Average Error: 58.0 → 0.6

Time: 9.5s

Precision: 64

Internal Precision: 128

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

↓

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

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Initial program 58.0
\[\frac{e^{x} - e^{-x}}{2}\]
Taylor expanded around 0 0.6
\[\leadsto \frac{\color{blue}{2 \cdot x + \left(\frac{1}{3} \cdot {x}^{3} + \frac{1}{60} \cdot {x}^{5}\right)}}{2}\]
Final simplification0.6
\[\leadsto \frac{2 \cdot x + \left({x}^{5} \cdot \frac{1}{60} + \frac{1}{3} \cdot {x}^{3}\right)}{2}\]

	Baseline	Herbie	Oracle	Span	%
Regimes	0.6	0.6	0.0	0.6	0%

herbie shell --seed 2018355 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))