Average Error: 33.6 → 33.6
Time: 27.3s
Precision: 64
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[e^{\left(\sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right) \cdot \sqrt[3]{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\]

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 33.6

    \[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]

  2. Taylor expanded around -inf 33.6

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

  4. Applied add-exp-log33.6

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

  6. Applied add-cube-cbrt33.6

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

  7. Final simplification33.6

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

Reproduce

herbie shell --seed 2019100 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))