Error

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Derivation

1. Split input into 3 regimes

2. if re < -9.654391066010857e+153

   1. Initial program 59.5

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

   2. Taylor expanded around -inf 7.2

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

   3. Simplified7.2

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

   if -9.654391066010857e+153 < re < 5.474516698358515e+115

   1. Initial program 20.0

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

   if 5.474516698358515e+115 < re

   1. Initial program 49.7

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

   2. Taylor expanded around inf 8.8

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

4. Final simplification16.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -9.654391066010857 \cdot 10^{+153}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 5.474516698358515 \cdot 10^{+115}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019004 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Details

Time bar (total: 1.6s)Debug log