Average Error: 0.0 → 0.0
Time: 5.7s
Precision: 64
Internal Precision: 576
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[(y.im \cdot x.re + \left(x.im \cdot y.re\right))_*\]

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

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

  2. Applied simplify0.0

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

  3. Taylor expanded around inf 0.0

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

  4. Applied simplify0.0

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

Runtime

Time bar (total: 5.7s)Debug logProfile

herbie shell --seed 2020178 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))