Average Error: 31.1 → 0.4
Time: 1.1m
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 31.1

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

  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: 1.1m)Debug logProfile

herbie shell --seed '#(1063027428 1192549564 1443466578 604016274 3637110559 1698629644)' 
(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))))