Error

Derivation

1. Initial program 4.1

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

2. Simplified0.1

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

4. Applied *-un-lft-identity0.1

   \[\leadsto \sqrt{e^{x} + \color{blue}{1 \cdot 1}}\]

5. Applied add-sqr-sqrt0.1

   \[\leadsto \sqrt{\color{blue}{\sqrt{e^{x}} \cdot \sqrt{e^{x}}} + 1 \cdot 1}\]

6. Applied hypot-def0.1

   \[\leadsto \color{blue}{\sqrt{\left(\sqrt{e^{x}}\right)^2 + 1^2}^*}\]

7. Final simplification0.1

   \[\leadsto \sqrt{\left(\sqrt{e^{x}}\right)^2 + 1^2}^*\]

Reproduce

herbie shell --seed 2019100 +o rules:numerics
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))