Average Error: 40.0 → 0.1

Time: 8.5s

Precision: 64

Internal Precision: 1344

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

↓

\[\sqrt{\frac{{\left(e^{x}\right)}^{3} + 1}{e^{x} \cdot e^{x} + \left(1 - e^{x}\right)}}\]

Error

Try it out

In
Out

Enter valid numbers for all inputs

Initial program 40.0
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
Initial simplification0.0
\[\leadsto \sqrt{e^{x} + 1}\]
Using strategy rm
Applied flip3-+0.1
\[\leadsto \sqrt{\color{blue}{\frac{{\left(e^{x}\right)}^{3} + {1}^{3}}{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}}}\]
Final simplification0.1
\[\leadsto \sqrt{\frac{{\left(e^{x}\right)}^{3} + 1}{e^{x} \cdot e^{x} + \left(1 - e^{x}\right)}}\]

	Baseline	Herbie	Oracle	Span	%
Regimes	0.1	0.1	0.0	0.0	0%

herbie shell --seed 2018274 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))