Error

Derivation

1. Initial program 60.6

   \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]

2. Initial simplification60.6

   \[\leadsto \cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]
3. Using strategy rm

4. Applied add-log-exp59.6

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

6. Applied add-sqr-sqrt59.6

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

7. Applied exp-prod59.6

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

8. Applied log-pow59.3

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

10. Applied add-cube-cbrt59.4

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

11. Applied log-prod59.4

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

12. Final simplification59.4

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

Reproduce

herbie shell --seed 2018362 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))

Details

Time bar (total: 5.7s)Debug log