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

Average Error: 0.5 → 0.5

Time: 2.1s

Precision: binary64

Math

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

↓

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

Error

Bits error versus x

Derivation

1. Initial program 0.5

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

2. Final simplification 0.5

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

Reproduce

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