Derivation

Split input into 2 regimes.
if re < 3.280266654840657e-252
1. Initial program 49.1
  \[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re - im \cdot im} + re\right)}\]
2. Applied taylor 0
  \[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(-1 \cdot re + re\right)}\]
3. Taylor expanded around -inf 0
  
  \[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(\color{blue}{-1 \cdot re} + re\right)}\]
if 3.280266654840657e-252 < re
1. Initial program 28.9
  \[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re - im \cdot im} + re\right)}\]
2. Using strategy rm
3. Applied square-unmult 28.9
  \[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re - \color{blue}{{im}^2}} + re\right)}\]
4. Applied square-unmult 28.9
  \[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{\color{blue}{{re}^2} - {im}^2} + re\right)}\]
5. Applied difference-of-squares 28.8
  \[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{\color{blue}{\left(re + im\right) \cdot \left(re - im\right)}} + re\right)}\]
6. Applied sqrt-prod 0.2
  \[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(\color{blue}{\sqrt{re + im} \cdot \sqrt{re - im}} + re\right)}\]
Recombined 2 regimes into one program.
Removed slow pow expressions

Runtime

Please include this information when filing a bug report:

herbie --seed '#(1052631102 1549666840 214851374 4124938917 336414485 3340135247)'
(FPCore (re im)
  :name "math.sqrt on complex, imaginary part, im greater than 0 branch"
  (* 0.5 (sqrt (* 2.0 (+ (sqrt (- (* re re) (* im im))) re)))))

Error

Derivation

`if re < 3.280266654840657e-252`

`if 3.280266654840657e-252 < re`

Runtime