Numerical examples 


Polynomial function of two variables: Rump equationThis example was proposed by S. M. Rump[1].The following polynomial is computed with two couples of values: P(x,y)= 9x^{4}  y^{4}+ 2y^{2}.
The first computed result is erroneous.
Without CADNA:P(10864,18817) = 2.0000000000000000 (exact value: 1)P(1/3,2/3) = 0.8024691358024691 With CADNA: CADNA software  University P. et M. Curie  LIP6 Selfvalidation detection: ON Mathematical instabilities detection: ON Branching instabilities detection: ON Intrinsic instabilities detection: ON Cancellation instabilities detection: ON  P(10864,18817) = @.0 (exact value: 1) P(1/3,2/3) = 0.802469135802469E+000  CADNA software  University P. et M. Curie  LIP6 There are 2 numerical instabilities 0 UNSTABLE DIVISION(S) 0 UNSTABLE POWER FUNCTION(S) 0 UNSTABLE MULTIPLICATION(S) 0 UNSTABLE BRANCHING(S) 0 UNSTABLE MATHEMATICAL FUNCTION(S) 0 UNSTABLE INTRINSIC FUNCTION(S) 2 UNSTABLE CANCELLATION(S) CommentsThe symbol @.0 means that the first result was computed with no significant digit.The second result was computed with 15 exact significant digits One can see the difference of accuracy between the two results even if they were provided with the same algorithm. It points out the importance of the data influence on the numerical quality of results given by an algorithm. References
the classical FORTRAN source code. the FORTRAN source code with CADNA. 