Average Error: 39.9 → 0.0

Time: 15.3s

Precision: 64

Internal Precision: 1344

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

↓

\[\sqrt{\frac{\left(e^{x} \cdot e^{x}\right) \cdot e^{x} + 1}{\left(1 - e^{x}\right) + e^{x} \cdot e^{x}}}\]

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Initial program 39.9
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
Initial simplification0.0
\[\leadsto \sqrt{e^{x} + 1}\]
Using strategy rm
Applied flip3-+0.0
\[\leadsto \sqrt{\color{blue}{\frac{{\left(e^{x}\right)}^{3} + {1}^{3}}{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}}}\]
Using strategy rm
Applied unpow30.0
\[\leadsto \sqrt{\frac{\color{blue}{\left(e^{x} \cdot e^{x}\right) \cdot e^{x}} + {1}^{3}}{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}}\]
Final simplification0.0
\[\leadsto \sqrt{\frac{\left(e^{x} \cdot e^{x}\right) \cdot e^{x} + 1}{\left(1 - e^{x}\right) + e^{x} \cdot e^{x}}}\]

	Baseline	Herbie	Oracle	Span	%
Regimes	0.0	0.0	0.0	0.0	100%

herbie shell --seed 2018340 +o rules:numerics
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))