Details

sample905.0ms

Algorithm: halfpoints

simplify474.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
3	418
2	93
1	35
0	19

prune57.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize420.0ms

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)))
0.8b	(/.p16 (.p16 (+.p16 alpha beta) (-.p16 beta alpha)) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)))

rewrite484.0ms

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:

17.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
341.0ms	(+.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))
108.0ms	(/.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 (/.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)))

simplify656.0ms

Counts

192 → 192

Iterations

Iter	Nodes
done	2000
2	461
1	118
0	60

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.5b

localize470.0ms

Local error

Found 4 expressions with local error:

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

rewrite472.0ms

Algorithm

rewrite-expression-head

Rules

51×	`p16-lft-identity-expand` `p16--un-lft-identity`
37×	`*p16-rgt-identity-expand`
30×	`p16-times-frac`
15×	`associate-/r*` `/p16-rgt-identity-expand`
14×	`p16-distribute-lft-out` `distribute-lft-out`
13×	`associate-r`
8×	`+p16-lft-identity-expand` `distribute-rgt-out` `introduce-quire` `+p16-rgt-identity-expand`
7×	`associate-/r/`
6×	`-p16-rgt-identity-expand`
5×	`associate-/l/`
4×	`associate-/l*`
3×	`associate-l` `insert-quire-fdp-add`
2×	`distribute-rgt-in` `associate-+l+` `associate-+r+` `distribute-lft-in` `distribute-lft1-in` `associate-l/` `associate-r/`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `p16-flip--` `*-commutative` `associate-+l-`

Counts

4 → 133

Calls

4 calls:

294.0ms	(+.p16 (/.p16 (.p16 (+.p16 beta alpha) (/.p16 (-.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))
22.0ms	(.p16 (+.p16 beta alpha) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))))
128.0ms	(/.p16 (.p16 (+.p16 beta alpha) (/.p16 (-.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)))
26.0ms	(/.p16 (-.p16 beta alpha) (+.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 (-.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 beta alpha) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i))))
0.0ms	(/.p16 (.p16 (+.p16 beta alpha) (/.p16 (-.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 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)))

simplify698.0ms

Counts

137 → 137

Iterations

Iter	Nodes
done	2004
2	546
1	121
0	54

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize601.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta)
0.2b	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 2.0))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta))) (real->posit16 1.0))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta))
0.7b	(/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

62×	`p16-lft-identity-expand` `p16--un-lft-identity`
45×	`p16-times-frac`
38×	`*p16-rgt-identity-expand`
16×	`p16-distribute-lft-out` `distribute-lft-out`
15×	`associate-/r*`
10×	`introduce-quire`
8×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `/p16-rgt-identity-expand` `+p16-rgt-identity-expand`
7×	`associate-+l+`
6×	`associate-/l*`
4×	`insert-quire-add` `distribute-rgt-out` `associate-+l-`
3×	`insert-quire-fdp-add` `associate-/l/`
2×	`distribute-rgt-in` `+-commutative` `associate-+r+` `distribute-lft-in` `associate-/r/`
1×	`associate-+r-` `p16-flip--`

Counts

4 → 124

Calls

4 calls:

15.0ms	(+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta)
8.0ms	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (+.p16 alpha beta) (.p16 (real->posit16 2) i)) (real->posit16 2.0))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta))) (real->posit16 1.0))
25.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 (*.p16 (real->posit16 2) i) alpha) beta))
133.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.7s

Counts

128 → 128

Iterations

Iter	Nodes
done	2001
3	1415
2	326
1	104
0	59

prune2.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize432.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.p16 (-.p16 beta alpha) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (*.p16 (real->posit16 2) i)) alpha (real->posit16 1.0)) beta (real->posit16 1.0))))
0.7b	(/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
2.6b	(quire16-mul-add (posit16->quire16 (*.p16 (real->posit16 2) i)) alpha (real->posit16 1.0))
9.3b	(quire16-mul-add (quire16-mul-add (posit16->quire16 (*.p16 (real->posit16 2) i)) alpha (real->posit16 1.0)) beta (real->posit16 1.0))

rewrite347.0ms

Algorithm

rewrite-expression-head

Rules

59×	`p16-lft-identity-expand` `p16--un-lft-identity`
45×	`p16-times-frac`
35×	`*p16-rgt-identity-expand`
16×	`p16-distribute-lft-out` `distribute-lft-out`
15×	`associate-/r*`
6×	`/p16-rgt-identity-expand` `associate-/l*`
4×	`distribute-rgt-out`
3×	`associate-/l/`
2×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `associate-/r/` `+p16-rgt-identity-expand`
1×	`p16-flip--`

Counts

4 → 87

Calls

4 calls:

3.0ms	(/.p16 (-.p16 beta alpha) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (*.p16 (real->posit16 2) i)) alpha (real->posit16 1.0)) beta (real->posit16 1.0))))
342.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
0.0ms	(quire16-mul-add (posit16->quire16 (*.p16 (real->posit16 2) i)) alpha (real->posit16 1.0))
0.0ms	(quire16-mul-add (quire16-mul-add (posit16->quire16 (*.p16 (real->posit16 2) i)) alpha (real->posit16 1.0)) beta (real->posit16 1.0))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (-.p16 beta alpha) (quire16->posit16 (quire16-mul-add (quire16-mul-add (posit16->quire16 (*.p16 (real->posit16 2) i)) alpha (real->posit16 1.0)) beta (real->posit16 1.0))))
0.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i)) (real->posit16 2.0)))
0.0ms	(quire16-mul-add (posit16->quire16 (*.p16 (real->posit16 2) i)) alpha (real->posit16 1.0))
0.0ms	(quire16-mul-add (quire16-mul-add (posit16->quire16 (*.p16 (real->posit16 2) i)) alpha (real->posit16 1.0)) beta (real->posit16 1.0))

simplify753.0ms

Counts

91 → 91

Iterations

Iter	Nodes
done	2005
4	866
3	398
2	190
1	55
0	37

prune835.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.3b

regimes1.1s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	24
0	24

end0.0ms

sample15.8s

Algorithm: halfpoints