Average Error: 30.8 → 0.4
Time: 37.2s
Precision: 64
Internal Precision: 384
\[\frac{\tan^{-1}_* \frac{im}{re} \cdot \log base - \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
↓
\[\left(\tan^{-1}_* \frac{im}{re} - 0\right) \cdot \frac{1}{\log base}\]

Error

Bits error versus re

Bits error versus im

Bits error versus base

Derivation

  1. Initial program 30.8

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

  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. Removed slow pow expressions.

Runtime

Time bar (total: 37.2s)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit
(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))))