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

Average Error: 0.4 → 0.0

Time: 758.0ms

Precision: binary64

Math

\[\frac{e^{-x}}{1 + e^{-x}}\]

↓

\[\frac{1}{1 + 1 \cdot e^{x}}\]

Error

Bits error versus x

Derivation

1. Initial program 0.4

   \[\frac{e^{-x}}{1 + e^{-x}}\]

2. Simplified 0.0

   \[\leadsto \color{blue}{\frac{1}{1 + 1 \cdot e^{x}}}\]

3. Final simplification 0.0

   \[\leadsto \frac{1}{1 + 1 \cdot e^{x}}\]

Reproduce

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