(/ (expm1 (/ (- N) l)) (expm1 (/ (- 1) l)))

Average Error: 9.9 → 9.9

Time: 920.0ms

Precision: binary64

Math

\[\frac{\mathsf{expm1}\left(\frac{-N}{\ell}\right)}{\mathsf{expm1}\left(\frac{-1}{\ell}\right)}\]

↓

\[\frac{\mathsf{expm1}\left(\frac{-N}{\ell}\right)}{\mathsf{expm1}\left(\frac{-1}{\ell}\right)}\]

Error

Bits error versus N

Bits error versus l

Derivation

1. Initial program 9.9

   \[\frac{\mathsf{expm1}\left(\frac{-N}{\ell}\right)}{\mathsf{expm1}\left(\frac{-1}{\ell}\right)}\]

2. Final simplification 9.9

   \[\leadsto \frac{\mathsf{expm1}\left(\frac{-N}{\ell}\right)}{\mathsf{expm1}\left(\frac{-1}{\ell}\right)}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (N l)
  :name "(/ (expm1 (/ (- N) l)) (expm1 (/ (- 1) l)))"
  :precision binary64
  (/ (expm1 (/ (neg N) l)) (expm1 (/ (neg 1.0) l))))