Details

sample147.0ms

Algorithm: halfpoints

simplify34.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	28
3	28
2	26
1	19
0	14

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.2b

localize225.0ms

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)))
0.5b	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
1.2b	(-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)

rewrite12.0ms

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:

6.0ms	(+.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)))
4.0ms	(-.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)

simplify3.3s

Counts

51 → 51

Iterations

Iter	Nodes
5	3047
4	731
3	242
2	84
1	48
0	35

prune2.7s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.9b

localize273.0ms

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)))
0.5b	(sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 re re)) im im)))
1.2b	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 re re)) im im))) re)
4.9b	(quire16-mul-add (posit16->quire16 (*.p16 re re)) im im)

rewrite7.0ms

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)))
5.0ms	(-.p16 (sqrt.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 re re)) im im))) re)
1.0ms	(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)

simplify3.5m

Counts

34 → 34

Iterations

Iter	Nodes
6	14722
5	1967
4	405
3	129
2	49
1	33
0	26

prune2.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.9b

localize300.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
1.1b	(/.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))
1.2b	(+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)
3.0b	(-.p16 (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))) (.p16 re re))

rewrite26.0ms

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)))
11.0ms	(/.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))
6.0ms	(+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)
6.0ms	(-.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))

simplify10.5s

Counts

78 → 78

Iterations

Iter	Nodes
4	12329
3	1588
2	348
1	84
0	48

prune4.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.8b

localize401.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 (real->posit16 1.0) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) 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 re re) (*.p16 im im))) re)))))
0.5b	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
1.2b	(-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

12×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
9×	`p16-times-frac`
6×	`/p16-rgt-identity-expand`
5×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
3×	`associate-/r` `associate-/l`
2×	`associate--l+` `p16-flip--` `associate-/r/`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `associate-/l/`

Counts

4 → 56

Calls

4 calls:

20.0ms	(/.p16 (real->posit16 1.0) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) 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 re re) (*.p16 im im))) re)))))
0.0ms	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
5.0ms	(-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.8s

Counts

60 → 60

Iterations

Iter	Nodes
5	2693
4	1078
3	300
2	86
1	49
0	35

prune3.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 1.7b

regimes765.0ms

Accuracy

0% (0.5b remaining)

Error of 2.1b against oracle of 1.7b and baseline of 2.1b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
1	15
0	15

end0.0ms

sample3.1s

Algorithm: halfpoints