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 simplify7.2

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

3. Taylor expanded around 0 7.1

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

4. Taylor expanded around -inf 62.6

   \[\leadsto 3 \cdot \color{blue}{\left(x.im \cdot e^{2 \cdot \left(\log -1 - \log \left(\frac{-1}{x.re}\right)\right)}\right)} - {x.im}^{3}\]

5. Applied simplify0.2

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

7. Applied associate-*l*0.2

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

Runtime

Time bar (total: 54.6s)Debug logProfile

herbie shell --seed '#(1071246582 2318319007 2683472949 3810440501 3233274817 2724848749)' 
(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)))