Error

Derivation

1. Split input into 5 regimes

2. if im < -3.3955093218469717e+145

   1. Initial program 59.9

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

   2. Applied simplify59.9

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

   3. Taylor expanded around -inf 0.5

      \[\leadsto \frac{\log base \cdot \log \color{blue}{\left(-1 \cdot im\right)}}{\log base \cdot \log base}\]

   4. Applied simplify0.4

      \[\leadsto \color{blue}{\frac{\log \left(-im\right)}{\log base}}\]

   if -3.3955093218469717e+145 < im < -1.3901459543564231e-276

   1. Initial program 20.1

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

   2. Applied simplify20.1

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

   4. Applied clear-num20.2

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

   5. Applied simplify20.1

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

   if -1.3901459543564231e-276 < im < 1.2864286111203345e-223

   1. Initial program 31.2

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

   2. Applied simplify31.2

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

   3. Taylor expanded around 0 0.5

      \[\leadsto \frac{\log base \cdot \log \color{blue}{re}}{\log base \cdot \log base}\]

   4. Applied simplify0.4

      \[\leadsto \color{blue}{\frac{\log re}{\log base}}\]

   if 1.2864286111203345e-223 < im < 9.303283361974231e+95

   1. Initial program 19.1

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

   2. Applied simplify19.1

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

   4. Applied associate-/l*19.1

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

   if 9.303283361974231e+95 < im

   1. Initial program 50.2

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

   2. Applied simplify50.2

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

   3. Taylor expanded around inf 0.5

      \[\leadsto \frac{\log base \cdot \log \color{blue}{im}}{\log base \cdot \log base}\]

   4. Applied simplify0.4

      \[\leadsto \color{blue}{\frac{\log im}{\log base}}\]
3. Recombined 5 regimes into one program.
4. Removed slow pow expressions.

Runtime

Time bar (total: 1.8m)Debug logProfile

herbie shell --seed '#(1062930989 876886121 3990119081 3032829768 3060892583 1929069376)' 
(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))))