Details

sample231.0ms

Algorithm: halfpoints

simplify53.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
3	28
2	26
1	19
0	12

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize171.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (real->posit16 1.0)) (real->posit16 2.0))
0.1b	(+.p16 (+.p16 alpha beta) (real->posit16 2.0))
0.3b	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (real->posit16 1.0))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0)))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

151×	`p16-lft-identity-expand` `p16--un-lft-identity`
111×	`*p16-rgt-identity-expand`
105×	`p16-times-frac`
50×	`p16-distribute-lft-out` `distribute-lft-out`
35×	`distribute-rgt-out`
28×	`/p16-rgt-identity-expand`
26×	`associate-/l*`
22×	`associate-/r/`
15×	`associate-/r*`
12×	`introduce-quire`
10×	`distribute-lft1-in`
8×	`-p16-rgt-identity-expand`
7×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
6×	`insert-quire-fdp-add`
4×	`associate-+r+`
3×	`associate-+l+` `associate-/l/`
2×	`+-commutative` `associate-+r-` `insert-quire-add` `associate-+l-`
1×	`p16-flip--`

Counts

4 → 233

Calls

4 calls:

150.0ms	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (real->posit16 1.0)) (real->posit16 2.0))
15.0ms	(+.p16 (+.p16 alpha beta) (real->posit16 2.0))
130.0ms	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (real->posit16 1.0))
22.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (real->posit16 1.0)) (real->posit16 2.0))
0.0ms	(+.p16 (+.p16 alpha beta) (real->posit16 2.0))
0.0ms	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (real->posit16 1.0))
0.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0)))

simplify2.1s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
3	1588
2	266
1	64
0	41

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize269.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))) (real->posit16 1.0)) (real->posit16 2.0))
0.2b	(+.p16 alpha (+.p16 beta (real->posit16 2.0)))
0.3b	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))) (real->posit16 1.0))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

101×	`p16-lft-identity-expand` `p16--un-lft-identity`
91×	`*p16-rgt-identity-expand`
78×	`p16-times-frac`
30×	`p16-distribute-lft-out` `distribute-rgt-out` `distribute-lft-out`
28×	`/p16-rgt-identity-expand`
26×	`associate-/l*`
22×	`associate-/r/`
10×	`distribute-lft1-in`
8×	`introduce-quire` `-p16-rgt-identity-expand`
6×	`associate-/r*` `+p16-lft-identity-expand` `+p16-rgt-identity-expand`
4×	`associate-+r-`
3×	`associate-+r+` `insert-quire-fdp-add` `associate-/l/`
2×	`+-commutative` `associate-+l+`
1×	`insert-quire-add` `p16-flip--` `associate-+l-`

Counts

4 → 182

Calls

4 calls:

52.0ms	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))) (real->posit16 1.0)) (real->posit16 2.0))
6.0ms	(+.p16 alpha (+.p16 beta (real->posit16 2.0)))
45.0ms	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))) (real->posit16 1.0))
16.0ms	(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))) (real->posit16 1.0)) (real->posit16 2.0))
0.0ms	(+.p16 alpha (+.p16 beta (real->posit16 2.0)))
0.0ms	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))) (real->posit16 1.0))
0.0ms	(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0))))

simplify1.8s

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
3	1426
2	220
1	54
0	36

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize286.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 alpha (+.p16 beta (real->posit16 2.0)))
0.3b	(+.p16 (/.p16 (real->posit16 1.0) (/.p16 (+.p16 alpha (+.p16 beta (real->posit16 2.0))) (-.p16 beta alpha))) (real->posit16 1.0))
0.3b	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 alpha (+.p16 beta (real->posit16 2.0))) (-.p16 beta alpha)))
0.5b	(/.p16 (+.p16 alpha (+.p16 beta (real->posit16 2.0))) (-.p16 beta alpha))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

87×	`p16-times-frac`
67×	`p16-lft-identity-expand` `p16--un-lft-identity`
65×	`*p16-rgt-identity-expand`
17×	`associate-/r*`
11×	`associate-/r/` `/p16-rgt-identity-expand`
8×	`introduce-quire` `-p16-rgt-identity-expand`
6×	`p16-distribute-lft-out` `+p16-lft-identity-expand` `+p16-rgt-identity-expand` `distribute-lft-out` `associate-/l*`
5×	`p16-flip--`
4×	`associate-+r-`
3×	`associate-+r+` `distribute-rgt-out` `insert-quire-fdp-add`
2×	`+-commutative` `associate-+l+` `associate-/l/`
1×	`insert-quire-add` `distribute-lft1-in` `associate-+l-`

Counts

4 → 142

Calls

4 calls:

5.0ms	(+.p16 alpha (+.p16 beta (real->posit16 2.0)))
57.0ms	(+.p16 (/.p16 (real->posit16 1.0) (/.p16 (+.p16 alpha (+.p16 beta (real->posit16 2.0))) (-.p16 beta alpha))) (real->posit16 1.0))
24.0ms	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 alpha (+.p16 beta (real->posit16 2.0))) (-.p16 beta alpha)))
17.0ms	(/.p16 (+.p16 alpha (+.p16 beta (real->posit16 2.0))) (-.p16 beta alpha))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 alpha (+.p16 beta (real->posit16 2.0)))
0.0ms	(+.p16 (/.p16 (real->posit16 1.0) (/.p16 (+.p16 alpha (+.p16 beta (real->posit16 2.0))) (-.p16 beta alpha))) (real->posit16 1.0))
0.0ms	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 alpha (+.p16 beta (real->posit16 2.0))) (-.p16 beta alpha)))
0.0ms	(/.p16 (+.p16 alpha (+.p16 beta (real->posit16 2.0))) (-.p16 beta alpha))

simplify3.1s

Counts

146 → 146

Iterations

Iter	Nodes
done	5008
4	1906
3	656
2	132
1	69
0	42

prune1.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.3b

localize229.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 alpha (+.p16 beta (real->posit16 2.0)))
0.2b	(/.p16 (real->posit16 1.0) (+.p16 alpha (+.p16 beta (real->posit16 2.0))))
0.3b	(+.p16 (*.p16 (-.p16 beta alpha) (/.p16 (real->posit16 1.0) (+.p16 alpha (+.p16 beta (real->posit16 2.0))))) (real->posit16 1.0))
0.6b	(*.p16 (-.p16 beta alpha) (/.p16 (real->posit16 1.0) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

21×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
18×	`p16-times-frac`
13×	`associate-r`
10×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
8×	`introduce-quire` `-p16-rgt-identity-expand` `/p16-rgt-identity-expand`
6×	`associate-+l+`
4×	`distribute-rgt-in` `associate-+r-` `distribute-lft-in`
3×	`associate-+r+` `associate-/r` `associate-l` `insert-quire-fdp-add` `associate-/l`
2×	`+-commutative` `associate-*l/` `associate-/r/`
1×	`insert-quire-add` `associate-r/` `p16-flip--` `-commutative` `associate-+l-` `associate-/l/`

Counts

4 → 92

Calls

4 calls:

12.0ms	(+.p16 alpha (+.p16 beta (real->posit16 2.0)))
7.0ms	(/.p16 (real->posit16 1.0) (+.p16 alpha (+.p16 beta (real->posit16 2.0))))
5.0ms	(+.p16 (*.p16 (-.p16 beta alpha) (/.p16 (real->posit16 1.0) (+.p16 alpha (+.p16 beta (real->posit16 2.0))))) (real->posit16 1.0))
7.0ms	(*.p16 (-.p16 beta alpha) (/.p16 (real->posit16 1.0) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 alpha (+.p16 beta (real->posit16 2.0)))
0.0ms	(/.p16 (real->posit16 1.0) (+.p16 alpha (+.p16 beta (real->posit16 2.0))))
0.0ms	(+.p16 (*.p16 (-.p16 beta alpha) (/.p16 (real->posit16 1.0) (+.p16 alpha (+.p16 beta (real->posit16 2.0))))) (real->posit16 1.0))
0.0ms	(*.p16 (-.p16 beta alpha) (/.p16 (real->posit16 1.0) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))))

simplify1.4m

Counts

96 → 96

Iterations

Iter	Nodes
done	5017
4	3475
3	933
2	374
1	73
0	40

prune1.1s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.3b

regimes517.0ms

Accuracy

0% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 0.8b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	13
0	13

end0.0ms

sample5.5s

Algorithm: halfpoints