Error

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Derivation

1. Split input into 4 regimes

2. if re < -3.269784804517612e+55

   1. Initial program 43.0

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

   2. Taylor expanded around -inf 10.2

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

   3. Simplified10.2

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

   if -3.269784804517612e+55 < re < -1.0663540637506733e-290 or 3.701775518637736e-256 < re < 1.5545837674343295e+102

   1. Initial program 20.2

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

   if -1.0663540637506733e-290 < re < 3.701775518637736e-256

   1. Initial program 29.2

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

   2. Taylor expanded around 0 34.1

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

   if 1.5545837674343295e+102 < re

   1. Initial program 50.4

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

   2. Taylor expanded around inf 8.4

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

4. Final simplification17.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -3.269784804517612 \cdot 10^{+55}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{elif}\;re \le -1.0663540637506733 \cdot 10^{-290}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{elif}\;re \le 3.701775518637736 \cdot 10^{-256}:\\ \;\;\;\;\log im\\ \mathbf{elif}\;re \le 1.5545837674343295 \cdot 10^{+102}:\\ \;\;\;\;\log \left(\sqrt{im \cdot im + re \cdot re}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

Reproduce

herbie shell --seed 2018365 
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))

Details

Time bar (total: 1.3s)Debug log