Cody

# Problem 44344. The 5th Root

Solution 1431563

Submitted on 1 Feb 2018 by Yu Wang
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### Test Suite

Test Status Code Input and Output
1   Pass
filetext = fileread('fifth_root.m'); assert(isempty(strfind(filetext, '^')),'^ forbidden') assert(isempty(strfind(filetext, 'power')),'power() forbidden') assert(isempty(strfind(filetext, 'mpower')),'mpower() forbidden') assert(isempty(strfind(filetext, 'realpow')),'realpow() forbidden') assert(isempty(strfind(filetext, 'nthroot')),'nthroot() forbidden') assert(isempty(strfind(filetext, 'roots')),'roots() forbidden')

2   Pass
n = 1/9765625; assert(abs(fifth_root(n)-1/25)<1e-5)

A = 1.0000 x_k1 = 0.8000 y = 0.3277 A = 1.0000 x_k1 = 0.8000 y = 0.3277 x_k = 0.8000 A = 0.3277 x_k1 = 0.6400 y = 0.1074 x_k = 0.6400 A = 0.1074 x_k1 = 0.5120 y = 0.0352 x_k = 0.5120 A = 0.0352 x_k1 = 0.4096 y = 0.0115 x_k = 0.4096 A = 0.0115 x_k1 = 0.3277 y = 0.0038 x_k = 0.3277 A = 0.0038 x_k1 = 0.2621 y = 0.0012 x_k = 0.2621 A = 0.0012 x_k1 = 0.2097 y = 4.0561e-04 x_k = 0.2097 A = 4.0561e-04 x_k1 = 0.1678 y = 1.3288e-04 x_k = 0.1678 A = 1.3288e-04 x_k1 = 0.1343 y = 4.3516e-05 x_k = 0.1343 A = 4.3516e-05 x_k1 = 0.1075 y = 1.4233e-05 x_k = 0.1075 A = 1.4233e-05 x_k1 = 0.0861 y = 4.6370e-06 x_k = 0.0861 A = 4.6370e-06 x_k1 = 0.0693 y = 1.4930e-06 x_k = 0.0693 A = 1.4930e-06 x_k1 = 0.0563 y = 4.6369e-07 x_k = 0.0563 A = 4.6369e-07 x_k1 = 0.0471 y = 1.2901e-07 x_k = 0.0471 A = 1.2901e-07 x_k1 = 0.0418 y = 2.5736e-08 x_k = 0.0418 A = 2.5736e-08 x_k1 = 0.0402 y = 1.9862e-09 x_k = 0.0402 A = 1.9862e-09 x_k1 = 0.0400 y = 1.5059e-11 x_k = 0.0400 f = 0.0400

3   Pass
n = 1/5555; assert(abs(fifth_root(n)-0.178263811215444)<1e-5)

A = 0.9998 x_k1 = 0.8000 y = 0.3276 A = 0.9998 x_k1 = 0.8000 y = 0.3276 x_k = 0.8000 A = 0.3276 x_k1 = 0.6401 y = 0.1073 x_k = 0.6401 A = 0.1073 x_k1 = 0.5123 y = 0.0351 x_k = 0.5123 A = 0.0351 x_k1 = 0.4104 y = 0.0115 x_k = 0.4104 A = 0.0115 x_k1 = 0.3296 y = 0.0037 x_k = 0.3296 A = 0.0037 x_k1 = 0.2667 y = 0.0012 x_k = 0.2667 A = 0.0012 x_k1 = 0.2205 y = 3.4098e-04 x_k = 0.2205 A = 3.4098e-04 x_k1 = 0.1916 y = 7.8325e-05 x_k = 0.1916 A = 7.8325e-05 x_k1 = 0.1800 y = 8.9400e-06 x_k = 0.1800 A = 8.9400e-06 x_k1 = 0.1783 y = 1.6759e-07 x_k = 0.1783 A = 1.6759e-07 x_k1 = 0.1783 y = 6.2342e-11 x_k = 0.1783 f = 0.1783

4   Pass
n = 1/3125; assert(abs(fifth_root(n)-1/5)<1e-5)

A = 0.9997 x_k1 = 0.8001 y = 0.3275 A = 0.9997 x_k1 = 0.8001 y = 0.3275 x_k = 0.8001 A = 0.3275 x_k1 = 0.6402 y = 0.1072 x_k = 0.6402 A = 0.1072 x_k1 = 0.5125 y = 0.0351 x_k = 0.5125 A = 0.0351 x_k1 = 0.4110 y = 0.0114 x_k = 0.4110 A = 0.0114 x_k1 = 0.3310 y = 0.0037 x_k = 0.3310 A = 0.0037 x_k1 = 0.2701 y = 0.0011 x_k = 0.2701 A = 0.0011 x_k1 = 0.2281 y = 2.9792e-04 x_k = 0.2281 A = 2.9792e-04 x_k1 = 0.2061 y = 5.2175e-05 x_k = 0.2061 A = 5.2175e-05 x_k1 = 0.2004 y = 2.8449e-06 x_k = 0.2004 A = 2.8449e-06 x_k1 = 0.2000 y = 1.0010e-08 x_k = 0.2000 A = 1.0010e-08 x_k1 = 0.2000 y = 1.2525e-13 x_k = 0.2000 f = 0.2000

5   Pass
n = 1/125; assert(abs(fifth_root(n)-0.380730787743176)<1e-5)

A = 0.9920 x_k1 = 0.8016 y = 0.3230 A = 0.9920 x_k1 = 0.8016 y = 0.3230 x_k = 0.8016 A = 0.3230 x_k1 = 0.6452 y = 0.1038 x_k = 0.6452 A = 0.1038 x_k1 = 0.5254 y = 0.0320 x_k = 0.5254 A = 0.0320 x_k1 = 0.4413 y = 0.0087 x_k = 0.4413 A = 0.0087 x_k1 = 0.3952 y = 0.0016 x_k = 0.3952 A = 0.0016 x_k1 = 0.3818 y = 1.0823e-04 x_k = 0.3818 A = 1.0823e-04 x_k1 = 0.3807 y = 5.7638e-07 x_k = 0.3807 A = 5.7638e-07 x_k1 = 0.3807 y = 1.6609e-11 x_k = 0.3807 f = 0.3807

6   Pass
n = 1/5; assert(abs(fifth_root(n)-0.724779663677696)<1e-5)

A = 0.8000 x_k1 = 0.8400 y = 0.2182 A = 0.8000 x_k1 = 0.8400 y = 0.2182 x_k = 0.8400 A = 0.2182 x_k1 = 0.7523 y = 0.0410 x_k = 0.7523 A = 0.0410 x_k1 = 0.7267 y = 0.0027 x_k = 0.7267 A = 0.0027 x_k1 = 0.7248 y = 1.4354e-05 x_k = 0.7248 A = 1.4354e-05 x_k1 = 0.7248 y = 4.1205e-10 x_k = 0.7248 A = 4.1205e-10 x_k1 = 0.7248 y = 2.7756e-17 x_k = 0.7248 f = 0.7248

7   Pass
n = 1; assert(abs(fifth_root(n)-1)<1e-5)

A = 0 x_k1 = 1 y = 0 f = 1

8   Pass
n = 5; assert(abs(fifth_root(n)-1.37972966146121)<1e-5)

A = -4 x_k1 = 1.8000 y = 13.8957 A = -4 x_k1 = 1.8000 y = 13.8957 x_k = 1.8000 A = 13.8957 x_k1 = 1.5353 y = 3.5292 x_k = 1.5353 A = 3.5292 x_k1 = 1.4082 y = 0.5378 x_k = 1.4082 A = 0.5378 x_k1 = 1.3809 y = 0.0205 x_k = 1.3809 A = 0.0205 x_k1 = 1.3797 y = 3.3411e-05 x_k = 1.3797 A = 3.3411e-05 x_k1 = 1.3797 y = 8.9299e-11 x_k = 1.3797 f = 1.3797

9   Pass
n = 25; assert(abs(fifth_root(n)-1.90365393871588)<1e-5)

A = -24 x_k1 = 5.8000 y = 6.5386e+03 A = -24 x_k1 = 5.8000 y = 6.5386e+03 x_k = 5.8000 A = 6.5386e+03 x_k1 = 4.6444 y = 2.1360e+03 x_k = 4.6444 A = 2.1360e+03 x_k1 = 3.7263 y = 693.4190 x_k = 3.7263 A = 693.4190 x_k1 = 3.0070 y = 220.8312 x_k = 3.0070 A = 220.8312 x_k1 = 2.4667 y = 66.3281 x_k = 2.4667 A = 66.3281 x_k1 = 2.1084 y = 16.6672 x_k = 2.1084 A = 16.6672 x_k1 = 1.9398 y = 2.4618 x_k = 1.9398 A = 2.4618 x_k1 = 1.9050 y = 0.0867 x_k = 1.9050 A = 0.0867 x_k1 = 1.9037 y = 1.1980e-04 x_k = 1.9037 A = 1.1980e-04 x_k1 = 1.9037 y = 2.2962e-10 x_k = 1.9037 A = 2.2962e-10 x_k1 = 1.9037 y = 1.0658e-14 x_k = 1.9037 f = 1.9037

10   Pass
n = 50; assert(abs(fifth_root(n)-2.18672414788656)<1e-5)

A = -49 x_k1 = 10.8000 y = 1.4688e+05 A = -49 x_k1 = 10.8000 y = 1.4688e+05 x_k = 10.8000 A = 1.4688e+05 x_k1 = 8.6407 y = 4.8117e+04 x_k = 8.6407 A = 4.8117e+04 x_k1 = 6.9144 y = 1.5754e+04 x_k = 6.9144 A = 1.5754e+04 x_k1 = 5.5359 y = 5.1492e+03 x_k = 5.5359 A = 5.1492e+03 x_k1 = 4.4394 y = 1.6742e+03 x_k = 4.4394 A = 1.6742e+03 x_k1 = 3.5772 y = 535.7784 x_k = 3.5772 A = 535.7784 x_k1 = 2.9229 y = 163.3208 x_k = 2.9229 A = 163.3208 x_k1 = 2.4753 y = 42.9259 x_k = 2.4753 A = 42.9259 x_k1 = 2.2466 y = 7.2321 x_k = 2.2466 A = 7.2321 x_k1 = 2.1898 y = 0.3564 x_k = 2.1898 A = 0.3564 x_k1 = 2.1867 y = 0.0010 x_k = 2.1867 A = 0.0010 x_k1 = 2.1867 y = 8.1234e-09 x_k = 2.1867 A = 8.1234e-09 x_k1 = 2.1867 y = 1.4211e-14 x_k = 2.1867 f = 2.1867

11   Pass
n = 500; assert(abs(fifth_root(n)-3.46572421577573)<1e-5)

A = -499 x_k1 = 100.8000 y = 1.0406e+10 A = -499 x_k1 = 100.8000 y = 1.0406e+10 x_k = 100.8000 A = 1.0406e+10 x_k1 = 80.6400 y = 3.4100e+09 x_k = 80.6400 A = 3.4100e+09 x_k1 = 64.5120 y = 1.1174e+09 x_k = 64.5120 A = 1.1174e+09 x_k1 = 51.6096 y = 3.6614e+08 x_k = 51.6096 A = 3.6614e+08 x_k1 = 41.2877 y = 1.1998e+08 x_k = 41.2877 A = 1.1998e+08 x_k1 = 33.0302 y = 3.9314e+07 x_k = 33.0302 A = 3.9314e+07 x_k1 = 26.4242 y = 1.2882e+07 x_k = 26.4242 A = 1.2882e+07 x_k1 = 21.1396 y = 4.2212e+06 x_k = 21.1396 A = 4.2212e+06 x_k1 = 16.9122 y = 1.3831e+06 x_k = 16.9122 A = 1.3831e+06 x_k1 = 13.5310 y = 4.5307e+05 x_k = 13.5310 A = 4.5307e+05 x_k1 = 10.8278 y = 1.4833e+05 x_k = 10.8278 A = 1.4833e+05 x_k1 = 8.6695 y = 4.8474e+04 x_k = 8.6695 A = 4.8474e+04 x_k1 = 6.9533 y = 1.5754e+04 x_k = 6.9533 A = 1.5754e+04 x_k1 = 5.6054 y = 5.0340e+03 x_k = 5.6054 A = 5.0340e+03 x_k1 = 4.5856 y = 1.5276e+03 x_k = 4.5856 A = 1.5276e+03 x_k1 = 3.8947 y = 396.0711 x_k = 3.8947 A = 396.0711 x_k1 = 3.5504 y = 64.1050 x_k = 3.5504 A = 64.1050 x_k1 = 3.4697 y = 2.8485 x_k = 3.4697 A = 2.8485 x_k1 = 3.4657 y = 0.0064 x_k = 3.4657 A = 0.0064 x_k1 = 3.4657 y = 3.3251e-08 x_k = 3.4657 A = 3.3251e-08 x_k1 = 3.4657 y = 1.7053e-13 x_k = 3.4657 f = 3.4657

12   Pass
n = 3125; assert(abs(fifth_root(n)-5)<1e-5)

A = -3124 x_k1 = 625.8000 y = 9.5979e+13 A = -3124 x_k1 = 625.8000 y = 9.5979e+13 x_k = 625.8000 A = 9.5979e+13 x_k1 = 500.6400 y = 3.1451e+13 x_k = 500.6400 A = 3.1451e+13 x_k1 = 400.5120 y = 1.0306e+13 x_k = 400.5120 A = 1.0306e+13 x_k1 = 320.4096 y = 3.3770e+12 x_k = 320.4096 A = 3.3770e+12 x_k1 = 256.3277 y = 1.1066e+12 x_k = 256.3277 A = 1.1066e+12 x_k1 = 205.0621 y = 3.6260e+11 x_k = 205.0621 A = 3.6260e+11 x_k1 = 164.0497 y = 1.1882e+11 x_k = 164.0497 A = 1.1882e+11 x_k1 = 131.2398 y = 3.8934e+10 x_k = 131.2398 A = 3.8934e+10 x_k1 = 104.9918 y = 1.2758e+10 x_k = 104.9918 A = 1.2758e+10 x_k1 = 83.9935 y = 4.1805e+09 x_k = 83.9935 A = 4.1805e+09 x_k1 = 67.1948 y = 1.3699e+09 x_k = 67.1948 A = 1.3699e+09 x_k1 = 53.7559 y = 4.4888e+08 x_k = 53.7559 A = 4.4888e+08 x_k1 = 43.0048 y = 1.4709e+08 x_k = 43.0048 A = 1.4709e+08 x_k1 = 34.4040 y = 4.8197e+07 x_k = 34.4040 A = 4.8197e+07 x_k1 = 27.5236 y = 1.5792e+07 x_k = 27.5236 A = 1.5792e+07 x_k1 = 22.0200 y = 5.1740e+06 x_k = 22.0200 A = 5.1740e+06 x_k1 = 17.6187 y = 1.6946e+06 x_k = 17.6187 A = 1.6946e+06 x_k1 = 14.1014 y = 5.5446e+05 x_k = 14.1014 A = 5.5446e+05 x_k1 = 11.2969 y = 1.8087e+05 x_k = 11.2969 A = 1.8087e+05 x_k1 = 9.0759 y = 5.8457e+04 x_k = 9.0759 A = 5.8457e+04 x_k1 = 7.3529 y = 1.8367e+04 x_k = 7.3529 A = 1.8367e+04 x_k1 = 6.0961 y = 5.2940e+03 x_k = 6.0961 A = 5.2940e+03 x_k1 = 5.3294 y = 1.1744e+03 x_k = 5.3294 A = 1.1744e+03 x_k1 = 5.0383 y = 121.4948 x_k = 5.0383 A = 121.4948 x_k1 = 5.0006 y = 1.8051 x_k = 5.0006 A = 1.8051 x_k1 = 5.0000 y = 4.1680e-04 x_k = 5.0000 A = 4.1680e-04 x_k1 = 5.0000 y = 2.2737e-11 x_k = 5.0000 f = 5.0000

13   Pass
n = 759375; assert(abs(fifth_root(n)-15)<1e-5)

A = -759374 x_k1 = 1.5188e+05 y = 8.0806e+25 A = -759374 x_k1 = 1.5188e+05 y = 8.0806e+25 x_k = 1.5188e+05 A = 8.0806e+25 x_k1 = 1.2150e+05 y = 2.6478e+25 x_k = 1.2150e+05 A = 2.6478e+25 x_k1 = 9.7201e+04 y = 8.6765e+24 x_k = 9.7201e+04 A = 8.6765e+24 x_k1 = 7.7760e+04 y = 2.8431e+24 x_k = 7.7760e+04 A = 2.8431e+24 x_k1 = 6.2208e+04 y = 9.3163e+23 x_k = 6.2208e+04 A = 9.3163e+23 x_k1 = 4.9767e+04 y = 3.0528e+23 x_k = 4.9767e+04 A = 3.0528e+23 x_k1 = 3.9813e+04 y = 1.0003e+23 x_k = 3.9813e+04 A = 1.0003e+23 x_k1 = 3.1851e+04 y = 3.2779e+22 x_k = 3.1851e+04 A = 3.2779e+22 x_k1 = 2.5481e+04 y = 1.0741e+22 x_k = 2.5481e+04 A = 1.0741e+22 x_k1 = 2.0384e+04 y = 3.5196e+21 x_k = 2.0384e+04 A = 3.5196e+21 x_k1 = 1.6308e+04 y = 1.1533e+21 x_k = 1.6308e+04 A = 1.1533e+21 x_k1 = 1.3046e+04 y = 3.7791e+20 x_k = 1.3046e+04 A = 3.7791e+20 x_k1 = 1.0437e+04 y = 1.2383e+20 x_k = 1.0437e+04 A = 1.2383e+20 x_k1 = 8.3495e+03 y = 4.0578e+19 x_k = 8.3495e+03 A = 4.0578e+19 x_k1 = 6.6796e+03 y = 1.3297e+19 x_k = 6.6796e+03 A = 1.3297e+19 x_k1 = 5.3437e+03 y = 4.3570e+18 x_k = 5.3437e+03 A = 4.3570e+18 x_k1 = 4.2749e+03 y = 1.4277e+18 x_k = 4.2749e+03 A = 1.4277e+18 x_k1 = 3.4199e+03 y = 4.6783e+17 x_k = 3.4199e+03 A = 4.6783e+17 x_k1 = 2.7360e+03 y = 1.5330e+17 x_k = 2.7360e+03 A = 1.5330e+17 x_k1 = 2.1888e+03 y = 5.0233e+16 x_k = 2.1888e+03 A = 5.0233e+16 x_k1 = 1.7510e+03 y = 1.6460e+16 x_k = 1.7510e+03 A = 1.6460e+16 x_k1 = 1.4008e+03 y = 5.3938e+15 x_k = 1.4008e+03 A = 5.3938e+15 x_k1 = 1.1206e+03 y = 1.7674e+15 x_k = 1.1206e+03 A = 1.7674e+15 x_k1 = 896.5165 y = 5.7915e+14 x_k = 896.5165 A = 5.7915e+14 x_k1 = 717.2132 y = 1.8978e+14 x_k = 717.2132 A = 1.8978e+14 x_k1 = 573.7706 y = 6.2186e+13 x_k = 573.7706 A = 6.2186e+13 x_k1 = 459.0164 y = 2.0377e+13 x_k = 459.0164 A = 2.0377e+13 x_k1 = 367.2132 y = 6.6771e+12 x_k = 367.2132 A = 6.6771e+12 x_k1 = 293.7705 y = 2.1880e+12 x_k = 293.7705 A = 2.1880e+12 x_k1 = 235.0164 y = 7.1695e+11 x_k = 235.0164 A = 7.1695e+11 x_k1 = 188.0132 y = 2.3493e+11 x_k = 188.0132 A = 2.3493e+11 x_k1 = 150.4107 y = 7.6982e+10 x_k = 150.4107 A = 7.6982e+10 x_k1 = 120.3288 y = 2.5225e+10 x_k = 120.3288 A = 2.5225e+10 x_k1 = 96.2638 y = 8.2656e+09 x_k = 96.2638 A = 8.2656e+09 x_k1 = 77.0128 y = 2.7083e+09 x_k = 77.0128 A = 2.7083e+09 x_k1 = 61.6146 y = 8.8725e+08 x_k = 61.6146 A = 8.8725e+08 x_k1 = 49.3022 y = 2.9053e+08 x_k = 49.3022 A = 2.9053e+08 x_k1 = 39.4675 y = 9.5003e+07 x_k = 39.4675 A = 9.5003e+07 x_k1 = 31.6366 y = 3.0932e+07 x_k = 31.6366 A = 3.0932e+07 x_k1 = 25.4609 y = 9.9402e+06 x_k = 25.4609 A = 9.9402e+06 x_k1 = 20.7301 y = 3.0689e+06 x_k = 20.7301 A = 3.0689e+06 x_k1 = 17.4065 y = 8.3854e+05 x_k = 17.4065 A = 8.3854e+05 x_k1 = 15.5796 y = 1.5849e+05 x_k = 15.5796 A = 1.5849e+05 x_k1 = 15.0415 y = 1.0575e+04 x_k = 15.0415 A = 1.0575e+04 x_k1 = 15.0002 y = 57.9428 x_k = 15.0002 A = 57.9428 x_k1 = 15.0000 y = 0.0018 x_k = 15.0000 A = 0.0018 x_k1 = 15 y = 0 x_k = 15 f = 15

14   Pass
n = 9765625; assert(abs(fifth_root(n)-25)<1e-5)

A = -9765624 x_k1 = 1.9531e+06 y = 2.8422e+31 A = -9765624 x_k1 = 1.9531e+06 y = 2.8422e+31 x_k = 1.9531e+06 A = 2.8422e+31 x_k1 = 1.5625e+06 y = 9.3132e+30 x_k = 1.5625e+06 A = 9.3132e+30 x_k1 = 1.2500e+06 y = 3.0518e+30 x_k = 1.2500e+06 A = 3.0518e+30 x_k1 = 1.0000e+06 y = 1.0000e+30 x_k = 1.0000e+06 A = 1.0000e+30 x_k1 = 8.0000e+05 y = 3.2768e+29 x_k = 8.0000e+05 A = 3.2768e+29 x_k1 = 6.4000e+05 y = 1.0737e+29 x_k = 6.4000e+05 A = 1.0737e+29 x_k1 = 5.1200e+05 y = 3.5184e+28 x_k = 5.1200e+05 A = 3.5184e+28 x_k1 = 4.0960e+05 y = 1.1529e+28 x_k = 4.0960e+05 A = 1.1529e+28 x_k1 = 3.2768e+05 y = 3.7779e+27 x_k = 3.2768e+05 A = 3.7779e+27 x_k1 = 2.6214e+05 y = 1.2379e+27 x_k = 2.6214e+05 A = 1.2379e+27 x_k1 = 2.0972e+05 y = 4.0565e+26 x_k = 2.0972e+05 A = 4.0565e+26 x_k1 = 1.6777e+05 y = 1.3292e+26 x_k = 1.6777e+05 A = 1.3292e+26 x_k1 = 1.3422e+05 y = 4.3556e+25 x_k = 1.3422e+05 A = 4.3556e+25 x_k1 = 1.0737e+05 y = 1.4273e+25 x_k = 1.0737e+05 A = 1.4273e+25 x_k1 = 8.5899e+04 y = 4.6768e+24 x_k = 8.5899e+04 A = 4.6768e+24 x_k1 = 6.8720e+04 y = 1.5325e+24 x_k = 6.8720e+04 A = 1.5325e+24 x_k1 = 5.4976e+04 y = 5.0217e+23 x_k = 5.4976e+04 A = 5.0217e+23 x_k1 = 4.3980e+04 y = 1.6455e+23 x_k = 4.3980e+04 A = 1.6455e+23 x_k1 = 3.5184e+04 y = 5.3920e+22 x_k = 3.5184e+04 A = 5.3920e+22 x_k1 = 2.8148e+04 y = 1.7669e+22 x_k = 2.8148e+04 A = 1.7669e+22 x_k1 = 2.2518e+04 y = 5.7896e+21 x_k = 2.2518e+04 A = 5.7896e+21 x_k1 = 1.8014e+04 y = 1.8971e+21 x_k = 1.8014e+04 A = 1.8971e+21 x_k1 = 1.4412e+04 y = 6.2166e+20 x_k = 1.4412e+04 A = 6.2166e+20 x_k1 = 1.1529e+04 y = 2.0370e+20 x_k = 1.1529e+04 A = 2.0370e+20 x_k1 = 9.2234e+03 y = 6.6750e+19 x_k = 9.2234e+03 A = 6.6750e+19 x_k1 = 7.3787e+03 y = 2.1873e+19 x_k = 7.3787e+03 A = 2.1873e+19 x_k1 = 5.9030e+03 y = 7.1672e+18 x_k = 5.9030e+03 A = 7.1672e+18 x_k1 = 4.7224e+03 y = 2.3485e+18 x_k = 4.7224e+03 A = 2.3485e+18 x_k1 = 3.7779e+03 y = 7.6957e+17 x_k = 3.7779e+03 A = 7.6957e+17 x_k1 = 3.0223e+03 y = 2.5217e+17 x_k = 3.0223e+03 A = 2.5217e+17 x_k1 = 2.4179e+03 y = 8.2632e+16 x_k = 2.4179e+03 A = 8.2632e+16 x_k1 = 1.9343e+03 y = 2.7077e+16 x_k = 1.9343e+03 A = 2.7077e+16 x_k1 = 1.5474e+03 y = 8.8726e+15 x_k = 1.5474e+03 A = 8.8726e+15 x_k1 = 1.2379e+03 y = 2.9074e+15 x_k = 1.2379e+03 A = 2.9074e+15 x_k1 = 990.3524 y = 9.5268e+14 x_k = 990.3524 A = 9.5268e+14 x_k1 = 792.2820 y = 3.1218e+14 x_k = 792.2820 A = 3.1218e+14 x_k1 = 633.8256 y = 1.0229e+14 x_k = 633.8256 A = 1.0229e+14 x_k1 = 507.0605 y = 3.3520e+13 x_k = 507.0605 A = 3.3520e+13 x_k1 = 405.6484 y = 1.0984e+13 x_k = 405.6484 A = 1.0984e+13 x_k1 = 324.5188 y = 3.5991e+12 x_k = 324.5188 A = 3.5991e+12 x_k1 = 259.6152 y = 1.1794e+12 x_k = 259.6152 A = 1.1794e+12 x_k1 = 207.6926 y = 3.8645e+11 x_k = 207.6926 A = 3.8645e+11 x_k1 = 166.1551 y = 1.2663e+11 x_k = 166.1551 A = 1.2663e+11 x_k1 = 132.9267 y = 4.1491e+10 x_k = 132.9267 A = 4.1491e+10 x_k1 = 106.3476 y = 1.3593e+10 x_k = 106.3476 A = 1.3593e+10 x_k1 = 85.0933 y = 4.4517e+09 x_k = 85.0933 A = 4.4517e+09 x_k1 = 68.1119 y = 1.4562e+09 x_k = 68.1119 A = 1.4562e+09 x_k1 = 54.5803 y = 4.7461e+08 x_k = 54.5803 A = 4.7461e+08 x_k1 = 43.8843 y = 1.5299e+08 x_k = 43.8843 A = 1.5299e+08 x_k1 = 35.6341 y = 4.7689e+07 x_k = 35.6341 A = 4.7689e+07 x_k1 = 29.7186 y = 1.3416e+07 x_k = 29.7186 A = 1.3416e+07 x_k1 = 26.2788 y = 2.7665e+06 x_k = 26.2788 A = 2.7665e+06 x_k1 = 25.1185 y = 2.3374e+05 x_k = 25.1185 A = 2.3374e+05 x_k1 = 25.0011 y = 2.1753e+03 x_k = 25.0011 A = 2.1753e+03 x_k1 = 25.0000 y = 0.1938 x_k = 25.0000 A = 0.1938 x_k1 = 25 y = 0 x_k = 25 f = 25

15   Pass
n = 312500000; assert(abs(fifth_root(n)-50)<1e-5)

A = -312499999 x_k1 = 6.2500e+07 y = 9.5367e+38 A = -312499999 x_k1 = 6.2500e+07 y = 9.5367e+38 x_k = 6.2500e+07 A = 9.5367e+38 x_k1 = 5.0000e+07 y = 3.1250e+38 x_k = 5.0000e+07 A = 3.1250e+38 x_k1 = 4.0000e+07 y = 1.0240e+38 x_k = 4.0000e+07 A = 1.0240e+38 x_k1 = 3.2000e+07 y = 3.3554e+37 x_k = 3.2000e+07 A = 3.3554e+37 x_k1 = 2.5600e+07 y = 1.0995e+37 x_k = 2.5600e+07 A = 1.0995e+37 x_k1 = 2.0480e+07 y = 3.6029e+36 x_k = 2.0480e+07 A = 3.6029e+36 x_k1 = 1.6384e+07 y = 1.1806e+36 x_k = 1.6384e+07 A = 1.1806e+36 x_k1 = 1.3107e+07 y = 3.8686e+35 x_k = 1.3107e+07 A = 3.8686e+35 x_k1 = 1.0486e+07 y = 1.2677e+35 x_k = 1.0486e+07 A = 1.2677e+35 x_k1 = 8.3886e+06 y = 4.1538e+34 x_k = 8.3886e+06 A = 4.1538e+34 x_k1 = 6.7109e+06 y = 1.3611e+34 x_k = 6.7109e+06 A = 1.3611e+34 x_k1 = 5.3687e+06 y = 4.4601e+33 x_k = 5.3687e+06 A = 4.4601e+33 x_k1 = 4.2950e+06 y = 1.4615e+33 x_k = 4.2950e+06 A = 1.4615e+33 x_k1 = 3.4360e+06 y = 4.7890e+32 x_k = 3.4360e+06 A = 4.7890e+32 x_k1 = 2.7488e+06 y = 1.5693e+32 x_k = 2.7488e+06 A = 1.5693e+32 x_k1 = 2.1990e+06 y = 5.1422e+31 x_k = 2.1990e+06 A = 5.1422e+31 x_k1 = 1.7592e+06 y = 1.6850e+31 x_k = 1.7592e+06 A = 1.6850e+31 x_k1 = 1.4074e+06 y = 5.5214e+30 x_k = 1.4074e+06 A = 5.5214e+30 x_k1 = 1.1259e+06 y = 1.8093e+30 x_k = 1.1259e+06 A = 1.8093e+30 x_k1 = 9.0072e+05 y = 5.9286e+29 x_k = 9.0072e+05 A = 5.9286e+29 x_k1 = 7.2058e+05 y = 1.9427e+29 x_k = 7.2058e+05 A = 1.9427e+29 x_k1 = 5.7646e+05 y = 6.3657e+28 x_k = 5.7646e+05 A = 6.3657e+28 x_k1 = 4.6117e+05 y = 2.0859e+28 x_k = 4.6117e+05 A = 2.0859e+28 x_k1 = 3.6893e+05 y = 6.8352e+27 x_k = 3.6893e+05 A = 6.8352e+27 x_k1 = 2.9515e+05 y = 2.2397e+27 x_k = 2.9515e+05 A = 2.2397e+27 x_k1 = 2.3612e+05 y = 7.3392e+26 x_k = 2.3612e+05 A = 7.3392e+26 x_k1 = 1.8889e+05 y = 2.4049e+26 x_k = 1.8889e+05 A = 2.4049e+26 x_k1 = 1.5112e+05 y = 7.8804e+25 x_k = 1.5112e+05 A = 7.8804e+25 x_k1 = 1.2089e+05 y = 2.5823e+25 x_k = 1.2089e+05 A = 2.5823e+25 x_k1 = 9.6714e+04 y = 8.4615e+24 x_k = 9.6714e+04 A = 8.4615e+24 x_k1 = 7.7371e+04 y = 2.7727e+24 x_k = 7.7371e+04 A = 2.7727e+24 x_k1 = 6.1897e+04 y = 9.0855e+23 x_k = 6.1897e+04 A = 9.0855e+23 x_k1 = 4.9518e+04 y = 2.9771e+23 x_k = 4.9518e+04 A = 2.9771e+23 x_k1 = 3.9614e+04 y = 9.7555e+22 x_k = 3.9614e+04 A = 9.7555e+22 x_k1 = 3.1691e+04 y = 3.1967e+22 x_k = 3.1691e+04 A = 3.1967e+22 x_k1 = 2.5353e+04 y = 1.0475e+22 x_k = 2.5353e+04 A = 1.0475e+22 x_k1 = 2.0282e+04 y = 3.4324e+21 x_k = 2.0282e+04 A = 3.4324e+21 x_k1 = 1.6226e+04 y = 1.1247e+21 x_k = 1.6226e+04 A = 1.1247e+21 x_k1 = 1.2981e+04 y = 3.6855e+20 x_k = 1.2981e+04 A = 3.6855e+20 x_k1 = 1.0385e+04 y = 1.2077e+20 x_k = 1.0385e+04 A = 1.2077e+20 x_k1 = 8.3077e+03 y = 3.9573e+19 x_k = 8.3077e+03 A = 3.9573e+19 x_k1 = 6.6461e+03 y = 1.2967e+19 x_k = 6.6461e+03 A = 1.2967e+19 x_k1 = 5.3169e+03 y = 4.2491e+18 x_k = 5.3169e+03 A = 4.2491e+18 x_k1 = 4.2535e+03 y = 1.3923e+18 x_k = 4.2535e+03 A = 1.3923e+18 x_k1 = 3.4028e+03 y = 4.5624e+17 x_k = 3.4028e+03 A = 4.5624e+17 x_k1 = 2.7223e+03 y = 1.4950e+17 x_k = 2.7223e+03 A = 1.4950e+17 x_k1 = 2.1778e+03 y = 4.8989e+16 x_k = 2.1778e+03 A = 4.8989e+16 x_k1 = 1.7422e+03 y = 1.6053e+16 x_k = 1.7422e+03 A = 1.6053e+16 x_k1 = 1.3938e+03 y = 5.2601e+15 x_k = 1.3938e+03 A = 5.2601e+15 x_k1 = 1.1150e+03 y = 1.7236e+15 x_k = 1.1150e+03 A = 1.7236e+15 x_k1 = 892.0299 y = 5.6480e+14 x_k = 892.0299 A = 5.6480e+14 x_k1 = 713.6240 y = 1.8507e+14 x_k = 713.6240 A = 1.8507e+14 x_k1 = 570.8994 y = 6.0645e+13 x_k = 570.8994 A = 6.0645e+13 x_k1 = 456.7201 y = 1.9872e+13 x_k = 456.7201 A = 1.9872e+13 x_k1 = 365.3776 y = 6.5116e+12 x_k = 365.3776 A = 6.5116e+12 x_k1 = 292.3055 y = 2.1336e+12 x_k = 292.3055 A = 2.1336e+12 x_k1 = 233.8530 y = 6.9907e+11 x_k = 233.8530 A = 6.9907e+11 x_k1 = 187.1033 y = 2.2899e+11 x_k = 187.1033 A = 2.2899e+11 x_k1 = 149.7336 y = 7.4953e+10 x_k = 149.7336 A = 7.4953e+10 x_k1 = 119.9112 y = 2.4479e+10 x_k = 119.9112 A = 2.4479e+10 x_k1 = 96.2313 y = 7.9399e+09 x_k = 96.2313 A = 7.9399e+09 x_k1 = 77.7138 y = 2.5221e+09 x_k = 77.7138 A = 2.5221e+09 x_k1 = 63.8846 y = 7.5160e+08 x_k = 63.8846 A = 7.5160e+08 x_k1 = 54.8600 y = 1.8441e+08 x_k = 54.8600 A = 1.8441e+08 x_k1 = 50.7881 y = 2.5417e+07 x_k = 50.7881 A = 2.5417e+07 x_k1 = 50.0241 y = 7.5330e+05 x_k = 50.0241 A = 7.5330e+05 x_k1 = 50.0000 y = 724.2605 x_k = 50.0000 A = 724.2605 x_k1 = 50.0000 y = 6.7145e-04 x_k = 50.0000 A = 6.7145e-04 x_k1 = 50 y = 0 x_k = 50 f = 50

16   Pass
n = 75937500000; assert(abs(fifth_root(n)-150)<1e-5)

A = -7.5937e+10 x_k1 = 1.5188e+10 y = 8.0804e+50 A = -7.5937e+10 x_k1 = 1.5188e+10 y = 8.0804e+50 x_k = 1.5188e+10 A = 8.0804e+50 x_k1 = 1.2150e+10 y = 2.6478e+50 x_k = 1.2150e+10 A = 2.6478e+50 x_k1 = 9.7200e+09 y = 8.6762e+49 x_k = 9.7200e+09 A = 8.6762e+49 x_k1 = 7.7760e+09 y = 2.8430e+49 x_k = 7.7760e+09 A = 2.8430e+49 x_k1 = 6.2208e+09 y = 9.3160e+48 x_k = 6.2208e+09 A = 9.3160e+48 x_k1 = 4.9766e+09 y = 3.0527e+48 x_k = 4.9766e+09 A = 3.0527e+48 x_k1 = 3.9813e+09 y = 1.0003e+48 x_k = 3.9813e+09 A = 1.0003e+48 x_k1 = 3.1850e+09 y = 3.2778e+47 x_k = 3.1850e+09 A = 3.2778e+47 x_k1 = 2.5480e+09 y = 1.0741e+47 x_k = 2.5480e+09 A = 1.0741e+47 x_k1 = 2.0384e+09 y = 3.5195e+46 x_k = 2.0384e+09 A = 3.5195e+46 x_k1 = 1.6307e+09 y = 1.1533e+46 x_k = 1.6307e+09 A = 1.1533e+46 x_k1 = 1.3046e+09 y = 3.7790e+45 x_k = 1.3046e+09 A = 3.7790e+45 x_k1 = 1.0437e+09 y = 1.2383e+45 x_k = 1.0437e+09 A = 1.2383e+45 x_k1 = 8.3494e+08 y = 4.0577e+44 x_k = 8.3494e+08 A = 4.0577e+44 x_k1 = 6.6795e+08 y = 1.3296e+44 x_k = 6.6795e+08 A = 1.3296e+44 x_k1 = 5.3436e+08 y = 4.3569e+43 x_k = 5.3436e+08 A = 4.3569e+43 x_k1 = 4.2749e+08 y = 1.4277e+43 x_k = 4.2749e+08 A = 1.4277e+43 x_k1 = 3.4199e+08 y = 4.6782e+42 x_k = 3.4199e+08 A = 4.6782e+42 x_k1 = 2.7359e+08 y = 1.5330e+42 x_k = 2.7359e+08 A = 1.5330e+42 x_k1 = 2.1887e+08 y = 5.0232e+41 x_k = 2.1887e+08 A = 5.0232e+41 x_k1 = 1.7510e+08 y = 1.6460e+41 x_k = 1.7510e+08 A = 1.6460e+41 x_k1 = 1.4008e+08 y = 5.3936e+40 x_k = 1.4008e+08 A = 5.3936e+40 x_k1 = 1.1206e+08 y = 1.7674e+40 x_k = 1.1206e+08 A = 1.7674e+40 x_k1 = 8.9651e+07 y = 5.7914e+39 x_k = 8.9651e+07 A = 5.7914e+39 x_k1 = 7.1721e+07 y = 1.8977e+39 x_k = 7.1721e+07 A = 1.8977e+39 x_k1 = 5.7377e+07 y = 6.2184e+38 x_k = 5.7377e+07 A = 6.2184e+38 x_k1 = 4.5901e+07 y = 2.0377e+38 x_k = 4.5901e+07 A = 2.0377e+38 x_k1 = 3.6721e+07 y = 6.6770e+37 x_k = 3.6721e+07 A = 6.6770e+37 x_k1 = 2.9377e+07 y = 2.1879e+37 x_k = 2.9377e+07 A = 2.1879e+37 x_k1 = 2.3502e+07 y = 7.1693e+36 x_k = 2.3502e+07 A = 7.1693e+36 x_k1 = 1.8801e+07 y = 2.3493e+36 x_k = 1.8801e+07 A = 2.3493e+36 x_k1 = 1.5041e+07 y = 7.6980e+35 x_k = 1.5041e+07 A = 7.6980e+35 x_k1 = 1.2033e+07 y = 2.5225e+35 x_k = 1.2033e+07 A = 2.5225e+35 x_k1 = 9.6262e+06 y = 8.2657e+34 x_k = 9.6262e+06 A = 8.2657e+34 x_k1 = 7.7010e+06 y = 2.7085e+34 x_k = 7.7010e+06 A = 2.7085e+34 x_k1 = 6.1608e+06 y = 8.8752e+33 x_k = 6.1608e+06 A = 8.8752e+33 x_k1 = 4.9286e+06 y = 2.9082e+33 x_k = 4.9286e+06 A = 2.9082e+33 x_k1 = 3.9429e+06 y = 9.5297e+32 x_k = 3.9429e+06 A = 9.5297e+32 x_k1 = 3.1543e+06 y = 3.1227e+32 x_k = 3.1543e+06 A = 3.1227e+32 x_k1 = 2.5235e+06 y = 1.0232e+32 x_k = 2.5235e+06 A = 1.0232e+32 x_k1 = 2.0188e+06 y = 3.3530e+31 x_k = 2.0188e+06 A = 3.3530e+31 x_k1 = 1.6150e+06 y = 1.0987e+31 x_k = 1.6150e+06 A = 1.0987e+31 x_k1 = 1.2920e+06 y = 3.6002e+30 x_k = 1.2920e+06 A = 3.6002e+30 x_k1 = 1.0336e+06 y = 1.1797e+30 x_k = 1.0336e+06 A = 1.1797e+30 x_k1 = 8.2689e+05 y = 3.8657e+29 x_k = 8.2689e+05 A = 3.8657e+29 x_k1 = 6.6151e+05 y = 1.2667e+29 x_k = 6.6151e+05 A = 1.2667e+29 x_k1 = 5.2921e+05 y = 4.1508e+28 x_k = 5.2921e+05 A = 4.1508e+28 x_k1 = 4.2337e+05 y = 1.3601e+28 x_k = 4.2337e+05 A = 1.3601e+28 x_k1 = 3.3869e+05 y = 4.4569e+27 x_k = 3.3869e+05 A = 4.4569e+27 x_k1 = 2.7095e+05 y = 1.4604e+27 x_k = 2.7095e+05 A = 1.4604e+27 x_k1 = 2.1676e+05 y = 4.7855e+26 x_k = 2.1676e+05 A = 4.7855e+26 x_k1 = 1.7341e+05 y = 1.5681e+26 x_k = 1.7341e+05 A = 1.5681e+26 x_k1 = 1.3873e+05 y = 5.1384e+25 x_k = 1.3873e+05 A = 5.1384e+25 x_k1 = 1.1098e+05 y = 1.6838e+25 x_k = 1.1098e+05 A = 1.6838e+25 x_k1 = 8.8786e+04 y = 5.5173e+24 x_k = 8.8786e+04 A = 5.5173e+24 x_k1 = 7.1029e+04 y = 1.8079e+24 x_k = 7.1029e+04 A = 1.8079e+24 x_k1 = 5.6823e+04 y = 5.9242e+23 x_k = 5.6823e+04 A = 5.9242e+23 x_k1 = 4.5459e+04 y = 1.9412e+23 x_k = 4.5459e+04 A = 1.9412e+23 x_k1 = 3.6367e+04 y = 6.3610e+22 x_k = 3.6367e+04 A = 6.3610e+22 x_k1 = 2.9093e+04 y = 2.0844e+22 x_k = 2.9093e+04 A = 2.0844e+22 x_k1 = 2.3275e+04 y = 6.8301e+21 x_k = 2.3275e+04 A = 6.8301e+21 x_k1 = 1.8620e+04 y = 2.2381e+21 x_k = 1.8620e+04 A = 2.2381e+21 x_k1 = 1.4896e+04 y = 7.3338e+20 x_k = 1.4896e+04 A = 7.3338e+20 x_k1 = 1.1917e+04 y = 2.4031e+20 x_k = 1.1917e+04 A = 2.4031e+20 x_k1 = 9.5333e+03 y = 7.8746e+19 x_k = 9.5333e+03 A = 7.8746e+19 x_k1 = 7.6267e+03 y = 2.5803e+19 x_k = 7.6267e+03 A = 2.5803e+19 x_k1 = 6.1013e+03 y = 8.4553e+18 x_k = 6.1013e+03 A = 8.4553e+18 x_k1 = 4.8811e+03 y = 2.7706e+18 x_k = 4.8811e+03 A = 2.7706e+18 x_k1 = 3.9049e+03 y = 9.0788e+17 x_k = 3.9049e+03 A = 9.0788e+17 x_k1 = 3.1239e+03 y = 2.9749e+17 x_k = 3.1239e+03 A = 2.9749e+17 x_k1 = 2.4991e+03 y = 9.7483e+16 x_k = 2.4991e+03 A = 9.7483e+16 x_k1 = 1.9993e+03 y = 3.1943e+16 x_k = 1.9993e+03 A = 3.1943e+16 x_k1 = 1.5994e+03 y = 1.0467e+16 x_k = 1.5994e+03 A = 1.0467e+16 x_k1 = 1.2795e+03 y = 3.4298e+15 x_k = 1.2795e+03 A = 3.4298e+15 x_k1 = 1.0236e+03 y = 1.1239e+15 x_k = 1.0236e+03 A = 1.1239e+15 x_k1 = 818.9290 y = 3.6825e+14 x_k = 818.9290 A = 3.6825e+14 x_k1 = 655.1769 y = 1.2065e+14 x_k = 655.1769 A = 1.2065e+14 x_k1 = 524.2240 y = 3.9514e+13 x_k = 524.2240 A = 3.9514e+13 x_k1 = 419.5803 y = 1.2928e+13 x_k = 419.5803 A = 1.2928e+13 x_k1 = 336.1543 y = 4.2164e+12 x_k = 336.1543 A = 4.2164e+12 x_k1 = 270.1128 y = 1.3620e+12 x_k = 270.1128 A = 1.3620e+12 x_k1 = 218.9433 y = 4.2717e+11 x_k = 218.9433 A = 4.2717e+11 x_k1 = 181.7640 y = 1.2246e+11 x_k = 181.7640 A = 1.2246e+11 x_k1 = 159.3253 y = 2.6728e+10 x_k = 159.3253 A = 2.6728e+10 x_k1 = 151.0296 y = 2.6421e+09 x_k = 151.0296 A = 2.6421e+09 x_k1 = 150.0139 y = 3.5297e+07 x_k = 150.0139 A = 3.5297e+07 x_k1 = 150.0000 y = 6.5589e+03 x_k = 150.0000 A = 6.5589e+03 x_k1 = 150.0000 y = 2.1362e-04 x_k = 150.0000 A = 2.1362e-04 x_k1 = 150 y = 0 x_k = 150 f = 150

17   Pass
n = 31250000000000; assert(abs(fifth_root(n)-500)<1e-5)

A = -3.1250e+13 x_k1 = 6.2500e+12 y = 9.5367e+63 A = -3.1250e+13 x_k1 = 6.2500e+12 y = 9.5367e+63 x_k = 6.2500e+12 A = 9.5367e+63 x_k1 = 5.0000e+12 y = 3.1250e+63 x_k = 5.0000e+12 A = 3.1250e+63 x_k1 = 4.0000e+12 y = 1.0240e+63 x_k = 4.0000e+12 A = 1.0240e+63 x_k1 = 3.2000e+12 y = 3.3554e+62 x_k = 3.2000e+12 A = 3.3554e+62 x_k1 = 2.5600e+12 y = 1.0995e+62 x_k = 2.5600e+12 A = 1.0995e+62 x_k1 = 2.0480e+12 y = 3.6029e+61 x_k = 2.0480e+12 A = 3.6029e+61 x_k1 = 1.6384e+12 y = 1.1806e+61 x_k = 1.6384e+12 A = 1.1806e+61 x_k1 = 1.3107e+12 y = 3.8686e+60 x_k = 1.3107e+12 A = 3.8686e+60 x_k1 = 1.0486e+12 y = 1.2677e+60 x_k = 1.0486e+12 A = 1.2677e+60 x_k1 = 8.3886e+11 y = 4.1538e+59 x_k = 8.3886e+11 A = 4.1538e+59 x_k1 = 6.7109e+11 y = 1.3611e+59 x_k = 6.7109e+11 A = 1.3611e+59 x_k1 = 5.3687e+11 y = 4.4601e+58 x_k = 5.3687e+11 A = 4.4601e+58 x_k1 = 4.2950e+11 y = 1.4615e+58 x_k = 4.2950e+11 A = 1.4615e+58 x_k1 = 3.4360e+11 y = 4.7890e+57 x_k = 3.4360e+11 A = 4.7890e+57 x_k1 = 2.7488e+11 y = 1.5693e+57 x_k = 2.7488e+11 A = 1.5693e+57 x_k1 = 2.1990e+11 y = 5.1422e+56 x_k = 2.1990e+11 A = 5.1422e+56 x_k1 = 1.7592e+11 y = 1.6850e+56 x_k = 1.7592e+11 A = 1.6850e+56 x_k1 = 1.4074e+11 y = 5.5214e+55 x_k = 1.4074e+11 A = 5.5214e+55 x_k1 = 1.1259e+11 y = 1.8093e+55 x_k = 1.1259e+11 A = 1.8093e+55 x_k1 = 9.0072e+10 y = 5.9286e+54 x_k = 9.0072e+10 A = 5.9286e+54 x_k1 = 7.2058e+10 y = 1.9427e+54 x_k = 7.2058e+10 A = 1.9427e+54 x_k1 = 5.7646e+10 y = 6.3657e+53 x_k = 5.7646e+10 A = 6.3657e+53 x_k1 = 4.6117e+10 y = 2.0859e+53 x_k = 4.6117e+10 A = 2.0859e+53 x_k1 = 3.6893e+10 y = 6.8352e+52 x_k = 3.6893e+10 A = 6.8352e+52 x_k1 = 2.9515e+10 y = 2.2397e+52 x_k = 2.9515e+10 A = 2.2397e+52 x_k1 = 2.3612e+10 y = 7.3392e+51 x_k = 2.3612e+10 A = 7.3392e+51 x_k1 = 1.8889e+10 y = 2.4049e+51 x_k = 1.8889e+10 A = 2.4049e+51 x_k1 = 1.5112e+10 y = 7.8804e+50 x_k = 1.5112e+10 A = 7.8804e+50 x_k1 = 1.2089e+10 y = 2.5822e+50 x_k = 1.2089e+10 A = 2.5822e+50 x_k1 = 9.6714e+09 y = 8.4615e+49 x_k = 9.6714e+09 A = 8.4615e+49 x_k1 = 7.7371e+09 y = 2.7727e+49 x_k = 7.7371e+09 A = 2.7727e+49 x_k1 = 6.1897e+09 y = 9.0855e+48 x_k = 6.1897e+09 A = 9.0855e+48 x_k1 = 4.9518e+09 y = 2.9771e+48 x_k = 4.9518e+09 A = 2.9771e+48 x_k1 = 3.9614e+09 y = 9.7555e+47 x_k = 3.9614e+09 A = 9.7555e+47 x_k1 = 3.1691e+09 y = 3.1967e+47 x_k = 3.1691e+09 A = 3.1967e+47 x_k1 = 2.5353e+09 y = 1.0475e+47 x_k = 2.5353e+09 A = 1.0475e+47 x_k1 = 2.0282e+09 y = 3.4324e+46 x_k = 2.0282e+09 A = 3.4324e+46 x_k1 = 1.6226e+09 y = 1.1247e+46 x_k = 1.6226e+09 A = 1.1247e+46 x_k1 = 1.2981e+09 y = 3.6855e+45 x_k = 1.2981e+09 A = 3.6855e+45 x_k1 = 1.0385e+09 y = 1.2077e+45 x_k = 1.0385e+09 A = 1.2077e+45 x_k1 = 8.3077e+08 y = 3.9573e+44 x_k = 8.3077e+08 A = 3.9573e+44 x_k1 = 6.6461e+08 y = 1.2967e+44 x_k = 6.6461e+08 A = 1.2967e+44 x_k1 = 5.3169e+08 y = 4.2491e+43 x_k = 5.3169e+08 A = 4.2491e+43 x_k1 = 4.2535e+08 y = 1.3923e+43 x_k = 4.2535e+08 A = 1.3923e+43 x_k1 = 3.4028e+08 y = 4.5624e+42 x_k = 3.4028e+08 A = 4.5624e+42 x_k1 = 2.7223e+08 y = 1.4950e+42 x_k = 2.7223e+08 A = 1.4950e+42 x_k1 = 2.1778e+08 y = 4.8989e+41 x_k = 2.1778e+08 A = 4.8989e+41 x_k1 = 1.7422e+08 y = 1.6053e+41 x_k = 1.7422e+08 A = 1.6053e+41 x_k1 = 1.3938e+08 y = 5.2601e+40 x_k = 1.3938e+08 A = 5.2601e+40 x_k1 = 1.1150e+08 y = 1.7236e+40 x_k = 1.1150e+08 A = 1.7236e+40 x_k1 = 8.9203e+07 y = 5.6480e+39 x_k = 8.9203e+07 A = 5.6480e+39 x_k1 = 7.1362e+07 y = 1.8507e+39 x_k = 7.1362e+07 A = 1.8507e+39 x_k1 = 5.7090e+07 y = 6.0645e+38 x_k = 5.7090e+07 A = 6.0645e+38 x_k1 = 4.5672e+07 y = 1.9872e+38 x_k = 4.5672e+07 A = 1.9872e+38 x_k1 = 3.6538e+07 y = 6.5117e+37 x_k = 3.6538e+07 A = 6.5117e+37 x_k1 = 2.9230e+07 y = 2.1338e+37 x_k = 2.9230e+07 A = 2.1338e+37 x_k1 = 2.3384e+07 y = 6.9919e+36 x_k = 2.3384e+07 A = 6.9919e+36 x_k1 = 1.8707e+07 y = 2.2911e+36 x_k = 1.8707e+07 A = 2.2911e+36 x_k1 = 1.4966e+07 y = 7.5075e+35 x_k = 1.4966e+07 A = 7.5075e+35 x_k1 = 1.1973e+07 y = 2.4601e+35 x_k = 1.1973e+07 A = 2.4601e+35 x_k1 = 9.5781e+06 y = 8.0611e+34 x_k = 9.5781e+06 A = 8.0611e+34 x_k1 = 7.6625e+06 y = 2.6415e+34 x_k = 7.6625e+06 A = 2.6415e+34 x_k1 = 6.1300e+06 y = 8.6556e+33 x_k = 6.1300e+06 A = 8.6556e+33 x_k1 = 4.9040e+06 y = 2.8363e+33 x_k = 4.9040e+06 A = 2.8363e+33 x_k1 = 3.9232e+06 y = 9.2939e+32 x_k = 3.9232e+06 A = 9.2939e+32 x_k1 = 3.1386e+06 y = 3.0454e+32 x_k = 3.1386e+06 A = 3.0454e+32 x_k1 = 2.5108e+06 y = 9.9792e+31 x_k = 2.5108e+06 A = 9.9792e+31 x_k1 = 2.0087e+06 y = 3.2700e+31 x_k = 2.0087e+06 A = 3.2700e+31 x_k1 = 1.6069e+06 y = 1.0715e+31 x_k = 1.6069e+06 A = 1.0715e+31 x_k1 = 1.2856e+06 y = 3.5111e+30 x_k = 1.2856e+06 A = 3.5111e+30 x_k1 = 1.0284e+06 y = 1.1505e+30 x_k = 1.0284e+06 A = 1.1505e+30 x_k1 = 8.2275e+05 y = 3.7700e+29 x_k = 8.2275e+05 A = 3.7700e+29 x_k1 = 6.5820e+05 y = 1.2354e+29 x_k = 6.5820e+05 A = 1.2354e+29 x_k1 = 5.2656e+05 y = 4.0480e+28 x_k = 5.2656e+05 A = 4.0480e+28 x_k1 = 4.2125e+05 y = 1.3265e+28 x_k = 4.2125e+05 A = 1.3265e+28 x_k1 = 3.3700e+05 y = 4.3466e+27 x_k = 3.3700e+05 A = 4.3466e+27 x_k1 = 2.6960e+05 y = 1.4243e+27 x_k = 2.6960e+05 A = 1.4243e+27 x_k1 = 2.1568e+05 y = 4.6671e+26 x_k = 2.1568e+05 A = 4.6671e+26 x_k1 = 1.7254e+05 y = 1.5293e+26 x_k = 1.7254e+05 A = 1.5293e+26 x_k1 = 1.3803e+05 y = 5.0112e+25 x_k = 1.3803e+05 A = 5.0112e+25 x_k1 = 1.1043e+05 y = 1.6421e+25 x_k = 1.1043e+05 A = 1.6421e+25 x_k1 = 8.8342e+04 y = 5.3808e+24 x_k = 8.8342e+04 A = 5.3808e+24 x_k1 = 7.0674e+04 y = 1.7632e+24 x_k = 7.0674e+04 A = 1.7632e+24 x_k1 = 5.6539e+04 y = 5.7776e+23 x_k = 5.6539e+04 A = 5.7776e+23 x_k1 = 4.5231e+04 y = 1.8932e+23 x_k = 4.5231e+04 A = 1.8932e+23 x_k1 = 3.6185e+04 y = 6.2036e+22 x_k = 3.6185e+04 A = 6.2036e+22 x_k1 = 2.8948e+04 y = 2.0328e+22 x_k = 2.8948e+04 A = 2.0328e+22 x_k1 = 2.3158e+04 y = 6.6611e+21 x_k = 2.3158e+04 A = 6.6611e+21 x_k1 = 1.8527e+04 y = 2.1827e+21 x_k = 1.8527e+04 A = 2.1827e+21 x_k1 = 1.4821e+04 y = 7.1523e+20 x_k = 1.4821e+04 A = 7.1523e+20 x_k1 = 1.1857e+04 y = 2.3437e+20 x_k = 1.1857e+04 A = 2.3437e+20 x_k1 = 9.4857e+03 y = 7.6797e+19 x_k = 9.4857e+03 A = 7.6797e+19 x_k1 = 7.5886e+03 y = 2.5165e+19 x_k = 7.5886e+03 A = 2.5165e+19 x_k1 = 6.0708e+03 y = 8.2460e+18 x_k = 6.0708e+03 A = 8.2460e+18 x_k1 = 4.8567e+03 y = 2.7020e+18 x_k = 4.8567e+03 A = 2.7020e+18 x_k1 = 3.8854e+03 y = 8.8540e+17 x_k = 3.8854e+03 A = 8.8540e+17 x_k1 = 3.1083e+03 y = 2.9012e+17 x_k = 3.1083e+03 A = 2.9012e+17 x_k1 = 2.4867e+03 y = 9.5058e+16 x_k = 2.4867e+03 A = 9.5058e+16 x_k1 = 1.9895e+03 y = 3.1140e+16 x_k = 1.9895e+03 A = 3.1140e+16 x_k1 = 1.5920e+03 y = 1.0196e+16 x_k = 1.5920e+03 A = 1.0196e+16 x_k1 = 1.2746e+03 y = 3.3328e+15 x_k = 1.2746e+03 A = 3.3328e+15 x_k1 = 1.0220e+03 y = 1.0839e+15 x_k = 1.0220e+03 A = 1.0839e+15 x_k1 = 823.3633 y = 3.4716e+14 x_k = 823.3633 A = 3.4716e+14 x_k1 = 672.2899 y = 1.0609e+14 x_k = 672.2899 A = 1.0609e+14 x_k1 = 568.4271 y = 2.8094e+13 x_k = 568.4271 A = 2.8094e+13 x_k1 = 514.6078 y = 4.8396e+12 x_k = 514.6078 A = 4.8396e+12 x_k1 = 500.8061 y = 2.5272e+11 x_k = 500.8061 A = 2.5272e+11 x_k1 = 500.0026 y = 8.0967e+08 x_k = 500.0026 A = 8.0967e+08 x_k1 = 500.0000 y = 8.3909e+03 x_k = 500.0000 A = 8.3909e+03 x_k1 = 500 y = 0 x_k = 500 f = 500

18   Pass
n = 52658067346875; assert(abs(fifth_root(n)-555)<1e-5)

A = -5.2658e+13 x_k1 = 1.0532e+13 y = 1.2956e+65 A = -5.2658e+13 x_k1 = 1.0532e+13 y = 1.2956e+65 x_k = 1.0532e+13 A = 1.2956e+65 x_k1 = 8.4253e+12 y = 4.2455e+64 x_k = 8.4253e+12 A = 4.2455e+64 x_k1 = 6.7402e+12 y = 1.3912e+64 x_k = 6.7402e+12 A = 1.3912e+64 x_k1 = 5.3922e+12 y = 4.5585e+63 x_k = 5.3922e+12 A = 4.5585e+63 x_k1 = 4.3137e+12 y = 1.4937e+63 x_k = 4.3137e+12 A = 1.4937e+63 x_k1 = 3.4510e+12 y = 4.8947e+62 x_k = 3.4510e+12 A = 4.8947e+62 x_k1 = 2.7608e+12 y = 1.6039e+62 x_k = 2.7608e+12 A = 1.6039e+62 x_k1 = 2.2086e+12 y = 5.2556e+61 x_k = 2.2086e+12 A = 5.2556e+61 x_k1 = 1.7669e+12 y = 1.7222e+61 x_k = 1.7669e+12 A = 1.7222e+61 x_k1 = 1.4135e+12 y = 5.6432e+60 x_k = 1.4135e+12 A = 5.6432e+60 x_k1 = 1.1308e+12 y = 1.8492e+60 x_k = 1.1308e+12 A = 1.8492e+60 x_k1 = 9.0466e+11 y = 6.0593e+59 x_k = 9.0466e+11 A = 6.0593e+59 x_k1 = 7.2373e+11 y = 1.9855e+59 x_k = 7.2373e+11 A = 1.9855e+59 x_k1 = 5.7898e+11 y = 6.5061e+58 x_k = 5.7898e+11 A = 6.5061e+58 x_k1 = 4.6319e+11 y = 2.1319e+58 x_k = 4.6319e+11 A = 2.1319e+58 x_k1 = 3.7055e+11 y = 6.9859e+57 x_k = 3.7055e+11 A = 6.9859e+57 x_k1 = 2.9644e+11 y = 2.2891e+57 x_k = 2.9644e+11 A = 2.2891e+57 x_k1 = 2.3715e+11 y = 7.5011e+56 x_k = 2.3715e+11 A = 7.5011e+56 x_k1 = 1.8972e+11 y = 2.4580e+56 x_k = 1.8972e+11 A = 2.4580e+56 x_k1 = 1.5178e+11 y = 8.0542e+55 x_k = 1.5178e+11 A = 8.0542e+55 x_k1 = 1.2142e+11 y = 2.6392e+55 x_k = 1.2142e+11 A = 2.6392e+55 x_k1 = 9.7137e+10 y = 8.6481e+54 x_k = 9.7137e+10 A = 8.6481e+54 x_k1 = 7.7710e+10 y = 2.8338e+54 x_k = 7.7710e+10 A = 2.8338e+54 x_k1 = 6.2168e+10 y = 9.2859e+53 x_k = 6.2168e+10 A = 9.2859e+53 x_k1 = 4.9734e+10 y = 3.0428e+53 x_k = 4.9734e+10 A = 3.0428e+53 x_k1 = 3.9787e+10 y = 9.9706e+52 x_k = 3.9787e+10 A = 9.9706e+52 x_k1 = 3.1830e+10 y = 3.2672e+52 x_k = 3.1830e+10 A = 3.2672e+52 x_k1 = 2.5464e+10 y = 1.0706e+52 x_k = 2.5464e+10 A = 1.0706e+52 x_k1 = 2.0371e+10 y = 3.5081e+51 x_k = 2.0371e+10 A = 3.5081e+51 x_k1 = 1.6297e+10 y = 1.1495e+51 x_k = 1.6297e+10 A = 1.1495e+51 x_k1 = 1.3038e+10 y = 3.7668e+50 x_k = 1.3038e+10 A = 3.7668e+50 x_k1 = 1.0430e+10 y = 1.2343e+50 x_k = 1.0430e+10 A = 1.2343e+50 x_k1 = 8.3440e+09 y = 4.0446e+49 x_k = 8.3440e+09 A = 4.0446e+49 x_k1 = 6.6752e+09 y = 1.3253e+49 x_k = 6.6752e+09 A = 1.3253e+49 x_k1 = 5.3402e+09 y = 4.3428e+48 x_k = 5.3402e+09 A = 4.3428e+48 x_k1 = 4.2721e+09 y = 1.4231e+48 x_k = 4.2721e+09 A = 1.4231e+48 x_k1 = 3.4177e+09 y = 4.6631e+47 x_k = 3.4177e+09 A = 4.6631e+47 x_k1 = 2.7342e+09 y = 1.5280e+47 x_k = 2.7342e+09 A = 1.5280e+47 x_k1 = 2.1873e+09 y = 5.0069e+46 x_k = 2.1873e+09 A = 5.0069e+46 x_k1 = 1.7499e+09 y = 1.6407e+46 x_k = 1.7499e+09 A = 1.6407e+46 x_k1 = 1.3999e+09 y = 5.3762e+45 x_k = 1.3999e+09 A = 5.3762e+45 x_k1 = 1.1199e+09 y = 1.7617e+45 x_k = 1.1199e+09 A = 1.7617e+45 x_k1 = 8.9593e+08 y = 5.7726e+44 x_k = 8.9593e+08 A = 5.7726e+44 x_k1 = 7.1674e+08 y = 1.8916e+44 x_k = 7.1674e+08 A = 1.8916e+44 x_k1 = 5.7340e+08 y = 6.1983e+43 x_k = 5.7340e+08 A = 6.1983e+43 x_k1 = 4.5872e+08 y = 2.0311e+43 x_k = 4.5872e+08 A = 2.0311e+43 x_k1 = 3.6697e+08 y = 6.6554e+42 x_k = 3.6697e+08 A = 6.6554e+42 x_k1 = 2.9358e+08 y = 2.1808e+42 x_k = 2.9358e+08 A = 2.1808e+42 x_k1 = 2.3486e+08 y = 7.1461e+41 x_k = 2.3486e+08 A = 7.1461e+41 x_k1 = 1.8789e+08 y = 2.3416e+41 x_k = 1.8789e+08 A = 2.3416e+41 x_k1 = 1.5031e+08 y = 7.6731e+40 x_k = 1.5031e+08 A = 7.6731e+40 x_k1 = 1.2025e+08 y = 2.5143e+40 x_k = 1.2025e+08 A = 2.5143e+40 x_k1 = 9.6200e+07 y = 8.2389e+39 x_k = 9.6200e+07 A = 8.2389e+39 x_k1 = 7.6960e+07 y = 2.6997e+39 x_k = 7.6960e+07 A = 2.6997e+39 x_k1 = 6.1568e+07 y = 8.8465e+38 x_k = 6.1568e+07 A = 8.8465e+38 x_k1 = 4.9254e+07 y = 2.8988e+38 x_k = 4.9254e+07 A = 2.8988e+38 x_k1 = 3.9403e+07 y = 9.4988e+37 x_k = 3.9403e+07 A = 9.4988e+37 x_k1 = 3.1523e+07 y = 3.1126e+37 x_k = 3.1523e+07 A = 3.1126e+37 x_k1 = 2.5218e+07 y = 1.0199e+37 x_k = 2.5218e+07 A = 1.0199e+37 x_k1 = 2.0175e+07 y = 3.3421e+36 x_k = 2.0175e+07 A = 3.3421e+36 x_k1 = 1.6140e+07 y = 1.0951e+36 x_k = 1.6140e+07 A = 1.0951e+36 x_k1 = 1.2912e+07 y = 3.5886e+35 x_k = 1.2912e+07 A = 3.5886e+35 x_k1 = 1.0329e+07 y = 1.1759e+35 x_k = 1.0329e+07 A = 1.1759e+35 x_k1 = 8.2635e+06 y = 3.8532e+34 x_k = 8.2635e+06 A = 3.8532e+34 x_k1 = 6.6108e+06 y = 1.2626e+34 x_k = 6.6108e+06 A = 1.2626e+34 x_k1 = 5.2886e+06 y = 4.1373e+33 x_k = 5.2886e+06 A = 4.1373e+33 x_k1 = 4.2309e+06 y = 1.3557e+33 x_k = 4.2309e+06 A = 1.3557e+33 x_k1 = 3.3847e+06 y = 4.4424e+32 x_k = 3.3847e+06 A = 4.4424e+32 x_k1 = 2.7078e+06 y = 1.4557e+32 x_k = 2.7078e+06 A = 1.4557e+32 x_k1 = 2.1662e+06 y = 4.7700e+31 x_k = 2.1662e+06 A = 4.7700e+31 x_k1 = 1.7330e+06 y = 1.5630e+31 x_k = 1.7330e+06 A = 1.5630e+31 x_k1 = 1.3864e+06 y = 5.1218e+30 x_k = 1.3864e+06 A = 5.1218e+30 x_k1 = 1.1091e+06 y = 1.6783e+30 x_k = 1.1091e+06 A = 1.6783e+30 x_k1 = 8.8729e+05 y = 5.4995e+29 x_k = 8.8729e+05 A = 5.4995e+29 x_k1 = 7.0983e+05 y = 1.8021e+29 x_k = 7.0983e+05 A = 1.8021e+29 x_k1 = 5.6786e+05 y = 5.9050e+28 x_k = 5.6786e+05 A = 5.9050e+28 x_k1 = 4.5429e+05 y = 1.9349e+28 x_k = 4.5429e+05 A = 1.9349e+28 x_k1 = 3.6343e+05 y = 6.3404e+27 x_k = 3.6343e+05 A = 6.3404e+27 x_k1 = 2.9075e+05 y = 2.0776e+27 x_k = 2.9075e+05 A = 2.0776e+27 x_k1 = 2.3260e+05 y = 6.8080e+26 x_k = 2.3260e+05 A = 6.8080e+26 x_k1 = 1.8608e+05 y = 2.2308e+26 x_k = 1.8608e+05 A = 2.2308e+26 x_k1 = 1.4886e+05 y = 7.3100e+25 x_k = 1.4886e+05 A = 7.3100e+25 x_k1 = 1.1909e+05 y = 2.3954e+25 x_k = 1.1909e+05 A = 2.3954e+25 x_k1 = 9.5272e+04 y = 7.8491e+24 x_k = 9.5272e+04 A = 7.8491e+24 x_k1 = 7.6217e+04 y = 2.5720e+24 x_k = 7.6217e+04 A = 2.5720e+24 x_k1 = 6.0974e+04 y = 8.4279e+23 x_k = 6.0974e+04 A = 8.4279e+23 x_k1 = 4.8779e+04 y = 2.7617e+23 x_k = 4.8779e+04 A = 2.7617e+23 x_k1 = 3.9023e+04 y = 9.0494e+22 x_k = 3.9023e+04 A = 9.0494e+22 x_k1 = 3.1219e+04 y = 2.9653e+22 x_k = 3.1219e+04 A = 2.9653e+22 x_k1 = 2.4975e+04 y = 9.7167e+21 x_k = 2.4975e+04 A = 9.7167e+21 x_k1 = 1.9980e+04 y = 3.1840e+21 x_k = 1.9980e+04 A = 3.1840e+21 x_k1 = 1.5984e+04 y = 1.0433e+21 x_k = 1.5984e+04 A = 1.0433e+21 x_k1 = 1.2787e+04 y = 3.4188e+20 x_k = 1.2787e+04 A = 3.4188e+20 x_k1 = 1.0230e+04 y = 1.1203e+20 x_k = 1.0230e+04 A = 1.1203e+20 x_k1 = 8.1838e+03 y = 3.6709e+19 x_k = 8.1838e+03 A = 3.6709e+19 x_k1 = 6.5470e+03 y = 1.2029e+19 x_k = 6.5470e+03 A = 1.2029e+19 x_k1 = 5.2376e+03 y = 3.9415e+18 x_k = 5.2376e+03 A = 3.9415e+18 x_k1 = 4.1901e+03 y = 1.2916e+18 x_k = 4.1901e+03 A = 1.2916e+18 x_k1 = 3.3521e+03 y = 4.2320e+17 x_k = 3.3521e+03 A = 4.2320e+17 x_k1 = 2.6818e+03 y = 1.3866e+17 x_k = 2.6818e+03 A = 1.3866e+17 x_k1 = 2.1456e+03 y = 4.5423e+16 x_k = 2.1456e+03 A = 4.5423e+16 x_k1 = 1.7170e+03 y = 1.4870e+16 x_k = 1.7170e+03 A = 1.4870e+16 x_k1 = 1.3748e+03 y = 4.8589e+15 x_k = 1.3748e+03 A = 4.8589e+15 x_k1 = 1.1028e+03 y = 1.5784e+15 x_k = 1.1028e+03 A = 1.5784e+15 x_k1 = 889.3590 y = 5.0374e+14 x_k = 889.3590 A = 5.0374e+14 x_k1 = 728.3212 y = 1.5228e+14 x_k = 728.3212 A = 1.5228e+14 x_k1 = 620.0855 y = 3.9018e+13 x_k = 620.0855 A = 3.9018e+13 x_k1 = 567.3026 y = 6.1009e+12 x_k = 567.3026 A = 6.1009e+12 x_k1 = 555.5221 y = 2.4817e+11 x_k = 555.5221 A = 2.4817e+11 x_k1 = 555.0010 y = 4.6521e+08 x_k = 555.0010 A = 4.6521e+08 x_k1 = 555.0000 y = 1.6439e+03 x_k = 555.0000 A = 1.6439e+03 x_k1 = 555 y = 0 x_k = 555 f = 555