Average Error: 60.6 → 48.2
Time: 34.1s
Precision: 64
Internal Precision: 128
\[\frac{x.im \cdot y.re - x.re \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
↓
\[0\]

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 60.6

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

  2. Initial simplification60.6

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

  3. Taylor expanded around inf 48.2

    \[\leadsto \color{blue}{0}\]

  4. Final simplification48.2

    \[\leadsto 0\]

Runtime

Time bar (total: 34.1s)Debug logProfile

herbie shell --seed 2018255 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, imaginary part"
  (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))