We report the CPU time, expressed in seconds, needed to compute the roots of univariate polynomials with the following functions:
The experiments have been performed on a Pentium 200 MMX with 64MB RAM under the Linux
operating system. 
The set of test polynomials has been divided into the following classes: 
| Spiralp(x) = (x+1) (x+1+a) (x+1+a+a2) ...
    (x+1+a+a2+... +an),  | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 200 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| n | MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | n | ||
| 10 | 1.51 | 1.53 | 26.3 | 20.4 | 24.5 | 17.5 | 13 | 16 | 1.63 | 73 | 250 | 59 | 45.6 | 156 | 36.8 | 10 | ||
| 15 | 13.8 | 13.7 | 231 | 102 | 129 | 16.8 | 7.4 | 9.4 | 13.8 | - | 957 | 238 | - | 69 | 17 | 15 | ||
| 20 | 91 | 84.4 | 1860 | 400 | F | 22 | 4.7 | - | 92.4 | - | - | - | - | - | - | 20 | ||
| 25 | 279 | 227 | - | 1557 | - | - | 6.8 | - | 276 | - | - | - | - | - | - | 25 | ||
| Timings on a Pentium 200 MMX | ||||||||||||||||||
 
 
  
   
| Geometric - 1p(x) = (x+1) (x+a) (x+a2) ... (x+an-1),  | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 200 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| n | MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | n | ||
| 10 | . | 0.04 | 1 | 7 | 3.1 | 25 | 175 | 75 | . | . | . | . | 10 | |||||
| 15 | . | 0.05 | 2.9 | 32.4 | 14.8 | 58 | 648 | 296 | . | . | . | . | 15 | |||||
| 20 | . | 0.08 | F | 280 | 61.8 | - | 3496 | 772 | . | . | . | . | 20 | |||||
| 25 | . | 0.45 | F | F | >36000 | - | - | >45000 | . | . | . | . | 25 | |||||
| Timings on a Pentium 200 MMX | ||||||||||||||||||
 
 
  
   
| Geometric - 2p(x) = (x+1)(x+a)(x+a2)...(x+an-1),  | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 200 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| n | MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | n | ||
| 10 | . | 0.03 | 5.9 | 6 | 14.4 | 197 | 200 | 480 | . | . | . | . | 10 | |||||
| 15 | . | 0.07 | 45 | 54.4 | 38 | 643 | 777 | 543 | . | . | . | . | 15 | |||||
| 20 | . | 0.11 | 255 | 424 | 205 | 2322 | 3853 | 1859 | . | . | . | . | 20 | |||||
| 25 | . | 0.6 | F | >36000 | F | - | >60000 | - | . | . | . | . | 25 | |||||
| Timings on a Pentium 200 MMX | ||||||||||||||||||
| Truncated exponentialp(x) = 1 + x/1! + x2/2! + ... + xn/n!, | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 200 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| n | MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | n | ||
| 50 | . | 0.7 | 17.6 | 8.2 | 27.6 | 25 | 12 | 39 | . | . | . | . | 50 | |||||
| 100 | . | 7.4 | 364 | 726 | 243 | 49 | 98 | 33 | . | . | . | . | 100 | |||||
| 200 | . | 66 | F | - | 2434 | - | - | 37 | . | . | . | . | 200 | |||||
| .Timings on a Pentium 200 MMX | ||||||||||||||||||
 
 
  
   
| Easy polynomialp(x) = 1 + 2x + 3x2 + ... + (n+1)xn, | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 200 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| n | MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | n | ||
| 50 | . | 0.4 | 15.7 | 5.7 | 21.3 | 39 | 14 | 53 | . | . | . | . | 50 | |||||
| 100 | . | 1.7 | 164 | 25 | 156 | 97 | 15 | 92 | . | . | . | . | 100 | |||||
| 200 | . | 8.5 | 772 | 169 | >9600 | 91 | 20 | >1136 | . | . | . | . | 200 | |||||
| 400 | . | 35 | . | . | . | 400 | ||||||||||||
| 800 | . | 150 | . | . | . | . | 800 | |||||||||||
| 1600 | . | 725 | 
 | 
 | 
 | 
 | 
 | 
 | . | . | . | . | 1600 | |||||
| Timings on a Pentium 200 MMX | ||||||||||||||||||
 
 
  
   
| Roots of unityp(x) = xn -1, | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 200 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| n | MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | n | ||
| 50 | . | 0.2 | 0.2 | 0.7 | 20 | 1 | 3.5 | 100 | . | . | . | . | 50 | |||||
| 100 | . | 0.5 | 0.4 | 1.4 | 155 | 0.8 | 2.8 | 310 | . | . | . | . | 100 | |||||
| 200 | . | 1.7 | 1 | 3.6 | 1823 | 0.6 | 2 | 1072 | . | . | . | . | 200 | |||||
| 400 | . | 7.4 | 3.5 | 10 | - | 0.5 | 1.4 | - | . | . | . | . | 400 | |||||
| 800 | . | 25.7 | 12.8 | 43 | - | 0.5 | 1.7 | - | . | . | . | . | 800 | |||||
| Timings on a Pentium 200 MMX | ||||||||||||||||||
 
 
  
   
| Wilkinson's polynomialp(x) = (x-1) (x-2) ... (x-n), | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 200 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| n | MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | n | ||
| 20 | . | 0.2 | 1.5 | 15.1 | 3.5 | 8 | 76 | 18 | . | . | . | . | 20 | |||||
| 40 | . | 1.6 | 40.6 | 181 | 30.1 | 25 | 113 | 19 | . | . | . | . | 40 | |||||
| 80 | . | 19 | 277 | 1266 | 357 | 15 | 67 | 19 | . | . | . | . | 80 | |||||
| 160 | . | 243 | - | - | - | - | - | - | . | . | . | . | 160 | |||||
| Timings on a Pentium 200 MMX | ||||||||||||||||||
 
 
  
   
| Characteristic polynomial - 1Characteristic polynomial of a n×n band
    Toeplitz matrix  | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 200 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| n | MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | n | ||
| 128 | . | 8.5 | 424 | F | F | 50 | - | - | . | . | . | . | 128 | |||||
| 256 | . | 90 | 3017 | F | F | 33 | - | - | . | . | . | . | 256 | |||||
| Timings on a Pentium 200 MMX | ||||||||||||||||||
 
 
  
   
| Characteristic polynomial - 2Characteristic polynomial of a n×n band
    Toeplitz matrix  | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 200 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| n | MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | n | ||
| 128 | . | 23 | 439 | F | F | 19 | - | - | . | . | . | . | 128 | |||||
| 256 | . | 301 | >3600 | F | F | >12 | - | - | . | . | . | . | 256 | |||||
| Timings on a Pentium 200 MMX | ||||||||||||||||||
| Kameny polynomialp(x) = (c2 x2 - 3)2
    + c2 x9, | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 400 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| n | MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | n | ||
| 6 | 0.02 | 0.02 | 3.7 | 4 | 1.8 | 185 | 200 | 90 | 0.2 | 83 | 36 | 24 | 415 | 180 | 120 | 6 | ||
| 10 | 0.12 | 0.05 | 3.2 | 67 | 5.2 | 64 | 1340 | 104 | 0.3 | F | 55 | 29 | - | 165 | 87 | 10 | ||
| 20 | 0.3 | 0.05 | 3.2 | >2000 | 36.5 | 64 | >40000 | 730 | 0.7 | F | >1300 | 77 | - | 1857 | 110 | 20 | ||
| Timings on a Pentium 200 MMX | ||||||||||||||||||
 
 
  
   
| Mignotte-like polynomialp(x) = xn + (a x + 1)m, | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 400 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| n | MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | n | ||
| 20 | 0.04 | 0.09 | 12 | 13 | 9.3 | 120 | 130 | 93 | 0.2 | 83 | 36 | 24 | 415 | 180 | 120 | 20 | ||
| 100 | 0.42 | 0.77 | 1650 | >2000 | 587 | 2142 | >2597 | 726 | 0.3 | F | 55 | 29 | - | 165 | 87 | 100 | ||
| 200 | 1.5 | 2.13 | - | - | - | - | - | - | 0.7 | F | >1300 | 77 | - | 1857 | 110 | 200 | ||
| 500 | 16.7 | 19.9 | - | - | - | - | - | - | . | 500 | ||||||||
| Timings on a Pentium 200 MMX | ||||||||||||||||||
 
 
  
   
| Roots with large and small moduli - 1p(x) = x500 + 10200 x499 + 10500 x495 + 10499 x480 + 103 x3 + 3 102 x2 + 1. | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 400 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | ||||
| 23.1 | 19.7 | F | F | F | - | - | - | . | . | . | . | |||||||
| Timings on a Pentium 200 MMX | ||||||||||||||||||
 
 
  
   
| Roots with large and small moduli - 2p(x) = (x12 - (1020 x -
    1)4) (1 + (1020 + x)4 x8) | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 1000 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | ||||
| 0.64 | 0.33 | 1699 | >3000 | 83 | 5048 | >9090 | 251 | 5.4 | - | - | 1485 | - | - | 275 | ||||
| Timings on a Pentium 200 MMX | ||||||||||||||||||
| Mandelbrot polynomial - 1p(x) defined according to the recurrence
    equation  | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 1000 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| n | MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | n | ||
| 31 | . | 0.25 | 2.6 | 1.8 | 4.5 | 10 | 7.2 | 18 | . | . | . | . | 31 | |||||
| 63 | . | 1.83 | 26 | 175 | 26 | 14 | 95 | 14 | . | . | . | . | 63 | |||||
| 127 | . | 18.5 | 363 | 1382 | 356 | 19 | 74 | 19 | . | . | . | . | 127 | |||||
| 255 | . | 213 | 2781 | - | 2544 | 13 | - | 12 | . | . | . | . | 255 | |||||
| 511 | . | 3272 | . | . | . | . | 511 | |||||||||||
| Timings on a Pentium 200 MMX | ||||||||||||||||||
 
 
  
   
| Mandelbrot polynomial - 2p(x) defined according to the recurrence
    equation  | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 1000 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| n | MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | n | ||
| 31 | . | 0.12 | . | . | . | . | 31 | |||||||||||
| 63 | . | 0.6 | . | . | . | . | 63 | |||||||||||
| 127 | . | 3.33 | . | . | . | . | 127 | |||||||||||
| 255 | . | 23.7 | . | . | . | . | 255 | |||||||||||
| 511 | . | 163 | . | . | . | . | 511 | |||||||||||
| 1023 | . | 1122 | . | . | . | . | 1023 | |||||||||||
| 2047 | . | 8537 | . | . | . | . | 2047 | |||||||||||
| Timings on a Pentium 200 MMX | ||||||||||||||||||
| Kirrinnis polynomialp(x) = (x4 - 1 / 16)m  
    (x4 - (1 / 2 + e)4) 16m/e4, | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 400 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| n | MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | n | ||
| 10 | . | 6.9 (0.01) | 54.3 | 0.02 | 0.23 | 8 (5430) | 0.003 (2) | 0.03 (23) | . | . | . | . | 10 | |||||
| 20 | . | 7.2 (0.02) | >3600 | 0.4 | 0.23 | >500 (>180000) | 0.05 (20) | 0.03 (11) | . | . | . | . | 20 | |||||
| 40 | . | 39.9 | - | 1.1 | 7.7 | - | 0.03 | 0.2 | . | . | . | . | 40 | |||||
| Timings on a Pentium 200 MMX | ||||||||||||||||||
| Modified Kirrinnis polynomialp(x) = (x4 - 1 / 16)m  
    (x4 - (1 / 2 + e)4)16m/e4+x4m+4, | ||||||||||||||||||
| Isolate | Approximate 50 digits | Approximate 400 digits | ||||||||||||||||
| CPU | CPU | Speedup | CPU | Speedup | ||||||||||||||
| n | MPSolve | MPSolve | Math | Maple | Pari | Math | Maple | Pari | MPSolve | Math | Maple | Pari | Math | Maple | Pari | n | ||
| 10 | . | 2.4 | 4 | 110 | 29 | 1.6 | 45 | 12 | . | . | . | . | 10 | |||||
| 20 | . | 11 | 27 | - | 174 | 2.4 | - | 16 | . | . | . | . | 20 | |||||
| 40 | . | 81 | 227 | - | 1512 | 2.8 | - | 19 | . | . | . | . | 40 | |||||
| Timings on a Pentium 200 MMX | ||||||||||||||||||