Error

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Derivation

1. Split input into 3 regimes

2. if re < -1.150911151621305e+154

   1. Initial program 59.3

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

   3. Applied add-exp-log59.3

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

   4. Taylor expanded around -inf 8.0

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

   5. Simplified8.0

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

   if -1.150911151621305e+154 < re < 1.2497447225446502e+148

   1. Initial program 20.1

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

   if 1.2497447225446502e+148 < re

   1. Initial program 58.0

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

   2. Taylor expanded around inf 7.9

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

4. Final simplification17.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -1.150911151621305 \cdot 10^{+154}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 1.2497447225446502 \cdot 10^{+148}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019005 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Details

Time bar (total: 8.6s)Debug log