Hyperbolic secant

Average Error: 0.0 → 0.0

Time: 1.5s

Precision: binary64

Math

\[\frac{2}{e^{x} + e^{-x}}\]

↓

\[\frac{-2}{\frac{-1}{e^{x}} - e^{x}}\]

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[\frac{2}{e^{x} + e^{-x}}\]
2. Using strategy rm

3. Applied frac-2neg 0.0

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

4. Simplified 0.0

   \[\leadsto \frac{-2}{\color{blue}{\frac{-1}{e^{x}} - e^{x}}}\]

5. Final simplification 0.0

   \[\leadsto \frac{-2}{\frac{-1}{e^{x}} - e^{x}}\]

Reproduce

herbie shell --seed 2020155 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (neg x)))))