Average Error: 0.0 → 0.0
Time: 2.0s
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. Final simplification0.0

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

Reproduce

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

Details

Time bar (total: 1.4s)Debug log

sample43.0ms

Algorithm
intervals
Results
27.0ms336×body80valid

simplify10.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(- (* x.re y.re) (* x.im y.im))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
1×flip--
1×add-cube-cbrt
1×add-exp-log
1×diff-log
1×add-cbrt-cube
1×flip3--
1×*-un-lft-identity
1×sub-neg
1×pow1
1×add-sqr-sqrt
Counts
1 → 12
Calls
1 calls:
Slowest
4.0ms
(- (* x.re y.re) (* x.im y.im))

series43.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
43.0ms
(- (* x.re y.re) (* x.im y.im))

simplify33.0ms

Counts
4 → 15
Calls
4 calls:
Slowest
22.0ms
(/ (exp (* x.re y.re)) (exp (* x.im y.im)))
5.0ms
(- (* y.re x.re) (* y.im x.im))
5.0ms
(- (* y.re x.re) (* y.im x.im))
0.0ms
0

prune118.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0.0b

end0.0ms

sample1.1s

Algorithm
intervals
Results
746.0ms10471×body80valid