Average Error: 34.3 → 34.3
Time: 26.7s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[{\left({\left(e^{\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right) \cdot \log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\right)}^{\left(\sqrt[3]{\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}} \cdot \sqrt[3]{\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\right)}\right)}^{\left(\sqrt[3]{\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\right)}\]

Error

Bits error versus a

Bits error versus c

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 add-cbrt-cube34.3

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

  7. Applied cbrt-prod34.3

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

  8. Applied exp-prod34.3

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

  10. Applied add-cube-cbrt34.3

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

  11. Applied pow-unpow34.3

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

  12. Final simplification34.3

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

Reproduce

herbie shell --seed 2019037 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))