Error

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Target

Derivation

1. Initial program 6.8

   \[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]

2. Initial simplification0.2

   \[\leadsto x.re \cdot \left(x.im \cdot \left(x.re + x.re\right)\right) + \left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)\]
3. Using strategy rm

4. Applied add-cube-cbrt0.7

   \[\leadsto x.re \cdot \left(x.im \cdot \left(x.re + x.re\right)\right) + \color{blue}{\left(\left(\sqrt[3]{x.im \cdot \left(x.re + x.im\right)} \cdot \sqrt[3]{x.im \cdot \left(x.re + x.im\right)}\right) \cdot \sqrt[3]{x.im \cdot \left(x.re + x.im\right)}\right)} \cdot \left(x.re - x.im\right)\]
5. Using strategy rm

6. Applied cbrt-prod0.7

   \[\leadsto x.re \cdot \left(x.im \cdot \left(x.re + x.re\right)\right) + \left(\left(\sqrt[3]{x.im \cdot \left(x.re + x.im\right)} \cdot \sqrt[3]{x.im \cdot \left(x.re + x.im\right)}\right) \cdot \color{blue}{\left(\sqrt[3]{x.im} \cdot \sqrt[3]{x.re + x.im}\right)}\right) \cdot \left(x.re - x.im\right)\]

7. Final simplification0.7

   \[\leadsto \left(x.re - x.im\right) \cdot \left(\left(\sqrt[3]{\left(x.im + x.re\right) \cdot x.im} \cdot \sqrt[3]{\left(x.im + x.re\right) \cdot x.im}\right) \cdot \left(\sqrt[3]{x.im + x.re} \cdot \sqrt[3]{x.im}\right)\right) + \left(\left(x.re + x.re\right) \cdot x.im\right) \cdot x.re\]

Runtime

Time bar (total: 4.6m)Debug logProfile

herbie shell --seed 2018214 
(FPCore (x.re x.im)
  :name "math.cube on complex, imaginary part"

  :herbie-target
  (+ (* (* x.re x.im) (* 2 x.re)) (* (* x.im (- x.re x.im)) (+ x.re x.im)))

  (+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re)))