Error

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Derivation

1. Split input into 4 regimes

2. if im < -5.693695950953394e-257 or 1.9463971507661055e-202 < im < 2.2194224750753604e+144

   1. Initial program 24.5

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

   if -5.693695950953394e-257 < im < -4.419307702247496e-287 or 3.46685258533055e-260 < im < 1.9463971507661055e-202

   1. Initial program 29.5

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

   2. Taylor expanded around inf 33.1

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

   if -4.419307702247496e-287 < im < 3.46685258533055e-260

   1. Initial program 29.6

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

   2. Taylor expanded around -inf 32.1

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

   3. Simplified32.1

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

   if 2.2194224750753604e+144 < im

   1. Initial program 55.9

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

   2. Taylor expanded around 0 6.6

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

4. Final simplification23.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;im \le -5.693695950953394 \cdot 10^{-257}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{elif}\;im \le -4.419307702247496 \cdot 10^{-287}:\\ \;\;\;\;re\\ \mathbf{elif}\;im \le 3.46685258533055 \cdot 10^{-260}:\\ \;\;\;\;-re\\ \mathbf{elif}\;im \le 1.9463971507661055 \cdot 10^{-202}:\\ \;\;\;\;re\\ \mathbf{elif}\;im \le 2.2194224750753604 \cdot 10^{+144}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;im\\ \end{array}\]

Reproduce

herbie shell --seed 2018360 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Details

Time bar (total: 1.1s)Debug log