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Derivation

1. Initial program 0.8

   \[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]

2. Initial simplification0.8

   \[\leadsto \frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
3. Using strategy rm

4. Applied add-sqr-sqrt0.8

   \[\leadsto \frac{\tan^{-1}_* \frac{im}{re}}{\color{blue}{\sqrt{\log 10} \cdot \sqrt{\log 10}}}\]

5. Applied *-un-lft-identity0.8

   \[\leadsto \frac{\color{blue}{1 \cdot \tan^{-1}_* \frac{im}{re}}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]

6. Applied times-frac0.8

   \[\leadsto \color{blue}{\frac{1}{\sqrt{\log 10}} \cdot \frac{\tan^{-1}_* \frac{im}{re}}{\sqrt{\log 10}}}\]
7. Using strategy rm

8. Applied div-inv0.8

   \[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \color{blue}{\left(\tan^{-1}_* \frac{im}{re} \cdot \frac{1}{\sqrt{\log 10}}\right)}\]

9. Final simplification0.8

   \[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \left(\tan^{-1}_* \frac{im}{re} \cdot \frac{1}{\sqrt{\log 10}}\right)\]

Runtime

Time bar (total: 9.3s)Debug logProfile

herbie shell --seed 2018296 +o rules:numerics
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  (/ (atan2 im re) (log 10)))