Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
Internal Precision: 128
\[x.re \cdot y.re - x.im \cdot y.im\]
↓
\[x.re \cdot y.re - x.im \cdot y.im\]

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Initial simplification0.0

    \[\leadsto x.re \cdot y.re - x.im \cdot y.im\]

  3. Final simplification0.0

    \[\leadsto x.re \cdot y.re - x.im \cdot y.im\]

Runtime

Time bar (total: 3.0s)Debug log

start37.0ms

Algorithm
intervals

setup14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (* x.re y.re) (* x.im y.im))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
1 → 12
Calls

1 calls. Slowest were:

2.0ms
(- (* x.re y.re) (* x.im y.im))

series35.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

35.0ms
(- (* x.re y.re) (* x.im y.im))

simplify33.0ms

Counts
4 → 15
Calls

4 calls. Slowest were:

20.0ms
(/ (exp (* x.re y.re)) (exp (* x.im y.im)))
6.0ms
(- (* y.re x.re) (* y.im x.im))
6.0ms
(- (* y.re x.re) (* y.im x.im))

prune192.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0.0b

herbie shell --seed 2018359 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))