(log (* (pow lam k) (exp (- k))))

Average Error: 58.2 → 56.1

Time: 6.0s

Precision: binary64

Math

\[\log \left({lam}^{k} \cdot e^{-k}\right)\]

↓

\[\log \left({lam}^{k}\right) - k\]

Error

Bits error versus lam

Bits error versus k

Derivation

1. Initial program 58.2

   \[\log \left({lam}^{k} \cdot e^{-k}\right)\]

2. Simplified 56.1

   \[\leadsto \color{blue}{\log \left({lam}^{k}\right) - k}\]

3. Final simplification 56.1

   \[\leadsto \log \left({lam}^{k}\right) - k\]

Reproduce

herbie shell --seed 2020153 
(FPCore (lam k)
  :name "(log (* (pow lam k) (exp (- k))))"
  :precision binary64
  (log (* (pow lam k) (exp (neg k)))))