Error

Try it out

Target

Derivation

1. Initial program 7.0

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

2. Simplified7.0

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

4. Applied associate-*l*7.0

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

5. Taylor expanded around 0 7.0

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

7. Applied unpow27.0

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

8. Applied associate-*r*0.2

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

10. Applied associate-*r*0.2

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

11. Final simplification0.2

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

Reproduce

herbie shell --seed 2019007 +o rules:numerics
(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)))

Details

Time bar (total: 10.0s)Debug log