Error

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Derivation

1. Split input into 3 regimes

2. if re < -1.6035446659814535e+64 or -6.356570007940982e-159 < re < -1.848688398750353e-171

   1. Initial program 43.4

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

   2. Taylor expanded around -inf 12.6

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

   3. Simplified12.6

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

   if -1.6035446659814535e+64 < re < -6.356570007940982e-159 or -1.848688398750353e-171 < re < 1.2372550508729309e+85

   1. Initial program 19.9

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

   if 1.2372550508729309e+85 < re

   1. Initial program 47.7

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

   2. Taylor expanded around inf 9.1

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

4. Final simplification16.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.6035446659814535 \cdot 10^{+64}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le -6.356570007940982 \cdot 10^{-159}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{elif}\;re \le -1.848688398750353 \cdot 10^{-171}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 1.2372550508729309 \cdot 10^{+85}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

Runtime

Time bar (total: 3.8s)Debug logProfile

herbie shell --seed 2018252 
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))