Average Error: 32.1 → 0.3

Time: 34.3s

Precision: 64

Internal Precision: 576

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

↓

\[\frac{\tan^{-1}_* \frac{im}{re}}{\log base}\]

Error

The X axis uses an exponential scale — Bits error versus `re`

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Derivation

Initial program 32.1
\[\frac{\tan^{-1}_* \frac{im}{re} \cdot \log base - \log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
Initial simplification0.3
\[\leadsto \frac{\tan^{-1}_* \frac{im}{re}}{\log base}\]
Final simplification0.3
\[\leadsto \frac{\tan^{-1}_* \frac{im}{re}}{\log base}\]

Runtime

herbie shell --seed 2018221 
(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))))