Error

Target

Derivation

1. Split input into 5 regimes.

2. if re < -5.237492387957813e+116

   1. Initial program 60.9

      \[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]
   2. Using strategy rm

   3. Applied flip-+ 60.9

      \[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \color{blue}{\frac{{\left(\sqrt{re \cdot re + im \cdot im}\right)}^2 - {re}^2}{\sqrt{re \cdot re + im \cdot im} - re}}}\]

   4. Applied associate-*r/ 60.9

      \[\leadsto 0.5 \cdot \sqrt{\color{blue}{\frac{2.0 \cdot \left({\left(\sqrt{re \cdot re + im \cdot im}\right)}^2 - {re}^2\right)}{\sqrt{re \cdot re + im \cdot im} - re}}}\]

   5. Applied sqrt-div 60.9

      \[\leadsto 0.5 \cdot \color{blue}{\frac{\sqrt{2.0 \cdot \left({\left(\sqrt{re \cdot re + im \cdot im}\right)}^2 - {re}^2\right)}}{\sqrt{\sqrt{re \cdot re + im \cdot im} - re}}}\]

   6. Applied simplify 47.0

      \[\leadsto 0.5 \cdot \frac{\color{blue}{\sqrt{\left(im \cdot 2.0\right) \cdot im}}}{\sqrt{\sqrt{re \cdot re + im \cdot im} - re}}\]

   7. Applied taylor 20.8

      \[\leadsto 0.5 \cdot \frac{\sqrt{\left(im \cdot 2.0\right) \cdot im}}{\sqrt{-1 \cdot re - re}}\]

   8. Taylor expanded around -inf 20.8

      \[\leadsto 0.5 \cdot \frac{\sqrt{\left(im \cdot 2.0\right) \cdot im}}{\sqrt{\color{blue}{-1 \cdot re} - re}}\]

   9. Applied simplify 20.8

      \[\leadsto \color{blue}{\frac{\sqrt{\left(2.0 \cdot im\right) \cdot im}}{\frac{\sqrt{\left(-re\right) - re}}{0.5}}}\]

   if -5.237492387957813e+116 < re < -2.321564696919607e-245

   1. Initial program 39.1

      \[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]
   2. Using strategy rm

   3. Applied flip-+ 39.0

      \[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \color{blue}{\frac{{\left(\sqrt{re \cdot re + im \cdot im}\right)}^2 - {re}^2}{\sqrt{re \cdot re + im \cdot im} - re}}}\]

   4. Applied simplify 30.2

      \[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \frac{\color{blue}{im \cdot im}}{\sqrt{re \cdot re + im \cdot im} - re}}\]

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

   1. Initial program 30.2

      \[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]

   2. Applied taylor 0

      \[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(im + re\right)}\]

   3. Taylor expanded around 0 0

      \[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(\color{blue}{im} + re\right)}\]

   if -2.837848394186995e-306 < re < 6.000404463137166e+126

   1. Initial program 20.2

      \[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]

   if 6.000404463137166e+126 < re

   1. Initial program 55.1

      \[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re + im \cdot im} + re\right)}\]

   2. Applied taylor 0.0

      \[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(re + re\right)}\]

   3. Taylor expanded around inf 0.0

      \[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(\color{blue}{re} + re\right)}\]
3. Recombined 5 regimes into one program.
4. Removed slow pow expressions

Runtime

Time bar (total: 11.7s) Debug logProfile

Please include this information when filing a bug report:

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

  :target
  (if (< re 0) (* 0.5 (* (sqrt 2) (sqrt (/ (sqr im) (- (sqrt (+ (sqr re) (sqr im))) re))))) (* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))))

  (* 0.5 (sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))))