Average Error: 0.0 → 0.0
Time: 2.2s
Precision: 64
Internal Precision: 128
\[x.re \cdot y.re - x.im \cdot y.im\]
↓
\[(x.re \cdot y.re + \left(y.im \cdot \left(-x.im\right)\right))_*\]

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

    \[x.re \cdot y.re - x.im \cdot y.im\]
  2. Using strategy rm

  3. Applied fma-neg0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019005 +o rules:numerics
(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: 1.9s)Debug log

sample33.0ms

Algorithm
intervals

simplify17.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

17.0ms
(- (* x.re y.re) (* x.im y.im))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Counts
1 → 16
Calls

1 calls. Slowest were:

5.0ms
(- (* x.re y.re) (* x.im y.im))

series61.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

61.0ms
(- (* x.re y.re) (* x.im y.im))

simplify75.0ms

Counts
6 → 19
Calls

6 calls. Slowest were:

32.0ms
(/ (exp (* x.re y.re)) (exp (* x.im y.im)))
17.0ms
(fma x.re y.re (- (* y.im x.im)))
9.0ms
(- (* y.re x.re) (* y.im x.im))

prune208.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(fma x.re y.re (- (* x.im y.im)))

series35.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

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

simplify37.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

18.0ms
(- (* y.re x.re) (* y.im x.im))
17.0ms
(- (* y.re x.re) (* y.im x.im))
1.0ms
0

prune167.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0.0b

end0.0ms

sample1.2s

Algorithm
intervals