Error

Try it out

Derivation

1. Split input into 3 regimes

2. if re < -3.0260633371563236e+95 or -1.6983590970193986e-164 < re < -3.151634490341881e-222

   1. Initial program 45.3

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

   2. Taylor expanded around -inf 17.1

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

   3. Simplified17.1

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

   if -3.0260633371563236e+95 < re < -1.6983590970193986e-164 or -3.151634490341881e-222 < re < 1.1887108504340247e+149

   1. Initial program 19.9

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

   if 1.1887108504340247e+149 < re

   1. Initial program 60.5

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

   2. Taylor expanded around inf 6.4

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

4. Final simplification17.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -3.0260633371563236 \cdot 10^{+95}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le -1.6983590970193986 \cdot 10^{-164}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{elif}\;re \le -3.151634490341881 \cdot 10^{-222}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 1.1887108504340247 \cdot 10^{+149}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

Runtime

Time bar (total: 3.7s)Debug logProfile

herbie shell --seed 2018249 
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))