Details

sample529.0ms

Algorithm: halfpoints

simplify503.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2074
3	418
2	93
1	35
0	19

prune69.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize265.0ms

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)))

rewrite277.0ms

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:

10.0ms	(+.p16 (+.p16 alpha beta) (*.p16 (real->posit16 2) i))
173.0ms	(+.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))
77.0ms	(/.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)))

simplify1.4s

Counts

192 → 192

Iterations

Iter	Nodes
3	3161
2	460
1	118
0	60

prune10.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize355.0ms

Local error

Found 4 expressions with local error:

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

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

31.0ms	(.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha)))) (/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2))))))
31.0ms	(+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha)))
54.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))))
6.0ms	(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.9s

Counts

129 → 129

Iterations

Iter	Nodes
3	3281
2	680
1	150
0	64

prune7.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize329.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

18.0ms	(+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta (+.p16 (real->posit16 2.0) alpha)))
5.0ms	(+.p16 beta (+.p16 (real->posit16 2.0) alpha))
28.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 beta (+.p16 (real->posit16 2.0) alpha))))
7.0ms	(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 beta (*.p16 i (real->posit16 2)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify8.4s

Counts

91 → 91

Iterations

Iter	Nodes
4	9290
3	1751
2	325
1	95
0	54

prune4.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize346.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

29×	`p16-lft-identity-expand` `p16--un-lft-identity`
23×	`*p16-rgt-identity-expand`
18×	`p16-times-frac`
17×	`introduce-quire`
12×	`insert-quire-fdp-add`
10×	`-p16-rgt-identity-expand`
8×	`/p16-rgt-identity-expand`
7×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
6×	`associate-+l+` `associate-+r-` `associate-/r` `associate-/l`
4×	`p16-distribute-lft-out` `distribute-lft-out`
3×	`associate-+l-` `associate-/l/`
2×	`distribute-rgt-in` `+-commutative` `associate-+r+` `distribute-lft-in` `associate-/r/`
1×	`insert-quire-add` `distribute-rgt-out` `p16-flip--`

Counts

4 → 96

Calls

4 calls:

4.0ms	(+.p16 beta (+.p16 (*.p16 i (real->posit16 2)) alpha))
30.0ms	(+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha)))
50.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (real->posit16 2.0) (+.p16 beta alpha))))
6.0ms	(/.p16 (-.p16 beta alpha) (+.p16 beta (+.p16 (*.p16 i (real->posit16 2)) alpha)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify11.3s

Counts

100 → 100

Iterations

Iter	Nodes
4	11953
3	1903
2	391
1	98
0	52

prune5.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

regimes1.7s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
1	22
0	22

end0.0ms

sample15.1s

Algorithm: halfpoints