(/ (- 1) (- (/ 1 (- (exp (* (- 2) x)) 1)) 1))

Average Error: 29.2 → 29.2

Time: 1.4s

Precision: binary64

Math

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

↓

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

Error

Bits error versus x

Derivation

1. Initial program 29.2

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

2. Final simplification 29.2

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

Reproduce

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