Details

sample230.0ms

Algorithm: halfpoints

simplify17.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	28
3	28
2	26
1	19
0	12

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize168.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (real->posit16 1.0)) (real->posit16 2.0))
0.1b	(+.p16 (+.p16 alpha beta) (real->posit16 2.0))
0.3b	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (real->posit16 1.0))
0.7b	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

151×	`p16-lft-identity-expand` `p16--un-lft-identity`
111×	`*p16-rgt-identity-expand`
105×	`p16-times-frac`
50×	`p16-distribute-lft-out` `distribute-lft-out`
35×	`distribute-rgt-out`
28×	`/p16-rgt-identity-expand`
26×	`associate-/l*`
22×	`associate-/r/`
15×	`associate-/r*`
12×	`introduce-quire`
10×	`distribute-lft1-in`
8×	`-p16-rgt-identity-expand`
7×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
6×	`insert-quire-fdp-add`
4×	`associate-+r+`
3×	`associate-+l+` `associate-/l/`
2×	`+-commutative` `associate-+r-` `insert-quire-add` `associate-+l-`
1×	`p16-flip--`

Counts

4 → 233

Calls

4 calls:

77.0ms	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (real->posit16 1.0)) (real->posit16 2.0))
17.0ms	(+.p16 (+.p16 alpha beta) (real->posit16 2.0))
71.0ms	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (real->posit16 1.0))
13.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.1s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
3	1588
2	266
1	64
0	41

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize166.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))) (real->posit16 1.0)) (real->posit16 2.0))
0.2b	(+.p16 alpha (+.p16 beta (real->posit16 2.0)))
0.3b	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))) (real->posit16 1.0))
0.7b	(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

101×	`p16-lft-identity-expand` `p16--un-lft-identity`
91×	`*p16-rgt-identity-expand`
78×	`p16-times-frac`
30×	`p16-distribute-lft-out` `distribute-rgt-out` `distribute-lft-out`
28×	`/p16-rgt-identity-expand`
26×	`associate-/l*`
22×	`associate-/r/`
10×	`distribute-lft1-in`
8×	`introduce-quire` `-p16-rgt-identity-expand`
6×	`associate-/r*` `+p16-lft-identity-expand` `+p16-rgt-identity-expand`
4×	`associate-+r-`
3×	`associate-+r+` `insert-quire-fdp-add` `associate-/l/`
2×	`+-commutative` `associate-+l+`
1×	`insert-quire-add` `p16-flip--` `associate-+l-`

Counts

4 → 182

Calls

4 calls:

42.0ms	(/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))) (real->posit16 1.0)) (real->posit16 2.0))
9.0ms	(+.p16 alpha (+.p16 beta (real->posit16 2.0)))
17.0ms	(+.p16 (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0)))) (real->posit16 1.0))
12.0ms	(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (real->posit16 2.0))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.6s

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
3	1426
2	220
1	54
0	36

prune996.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize289.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.p16 (+.p16 alpha beta) (real->posit16 2.0))
0.3b	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0)))
0.3b	(+.p16 (*.p16 (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (-.p16 beta alpha)) (real->posit16 1.0))
0.6b	(*.p16 (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (-.p16 beta alpha))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

104×	`p16-lft-identity-expand` `p16--un-lft-identity`
72×	`p16-times-frac`
56×	`*p16-rgt-identity-expand`
40×	`associate-l`
32×	`p16-distribute-lft-out` `distribute-lft-out`
12×	`associate-/r*` `introduce-quire`
11×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
9×	`associate-+l+`
8×	`distribute-rgt-out` `-p16-rgt-identity-expand` `/p16-rgt-identity-expand`
6×	`distribute-rgt-in` `distribute-lft-in` `insert-quire-fdp-add`
4×	`associate-+r+` `sub-neg`
3×	`associate-r` `associate-/l*`
2×	`+-commutative` `associate-+r-` `insert-quire-add` `associate-*r/` `associate-/r/` `associate-+l-`
1×	`associate-l/` `p16-flip--` `-commutative` `associate-/l/`

Counts

4 → 174

Calls

4 calls:

8.0ms	(+.p16 (+.p16 alpha beta) (real->posit16 2.0))
21.0ms	(/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0)))
8.0ms	(+.p16 (*.p16 (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (-.p16 beta alpha)) (real->posit16 1.0))
18.0ms	(*.p16 (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (-.p16 beta alpha))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify38.8s

Counts

178 → 178

Iterations

Iter	Nodes
done	5086
4	3638
3	1426
2	408
1	107
0	52

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.4b

localize298.0ms

Local error

Found 4 expressions with local error:

0.3b	(+.p16 (.p16 beta (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0)))) (.p16 (neg.p16 alpha) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0)))))
0.3b	(+.p16 (+.p16 (.p16 beta (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0)))) (.p16 (neg.p16 alpha) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))))) (real->posit16 1.0))
0.3b	(*.p16 (neg.p16 alpha) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))))
0.4b	(*.p16 beta (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

99×	`p16-lft-identity-expand` `p16--un-lft-identity`
80×	`associate-r`
72×	`p16-times-frac`
61×	`*p16-rgt-identity-expand`
30×	`p16-distribute-lft-out` `distribute-lft-out`
18×	`introduce-quire`
15×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
14×	`insert-quire-fdp-add`
10×	`distribute-rgt-out` `-p16-rgt-identity-expand`
8×	`distribute-rgt-in` `associate-+r+` `insert-quire-add` `distribute-lft-in`
7×	`associate-+l+` `/p16-rgt-identity-expand`
5×	`associate-+l-`
3×	`associate-+r-` `associate-l`
2×	`+-commutative` `associate-r/` `associate-/r/` `-commutative`
1×	`distribute-lft1-in` `associate-*l/`

Counts

4 → 182

Calls

4 calls:

7.0ms	(+.p16 (.p16 beta (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0)))) (.p16 (neg.p16 alpha) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0)))))
9.0ms	(+.p16 (+.p16 (.p16 beta (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0)))) (.p16 (neg.p16 alpha) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))))) (real->posit16 1.0))
15.0ms	(*.p16 (neg.p16 alpha) (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))))
16.0ms	(*.p16 beta (/.p16 (real->posit16 1.0) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.7s

Counts

186 → 186

Iterations

Iter	Nodes
done	5436
3	861
2	323
1	108
0	51

prune2.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.3b

regimes649.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	16
0	16

end0.0ms

sample4.9s

Algorithm: halfpoints