Error

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Derivation

1. Split input into 4 regimes

2. if re < -2.139770464496479e+66

   1. Initial program 43.8

      \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]

   2. Taylor expanded around -inf 10.2

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

   3. Simplified10.2

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

   if -2.139770464496479e+66 < re < -1.7386973165922955e-170 or 4.948363111980352e-288 < re < 5.516607425614895e-204 or 1.9758932018135865e-175 < re < 0.15853601375624227

   1. Initial program 18.7

      \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]

   if -1.7386973165922955e-170 < re < 4.948363111980352e-288 or 5.516607425614895e-204 < re < 1.9758932018135865e-175

   1. Initial program 29.6

      \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]

   2. Taylor expanded around 0 34.2

      \[\leadsto \log \color{blue}{im}\]

   if 0.15853601375624227 < re

   1. Initial program 38.8

      \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]

   2. Taylor expanded around inf 13.2

      \[\leadsto \log \color{blue}{re}\]
3. Recombined 4 regimes into one program.

4. Final simplification18.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -2.139770464496479 \cdot 10^{+66}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le -1.7386973165922955 \cdot 10^{-170}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{elif}\;re \le 4.948363111980352 \cdot 10^{-288}:\\ \;\;\;\;\log im\\ \mathbf{elif}\;re \le 5.516607425614895 \cdot 10^{-204}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{elif}\;re \le 1.9758932018135865 \cdot 10^{-175}:\\ \;\;\;\;\log im\\ \mathbf{elif}\;re \le 0.15853601375624227:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

Runtime

Time bar (total: 3.7s)Debug logProfile

herbie shell --seed 2018340 
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))