Average Error: 0.0 → 0.0
Time: 2.6s
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 2018360 +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: 531.0ms)Debug log

start32.0ms

Algorithm
intervals

setup27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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 → 16
Calls

1 calls. Slowest were:

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

series34.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

34.0ms
(- (* x.re y.re) (* x.im y.im))

simplify69.0ms

Counts
6 → 19
Calls

6 calls. Slowest were:

26.0ms
(fma x.re y.re (- (* y.im x.im)))
18.0ms
(/ (exp (* x.re y.re)) (exp (* x.im y.im)))
9.0ms
(- (* y.re x.re) (* y.im x.im))

prune186.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

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)))

series43.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

43.0ms
(fma x.re y.re (- (* x.im y.im)))

simplify19.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

9.0ms
(- (* y.re x.re) (* y.im x.im))
9.0ms
(- (* y.re x.re) (* y.im x.im))
0.0ms
0

prune99.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0.0b