Average Error: 0.0 → 0.0

Time: 6.0min

Precision: binary64

Falling back on racket egraph because egg-herbie package not installed (more)

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

↓

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

Error

The X axis uses an exponential scale — Bits error versus x

The X axis uses an exponential scale — Bits error versus x

Derivation

Initial program 0.0
\[\frac{2}{e^{x} + e^{-x}}\]
Using strategy rm
Applied add-sqr-sqrt0.0
\[\leadsto \color{blue}{\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{\frac{2}{e^{x} + e^{-x}}}}\]
Final simplification0.0
\[\leadsto \sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{\frac{2}{e^{x} + e^{-x}}}\]

Reproduce

herbie shell --seed 2020181 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (neg x)))))