Error

Target

Derivation

1. Initial program 37.8

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

2. Initial simplification13.2

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

4. Applied add-sqr-sqrt14.2

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

6. Applied add-sqr-sqrt14.5

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

7. Final simplification14.5

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

Runtime

Time bar (total: 16.2s)Debug logProfile

herbie shell --seed 2018351 +o rules:numerics
(FPCore (re im)
  :name "math.sqrt on complex, real part"

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

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