Average Error: 0.0 → 0.0
Time: 6.0s
Precision: 64
Internal Precision: 576
\[x.re \cdot y.re - x.im \cdot y.im\]
↓
\[(x.re \cdot y.re + \left(-y.im \cdot x.im\right))_* + (\left(-y.im\right) \cdot x.im + \left(y.im \cdot x.im\right))_*\]

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Try it out

  1. Inputs

  2. Original Output:

    Herbie Output:

Derivation

  1. Initial program 0.0

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

  3. Applied prod-diff0.0

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

Runtime

Time bar (total: 6.0s)Debug logProfile

herbie shell --seed '#(1072361757 3390613284 2339397988 1175251238 145061547 3101881848)' +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))