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Derivation

1. Split input into 3 regimes

2. if re < -1.4072346371405111e+153

   1. Initial program 59.0

      \[\sqrt{re \cdot re + im \cdot im}\]

   2. Taylor expanded around -inf 7.4

      \[\leadsto \color{blue}{-1 \cdot re}\]

   3. Simplified7.4

      \[\leadsto \color{blue}{-re}\]

   if -1.4072346371405111e+153 < re < 7.806807759685719e+146

   1. Initial program 19.4

      \[\sqrt{re \cdot re + im \cdot im}\]

   if 7.806807759685719e+146 < re

   1. Initial program 57.2

      \[\sqrt{re \cdot re + im \cdot im}\]

   2. Taylor expanded around inf 7.9

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

4. Final simplification16.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.4072346371405111 \cdot 10^{+153}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 7.806807759685719 \cdot 10^{+146}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Runtime

Time bar (total: 2.0s)Debug logProfile

herbie shell --seed 2018263 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))