Details

sample1.2s

Algorithm: halfpoints

simplify1.3s

Counts

1 → 1

Iterations

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

prune68.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.4b

localize296.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 i (+.p16 (+.p16 alpha beta) i))
0.2b	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))
1.3b	(/.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)))
3.5b	(/.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))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

17.0ms	(*.p16 i (+.p16 (+.p16 alpha beta) i))
5.0ms	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))
7.0ms	(/.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)))
15.0ms	(/.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 i (+.p16 (+.p16 alpha beta) i))
0.0ms	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) 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))))

simplify1.1s

Counts

130 → 130

Iterations

Iter	Nodes
done	2000
3	2000
2	828
1	161
0	65

prune6.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.8b

localize479.0ms

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

rewrite240.0ms

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:

95.0ms	(/.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)))
77.0ms	(/.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)))
25.0ms	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))
35.0ms	(/.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)))

simplify1.3s

Counts

408 → 408

Iterations

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

prune20.0s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 0.5b

localize1.1s

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 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
1.3b	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 (real->posit16 1.0) (*.p16 i (real->posit16 2))) (+.p16 alpha beta)))
1.4b	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

318×	`p16-times-frac`
251×	`p16-lft-identity-expand` `p16--un-lft-identity`
227×	`*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/`
16×	`p16-distribute-lft-out` `distribute-lft-out`
4×	`+p16-lft-identity-expand` `distribute-rgt-out` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
3×	`associate-/l/`
1×	`p16-flip--`

Counts

4 → 290

Calls

4 calls:

84.0ms	(/.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)))
3.0ms	(/.p16 i (+.p16 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
53.0ms	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 (real->posit16 1.0) (*.p16 i (real->posit16 2))) (+.p16 alpha beta)))
11.0ms	(/.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 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
0.0ms	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 (real->posit16 1.0) (*.p16 i (real->posit16 2))) (+.p16 alpha beta)))
0.0ms	(/.p16 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

simplify966.0ms

Counts

294 → 294

Iterations

Iter	Nodes
done	2016
3	2016
2	846
1	145
0	62

prune17.6s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 0.4b

localize570.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

70×	`p16-lft-identity-expand` `p16--un-lft-identity`
54×	`p16-times-frac`
46×	`*p16-rgt-identity-expand`
18×	`associate-/r*`
16×	`p16-distribute-lft-out` `distribute-lft-out`
13×	`associate-l`
11×	`/p16-rgt-identity-expand`
6×	`associate-/l*`
4×	`+p16-lft-identity-expand` `distribute-rgt-out` `introduce-quire` `-p16-rgt-identity-expand` `associate-/r/` `+p16-rgt-identity-expand`
3×	`associate-r`
2×	`associate-/l/`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 127

Calls

4 calls:

4.0ms	(/.p16 i (+.p16 beta (+.p16 alpha (*.p16 i (real->posit16 2)))))
12.0ms	(.p16 (/.p16 (+.p16 alpha (-.p16 (+.p16 (.p16 (real->posit16 2) i) beta) (real->posit16 1.0))) (+.p16 (.p16 alpha beta) (.p16 i (+.p16 (+.p16 alpha beta) i)))) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 alpha beta)))
38.0ms	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 (real->posit16 1.0) (*.p16 i (real->posit16 2))) (+.p16 alpha beta)))
10.0ms	(/.p16 (+.p16 alpha (-.p16 (+.p16 (.p16 (real->posit16 2) i) beta) (real->posit16 1.0))) (+.p16 (.p16 alpha beta) (*.p16 i (+.p16 (+.p16 alpha beta) i))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.2s

Counts

131 → 131

Iterations

Iter	Nodes
done	2012
3	2012
2	814
1	168
0	57

prune9.7s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 0.4b

regimes2.7s

Accuracy

0% (0.9b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	32
0	32

end0.0ms

sample33.6s

Algorithm: halfpoints