Details

sample1.4s

Algorithm: halfpoints

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2011
4	2011
3	1591
2	264
1	60
0	19

prune87.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize500.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.2b	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
1.4b	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
3.2b	(/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

58×	`p16-times-frac`
36×	`/p16-rgt-identity-expand`
29×	`associate-/r/`
28×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
24×	`difference-of-squares`
11×	`associate-l/` `associate-r/`
8×	`associate-/r` `introduce-quire` `difference-of-sqr-1` `-p16-rgt-identity-expand` `associate-/l`
6×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
5×	`associate-/l/`
4×	`associate-+r+`
2×	`+-commutative` `associate-+l+` `associate-+r-` `insert-quire-add` `insert-quire-fdp-add` `associate-+l-`
1×	`p16-flip--`

Counts

4 → 124

Calls

4 calls:

16.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
18.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
24.0ms	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
14.0ms	(/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.0ms	(/.p16 (/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (real->posit16 1.0)))
0.0ms	(/.p16 (.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))))

simplify1.4s

Counts

128 → 128

Iterations

Iter	Nodes
done	2008
3	2008
2	873
1	149
0	58

prune2.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.7b

localize461.0ms

Local error

Found 4 expressions with local error:

0.7b	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.7b	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
1.3b	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))
1.3b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

478×	`p16-times-frac`
339×	`p16-lft-identity-expand` `p16--un-lft-identity`
323×	`*p16-rgt-identity-expand`
84×	`distribute-lft-out--`
48×	`p16-distribute-lft-out` `distribute-lft-out`
44×	`/p16-rgt-identity-expand`
42×	`distribute-rgt-out--`
38×	`associate-/r/`
37×	`associate-/r*`
24×	`distribute-rgt-out` `associate-/l*`
8×	`distribute-lft1-in`
5×	`associate-/l/`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
1×	`associate-*r/` `p16-flip--`

Counts

4 → 404

Calls

4 calls:

114.0ms	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
91.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
13.0ms	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))
15.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.0ms	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))
0.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

simplify1.7s

Counts

408 → 408

Iterations

Iter	Nodes
done	2014
3	2014
2	947
1	167
0	71

prune2.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.4b

localize585.0ms

Local error

Found 4 expressions with local error:

0.7b	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.9b	(/.p16 i (+.p16 (+.p16 (real->posit16 1.0) (*.p16 i (real->posit16 2))) (+.p16 alpha beta)))
1.1b	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
1.3b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

291×	`p16-times-frac`
218×	`p16-lft-identity-expand` `p16--un-lft-identity`
212×	`*p16-rgt-identity-expand`
84×	`distribute-lft-out--`
42×	`distribute-rgt-out--`
30×	`associate-/r*`
23×	`/p16-rgt-identity-expand`
19×	`associate-/l*`
18×	`associate-/r/`
4×	`p16-distribute-lft-out` `+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand` `distribute-lft-out`
3×	`associate-/l/`
1×	`distribute-rgt-out` `p16-flip--`

Counts

4 → 263

Calls

4 calls:

95.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
15.0ms	(/.p16 i (+.p16 (+.p16 (real->posit16 1.0) (*.p16 i (real->posit16 2))) (+.p16 alpha beta)))
21.0ms	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
12.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.0ms	(/.p16 i (+.p16 (+.p16 (real->posit16 1.0) (*.p16 i (real->posit16 2))) (+.p16 alpha beta)))
0.0ms	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
0.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

simplify1.4s

Counts

267 → 267

Iterations

Iter	Nodes
done	2020
3	2020
2	843
1	145
0	62

prune2.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.4b

localize504.0ms

Local error

Found 4 expressions with local error:

0.7b	(/.p16 (.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 (+.p16 alpha beta) i))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.9b	(/.p16 i (+.p16 (+.p16 (real->posit16 1.0) (*.p16 i (real->posit16 2))) (+.p16 alpha beta)))
1.1b	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
1.3b	(.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 (+.p16 alpha beta) i))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

43×	`p16-lft-identity-expand` `p16--un-lft-identity`
37×	`*p16-rgt-identity-expand`
30×	`p16-times-frac`
27×	`associate-/r*`
13×	`associate-r`
12×	`/p16-rgt-identity-expand` `distribute-lft-out--`
6×	`+p16-lft-identity-expand` `distribute-rgt-out--` `+p16-rgt-identity-expand`
5×	`associate-/r/`
4×	`p16-distribute-lft-out` `introduce-quire` `-p16-rgt-identity-expand` `distribute-lft-out` `associate-/l*` `associate-/l/`
3×	`associate-l`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `associate-r/`
1×	`distribute-rgt-out` `p16-flip--` `*-commutative`

Counts

4 → 115

Calls

4 calls:

65.0ms	(/.p16 (.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 (+.p16 alpha beta) i))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
13.0ms	(/.p16 i (+.p16 (+.p16 (real->posit16 1.0) (*.p16 i (real->posit16 2))) (+.p16 alpha beta)))
21.0ms	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
8.0ms	(.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 (+.p16 alpha beta) i))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 (+.p16 alpha beta) i))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))) (-.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 1.0)))
0.0ms	(/.p16 i (+.p16 (+.p16 (real->posit16 1.0) (*.p16 i (real->posit16 2))) (+.p16 alpha beta)))
0.0ms	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
0.0ms	(.p16 (+.p16 (.p16 alpha beta) (.p16 i (+.p16 (+.p16 alpha beta) i))) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))))

simplify1.4s

Counts

119 → 119

Iterations

Iter	Nodes
done	2011
3	2011
2	682
1	155
0	58

prune2.0s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 0.4b

regimes2.1s

Accuracy

0% (0.9b remaining)

Error of 1.4b against oracle of 0.5b and baseline of 1.4b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	29
0	29

end0.0ms

sample33.8s

Algorithm: halfpoints