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

Average Error: 51.0 → 51.0

Time: 2.4s

Precision: binary64

Math

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

↓

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

Error

Bits error versus x

Derivation

1. Initial program 51.0

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

2. Final simplification 51.0

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

Reproduce

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