Average Error: 34.4 → 34.4
Time: 24.2s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[\sqrt{e^{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}} \cdot \sqrt{e^{\log \left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)}}\]

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.4

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

  3. Applied add-exp-log34.4

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

  5. Applied add-sqr-sqrt34.4

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

  6. Final simplification34.4

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

Reproduce

herbie shell --seed 2019030 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))