Error

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Derivation

1. Split input into 4 regimes

2. if re < -1.3034612690171742e+154

   1. Initial program 59.4

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

   2. Taylor expanded around -inf 7.6

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

   3. Simplified7.6

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

   if -1.3034612690171742e+154 < re < -5.536443801166738e-261 or 2.727916884694162e-303 < re < 3.0959742777573048e+147

   1. Initial program 18.9

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

   if -5.536443801166738e-261 < re < 2.727916884694162e-303

   1. Initial program 31.2

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

   2. Taylor expanded around 0 31.3

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

   if 3.0959742777573048e+147 < re

   1. Initial program 57.9

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

   2. Taylor expanded around inf 7.7

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

4. Final simplification16.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.3034612690171742 \cdot 10^{+154}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le -5.536443801166738 \cdot 10^{-261}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{elif}\;re \le 2.727916884694162 \cdot 10^{-303}:\\ \;\;\;\;im\\ \mathbf{elif}\;re \le 3.0959742777573048 \cdot 10^{+147}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019022 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Details

Time bar (total: 1.9s)Debug log