Average Error: 33.6 → 33.7
Time: 38.3s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[e^{\left(\sqrt[3]{\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)} \cdot \sqrt[3]{\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)}\right) \cdot \sqrt[3]{\log \left(\sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt{\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}\right)}}\]

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 33.6

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

  3. Applied add-sqr-sqrt33.7

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

  5. Applied add-exp-log33.7

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

  7. Applied add-cube-cbrt33.7

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

  8. Final simplification33.7

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

Runtime

Time bar (total: 38.3s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes33.733.733.60.10%
herbie shell --seed 2018353 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))