Details

sample87.0ms

Algorithm: halfpoints

simplify385.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	12
0	7

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize132.0ms

Local error

Found 2 expressions with local error:

0.1b	(sqrt.p16 (+.p16 x (real->posit16 1)))
0.8b	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

0.0ms	(sqrt.p16 (+.p16 x (real->posit16 1)))
6.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

series0.0ms

Counts

2 → 2

Calls

2 calls:

0.0ms	(sqrt.p16 (+.p16 x (real->posit16 1)))
0.0ms	(-.p16 (sqrt.p16 (+.p16 x (real->posit16 1))) (sqrt.p16 x))

simplify1.1s

Counts

35 → 35

Iterations

Iter	Nodes
done	5002
3	834
2	126
1	37
0	23

prune345.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize232.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.1b	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.1b	(*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.8b	(-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

41×	`p16-lft-identity-expand` `p16--un-lft-identity`
19×	`*p16-rgt-identity-expand`
16×	`introduce-quire`
14×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
12×	`p16-distribute-lft-out` `associate-l` `-p16-rgt-identity-expand` `distribute-lft-out`
8×	`associate-r` `distribute-lft-out--`
6×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `/p16-rgt-identity-expand` `insert-quire-fdp-add`
4×	`associate-+l+` `associate-+r+`
3×	`sub-neg` `distribute-rgt-out` `insert-quire-fdp-sub` `associate--r-`
2×	`+-commutative` `associate-+r-` `insert-quire-add` `distribute-rgt-out--` `associate-*r/` `p16-flip--` `associate-+l-` `associate--r+`
1×	`associate--l-` `insert-quire-sub` `associate-l/` `-commutative`

Counts

4 → 125

Calls

4 calls:

5.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
7.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
20.0ms	(*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
8.0ms	(-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.0ms	(*.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.0ms	(-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))

simplify4.7s

Counts

129 → 129

Iterations

Iter	Nodes
done	5000
3	4756
2	600
1	99
0	42

prune857.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize271.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.1b	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.1b	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.2b	(+.p16 (.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (neg.p16 (sqrt.p16 x))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

31×	`p16-lft-identity-expand` `p16--un-lft-identity`
18×	`introduce-quire`
16×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
13×	`p16-distribute-lft-out` `*p16-rgt-identity-expand` `distribute-lft-out`
12×	`associate-+l+` `associate-+r+` `-p16-rgt-identity-expand`
10×	`insert-quire-fdp-add`
4×	`distribute-rgt-in` `+-commutative` `associate-+r-` `insert-quire-add` `distribute-lft-in` `/p16-rgt-identity-expand` `associate-+l-`
3×	`distribute-rgt-out`

Counts

4 → 111

Calls

4 calls:

10.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
10.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
9.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
10.0ms	(+.p16 (.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (neg.p16 (sqrt.p16 x))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.0ms	(+.p16 (.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (.p16 (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (neg.p16 (sqrt.p16 x))))

simplify15.2s

Counts

115 → 115

Iterations

Iter	Nodes
done	5038
3	3421
2	378
1	86
0	40

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize252.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.1b	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.1b	(*.p16 (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.8b	(-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

41×	`p16-lft-identity-expand` `p16--un-lft-identity`
19×	`*p16-rgt-identity-expand`
16×	`introduce-quire`
12×	`p16-distribute-lft-out` `associate-r` `distribute-lft-out`
10×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
8×	`associate-l` `distribute-lft-out--`
6×	`/p16-rgt-identity-expand` `insert-quire-fdp-add`
4×	`associate-+l+` `associate-+r+`
3×	`distribute-rgt-out` `insert-quire-fdp-sub`
2×	`+-commutative` `associate-+r-` `insert-quire-add` `distribute-rgt-out--` `associate-*l/` `associate--l+` `p16-flip--` `associate-+l-` `associate--r+`
1×	`associate--l-` `distribute-rgt-in` `insert-quire-sub` `sub-neg` `distribute-lft-in` `associate-r/` `-commutative` `associate--r-`

Counts

4 → 115

Calls

4 calls:

5.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
5.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
11.0ms	(*.p16 (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
7.0ms	(-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.0ms	(*.p16 (-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x)))
0.0ms	(-.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))

simplify1.4s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
2	648
1	88
0	39

prune839.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

regimes113.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 0.7b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample1.5s

Algorithm: halfpoints