Error

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Derivation

1. Initial program 0.0

   \[\frac{2}{e^{x} + e^{-x}}\]
2. Using strategy rm

3. Applied add-log-exp0.1

   \[\leadsto \color{blue}{\log \left(e^{\frac{2}{e^{x} + e^{-x}}}\right)}\]
4. Using strategy rm

5. Applied add-sqr-sqrt0.1

   \[\leadsto \log \color{blue}{\left(\sqrt{e^{\frac{2}{e^{x} + e^{-x}}}} \cdot \sqrt{e^{\frac{2}{e^{x} + e^{-x}}}}\right)}\]

6. Applied log-prod0.1

   \[\leadsto \color{blue}{\log \left(\sqrt{e^{\frac{2}{e^{x} + e^{-x}}}}\right) + \log \left(\sqrt{e^{\frac{2}{e^{x} + e^{-x}}}}\right)}\]

7. Final simplification0.1

   \[\leadsto \log \left(\sqrt{e^{\frac{2}{e^{x} + e^{-x}}}}\right) + \log \left(\sqrt{e^{\frac{2}{e^{x} + e^{-x}}}}\right)\]

Reproduce

herbie shell --seed 2018365 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))

Details

Time bar (total: 3.1s)Debug log