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

↓

\[\frac{(\left((\left(x \cdot x\right) \cdot \frac{1}{3} + 2)_*\right) \cdot x + \left(\frac{1}{60} \cdot {x}^{5}\right))_*}{2}\]

Derivation

Initial program 57.8
\[\frac{e^{x} - e^{-x}}{2}\]
Taylor expanded around 0 0.8
\[\leadsto \frac{\color{blue}{\frac{1}{3} \cdot {x}^{3} + \left(\frac{1}{60} \cdot {x}^{5} + 2 \cdot x\right)}}{2}\]
Simplified0.8
\[\leadsto \frac{\color{blue}{(\left((\left(x \cdot x\right) \cdot \frac{1}{3} + 2)_*\right) \cdot x + \left(\frac{1}{60} \cdot {x}^{5}\right))_*}}{2}\]
Final simplification0.8
\[\leadsto \frac{(\left((\left(x \cdot x\right) \cdot \frac{1}{3} + 2)_*\right) \cdot x + \left(\frac{1}{60} \cdot {x}^{5}\right))_*}{2}\]

Runtime

herbie shell --seed 2018215 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))