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

Average Error: 0.5 → 0.5

Time: 1.6s

Precision: binary64

Math

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

↓

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

Error

Bits error versus x

Derivation

1. Initial program 0.5

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

2. Final simplification 0.5

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

Reproduce

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