Error

Try it out

Derivation

1. Split input into 4 regimes

2. if re < -2.5610637130855064e+108

   1. Initial program 49.1

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

   2. Taylor expanded around -inf 10.1

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

   3. Simplified10.1

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

   if -2.5610637130855064e+108 < re < -1.5860187489394888e-287 or 3.788519408795228e-242 < re < 3.1963818951378107e+122

   1. Initial program 19.3

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

   if -1.5860187489394888e-287 < re < 3.788519408795228e-242

   1. Initial program 31.5

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

   2. Taylor expanded around 0 33.4

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

   if 3.1963818951378107e+122 < re

   1. Initial program 51.6

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

   2. Taylor expanded around inf 8.7

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

4. Final simplification17.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -2.5610637130855064 \cdot 10^{+108}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le -1.5860187489394888 \cdot 10^{-287}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{elif}\;re \le 3.788519408795228 \cdot 10^{-242}:\\ \;\;\;\;im\\ \mathbf{elif}\;re \le 3.1963818951378107 \cdot 10^{+122}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019010 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Details

Time bar (total: 2.0s)Debug log