(log (- 1 (exp (- x))))

Average Error: 30.8 → 30.8

Time: 3.1s

Precision: binary64

Math

\[\log \left(1 - e^{-x}\right)\]

↓

\[\log \left(1 - e^{-x}\right)\]

Error

Bits error versus x

Derivation

1. Initial program 30.8

   \[\log \left(1 - e^{-x}\right)\]

2. Final simplification 30.8

   \[\leadsto \log \left(1 - e^{-x}\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(log (- 1 (exp (- x))))"
  :precision binary64
  (log (- 1.0 (exp (neg x)))))