Average Error: 0.9 → 0.8
Time: 10.2s
Precision: 64
Internal precision: 128
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
⬇
\[\frac{1}{{\left(\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right)}^{3}}\]

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.9

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

  3. Applied clear-num 1.0

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

  5. Applied add-cube-cbrt 0.8

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

  7. Applied pow3 0.8

    \[\leadsto \frac{1}{\color{blue}{{\left(\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right)}^{3}}}\]
  8. Removed slow pow expressions

Runtime

Time bar (total: 10.2s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(2531553256 3777197841 433815218 667484030 2077417930 1834909037)'
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  (/ (atan2 im re) (log 10)))