Average Error: 0.0 → 0.0
Time: 3.4s
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. Initial simplification0.0

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

  4. Applied fma-neg0.0

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

  5. Final simplification0.0

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

Runtime

Time bar (total: 3.4s)Debug log

start74.0ms

Algorithm
intervals

setup18.0ms

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

rewrite30.0ms

Algorithm
rewrite-expression-head
Counts
1 → 16
Calls

1 calls. Slowest were:

30.0ms
(- (* x.re y.re) (* x.im y.im))

series45.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

45.0ms
(- (* x.re y.re) (* x.im y.im))

simplify68.0ms

Counts
6 → 19
Calls

6 calls. Slowest were:

23.0ms
(/ (exp (* x.re y.re)) (exp (* x.im y.im)))
18.0ms
(fma x.re y.re (- (* y.im x.im)))
9.0ms
(fma (- y.im) x.im (* y.im x.im))

prune184.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

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

series51.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

51.0ms
(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))
18.0ms
(- (* y.re x.re) (* y.im x.im))
1.0ms
0

prune163.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0.0b

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