Error

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Derivation

1. Split input into 3 regimes

2. if re < -5.061381323129702e+137

   1. Initial program 54.5

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

   2. Taylor expanded around -inf 7.9

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

   3. Simplified7.9

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

   if -5.061381323129702e+137 < re < 1.7906814815354527e+113

   1. Initial program 20.6

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

   if 1.7906814815354527e+113 < re

   1. Initial program 51.2

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

   2. Taylor expanded around inf 10.0

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

4. Final simplification17.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -5.061381323129702 \cdot 10^{+137}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 1.7906814815354527 \cdot 10^{+113}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019008 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Details

Time bar (total: 1.9s)Debug log