Error

Derivation

1. Initial program 7.3

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

3. Applied difference-of-squares7.3

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

4. Applied associate-*l*0.2

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

6. Applied add-cube-cbrt0.7

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

8. Applied cbrt-prod0.7

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

Runtime

Time bar (total: 6.9m)Debug logProfile

herbie shell --seed '#(1072840222 1305617769 1692503039 1353360431 4178980589 1488672652)' 
(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)))