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

⬇

\[\begin{array}{l} \mathbf{if}\;re \le -2.0506543985785498 \cdot 10^{+132}:\\ \;\;\;\;-re\\ \mathbf{if}\;re \le -9.729387694827135 \cdot 10^{-250}:\\ \;\;\;\;\sqrt{re \cdot re + im \cdot im}\\ \mathbf{if}\;re \le 1.1913008854416164 \cdot 10^{-287}:\\ \;\;\;\;im\\ \mathbf{if}\;re \le 2.4228660641686305 \cdot 10^{+144}:\\ \;\;\;\;\sqrt{re \cdot re + im \cdot im}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Derivation

Split input into 4 regimes.
if re < -2.0506543985785498e+132
1. Initial program 54.0
  \[\sqrt{re \cdot re + im \cdot im}\]
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 -2.0506543985785498e+132 < re < -9.729387694827135e-250 or 1.1913008854416164e-287 < re < 2.4228660641686305e+144
1. Initial program 18.7
  \[\sqrt{re \cdot re + im \cdot im}\]
if -9.729387694827135e-250 < re < 1.1913008854416164e-287
1. Initial program 46.4
  \[\sqrt{re \cdot re + im \cdot im}\]
2. Applied taylor 0
  \[\leadsto im\]
3. Taylor expanded around 0 0
  
  \[\leadsto \color{blue}{im}\]
if 2.4228660641686305e+144 < re
1. Initial program 57.3
  \[\sqrt{re \cdot re + im \cdot im}\]
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 --seed '#(1184208345 2389244311 1807722534 1482994180 2388527835 2813794003)'
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Error

Derivation

`if re < -2.0506543985785498e+132`

`if -2.0506543985785498e+132 < re < -9.729387694827135e-250 or 1.1913008854416164e-287 < re < 2.4228660641686305e+144`

`if -9.729387694827135e-250 < re < 1.1913008854416164e-287`

`if 2.4228660641686305e+144 < re`

Runtime