Average Error: 34.1 → 34.1
Time: 28.6s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[{e}^{\left(\sqrt[3]{\left(\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\right) \cdot \left(\left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)}\right)}\]

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.1

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

  3. Applied add-exp-log34.1

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

  5. Applied pow134.1

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

  6. Applied log-pow34.1

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

  7. Applied exp-prod34.1

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

  8. Simplified34.1

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

  10. Applied add-cbrt-cube34.1

    \[\leadsto {e}^{\color{blue}{\left(\sqrt[3]{\left(\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)}}\]
  11. Using strategy rm

  12. Applied add-cube-cbrt34.1

    \[\leadsto {e}^{\left(\sqrt[3]{\left(\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)}}\right)}\]

  13. Final simplification34.1

    \[\leadsto {e}^{\left(\sqrt[3]{\left(\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\right) \cdot \left(\left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)}\right)}\]

Reproduce

herbie shell --seed 2019089 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))