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

Average Error: 0.1 → 0.1

Time: 1.5s

Precision: binary64

Math

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

↓

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

Error

Bits error versus j

Bits error versus x

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Reproduce

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