Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
Internal Precision: 128
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[(x.re \cdot y.im + \left(x.im \cdot y.re\right))_*\]

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. Initial simplification0.0

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

  3. Final simplification0.0

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

Runtime

Time bar (total: 3.1s)Debug log

start53.0ms

Algorithm
intervals

setup19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
0 → 0
Calls

0 calls. Slowest were:

series0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

simplify0.0ms

Counts
0 → 0
Calls

0 calls. Slowest were:

prune4.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

herbie shell --seed 2018359 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))