Average Error: 0.0 → 0.0
Time: 1.3m
Precision: 64
Internal Precision: 384
\[x.re \cdot y.re - x.im \cdot y.im\]
↓
\[(x.re \cdot y.re + \left(-y.im \cdot x.im\right))_* + (\left(-y.im\right) \cdot x.im + \left(y.im \cdot x.im\right))_*\]

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

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: 1.3m)Debug logProfile

herbie shell --seed '#(1070706311 3771791028 4128836681 4194990999 2341756049 504035650)' +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))