Details

sample130.0ms

Algorithm: halfpoints

simplify57.0ms

Counts

1 → 1

Iterations

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

prune38.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.3b

localize323.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (real->posit16 0.5) (sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re))))
0.4b	(sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (*.p16 im im))) re)))
0.6b	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
1.2b	(-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
6×	`p16-lft-identity-expand` `/p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
5×	`introduce-quire` `-p16-rgt-identity-expand`
3×	`associate-r` `associate-l`
2×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
1×	`associate--l-` `insert-quire-sub` `sub-neg` `associate-l/` `associate-r/` `p16-flip--` `*-commutative`

Counts

4 → 51

Calls

4 calls:

4.0ms	(.p16 (real->posit16 0.5) (sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re))))
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)))
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 0.5) (sqrt.p16 (.p16 (real->posit16 2.0) (-.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re))))
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)

simplify49.4s

Counts

55 → 55

Iterations

Iter	Nodes
done	5466
5	5466
4	646
3	240
2	101
1	49
0	34

prune2.8s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 2.0b

localize293.0ms

Local error

Found 4 expressions with local error:

0.6b	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
0.9b	(/.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))
1.1b	(+.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) re)
2.8b	(-.p16 (.p16 (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im))) (sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))) (.p16 re re))

rewrite36.0ms

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:

9.0ms	(sqrt.p16 (+.p16 (.p16 re re) (.p16 im im)))
12.0ms	(/.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)
7.0ms	(-.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))

simplify1.8s

Counts

78 → 78

Iterations

Iter	Nodes
done	2158
4	2158
3	1638
2	351
1	85
0	48

prune5.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.8b

localize256.0ms

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)))))
0.6b	(sqrt.p16 (+.p16 (.p16 im im) (.p16 re re)))
1.2b	(-.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)

simplify1.1s

Counts

104 → 104

Iterations

Iter	Nodes
done	2003
5	2003
4	1123
3	290
2	89
1	59
0	38

prune5.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.8b

localize270.0ms

Local error

Found 4 expressions with local error:

1.0b	(.p16 (+.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re) (/.p16 (-.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re) (+.p16 (sqrt.p16 (+.p16 (.p16 im im) (*.p16 re re))) re)))
1.1b	(+.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re)
1.1b	(+.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re)
1.2b	(-.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

8.0ms	(.p16 (+.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re) (/.p16 (-.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re) (+.p16 (sqrt.p16 (+.p16 (.p16 im im) (*.p16 re re))) re)))
3.0ms	(+.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re)
3.0ms	(+.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re)
10.0ms	(-.p16 (sqrt.p16 (+.p16 (.p16 im im) (.p16 re re))) re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.9s

Counts

75 → 75

Iterations

Iter	Nodes
done	2001
3	2001
2	369
1	86
0	44

prune3.8s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 1.8b

regimes602.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	14
0	14

end0.0ms

sample2.4s

Algorithm: halfpoints