Error

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Derivation

1. Split input into 4 regimes

2. if re < -2.0237663893503905e+121

   1. Initial program 51.5

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

   2. Taylor expanded around -inf 9.2

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

   3. Simplified9.2

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

   if -2.0237663893503905e+121 < re < 6.288295134269618e-140 or 1.1925302764880028e-107 < re < 3.539643897265089e+114

   1. Initial program 20.3

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

   if 6.288295134269618e-140 < re < 1.1925302764880028e-107

   1. Initial program 18.9

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

   2. Taylor expanded around 0 38.7

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

   if 3.539643897265089e+114 < re

   1. Initial program 50.5

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

   2. Taylor expanded around inf 9.2

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

4. Final simplification17.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -2.0237663893503905 \cdot 10^{+121}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 6.288295134269618 \cdot 10^{-140}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{elif}\;re \le 1.1925302764880028 \cdot 10^{-107}:\\ \;\;\;\;im\\ \mathbf{elif}\;re \le 3.539643897265089 \cdot 10^{+114}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019007 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Details

Time bar (total: 2.0s)Debug log