(/ (exp x1) (exp (+ x1 x2)))

Average Error: 1.0 → 0

Time: 1.2s

Precision: binary64

Math

\[\frac{e^{x1}}{e^{x1 + x2}}\]

↓

\[e^{-x2}\]

Error

Bits error versus x1

Bits error versus x2

Derivation

1. Initial program 1.0

   \[\frac{e^{x1}}{e^{x1 + x2}}\]

2. Simplified 0

   \[\leadsto \color{blue}{e^{-x2}}\]

3. Final simplification 0

   \[\leadsto e^{-x2}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x1 x2)
  :name "(/ (exp x1) (exp (+ x1 x2)))"
  :precision binary64
  (/ (exp x1) (exp (+ x1 x2))))