Average Error: 31.2 → 0.3
Time: 14.6s
Precision: 64
Internal precision: 128
\[\frac{\tan^{-1}_* \frac{im}{re} \cdot \log base - \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
⬇
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log base} - 0\]

Error

Bits error versus re

Bits error versus im

Bits error versus base

Derivation

  1. Initial program 31.2

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

  2. Applied simplify 0.3

    \[\leadsto \color{blue}{\frac{\tan^{-1}_* \frac{im}{re}}{\log base} - 0}\]
  3. Removed slow pow expressions

Runtime

Time bar (total: 14.6s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(1937128464 1473633845 3441730828 2458929433 4027796092 2874239299)'
(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))))