Error

Derivation

1. Initial program 0.0

   \[x.re \cdot y.im + x.im \cdot y.re\]

2. Simplified0.0

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

3. Taylor expanded around -inf 0.0

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

4. Simplified0.0

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

5. Final simplification0.0

   \[\leadsto (y.re \cdot x.im + \left(y.im \cdot x.re\right))_*\]

Reproduce

herbie shell --seed 2019008 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))

Details

Time bar (total: 1.8s)Debug log