Error

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 difference-of-squares30.0

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

4. Applied sqrt-prod0.1

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

6. Applied sqrt-prod0.5

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

Runtime

Time bar (total: 53.4s)Debug logProfile

herbie shell --seed '#(1070578969 3140398606 632207097 462683394 1189254563 964980650)' 
(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)))))