Average Error: 25.3 → 25.3
Time: 10.8s
Precision: 64
Internal precision: 384
\[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
⬇
\[\frac{y.re \cdot x.re + x.im \cdot y.im}{y.im \cdot y.im + {y.re}^2}\]

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 25.3

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

  2. Applied simplify 25.3

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

Runtime

Time bar (total: 10.8s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(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))))