Error

Derivation

1. Initial program 7.1

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

2. Applied simplify0.2

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

3. Taylor expanded around 0 7.0

   \[\leadsto \color{blue}{3 \cdot \left({x.re}^{2} \cdot x.im\right) - {x.im}^{3}}\]
4. Using strategy rm

5. Applied add-cube-cbrt7.3

   \[\leadsto 3 \cdot \left({x.re}^{2} \cdot x.im\right) - \color{blue}{\left(\sqrt[3]{{x.im}^{3}} \cdot \sqrt[3]{{x.im}^{3}}\right) \cdot \sqrt[3]{{x.im}^{3}}}\]

6. Applied prod-diff7.3

   \[\leadsto \color{blue}{(3 \cdot \left({x.re}^{2} \cdot x.im\right) + \left(-\sqrt[3]{{x.im}^{3}} \cdot \left(\sqrt[3]{{x.im}^{3}} \cdot \sqrt[3]{{x.im}^{3}}\right)\right))_* + (\left(-\sqrt[3]{{x.im}^{3}}\right) \cdot \left(\sqrt[3]{{x.im}^{3}} \cdot \sqrt[3]{{x.im}^{3}}\right) + \left(\sqrt[3]{{x.im}^{3}} \cdot \left(\sqrt[3]{{x.im}^{3}} \cdot \sqrt[3]{{x.im}^{3}}\right)\right))_*}\]

7. Applied simplify0.2

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

8. Applied simplify0.2

   \[\leadsto (x.re \cdot \left(\left(x.re \cdot x.im\right) \cdot 3\right) + \left(\left(-x.im\right) \cdot \left(x.im \cdot x.im\right)\right))_* + \color{blue}{0}\]

Runtime

Time bar (total: 54.7s)Debug logProfile

herbie shell --seed 2018201 +o rules:numerics
(FPCore (x.re x.im)
  :name "math.cube on complex, imaginary part"
  (+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re)))