Average Error: 30.0 → 0.1
Time: 14.1s
Precision: 64
Internal precision: 3968
\[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re \cdot re - im \cdot im} + re\right)}\]
⬇
\[0.5 \cdot \sqrt{2.0 \cdot \left(\sqrt{re + im} \cdot \sqrt{re - im} + re\right)}\]

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 30.0

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

  3. Applied square-unmult 30.0

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

  4. Applied square-unmult 30.0

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

  5. Applied difference-of-squares 30.0

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

  6. Applied sqrt-prod 0.1

    \[\leadsto 0.5 \cdot \sqrt{2.0 \cdot \left(\color{blue}{\sqrt{re + im} \cdot \sqrt{re - im}} + re\right)}\]
  7. Removed slow pow expressions

Runtime

Time bar (total: 14.1s) 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, imaginary part, im greater than 0 branch"
  (* 0.5 (sqrt (* 2.0 (+ (sqrt (- (* re re) (* im im))) re)))))