Error

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Derivation

1. Split input into 3 regimes

2. if re < -1.747299818609954e+153

   1. Initial program 61.6

      \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
   2. Using strategy rm

   3. Applied add-exp-log61.6

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

   4. Taylor expanded around -inf 6.8

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

   5. Simplified6.8

      \[\leadsto \log \color{blue}{\left(-re\right)}\]

   if -1.747299818609954e+153 < re < 1.0209258191409414e+147

   1. Initial program 20.8

      \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
   2. Using strategy rm

   3. Applied add-exp-log20.8

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

   if 1.0209258191409414e+147 < re

   1. Initial program 60.3

      \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
   2. Using strategy rm

   3. Applied add-exp-log60.3

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

   4. Taylor expanded around inf 6.6

      \[\leadsto \log \color{blue}{re}\]
3. Recombined 3 regimes into one program.

4. Final simplification17.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.747299818609954 \cdot 10^{+153}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 1.0209258191409414 \cdot 10^{+147}:\\ \;\;\;\;\log \left(\sqrt{e^{\log \left(im \cdot im + re \cdot re\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

Reproduce

herbie shell --seed 2019005 
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))

Details

Time bar (total: 4.0s)Debug log