Average Error: 39.7 → 0.1

Time: 1.4m

Precision: 64

Internal Precision: 128

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

↓

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

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Initial program 39.7
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
Initial simplification0.0
\[\leadsto \sqrt{e^{x} + 1}\]
Using strategy rm
Applied flip3-+0.1
\[\leadsto \sqrt{\color{blue}{\frac{{\left(e^{x}\right)}^{3} + {1}^{3}}{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}}}\]
Applied sqrt-div0.1
\[\leadsto \color{blue}{\frac{\sqrt{{\left(e^{x}\right)}^{3} + {1}^{3}}}{\sqrt{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}}}\]
Simplified0.1
\[\leadsto \frac{\color{blue}{\sqrt{1 + {\left(e^{x}\right)}^{3}}}}{\sqrt{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}}\]
Final simplification0.1
\[\leadsto \frac{\sqrt{1 + {\left(e^{x}\right)}^{3}}}{\sqrt{e^{x} \cdot e^{x} + \left(1 - e^{x}\right)}}\]

herbie shell --seed 2018336 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))