Average Error: 0.8 → 0.8
Time: 13.7s
Precision: 64
Internal Precision: 576
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
↓
\[\frac{1}{\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}} \cdot \left(\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}} \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right)}\]

Error

Bits error versus re

Bits error versus im

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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 *-un-lft-identity0.8

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

  5. Applied associate-/l*1.0

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

  7. Applied add-cube-cbrt0.8

    \[\leadsto \frac{1}{\color{blue}{\left(\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}} \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right) \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}}}\]

  8. Final simplification0.8

    \[\leadsto \frac{1}{\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}} \cdot \left(\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}} \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right)}\]

Runtime

Time bar (total: 13.7s)Debug logProfile

herbie shell --seed 2018258 
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  (/ (atan2 im re) (log 10)))