Error

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Derivation

1. Initial program 37.5

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

2. Initial simplification13.1

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

4. Applied sqrt-prod13.4

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

5. Final simplification13.4

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

Reproduce

herbie shell --seed 2018362 +o rules:numerics
(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)))))

Details

Time bar (total: 8.7s)Debug log