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

↓

\[\begin{array}{l} \mathbf{if}\;re \le -4.9066085980367 \cdot 10^{+122}:\\ \;\;\;\;\log \left(-re\right)\\ \mathbf{if}\;re \le -1.4664875883069754 \cdot 10^{-130}:\\ \;\;\;\;\log \left(\sqrt{re \cdot re + im \cdot im}\right)\\ \mathbf{if}\;re \le -3.5689365038231576 \cdot 10^{-250}:\\ \;\;\;\;\log im\\ \mathbf{if}\;re \le 5.78951180277367 \cdot 10^{+88}:\\ \;\;\;\;\log \left(\sqrt{re \cdot re + im \cdot im}\right)\\ \mathbf{else}:\\ \;\;\;\;\log re\\ \end{array}\]

Derivation

Split input into 4 regimes
if re < -4.9066085980367e+122
1. Initial program 54.6
  \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
2. Taylor expanded around -inf 7.7
  \[\leadsto \log \color{blue}{\left(-1 \cdot re\right)}\]
3. Applied simplify7.7
  \[\leadsto \color{blue}{\log \left(-re\right)}\]
if -4.9066085980367e+122 < re < -1.4664875883069754e-130 or -3.5689365038231576e-250 < re < 5.78951180277367e+88
1. Initial program 19.8
  \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
if -1.4664875883069754e-130 < re < -3.5689365038231576e-250
1. Initial program 26.6
  \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
2. Taylor expanded around 0 35.4
  \[\leadsto \log \color{blue}{im}\]
if 5.78951180277367e+88 < re
1. Initial program 47.6
  \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
2. Taylor expanded around inf 9.0
  \[\leadsto \log \color{blue}{re}\]
Recombined 4 regimes into one program.

Runtime

herbie shell --seed '#(1072330854 3074818769 591214268 3603999196 3863745332 3332387116)' 
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))

Error

Derivation

`if re < -4.9066085980367e+122`

`if -4.9066085980367e+122 < re < -1.4664875883069754e-130 or -3.5689365038231576e-250 < re < 5.78951180277367e+88`

`if -1.4664875883069754e-130 < re < -3.5689365038231576e-250`

`if 5.78951180277367e+88 < re`

Runtime