Error

Try it out

Derivation

1. Split input into 4 regimes

2. if re < -5.087015824912348e+107

   1. Initial program 51.7

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

   2. Taylor expanded around -inf 8.5

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

   3. Simplified8.5

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

   if -5.087015824912348e+107 < re < 7.158781234828456e-138 or 1.1925302764880028e-107 < re < 4.3619401585985797e+95

   1. Initial program 21.0

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

   if 7.158781234828456e-138 < re < 1.1925302764880028e-107

   1. Initial program 19.8

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

   2. Taylor expanded around 0 36.7

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

   if 4.3619401585985797e+95 < re

   1. Initial program 50.2

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

   2. Taylor expanded around inf 8.7

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

4. Final simplification17.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -5.087015824912348 \cdot 10^{+107}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le 7.158781234828456 \cdot 10^{-138}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{elif}\;re \le 1.1925302764880028 \cdot 10^{-107}:\\ \;\;\;\;\log im\\ \mathbf{elif}\;re \le 4.3619401585985797 \cdot 10^{+95}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

Reproduce

herbie shell --seed 2019007 
(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