Details

sample88.0ms

Algorithm: halfpoints

simplify27.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
3	28
2	26
1	19
0	14

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize257.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (.p16 re re) (.p16 im im))
0.4b	(sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (*.p16 im im))) re)))
0.4b	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
1.1b	(-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

7×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
4×	`p16-lft-identity-expand` `/p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
2×	`associate-+l+` `associate-+r+` `associate--l+`
1×	`associate--l-` `+-commutative` `insert-quire-sub` `associate-+r-` `sub-neg` `insert-quire-add` `p16-flip--` `insert-quire-fdp-add` `associate-+l-`

Counts

4 → 47

Calls

4 calls:

4.0ms	(+.p16 (.p16 re re) (.p16 im im))
0.0ms	(sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (*.p16 im im))) re)))
0.0ms	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
3.0ms	(-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (.p16 re re) (.p16 im im))
0.0ms	(sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (*.p16 im im))) re)))
0.0ms	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
0.0ms	(-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)

simplify5.1s

Counts

51 → 51

Iterations

Iter	Nodes
done	5131
5	3200
4	737
3	243
2	85
1	49
0	35

prune992.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.7b

localize268.0ms

Local error

Found 4 expressions with local error:

0.4b	(sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 re re)) im im))) re)))
0.4b	(sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 re re)) im im)))
1.1b	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 re re)) im im))) re)
4.7b	(quire16-mul-add (posit16->quire16 (*.p16 re re)) im im)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
3×	`p16-lft-identity-expand` `/p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
2×	`associate--l+`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `p16-flip--`

Counts

4 → 30

Calls

4 calls:

0.0ms	(sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 re re)) im im))) re)))
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 re re)) im im)))
2.0ms	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 re re)) im im))) re)
0.0ms	(quire16-mul-add (posit16->quire16 (*.p16 re re)) im im)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 re re)) im im))) re)))
0.0ms	(sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 re re)) im im)))
0.0ms	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 re re)) im im))) re)
0.0ms	(quire16-mul-add (posit16->quire16 (*.p16 re re)) im im)

simplify3.3s

Counts

34 → 34

Iterations

Iter	Nodes
done	5027
5	2145
4	413
3	130
2	50
1	34
0	26

prune830.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.7b

localize304.0ms

Local error

Found 4 expressions with local error:

0.4b	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
0.8b	(/.p16 (-.p16 (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))) (.p16 re re)) (+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re))
1.3b	(+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)
2.9b	(-.p16 (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))) (.p16 re re))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
12×	`p16-times-frac`
9×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
7×	`introduce-quire` `-p16-rgt-identity-expand`
6×	`associate--l+` `/p16-rgt-identity-expand`
5×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `p16-flip--` `associate--r+` `associate-/l/`
1×	`associate--l-` `+-commutative` `insert-quire-sub` `sub-neg` `insert-quire-add` `associate-/r/` `associate-+l-` `insert-quire-fdp-sub` `associate--r-`

Counts

4 → 74

Calls

4 calls:

0.0ms	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
6.0ms	(/.p16 (-.p16 (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))) (.p16 re re)) (+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re))
3.0ms	(+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)
3.0ms	(-.p16 (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))) (.p16 re re))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
0.0ms	(/.p16 (-.p16 (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))) (.p16 re re)) (+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re))
0.0ms	(+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)
0.0ms	(-.p16 (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))) (.p16 re re))

simplify1.9s

Counts

78 → 78

Iterations

Iter	Nodes
done	5019
3	1638
2	351
1	85
0	48

prune1.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 1.5b

localize403.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 (real->posit16 1.0) (/.p16 (real->posit16 1.0) (-.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re)))
0.4b	(sqrt.p16 (.p16 (real->posit16 2.0) (/.p16 (real->posit16 1.0) (/.p16 (real->posit16 1.0) (-.p16 (sqrt.p16 (+.p16 (.p16 im im) (*.p16 re re))) re)))))
0.4b	(sqrt.p16 (+.p16 (.p16 im im) (.p16 re re)))
1.1b	(-.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

78×	`p16-times-frac`
47×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
14×	`associate-/r*`
9×	`associate-/r/` `/p16-rgt-identity-expand`
5×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `p16-flip--` `+p16-rgt-identity-expand`
3×	`associate-/l*`
2×	`associate--l+`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `remove-double-div.p16` `associate-/l/`

Counts

4 → 100

Calls

4 calls:

9.0ms	(/.p16 (real->posit16 1.0) (/.p16 (real->posit16 1.0) (-.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re)))
0.0ms	(sqrt.p16 (.p16 (real->posit16 2.0) (/.p16 (real->posit16 1.0) (/.p16 (real->posit16 1.0) (-.p16 (sqrt.p16 (+.p16 (.p16 im im) (*.p16 re re))) re)))))
0.0ms	(sqrt.p16 (+.p16 (.p16 im im) (.p16 re re)))
5.0ms	(-.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (real->posit16 1.0) (/.p16 (real->posit16 1.0) (-.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re)))
0.0ms	(sqrt.p16 (.p16 (real->posit16 2.0) (/.p16 (real->posit16 1.0) (/.p16 (real->posit16 1.0) (-.p16 (sqrt.p16 (+.p16 (.p16 im im) (*.p16 re re))) re)))))
0.0ms	(sqrt.p16 (+.p16 (.p16 im im) (.p16 re re)))
0.0ms	(-.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re)

simplify5.8s

Counts

104 → 104

Iterations

Iter	Nodes
done	5073
5	4914
4	1123
3	290
2	89
1	59
0	38

prune956.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 1.5b

regimes531.0ms

Accuracy

0% (0.4b remaining)

Error of 2.1b against oracle of 1.6b and baseline of 2.1b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	15
0	15

end0.0ms

sample2.9s

Algorithm: halfpoints