python - Is there an error of precision in that program? -

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i'm trying verify sum , seems in program don't find 0, there error ?

from mpmath import * mp.dps = 1500  a=mpf(0.1) p=mpf(2.)  def f1(x):   return (a-(mpf(1)-mp.sqrt(1-x**2)))**p*x  def f2(x):   return x*(x-a)**p  def f3(x):   return x**p  i=mp.quad(f1,[0,mp.sqrt(mpf(1)-mpf(0.9)**mpf(2))]) j=mp.quad(f2,[0,a]) k=mp.quad(f3,[0,a])  print i,j,k print mp.fabs(i)+mp.fabs(j)-mp.fabs(k)

even 1500 digits don't find 0.

when creating mpf instances python float, value enter in code first converted 53-bit value , converted high-precision value. working values not expecting.

if working high-precision code, should either initialize string or integer. try following instead:

from mpmath import * mp.dps = 1500  a=mpf("0.1") p=mpf(2)  def f1(x):   return (a-(mpf(1)-mp.sqrt(1-x**2)))**p*x  def f2(x):   return x*(x-a)**p  def f3(x):   return x**p  i=mp.quad(f1,[0,mp.sqrt(mpf(1)-mpf("0.9")**mpf(2))]) j=mp.quad(f2,[0,a]) k=mp.quad(f3,[0,a])  print i,j,k print mp.fabs(i)+mp.fabs(j)-mp.fabs(k)

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