(/ 1 (+ (pow e x) (pow e (- x))))

Average Error: 0.0 → 0.0

Time: 1.4s

Precision: binary64

Math

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

↓

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

Error

Bits error versus e

Bits error versus x

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020152 
(FPCore (e x)
  :name "(/ 1 (+ (pow e x) (pow e (- x))))"
  :precision binary64
  (/ 1.0 (+ (pow e x) (pow e (neg x)))))