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Derivation

1. Initial program 39.9

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

2. Initial simplification0.0

   \[\leadsto \sqrt{e^{x} + 1}\]
3. Using strategy rm

4. Applied flip3-+0.1

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

5. Applied sqrt-div0.1

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

6. Final simplification0.1

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

Reproduce

herbie shell --seed 2018360 +o rules:numerics
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))

Details

Time bar (total: 8.1s)Debug log