Average Error: 0.0 → 0.0
Time: 14.2s
Precision: 64
Internal Precision: 576
\[x.re \cdot y.re - x.im \cdot y.im\]
↓
\[(y.im \cdot \left(-x.im\right) + \left(x.re \cdot y.re\right))_*\]

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. Initial simplification0.0

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

  3. Final simplification0.0

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

Runtime

Time bar (total: 14.2s)Debug logProfile

herbie shell --seed 2018221 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))