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

⬇

\[\begin{array}{l} \mathbf{if}\;re \le -2.674059323268242 \cdot 10^{+128}:\\ \;\;\;\;-re\\ \mathbf{if}\;re \le -2.321564696919607 \cdot 10^{-245}:\\ \;\;\;\;\sqrt{re \cdot re + im \cdot im}\\ \mathbf{if}\;re \le -2.837848394186995 \cdot 10^{-306}:\\ \;\;\;\;im\\ \mathbf{if}\;re \le 2.540188601643307 \cdot 10^{+151}:\\ \;\;\;\;\sqrt{re \cdot re + im \cdot im}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Derivation

Split input into 4 regimes.
if re < -2.674059323268242e+128
1. Initial program 53.9
  \[\sqrt{re \cdot re + im \cdot im}\]
2. Applied taylor 0
  \[\leadsto -1 \cdot re\]
3. Taylor expanded around -inf 0
  
  \[\leadsto \color{blue}{-1 \cdot re}\]
4. Applied simplify 0
  \[\leadsto \color{blue}{-re}\]
if -2.674059323268242e+128 < re < -2.321564696919607e-245 or -2.837848394186995e-306 < re < 2.540188601643307e+151
1. Initial program 19.1
  \[\sqrt{re \cdot re + im \cdot im}\]
if -2.321564696919607e-245 < re < -2.837848394186995e-306
1. Initial program 45.8
  \[\sqrt{re \cdot re + im \cdot im}\]
2. Applied taylor 0
  \[\leadsto im\]
3. Taylor expanded around 0 0
  
  \[\leadsto \color{blue}{im}\]
if 2.540188601643307e+151 < re
1. Initial program 59.1
  \[\sqrt{re \cdot re + im \cdot im}\]
2. Applied taylor 0
  \[\leadsto re\]
3. Taylor expanded around inf 0
  
  \[\leadsto \color{blue}{re}\]
Recombined 4 regimes into one program.
Removed slow pow expressions

Runtime

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Error

Derivation

`if re < -2.674059323268242e+128`

`if -2.674059323268242e+128 < re < -2.321564696919607e-245 or -2.837848394186995e-306 < re < 2.540188601643307e+151`

`if -2.321564696919607e-245 < re < -2.837848394186995e-306`

`if 2.540188601643307e+151 < re`

Runtime