(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))

Average Error: 58.1 → 58.1

Time: 2.5s

Precision: binary64

Math

\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]

↓

\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]

Error

Bits error versus x

Derivation

1. Initial program 58.1

   \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]

2. Final simplification 58.1

   \[\leadsto \frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]

Reproduce

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