Details

sample630.0ms

Algorithm: halfpoints

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2213
3	420
2	97
1	35
0	19

prune92.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize350.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.2b	(+.p16 (/.p16 (/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0))) (real->posit16 1.0))
0.5b	(/.p16 (/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
0.7b	(/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

rewrite358.0ms

Algorithm

rewrite-expression-head

Rules

126×	`p16-times-frac`
117×	`p16-lft-identity-expand` `p16--un-lft-identity`
67×	`*p16-rgt-identity-expand`
38×	`p16-distribute-lft-out` `distribute-lft-out`
26×	`/p16-rgt-identity-expand`
19×	`associate-/r/`
15×	`associate-/r*`
14×	`distribute-rgt-out`
10×	`introduce-quire`
8×	`-p16-rgt-identity-expand` `associate-/l*`
7×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
5×	`associate-/l/`
4×	`associate-+r+` `insert-quire-fdp-add`
3×	`associate-+l+`
2×	`+-commutative` `associate-+r-` `insert-quire-add` `distribute-lft1-in` `associate-*r/` `associate-+l-`
1×	`associate-*l/` `p16-flip--`

Counts

4 → 188

Calls

4 calls:

11.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
246.0ms	(+.p16 (/.p16 (/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0))) (real->posit16 1.0))
72.0ms	(/.p16 (/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
24.0ms	(/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.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 (/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0))) (real->posit16 1.0))
0.0ms	(/.p16 (/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
0.0ms	(/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

simplify3.4s

Counts

192 → 192

Iterations

Iter	Nodes
done	5018
3	3484
2	472
1	118
0	60

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.4b

localize252.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0)))) (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta alpha))))
0.2b	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0)))) (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta alpha)))) (real->posit16 1.0))
0.5b	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta alpha)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

48.0ms	(.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0)))) (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta alpha))))
8.0ms	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0)))) (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta alpha)))) (real->posit16 1.0))
65.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))))
11.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta alpha)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0)))) (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta alpha))))
0.0ms	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0)))) (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta alpha)))) (real->posit16 1.0))
0.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))))
0.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta alpha)))

simplify3.7s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
3	3845
2	833
1	133
0	58

prune2.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize275.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 beta alpha))) (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))))) (real->posit16 1.0))
0.2b	(.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 beta alpha))) (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0)))))
0.6b	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta alpha)))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

8.0ms	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 beta alpha))) (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))))) (real->posit16 1.0))
72.0ms	(.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 beta alpha))) (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0)))))
20.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta alpha)))
48.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 beta alpha))) (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))))) (real->posit16 1.0))
0.0ms	(.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 beta alpha))) (/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0)))))
0.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta alpha)))
0.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))))

simplify3.0s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
3	3453
2	781
1	130
0	58

prune1.7s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.3b

localize396.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 beta alpha))) (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha))))
0.4b	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha)))
0.6b	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta alpha)))
0.6b	(/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

174×	`p16-times-frac`
106×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
46×	`associate-r`
20×	`associate-/r*` `associate-/r/`
17×	`/p16-rgt-identity-expand`
13×	`associate-l`
9×	`associate-/l*`
8×	`p16-flip--`
6×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
4×	`introduce-quire` `-p16-rgt-identity-expand`
3×	`associate-/l/`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`associate-l/` `associate-r/` `*-commutative`

Counts

4 → 194

Calls

4 calls:

54.0ms	(.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 beta alpha))) (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha))))
55.0ms	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha)))
13.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta alpha)))
51.0ms	(/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 beta alpha))) (/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha))))
0.0ms	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha)))
0.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta alpha)))
0.0ms	(/.p16 (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))) (-.p16 beta alpha))

simplify2.2s

Counts

198 → 198

Iterations

Iter	Nodes
done	5001
3	1795
2	581
1	153
0	63

prune1.8s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.3b

regimes1.5s

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	22
0	22

end0.0ms

sample15.1s

Algorithm: halfpoints