Error

Derivation

1. Initial program 34.3

   \[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
2. Using strategy rm

3. Applied add-exp-log34.3

   \[\leadsto \color{blue}{e^{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\]
4. Using strategy rm

5. Applied pow134.3

   \[\leadsto e^{\log \color{blue}{\left({\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}^{1}\right)}}\]

6. Applied log-pow34.3

   \[\leadsto e^{\color{blue}{1 \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\]

7. Applied exp-prod34.3

   \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left(\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\right)}}\]

8. Simplified34.3

   \[\leadsto {\color{blue}{e}}^{\left(\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\right)}\]
9. Using strategy rm

10. Applied add-sqr-sqrt34.3

    \[\leadsto {e}^{\left(\log \color{blue}{\left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)}\right)}\]

11. Applied log-prod34.3

    \[\leadsto {e}^{\color{blue}{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) + \log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right)}}\]

12. Applied unpow-prod-up34.3

    \[\leadsto \color{blue}{{e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right)} \cdot {e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right)}}\]

13. Final simplification34.3

    \[\leadsto {e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right)} \cdot {e}^{\left(\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)\right)}\]

Reproduce

herbie shell --seed 2018365 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))

Details

Time bar (total: 5.4s)Debug log