Error

Try it out

Derivation

1. Split input into 4 regimes

2. if im < -1.3392627148502294e+154 or 2.5071549499226937e-304 < im < 1.2965675590706139e-281

   1. Initial program 57.5

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

   2. Taylor expanded around -inf 53.7

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

   3. Simplified53.7

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

   if -1.3392627148502294e+154 < im < -1.7597295040722402e-173 or 2.51415582484853e-199 < im < 2.65467171931929e+92

   1. Initial program 17.2

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

   if -1.7597295040722402e-173 < im < 2.5071549499226937e-304 or 1.2965675590706139e-281 < im < 2.51415582484853e-199

   1. Initial program 30.8

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

   2. Taylor expanded around inf 32.6

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

   if 2.65467171931929e+92 < im

   1. Initial program 48.8

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

   2. Taylor expanded around 0 9.9

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

4. Final simplification23.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;im \le -1.3392627148502294 \cdot 10^{+154}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;im \le -1.7597295040722402 \cdot 10^{-173}:\\ \;\;\;\;\log \left(\sqrt{re \cdot re + im \cdot im}\right)\\ \mathbf{elif}\;im \le 2.5071549499226937 \cdot 10^{-304}:\\ \;\;\;\;\log re\\ \mathbf{elif}\;im \le 1.2965675590706139 \cdot 10^{-281}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;im \le 2.51415582484853 \cdot 10^{-199}:\\ \;\;\;\;\log re\\ \mathbf{elif}\;im \le 2.65467171931929 \cdot 10^{+92}:\\ \;\;\;\;\log \left(\sqrt{re \cdot re + im \cdot im}\right)\\ \mathbf{else}:\\ \;\;\;\;\log im\\ \end{array}\]

Runtime

Time bar (total: 3.1s)Debug logProfile

herbie shell --seed 2018346 
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))