Average Error: 33.8 → 33.4
Time: 32.2s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[\left(\left(\cosh c\right) \bmod \left(\sqrt[3]{\log_* (1 + a)} \cdot \left(\sqrt[3]{\log_* (1 + a)} \cdot \left(\sqrt[3]{\sqrt[3]{\log_* (1 + a)}} \cdot \left(\sqrt[3]{\sqrt[3]{\log_* (1 + a)}} \cdot \left(e^{\log \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{\log_* (1 + a)}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{\log_* (1 + a)}}}\right)} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{\log_* (1 + a)}}}\right)\right)\right)\right)\right)\right)\]

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 33.8

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

  3. Applied add-cube-cbrt33.4

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

  5. Applied add-cube-cbrt33.4

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

  7. Applied add-cube-cbrt33.4

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

  9. Applied add-exp-log33.4

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

  10. Final simplification33.4

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

Reproduce

herbie shell --seed 2019051 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))