Details

sample439.0ms

Algorithm: halfpoints

simplify782.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2003
4	2003
3	418
2	93
1	35
0	19

prune107.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize432.0ms

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

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

126×	`p16-times-frac`
104×	`p16-lft-identity-expand` `p16--un-lft-identity`
56×	`*p16-rgt-identity-expand`
32×	`p16-distribute-lft-out` `distribute-lft-out`
22×	`/p16-rgt-identity-expand`
15×	`associate-/r*` `associate-/r/`
8×	`distribute-rgt-out` `introduce-quire` `-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` `associate-*r/` `insert-quire-fdp-add` `associate-+l-`
1×	`associate-*l/` `p16-flip--`

Counts

4 → 165

Calls

4 calls:

12.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
18.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
124.0ms	(/.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)))
13.0ms	(/.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 alpha beta) (*.p16 (real->posit16 2) i))
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)))

simplify632.0ms

Counts

169 → 169

Iterations

Iter	Nodes
done	2001
3	2001
2	426
1	110
0	55

prune7.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize263.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
0.3b	(.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 beta alpha))
0.5b	(/.p16 (.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 beta alpha)) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
0.5b	(/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

38×	`p16-lft-identity-expand` `p16--un-lft-identity`
30×	`p16-times-frac`
26×	`*p16-rgt-identity-expand`
15×	`associate-/r*`
13×	`associate-l`
11×	`/p16-rgt-identity-expand`
8×	`p16-distribute-lft-out` `distribute-lft-out`
7×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
6×	`introduce-quire` `-p16-rgt-identity-expand`
5×	`associate-/l/`
4×	`associate-r/` `associate-/l`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-/r/`
2×	`associate-+r+` `sub-neg` `distribute-rgt-out` `associate-*l/` `p16-flip--`
1×	`+-commutative` `associate-+l+` `associate-+r-` `insert-quire-add` `*-commutative` `insert-quire-fdp-add` `associate-+l-`

Counts

4 → 113

Calls

4 calls:

12.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
11.0ms	(.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 beta alpha))
61.0ms	(/.p16 (.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 beta alpha)) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
13.0ms	(/.p16 (+.p16 alpha beta) (+.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 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 beta alpha))
0.0ms	(/.p16 (.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 beta alpha)) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
0.0ms	(/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

simplify1.0s

Counts

117 → 117

Iterations

Iter	Nodes
done	2006
3	2006
2	656
1	143
0	65

prune8.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize448.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i)))
0.3b	(.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 beta alpha))
0.5b	(/.p16 (.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 beta alpha)) (+.p16 (+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i))) (real->posit16 2.0)))
0.5b	(/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

38×	`p16-lft-identity-expand` `p16--un-lft-identity`
30×	`p16-times-frac`
26×	`*p16-rgt-identity-expand`
15×	`associate-/r*`
13×	`associate-l`
11×	`/p16-rgt-identity-expand`
8×	`p16-distribute-lft-out` `distribute-lft-out`
6×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
5×	`associate-/l/`
4×	`introduce-quire` `associate-r/` `associate-/l`
3×	`distribute-rgt-in` `associate-+r-` `distribute-lft-in` `associate-r` `associate-/r/`
2×	`sub-neg` `distribute-rgt-out` `associate-*l/` `p16-flip--`
1×	`+-commutative` `associate-+r+` `*-commutative`

Counts

4 → 109

Calls

4 calls:

4.0ms	(+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i)))
10.0ms	(.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 beta alpha))
28.0ms	(/.p16 (.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (-.p16 beta alpha)) (+.p16 (+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i))) (real->posit16 2.0)))
13.0ms	(/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.1s

Counts

113 → 113

Iterations

Iter	Nodes
done	2007
3	2007
2	492
1	132
0	59

prune7.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize427.0ms

Local error

Found 4 expressions with local error:

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

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

1460×	`p16-times-frac`
915×	`p16-lft-identity-expand` `p16--un-lft-identity`
639×	`*p16-rgt-identity-expand`
184×	`p16-distribute-lft-out` `distribute-lft-out`
74×	`associate-/r/`
64×	`/p16-rgt-identity-expand`
47×	`associate-/r*`
46×	`distribute-rgt-out`
28×	`associate-/l*`
15×	`p16-flip--`
6×	`-p16-rgt-identity-expand`
4×	`+p16-lft-identity-expand` `introduce-quire` `+p16-rgt-identity-expand`
3×	`associate-+r-` `associate-/l/`
1×	`+-commutative` `associate-+r+`

Counts

4 → 696

Calls

4 calls:

8.0ms	(+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i)))
42.0ms	(/.p16 (/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))) (/.p16 (+.p16 (+.p16 alpha (+.p16 beta (.p16 (real->posit16 2) i))) (real->posit16 2.0)) (-.p16 beta alpha)))
42.0ms	(/.p16 (+.p16 (+.p16 alpha (+.p16 beta (*.p16 (real->posit16 2) i))) (real->posit16 2.0)) (-.p16 beta alpha))
40.0ms	(/.p16 (+.p16 alpha beta) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.5s

Counts

700 → 700

Iterations

Iter	Nodes
done	2005
3	2005
2	857
1	196
0	81

prune36.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

regimes1.7s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	23
0	23

end0.0ms

sample14.3s

Algorithm: halfpoints