0.064 0.017 0.100 0.000 0.500 1.297 0.000 1.625
Problem 234 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 31 114 0 1287 0 188 25
normalized size 1 1.00 1.00 3.68 0.00 41.52 0.00 6.06 0.81
time (sec) N/A 0.027 0.024 0.109 0.000 0.481 0.000 0.322 1.571
Problem 235 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 56 56 56 0 0 3527 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 62.98 0.00 0.00 -0.02
time (sec) N/A 0.113 0.050 0.335 0.000 0.611 0.000 0.000 0.000
Problem 236 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 51 51 123 0 0 1565 0 0 -1
normalized size 1 1.00 2.41 0.00 0.00 30.69 0.00 0.00 -0.02
time (sec) N/A 0.095 6.180 0.360 0.000 0.599 0.000 0.000 0.000
Problem 237 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 88 88 107 0 0 5711 0 0 -1
normalized size 1 1.00 1.22 0.00 0.00 64.90 0.00 0.00 -0.01
time (sec) N/A 0.166 0.469 0.362 0.000 0.986 0.000 0.000 0.000
Problem 238 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 67 322 0 3991 0 0 70
normalized size 1 1.00 0.93 4.47 0.00 55.43 0.00 0.00 0.97
time (sec) N/A 0.163 0.113 0.084 0.000 0.864 0.000 0.000 2.521
Problem 239 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 188 328 0 6973 0 0 -1
normalized size 1 1.00 2.24 3.90 0.00 83.01 0.00 0.00 -0.01
time (sec) N/A 0.130 2.452 0.099 0.000 0.832 0.000 0.000 0.000
Problem 240 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 52 52 52 287 0 2525 0 0 45
normalized size 1 1.00 1.00 5.52 0.00 48.56 0.00 0.00 0.87
time (sec) N/A 0.123 0.130 0.081 0.000 0.536 0.000 0.000 2.060
Problem 241 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 112 289 0 2281 0 0 -1
normalized size 1 1.00 2.11 5.45 0.00 43.04 0.00 0.00 -0.02
time (sec) N/A 0.099 1.833 0.084 0.000 0.553 0.000 0.000 0.000
Problem 242 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 41 273 0 2277 51 0 41
normalized size 1 1.00 0.84 5.57 0.00 46.47 1.04 0.00 0.84
time (sec) N/A 0.086 0.035 0.083 0.000 0.669 23.264 0.000 1.942
Problem 243 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 56 56 223 272 0 2509 0 0 -1
normalized size 1 1.00 3.98 4.86 0.00 44.80 0.00 0.00 -0.02
time (sec) N/A 0.043 4.600 0.092 0.000 0.716 0.000 0.000 0.000
Problem 244 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 70 0 0 6955 0 0 -1
normalized size 1 1.00 0.90 0.00 0.00 89.17 0.00 0.00 -0.01
time (sec) N/A 0.146 0.077 0.332 0.000 1.007 0.000 0.000 0.000
Problem 245 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 230 0 0 3929 0 0 -1
normalized size 1 1.00 2.71 0.00 0.00 46.22 0.00 0.00 -0.01
time (sec) N/A 0.161 7.990 0.341 0.000 0.927 0.000 0.000 0.000
Problem 246 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F(-1) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 231 549 0 0 0 0 -1
normalized size 1 1.00 1.96 4.65 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.220 2.033 0.098 0.000 0.000 0.000 0.000 0.000
Problem 247 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 68 469 0 7033 0 0 92
normalized size 1 1.00 0.81 5.58 0.00 83.73 0.00 0.00 1.10
time (sec) N/A 0.181 0.116 0.101 0.000 1.579 0.000 0.000 4.013
Problem 248 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 132 491 0 5719 0 0 -1
normalized size 1 1.00 1.47 5.46 0.00 63.54 0.00 0.00 -0.01
time (sec) N/A 0.138 3.126 0.096 0.000 1.803 0.000 0.000 0.000
Problem 249 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 63 435 0 6621 0 0 82
normalized size 1 1.00 0.85 5.88 0.00 89.47 0.00 0.00 1.11
time (sec) N/A 0.144 0.093 0.083 0.000 1.431 0.000 0.000 3.824
Problem 250 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 88 88 259 454 0 6507 0 0 -1
normalized size 1 1.00 2.94 5.16 0.00 73.94 0.00 0.00 -0.01
time (sec) N/A 0.132 7.823 0.091 0.000 1.597 0.000 0.000 0.000
Problem 251 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 43 420 0 5779 73 0 76
normalized size 1 1.00 0.61 6.00 0.00 82.56 1.04 0.00 1.09
time (sec) N/A 0.103 0.047 0.084 0.000 1.396 30.763 0.000 3.556
Problem 252 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 93 93 976 420 0 6933 0 0 -1
normalized size 1 1.00 10.49 4.52 0.00 74.55 0.00 0.00 -0.01
time (sec) N/A 0.085 7.711 0.095 0.000 1.482 0.000 0.000 0.000
Problem 253 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F(-1) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 108 108 73 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 0.208 0.072 0.334 0.000 0.000 0.000 0.000 0.000
Problem 254 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 131 131 246 0 0 10671 0 0 -1
normalized size 1 1.00 1.88 0.00 0.00 81.46 0.00 0.00 -0.01
time (sec) N/A 0.242 7.766 0.350 0.000 2.491 0.000 0.000 0.000
Problem 255 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 35 62 0 543 0 58 63
normalized size 1 1.00 1.40 2.48 0.00 21.72 0.00 2.32 2.52
time (sec) N/A 0.019 0.023 0.131 0.000 0.446 0.000 0.119 0.171
Problem 256 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F C F C B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 37 66 0 175 0 58 22
normalized size 1 1.00 1.37 2.44 0.00 6.48 0.00 2.15 0.81
time (sec) N/A 0.020 0.021 0.125 0.000 0.407 0.000 0.137 1.200
Problem 257 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 112 95 163 194 2074 100 142 91
normalized size 1 1.26 1.07 1.83 2.18 23.30 1.12 1.60 1.02
time (sec) N/A 0.075 0.761 0.016 0.413 0.430 0.620 0.159 1.157
Problem 258 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A B B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 40 41 73 95 102 25 38
normalized size 1 1.00 1.05 1.08 1.92 2.50 2.68 0.66 1.00
time (sec) N/A 0.066 0.072 0.064 0.412 0.527 0.559 0.114 0.097
Problem 259 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 166 620 0 0 0 0 -1
normalized size 1 1.00 1.34 5.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.242 4.810 0.240 0.000 0.000 0.000 0.000 0.000
Problem 260 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 86 116 0 5136 0 0 -1
normalized size 1 1.00 0.97 1.30 0.00 57.71 0.00 0.00 -0.01
time (sec) N/A 0.128 0.062 0.118 0.000 0.649 0.000 0.000 0.000
Problem 261 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 40 37 0 1286 0 0 -1
normalized size 1 1.00 1.00 0.92 0.00 32.15 0.00 0.00 -0.02
time (sec) N/A 0.078 0.018 0.128 0.000 0.639 0.000 0.000 0.000
Problem 262 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 73 431 0 3914 0 0 -1
normalized size 1 1.00 0.99 5.82 0.00 52.89 0.00 0.00 -0.01
time (sec) N/A 0.123 0.544 0.119 0.000 0.807 0.000 0.000 0.000
Problem 263 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 113 637 0 0 0 0 -1
normalized size 1 1.00 0.96 5.40 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.199 0.853 0.137 0.000 0.000 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 [258] had the largest ratio of [.6250]

Table 2.1:Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 5 5 1.00 21 0.238
2 A 3 2 1.00 21 0.095
3 A 4 4 1.00 21 0.190
4 A 3 2 1.00 19 0.105
5 A 3 3 1.00 19 0.158
6 A 3 2 1.00 21 0.095
7 A 4 4 1.00 21 0.190
8 A 3 2 1.00 21 0.095
9 A 6 5 1.00 23 0.217
10 A 3 2 1.00 23 0.087
11 A 5 5 1.00 23 0.217
12 A 3 2 1.00 21 0.095
13 A 4 3 1.00 21 0.143
14 A 3 2 1.00 23 0.087
15 A 5 5 1.00 23 0.217
16 A 3 2 1.00 23 0.087
17 A 6 5 1.00 23 0.217
18 A 3 2 1.00 23 0.087
19 A 6 5 1.14 23 0.217
20 A 3 2 1.00 21 0.095
21 A 4 3 1.00 21 0.143
22 A 3 2 1.00 23 0.087
23 A 6 5 1.00 23 0.217
24 A 3 2 1.00 23 0.087
25 A 6 6 1.00 23 0.261
26 A 4 4 1.00 23 0.174
27 A 5 5 1.00 23 0.217
28 A 3 3 1.00 21 0.143
29 A 4 4 1.00 21 0.190
30 A 3 3 1.00 23 0.130
31 A 5 5 1.00 23 0.217
32 A 4 4 1.00 23 0.174
33 A 7 6 1.00 23 0.261
34 A 5 4 1.00 23 0.174
35 A 6 6 1.00 23 0.261
36 A 4 4 1.00 21 0.190
37 A 5 5 1.00 21 0.238
38 A 4 4 1.00 23 0.174
39 A 6 6 1.00 23 0.261
40 A 5 4 1.00 23 0.174
41 A 8 6 1.00 23 0.261
42 A 6 5 1.00 23 0.217
43 A 7 6 1.00 23 0.261
44 A 5 4 1.00 21 0.190
45 A 6 6 1.00 21 0.286
46 A 5 4 1.00 23 0.174
47 A 7 6 1.00 23 0.261
48 A 6 5 1.00 23 0.217
49 A 8 5 1.00 21 0.238
50 A 9 6 1.00 21 0.286
51 A 7 5 1.00 21 0.238
52 A 7 6 1.00 19 0.316
53 A 5 3 1.00 19 0.158
54 A 3 2 1.00 21 0.095
55 A 6 3 1.00 21 0.143
56 A 3 2 1.00 21 0.095
57 A 8 5 1.21 23 0.217
58 A 12 8 1.00 23 0.348
59 A 7 5 1.23 23 0.217
60 A 10 8 1.00 21 0.381
61 A 8 5 1.00 21 0.238
62 A 3 2 1.00 23 0.087
63 A 9 5 1.00 23 0.217
64 A 3 2 1.00 23 0.087
65 A 8 5 1.11 23 0.217
66 A 20 8 1.00 23 0.348
67 A 7 5 1.10 23 0.217
68 A 17 8 1.00 21 0.381
69 A 13 5 1.00 21 0.238
70 A 3 2 1.00 23 0.087
71 A 14 6 1.00 23 0.261
72 A 3 2 1.00 23 0.087
73 A 11 10 1.00 23 0.435
74 A 0 0 0.00 0 0.000
75 A 11 10 1.00 23 0.435
76 A 0 0 0.00 0 0.000
77 A 0 0 0.00 0 0.000
78 A 8 8 1.00 23 0.348
79 A 0 0 0.00 0 0.000
80 A 12 11 1.00 23 0.478
81 A 4 4 1.00 21 0.190
82 A 2 1 1.00 21 0.048
83 A 3 3 1.00 21 0.143
84 A 3 3 1.00 19 0.158
85 A 3 3 1.00 19 0.158
86 A 2 1 1.00 21 0.048
87 A 4 4 1.00 21 0.190
88 A 3 2 1.00 21 0.095
89 A 4 4 1.00 23 0.174
90 A 4 3 1.00 23 0.130
91 A 5 4 1.00 23 0.174
92 A 5 4 1.00 21 0.190
93 A 4 4 1.00 21 0.190
94 A 3 2 1.00 23 0.087
95 A 5 5 1.00 23 0.217
96 A 3 2 1.00 23 0.087
97 A 6 5 1.00 23 0.217
98 A 5 4 1.00 23 0.174
99 A 5 4 1.00 23 0.174
100 A 6 5 1.00 21 0.238
101 A 5 5 1.00 21 0.238
102 A 3 2 1.00 23 0.087
103 A 6 6 1.00 23 0.261
104 A 3 2 1.00 23 0.087
105 A 6 6 1.00 23 0.261
106 A 4 3 1.00 23 0.130
107 A 5 5 1.00 23 0.217
108 A 3 3 1.00 21 0.143
109 A 2 2 1.00 21 0.095
110 A 2 2 1.00 23 0.087
111 A 4 4 1.00 23 0.174
112 A 3 3 1.00 23 0.130
113 A 5 5 1.00 23 0.217
114 A 4 3 1.00 23 0.130
115 A 5 4 1.00 23 0.174
116 A 6 6 1.00 23 0.261
117 A 5 4 1.00 21 0.190
118 A 3 3 1.00 21 0.143
119 A 3 3 1.00 23 0.130
120 A 3 3 1.00 23 0.130
121 A 3 3 1.00 23 0.130
122 A 5 5 1.00 23 0.217
123 A 5 4 1.00 23 0.174
124 A 6 6 1.00 23 0.261
125 A 7 6 1.00 23 0.261
126 A 6 5 1.00 21 0.238
127 A 4 4 1.00 21 0.190
128 A 4 3 1.00 23 0.130
129 A 4 4 1.00 23 0.174
130 A 4 4 1.00 23 0.174
131 A 4 3 1.00 23 0.130
132 A 4 4 1.00 23 0.174
133 A 6 6 1.00 23 0.261
134 A 4 3 1.00 21 0.143
135 A 3 3 1.00 21 0.143
136 A 3 3 1.00 21 0.143
137 A 2 2 1.00 19 0.105
138 A 3 2 1.00 12 0.167
139 A 3 2 1.00 19 0.105
140 A 2 2 1.00 21 0.095
141 A 3 3 1.00 21 0.143
142 A 4 4 1.00 21 0.190
143 A 4 4 1.00 21 0.190
144 A 4 3 1.00 23 0.130
145 A 4 3 1.00 23 0.130
146 A 4 3 1.00 23 0.130
147 A 4 3 1.00 21 0.143
148 A 4 3 1.00 14 0.214
149 A 4 3 1.00 21 0.143
150 A 4 3 1.00 23 0.130
151 A 4 3 1.00 23 0.130
152 A 4 3 1.00 23 0.130
153 A 4 3 1.00 23 0.130
154 A 4 3 1.00 23 0.130
155 A 4 3 1.00 23 0.130
156 A 4 3 1.00 23 0.130
157 A 4 3 1.00 23 0.130
158 A 4 3 1.00 23 0.130
159 A 4 3 1.00 21 0.143
160 A 4 3 1.00 14 0.214
161 A 4 3 1.00 21 0.143
162 A 4 3 1.00 23 0.130
163 A 4 3 1.00 23 0.130
164 A 4 3 1.00 23 0.130
165 A 4 3 1.00 23 0.130
166 A 4 3 1.00 23 0.130
167 A 4 3 1.00 23 0.130
168 A 4 3 1.00 14 0.214
169 A 4 3 1.00 14 0.214
170 A 4 3 1.00 23 0.130
171 A 5 5 1.00 23 0.217
172 A 4 3 1.00 23 0.130
173 A 4 4 1.00 23 0.174
174 A 5 4 1.00 21 0.190
175 A 3 3 1.00 14 0.214
176 A 4 3 1.00 21 0.143
177 A 5 5 1.00 23 0.217
178 A 4 3 1.00 23 0.130
179 A 6 6 1.00 23 0.261
180 A 4 3 1.00 23 0.130
181 A 5 5 1.00 23 0.217
182 A 4 3 1.00 23 0.130
183 A 5 5 1.00 23 0.217
184 A 4 3 1.00 21 0.143
185 A 5 5 1.00 14 0.357
186 A 4 3 1.00 21 0.143
187 A 6 6 1.00 23 0.261
188 A 4 3 1.00 23 0.130
189 A 7 6 1.00 23 0.261
190 A 6 6 1.00 23 0.261
191 A 4 3 1.00 23 0.130
192 A 6 6 1.00 23 0.261
193 A 4 3 1.00 23 0.130
194 A 6 6 1.00 23 0.261
195 A 4 3 1.00 21 0.143
196 A 6 6 1.00 14 0.429
197 A 4 3 1.00 21 0.143
198 A 7 7 1.00 23 0.304
199 A 4 3 1.00 23 0.130
200 A 8 7 1.00 23 0.304
201 A 7 6 1.00 14 0.429
202 A 3 3 1.00 12 0.250
203 A 4 4 1.00 10 0.400
204 A 4 4 1.00 12 0.333
205 A 5 5 1.00 10 0.500
206 A 3 3 1.00 12 0.250
207 A 3 3 1.00 10 0.300
208 A 7 6 1.00 17 0.353
209 A 8 7 1.00 17 0.412
210 A 6 6 1.00 17 0.353
211 A 7 6 1.00 17 0.353
212 A 5 5 1.00 15 0.333
213 A 6 5 1.00 12 0.417
214 A 7 5 1.00 15 0.333
215 A 5 5 1.00 17 0.294
216 A 8 6 1.00 17 0.353
217 A 6 6 1.00 17 0.353
218 A 9 7 1.00 17 0.412
219 A 7 6 1.00 17 0.353
220 A 8 7 1.00 17 0.412
221 A 6 5 1.00 15 0.333
222 A 7 6 1.00 12 0.500
223 A 8 6 1.00 15 0.400
224 A 7 6 1.00 17 0.353
225 A 5 5 1.00 10 0.500
226 A 6 5 1.00 12 0.417
227 A 6 6 1.00 10 0.600
228 A 7 6 1.00 12 0.500
229 A 6 5 1.00 17 0.294
230 A 7 6 1.00 17 0.353
231 A 5 5 1.00 17 0.294
232 A 6 5 1.00 17 0.294
233 A 4 4 1.00 15 0.267
234 A 3 3 1.00 12 0.250
235 A 7 5 1.00 15 0.333
236 A 5 5 1.00 17 0.294
237 A 8 6 1.00 17 0.353
238 A 6 5 1.00 17 0.294
239 A 7 6 1.00 17 0.353
240 A 5 5 1.00 17 0.294
241 A 4 4 1.00 17 0.235
242 A 5 5 1.00 15 0.333
243 A 4 4 1.00 12 0.333
244 A 8 6 1.00 15 0.400
245 A 6 6 1.00 17 0.353
246 A 8 7 1.00 17 0.412
247 A 6 5 1.00 17 0.294
248 A 6 6 1.00 17 0.353
249 A 6 6 1.00 17 0.353
250 A 6 6 1.00 17 0.353
251 A 6 5 1.00 15 0.333
252 A 6 6 1.00 12 0.500
253 A 9 7 1.00 15 0.467
254 A 7 7 1.00 17 0.412
255 A 3 3 1.00 10 0.300
256 A 3 3 1.00 12 0.250
257 A 6 4 1.26 14 0.286
258 A 6 5 1.00 8 0.625
259 A 9 8 1.00 15 0.533
260 A 8 7 1.00 15 0.467
261 A 4 4 1.00 15 0.267
262 A 6 6 1.00 15 0.400
263 A 7 7 1.00 15 0.467

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