Error

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Derivation

1. Split input into 3 regimes

2. if re < -1.6813385983305504e+75

   1. Initial program 45.1

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

   2. Taylor expanded around -inf 9.5

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

   3. Simplified9.5

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

   if -1.6813385983305504e+75 < re < 1.509340664542111e+112

   1. Initial program 21.2

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

   if 1.509340664542111e+112 < re

   1. Initial program 51.3

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

   2. Taylor expanded around inf 7.4

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

4. Final simplification16.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.6813385983305504 \cdot 10^{+75}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 1.509340664542111 \cdot 10^{+112}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

Reproduce

herbie shell --seed 2019004 
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))

Details

Time bar (total: 2.2s)Debug log