Details

sample1.3s

Algorithm: halfpoints

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5014
3	1591
2	264
1	60
0	19

prune73.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.0b

localize403.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.p16 i (+.p16 (+.p16 alpha beta) i))
0.2b	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) 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)))
3.3b	(/.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))))

rewrite63.0ms

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:

12.0ms	(*.p16 i (+.p16 (+.p16 alpha beta) i))
8.0ms	(+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i)))
21.0ms	(/.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 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))))

simplify1.3s

Counts

130 → 130

Iterations

Iter	Nodes
done	5008
2	828
1	161
0	65

prune1.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.8b

localize404.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.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 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
1.4b	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

rewrite281.0ms

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:

131.0ms	(/.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)))
100.0ms	(/.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 (+.p16 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
15.0ms	(/.p16 (.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 (.p16 beta alpha) (.p16 i (+.p16 (+.p16 alpha beta) i))) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
0.0ms	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

simplify2.3s

Counts

408 → 408

Iterations

Iter	Nodes
done	5000
2	997
1	166
0	71

prune2.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.5b

localize503.0ms

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

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

291×	`p16-times-frac`
221×	`p16-lft-identity-expand` `p16--un-lft-identity`
219×	`*p16-rgt-identity-expand`
84×	`distribute-lft-out--`
42×	`distribute-rgt-out--`
37×	`associate-/r*`
23×	`/p16-rgt-identity-expand`
19×	`associate-/l*`
18×	`associate-/r/`
6×	`p16-distribute-lft-out` `distribute-lft-out`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
3×	`distribute-rgt-out` `associate-/l/`
1×	`distribute-rgt1-in` `p16-flip--`

Counts

4 → 270

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)))
47.0ms	(/.p16 i (+.p16 (real->posit16 1.0) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta)))
17.0ms	(/.p16 (+.p16 alpha (+.p16 beta i)) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta))
17.0ms	(/.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 (real->posit16 1.0) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta)))
0.0ms	(/.p16 (+.p16 alpha (+.p16 beta i)) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) 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)))

simplify2.1s

Counts

274 → 274

Iterations

Iter	Nodes
done	5000
2	934
1	143
0	64

prune2.3s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 0.4b

localize567.0ms

Local error

Found 4 expressions with local error:

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

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

46×	`p16-lft-identity-expand` `p16--un-lft-identity`
44×	`*p16-rgt-identity-expand`
34×	`associate-/r*`
30×	`p16-times-frac`
13×	`associate-r`
12×	`/p16-rgt-identity-expand` `distribute-lft-out--`
6×	`p16-distribute-lft-out` `+p16-lft-identity-expand` `distribute-rgt-out--` `+p16-rgt-identity-expand` `distribute-lft-out`
5×	`associate-/r/`
4×	`introduce-quire` `-p16-rgt-identity-expand` `associate-/l*` `associate-/l/`
3×	`distribute-rgt-out` `associate-l`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `associate-r/`
1×	`distribute-rgt1-in` `p16-flip--` `*-commutative`

Counts

4 → 122

Calls

4 calls:

51.0ms	(/.p16 (.p16 (+.p16 (.p16 alpha beta) (.p16 (+.p16 (+.p16 alpha beta) i) 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)))
29.0ms	(/.p16 i (+.p16 (real->posit16 1.0) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta)))
17.0ms	(/.p16 (+.p16 alpha (+.p16 beta i)) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta))
11.0ms	(.p16 (+.p16 (.p16 alpha beta) (.p16 (+.p16 (+.p16 alpha beta) i) 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 (+.p16 (+.p16 alpha beta) i) 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 (real->posit16 1.0) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta)))
0.0ms	(/.p16 (+.p16 alpha (+.p16 beta i)) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta))
0.0ms	(.p16 (+.p16 (.p16 alpha beta) (.p16 (+.p16 (+.p16 alpha beta) i) i)) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))))

simplify1.9s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	613
1	150
0	60

prune1.5s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 0.4b

regimes2.2s

Accuracy

0% (0.9b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	27
0	27

end0.0ms

sample32.6s

Algorithm: halfpoints