Average Error: 0.9 → 0.5
Time: 17.9s
Precision: 64
Ground Truth: 128
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
⬇
\[\frac{1}{{\left(\sqrt[3]{{\left(\sqrt[3]{\frac{\log 10}{\tan^{-1}_* \frac{im}{re}}}\right)}^3}\right)}^3}\]

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 0.9

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

  7. Applied add-cube-cbrt 0.5

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

Runtime

Total time: 17.9s Debug log

Please include this information when filing a bug report:

herbie --seed '#(716253325 3392695753 2850131074 4052890301 3778115962 4137927804)'
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  (/ (atan2 im re) (log 10)))