Error

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Derivation

1. Initial program 31.3

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

2. Simplified0.4

   \[\leadsto \color{blue}{\frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log base}}\]
3. Using strategy rm

4. Applied pow10.4

   \[\leadsto \frac{\log \color{blue}{\left({\left(\sqrt{re^2 + im^2}^*\right)}^{1}\right)}}{\log base}\]

5. Applied log-pow0.4

   \[\leadsto \frac{\color{blue}{1 \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}}{\log base}\]

6. Applied associate-/l*0.4

   \[\leadsto \color{blue}{\frac{1}{\frac{\log base}{\log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
7. Using strategy rm

8. Applied associate-/r/0.4

   \[\leadsto \color{blue}{\frac{1}{\log base} \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}\]

9. Final simplification0.4

   \[\leadsto \frac{1}{\log base} \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\]

Reproduce

herbie shell --seed 2019007 +o rules:numerics
(FPCore (re im base)
  :name "math.log/2 on complex, real part"
  (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))))

Details

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