Average Error: 34.7 → 34.8
Time: 27.1s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[e^{\log \left(\sqrt[3]{\left(\left(e^{\log \left(\cosh c\right)}\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)} \cdot e^{\log \left(\sqrt[3]{\left(\left(e^{\log \left(\cosh c\right)}\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\left(\left(e^{\log \left(\cosh c\right)}\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)}\]

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.7

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

  3. Applied add-exp-log34.7

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

  5. Applied add-exp-log34.7

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

  7. Applied add-cube-cbrt34.8

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

  8. Applied log-prod34.8

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

  9. Applied exp-sum34.8

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

  10. Final simplification34.8

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

Reproduce

herbie shell --seed 2019052 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))