Average Error: 31.8 → 0.7
Time: 28.9s
Precision: 64
Internal Precision: 384
\[\frac{\tan^{-1}_* \frac{im}{re} \cdot \log base - \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
↓
\[\left(\tan^{-1}_* \frac{im}{re} - 0\right) \cdot \sqrt[3]{\frac{\frac{1}{\log base}}{\log base \cdot \log base}}\]

Error

Bits error versus re

Bits error versus im

Bits error versus base

Derivation

  1. Initial program 31.8

    \[\frac{\tan^{-1}_* \frac{im}{re} \cdot \log base - \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]

  2. Applied simplify0.3

    \[\leadsto \color{blue}{\frac{\tan^{-1}_* \frac{im}{re} - 0}{\log base}}\]
  3. Using strategy rm

  4. Applied div-inv0.4

    \[\leadsto \color{blue}{\left(\tan^{-1}_* \frac{im}{re} - 0\right) \cdot \frac{1}{\log base}}\]
  5. Using strategy rm

  6. Applied add-cbrt-cube0.8

    \[\leadsto \left(\tan^{-1}_* \frac{im}{re} - 0\right) \cdot \color{blue}{\sqrt[3]{\left(\frac{1}{\log base} \cdot \frac{1}{\log base}\right) \cdot \frac{1}{\log base}}}\]

  7. Applied simplify0.7

    \[\leadsto \left(\tan^{-1}_* \frac{im}{re} - 0\right) \cdot \sqrt[3]{\color{blue}{\frac{\frac{1}{\log base}}{\log base \cdot \log base}}}\]

Runtime

Time bar (total: 28.9s)Debug logProfile

herbie shell --seed '#(1070100504 930361288 1279167582 284574201 1450237281 2578255382)' 
(FPCore (re im base)
  :name "math.log/2 on complex, imaginary part"
  (/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0)) (+ (* (log base) (log base)) (* 0 0))))