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

Average Error: 1.3 → 0

Time: 936.0ms

Precision: binary64

Math

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

↓

\[e^{-1}\]

Error

Bits error versus x

Derivation

1. Initial program 1.3

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

2. Simplified 0

   \[\leadsto \color{blue}{e^{-1}}\]

3. Final simplification 0

   \[\leadsto e^{-1}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ (exp (- x 1)) (exp x))"
  :precision binary64
  (/ (exp (- x 1.0)) (exp x)))