Average Error: 0.8 → 0.7
Time: 25.3s
Precision: 64
Internal Precision: 384
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
↓
\[\frac{\frac{1}{\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}} \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}}}{\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}}\]

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.8

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

  3. Applied clear-num1.0

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

  5. Applied add-cube-cbrt0.9

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

  6. Applied associate-/r*0.7

    \[\leadsto \color{blue}{\frac{\frac{1}{\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}} \cdot \sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}}}{\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}}}\]
  7. Removed slow pow expressions.

Runtime

Time bar (total: 25.3s)Debug logProfile

herbie shell --seed '#(1062930989 876886121 3990119081 3032829768 3060892583 1929069376)' 
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  (/ (atan2 im re) (log 10)))