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

↓

\[\begin{array}{l} \mathbf{if}\;re \le -1.863416131836119 \cdot 10^{+102}:\\ \;\;\;\;-re\\ \mathbf{if}\;re \le 3.778966780440601 \cdot 10^{+153}:\\ \;\;\;\;\sqrt{re \cdot re + im \cdot im}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Derivation

Split input into 3 regimes
if re < -1.863416131836119e+102
1. Initial program 48.2
  \[\sqrt{re \cdot re + im \cdot im}\]
2. Taylor expanded around -inf 9.6
  \[\leadsto \color{blue}{-1 \cdot re}\]
3. Applied simplify9.6
  \[\leadsto \color{blue}{-re}\]
if -1.863416131836119e+102 < re < 3.778966780440601e+153
1. Initial program 20.2
  \[\sqrt{re \cdot re + im \cdot im}\]
if 3.778966780440601e+153 < re
1. Initial program 59.0
  \[\sqrt{re \cdot re + im \cdot im}\]
2. Taylor expanded around inf 7.7
  \[\leadsto \color{blue}{re}\]
Recombined 3 regimes into one program.

Runtime

herbie shell --seed '#(1071725047 233389029 2036512464 3988615230 2972226563 1111574017)' 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Error

Derivation

`if re < -1.863416131836119e+102`

`if -1.863416131836119e+102 < re < 3.778966780440601e+153`

`if 3.778966780440601e+153 < re`

Runtime