Details

sample1.5s

Algorithm: halfpoints

simplify845.0ms

Counts

1 → 1

Iterations

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

prune90.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize305.0ms

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)))
3.5b	(/.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))))

rewrite31.0ms

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:

8.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
8.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) 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)))
6.0ms	(/.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))))

simplify627.0ms

Counts

128 → 128

Iterations

Iter	Nodes
done	2008
2	873
1	149
0	58

prune2.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.8b

localize618.0ms

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)))
0.6b	(/.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)))
1.4b	(/.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)))

rewrite313.0ms

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)))
114.0ms	(/.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)))
27.0ms	(/.p16 (.p16 i (+.p16 (+.p16 alpha beta) i)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))
24.0ms	(/.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)))

simplify1.0s

Counts

408 → 408

Iterations

Iter	Nodes
done	2002
2	947
1	167
0	71

prune2.7s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 0.5b

localize637.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.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)))
0.7b	(/.p16 (/.p16 i (real->posit16 1.0)) (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)) (/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))))
1.0b	(/.p16 (+.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)))

rewrite446.0ms

Algorithm

rewrite-expression-head

Rules

3385×	`p16-times-frac`
1911×	`p16-lft-identity-expand` `p16--un-lft-identity`
1781×	`*p16-rgt-identity-expand`
390×	`p16-distribute-lft-out` `distribute-lft-out`
370×	`associate-/r/`
369×	`/p16-rgt-identity-expand`
269×	`associate-/r*`
195×	`distribute-rgt-out`
84×	`distribute-lft-out--`
65×	`distribute-lft1-in`
42×	`distribute-rgt-out--`
23×	`associate-/l*`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand` `associate-/l/`
1×	`p16-flip--`

Counts

4 → 1511

Calls

4 calls:

109.0ms	(/.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)))
168.0ms	(/.p16 (/.p16 i (real->posit16 1.0)) (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)) (/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))))
44.0ms	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
25.0ms	(/.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 (/.p16 i (real->posit16 1.0)) (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)) (/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))))
0.0ms	(/.p16 (+.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)))

simplify1.0s

Counts

1515 → 1515

Iterations

Iter	Nodes
done	2032
2	843
1	234
0	89

prune3.5s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 0.4b

localize557.0ms

Local error

Found 4 expressions with local error:

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

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

3121×	`p16-times-frac`
1730×	`p16-lft-identity-expand` `p16--un-lft-identity`
1600×	`*p16-rgt-identity-expand`
390×	`p16-distribute-lft-out` `distribute-lft-out`
357×	`/p16-rgt-identity-expand`
356×	`associate-/r/`
257×	`associate-/r*`
195×	`distribute-rgt-out`
65×	`distribute-lft1-in`
13×	`associate-l`
10×	`associate-/l*`
4×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
3×	`associate-r` `associate-/l/`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 1348

Calls

4 calls:

82.0ms	(/.p16 (/.p16 i (real->posit16 1.0)) (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)) (/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))))
26.0ms	(.p16 (/.p16 (+.p16 (.p16 (real->posit16 2) i) (-.p16 (+.p16 alpha 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)))
41.0ms	(/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))
77.0ms	(/.p16 (+.p16 (.p16 (real->posit16 2) i) (-.p16 (+.p16 alpha 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 (/.p16 i (real->posit16 1.0)) (/.p16 (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 1.0)) (/.p16 (+.p16 (+.p16 alpha beta) i) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))))
0.0ms	(.p16 (/.p16 (+.p16 (.p16 (real->posit16 2) i) (-.p16 (+.p16 alpha 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 alpha beta) (*.p16 (real->posit16 2) i)))
0.0ms	(/.p16 (+.p16 (.p16 (real->posit16 2) i) (-.p16 (+.p16 alpha beta) (real->posit16 1.0))) (+.p16 (.p16 alpha beta) (*.p16 i (+.p16 (+.p16 alpha beta) i))))

simplify1.3s

Counts

1352 → 1352

Iterations

Iter	Nodes
done	2003
2	957
1	266
0	88

prune2.2s

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

simplify11.0ms

Iterations

Iter	Nodes
done	27
0	27

end0.0ms

sample28.1s

Algorithm: halfpoints