Error

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Derivation

1. Split input into 3 regimes

2. if re < -2.0059171689987356e+152

   1. Initial program 58.7

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

   2. Taylor expanded around -inf 6.8

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

   3. Simplified6.8

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

   if -2.0059171689987356e+152 < re < 8.497170838155968e+123

   1. Initial program 19.4

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

   if 8.497170838155968e+123 < re

   1. Initial program 52.5

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

   2. Taylor expanded around inf 9.3

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

4. Final simplification16.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -2.0059171689987356 \cdot 10^{+152}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 8.497170838155968 \cdot 10^{+123}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2018362 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Details

Time bar (total: 1.1s)Debug log