Error

Try it out

Derivation

1. Initial program 0.0

   \[x.re \cdot y.re - x.im \cdot y.im\]
2. Using strategy rm

3. Applied flip--25.3

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

5. Applied difference-of-squares25.2

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

6. Applied associate-/l*1.0

   \[\leadsto \color{blue}{\frac{x.re \cdot y.re + x.im \cdot y.im}{\frac{x.re \cdot y.re + x.im \cdot y.im}{x.re \cdot y.re - x.im \cdot y.im}}}\]

7. Final simplification1.0

   \[\leadsto \frac{x.im \cdot y.im + x.re \cdot y.re}{\frac{x.im \cdot y.im + x.re \cdot y.re}{x.re \cdot y.re - x.im \cdot y.im}}\]

Runtime

Time bar (total: 30.4s)Debug logProfile

herbie shell --seed 2018285 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))