Error

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Derivation

1. Split input into 4 regimes

2. if re < -2.158725719313022e+148

   1. Initial program 57.6

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

   2. Taylor expanded around -inf 7.5

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

   3. Simplified7.5

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

   if -2.158725719313022e+148 < re < -1.8470168009869996e-301 or 4.2122813192253714e-256 < re < 1.7910245925154982e+121

   1. Initial program 18.9

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

   if -1.8470168009869996e-301 < re < 4.2122813192253714e-256

   1. Initial program 28.2

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

   2. Taylor expanded around 0 34.4

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

   if 1.7910245925154982e+121 < re

   1. Initial program 51.7

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

   2. Taylor expanded around inf 8.7

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

4. Final simplification16.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -2.158725719313022 \cdot 10^{+148}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le -1.8470168009869996 \cdot 10^{-301}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{elif}\;re \le 4.2122813192253714 \cdot 10^{-256}:\\ \;\;\;\;im\\ \mathbf{elif}\;re \le 1.7910245925154982 \cdot 10^{+121}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2018365 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Details

Time bar (total: 9.1s)Debug log