Error

Try it out

Derivation

1. Split input into 3 regimes

2. if re < -1.98901646800801e+52

   1. Initial program 42.5

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

   2. Taylor expanded around -inf 10.7

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

   3. Simplified10.7

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

   if -1.98901646800801e+52 < re < 2.7167323166120062e+127

   1. Initial program 21.0

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

   if 2.7167323166120062e+127 < re

   1. Initial program 55.1

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

   2. Taylor expanded around inf 7.1

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

4. Final simplification16.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.98901646800801 \cdot 10^{+52}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 2.7167323166120062 \cdot 10^{+127}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

Reproduce

herbie shell --seed 2019021 
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))

Details

Time bar (total: 2.4s)Debug log