Details

sample78.0ms

Algorithm: halfpoints

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	12
0	7

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize129.0ms

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))

rewrite8.0ms

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)))
7.0ms	(-.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))

simplify1.2s

Counts

35 → 35

Iterations

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

prune312.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize247.0ms

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`
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))
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))

simplify5.0s

Counts

129 → 129

Iterations

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

prune858.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize264.0ms

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

9.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
5.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
12.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
6.0ms	(+.p16 (.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (.p16 (neg.p16 (sqrt.p16 x)) (+.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 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.0ms	(+.p16 (.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))) (.p16 (neg.p16 (sqrt.p16 x)) (+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))))

simplify3.6s

Counts

110 → 110

Iterations

Iter	Nodes
done	5007
3	2440
2	290
1	73
0	39

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

localize311.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (sqrt.p16 x) (neg.p16 (sqrt.p16 x)))
0.1b	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
0.3b	(*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x)))
0.3b	(+.p16 (.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (.p16 (sqrt.p16 x) (neg.p16 (sqrt.p16 x))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

17×	`p16-lft-identity-expand` `p16--un-lft-identity`
16×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
11×	`*p16-rgt-identity-expand`
10×	`introduce-quire`
8×	`distribute-rgt-in` `associate-+l+` `associate-+r+` `distribute-lft-in` `-p16-rgt-identity-expand` `/p16-rgt-identity-expand`
6×	`associate-r` `associate-l`
4×	`p16-distribute-lft-out` `insert-quire-fdp-add` `distribute-lft-out`
2×	`+-commutative` `associate-+r-` `insert-quire-add` `associate-l/` `associate-r/` `*-commutative` `associate-+l-`
1×	`distribute-rgt-out` `sqrt-sqrd.p16`

Counts

4 → 96

Calls

4 calls:

6.0ms	(*.p16 (sqrt.p16 x) (neg.p16 (sqrt.p16 x)))
10.0ms	(+.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 x))
5.0ms	(*.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x)))
12.0ms	(+.p16 (.p16 (sqrt.p16 (+.p16 (real->posit16 1) x)) (sqrt.p16 (+.p16 (real->posit16 1) x))) (.p16 (sqrt.p16 x) (neg.p16 (sqrt.p16 x))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify3.1m

Counts

100 → 100

Iterations

Iter	Nodes
done	5003
3	3082
2	305
1	73
0	45

prune704.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

regimes104.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
1	13
0	11

end0.0ms

sample1.2s

Algorithm: halfpoints

Details

sample78.0ms

simplify6.0ms

prune17.0ms

localize129.0ms

rewrite8.0ms

series0.0ms

simplify1.2s

prune312.0ms

localize247.0ms

rewrite31.0ms

series0.0ms

simplify5.0s

prune858.0ms

localize264.0ms

rewrite36.0ms

series0.0ms

simplify3.6s

prune1.3s

localize311.0ms

rewrite38.0ms

series0.0ms

simplify3.1m

prune704.0ms

regimes104.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

end6.6m