Error

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Derivation

1. Split input into 3 regimes

2. if re < -4.59728319839016e+152

   1. Initial program 59.1

      \[\sqrt{re \cdot re + im \cdot im}\]
   2. Using strategy rm

   3. Applied add-cbrt-cube59.4

      \[\leadsto \color{blue}{\sqrt[3]{\left(\sqrt{re \cdot re + im \cdot im} \cdot \sqrt{re \cdot re + im \cdot im}\right) \cdot \sqrt{re \cdot re + im \cdot im}}}\]

   4. Taylor expanded around -inf 8.1

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

   5. Simplified8.1

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

   if -4.59728319839016e+152 < re < 6.173118775452133e+146

   1. Initial program 19.8

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

   if 6.173118775452133e+146 < re

   1. Initial program 57.6

      \[\sqrt{re \cdot re + im \cdot im}\]
   2. Using strategy rm

   3. Applied add-cbrt-cube59.5

      \[\leadsto \color{blue}{\sqrt[3]{\left(\sqrt{re \cdot re + im \cdot im} \cdot \sqrt{re \cdot re + im \cdot im}\right) \cdot \sqrt{re \cdot re + im \cdot im}}}\]

   4. Taylor expanded around inf 7.4

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

4. Final simplification16.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -4.59728319839016 \cdot 10^{+152}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 6.173118775452133 \cdot 10^{+146}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019018 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Details

Time bar (total: 8.3s)Debug log