Average Error: 34.0 → 34.0
Time: 27.4s
Precision: 64
Internal Precision: 128
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
↓
\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]

Error

Bits error versus a

Bits error versus c

Derivation

  1. Initial program 34.0

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

  3. Applied add-exp-log34.0

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

  4. Taylor expanded around -inf 34.0

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

  5. Final simplification34.0

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

Reproduce

herbie shell --seed 2019072 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))