Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
Internal Precision: 128
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[x.im \cdot y.re + x.re \cdot y.im\]

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

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019022 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))

Details

Time bar (total: 1.2s)Debug log

sample42.0ms

Algorithm
intervals
Results
27.0ms349×body80valid

simplify5.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
5.0ms
(+ (* x.re y.im) (* x.im y.re))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
1×flip-+
1×add-cube-cbrt
1×add-exp-log
1×add-cbrt-cube
1×flip3-+
1×*-un-lft-identity
1×sum-log
1×+-commutative
1×pow1
1×add-sqr-sqrt
Counts
1 → 11
Calls
1 calls:
Slowest
4.0ms
(+ (* x.re y.im) (* x.im y.re))

series52.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
52.0ms
(+ (* x.re y.im) (* x.im y.re))

simplify22.0ms

Counts
4 → 14
Calls
4 calls:
Slowest
12.0ms
(* (exp (* x.re y.im)) (exp (* x.im y.re)))
5.0ms
(+ (* y.re x.im) (* y.im x.re))
4.0ms
(+ (* y.re x.im) (* y.im x.re))
1.0ms
0

prune97.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0.0b

end0.0ms

sample944.0ms

Algorithm
intervals
Results
734.0ms10488×body80valid