Average Error: 26.1 → 26.1
Time: 24.3s
Precision: 64
Internal precision: 128
\[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
⬇
\[\frac{y.im \cdot x.im + y.re \cdot x.re}{{y.re}^2 + y.im \cdot y.im}\]

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 26.1

    \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]

  2. Applied simplify 26.1

    \[\leadsto \color{blue}{\frac{y.im \cdot x.im + y.re \cdot x.re}{{y.re}^2 + y.im \cdot y.im}}\]
  3. Removed slow pow expressions

Runtime

Time bar (total: 24.3s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(2904472013 2086908781 242677623 3011524023 3242740239 2621738943)'
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, real part"
  (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))