Find a numerical failure before trusting an experiment
Does an apparently sensible floating-point answer survive a separately formulated reference calculation?
Make this plan your own ↓Read, edit and export without an account. This is preparation; no run or result is claimed.
Make the question your own.
6 sources · Exact preparation context
- Stable log-sum-exp on overflowing inputs →
Original local preparation by the Executable Science seed collection; upstream API references remain separately attributed.
Record revision: bfc289dd93ab5b26a9bfd816db2795d570359634047db91c03ab3ea12851c73c
- Rationalization and subtractive cancellation →
Original local preparation by the Executable Science seed collection; upstream API references remain separately attributed.
Record revision: 7a80d374026a33a68ab7a6745f61b57e888971072c62686eb6c98a7c5199d49b
- Summation with a large dynamic range →
Original local preparation by the Executable Science seed collection; upstream API references remain separately attributed.
Record revision: fc05aa85f1064ba3c5e31c5bf543f5e755e7ca7ae01d5dd726514b439215047d
- Variance estimation for nearly equal large values →
Original local preparation by the Executable Science seed collection; upstream API references remain separately attributed.
Record revision: e8fd26805262efa9b371a47a1d4236feb069fa7d1cf53782ac604793d274718c
- mpmath →
Preserve the upstream project name, version, repository link, applicable notices, and contributor attribution when preparing an artifact for reuse.
Record revision: 1a802838d72e468d8b8f93988487f58e6dc07f672dcfc1de68eccfdb8b317398
- NumPy →
Preserve the upstream project name, version, repository link, applicable notices, and contributor attribution when preparing an artifact for reuse.
Record revision: a421afa7537135f9209d979f4724e94f1c23f2cb7885fca8655adeaf82a7dc0c
Source links open the current listing. This plan retains the revisions above; listing review does not grant permission to copy or adapt source files.
Before carrying out this plan
- Four original cases are prepared for the qualified standard-library runtime.
- External packages remain unexecuted; their environment needs qualification.
Limits to keep in view
- Passing these inputs does not establish a general error bound.
- No external library was executed by catalog preparation.
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What to compare
Use exact represented float values when constructing an error, and preserve the explicit sequential summation baseline. A rounded reference is not an exact oracle.
Useful outputs
- Fixed adversarial inputs and exact/high-precision references.
- Baseline and stable-form outputs with absolute error, overflow and cancellation recorded separately.
- A minimal regression fixture tied to the exact source/runtime version.
Inputs and prerequisites
- Four original cases are prepared for the qualified standard-library runtime.
- External packages remain unexecuted; their environment needs qualification.
What this work would not establish
- Passing these inputs does not establish a general error bound.
- No external library was executed by catalog preparation.
Start with these sources.
Stable log-sum-exp on overflowing inputs
Executable Science local pilot drafts
Compare naive exponentiation with a shifted log-sum-exp calculation and a 70-digit Decimal reference on three fixed large inputs.
Investigate Can a shifted calculation retain an accurate finite result when direct exponentiation overflows?
Rationalization and subtractive cancellation
Executable Science local pilot drafts
Measure loss of precision in sqrt(x+1)-sqrt(x) at x=10^16 and compare an algebraically rationalized expression with a high-precision reference.
Investigate How much error is removed by changing the expression while preserving its exact-arithmetic meaning?
Summation with a large dynamic range
Executable Science local pilot drafts
Compare sequential sum and math.fsum on a repeated cancellation pattern, with a Fraction reference for the exact represented inputs.
Investigate Which summation strategy preserves the small contributions in this adversarial finite sequence?
Variance estimation for nearly equal large values
Executable Science local pilot drafts
Compare a raw second-moment formula, Welford accumulation, and statistics.pvariance on five large observations with an exact population variance of two.
Investigate How does cancellation affect variance calculations when location is much larger than spread?
mpmath
Upstream project repository
Arbitrary-precision real and complex arithmetic with special functions and numerical calculus.
Investigate How does precision growth change the residual in a cancellation-sensitive special-function identity?
NumPy
Upstream project repository
Multidimensional array operations and numerical linear algebra for scientific Python.
Investigate How do sequential and pairwise array reductions behave on cancellation-heavy inputs?