(/ (+ (- (exp (- x)) 1) x) (pow x 2))

Average Error: 50.8 → 50.8

Time: 2.8s

Precision: binary64

Math

\[\frac{\left(e^{-x} - 1\right) + x}{{x}^{2}}\]

↓

\[\frac{\left(e^{-x} - 1\right) + x}{{x}^{2}}\]

Error

Bits error versus x

Derivation

1. Initial program 50.8

   \[\frac{\left(e^{-x} - 1\right) + x}{{x}^{2}}\]

2. Final simplification 50.8

   \[\leadsto \frac{\left(e^{-x} - 1\right) + x}{{x}^{2}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(/ (+ (- (exp (- x)) 1) x) (pow x 2))"
  :precision binary64
  (/ (+ (- (exp (neg x)) 1.0) x) (pow x 2.0)))