Details

sample642.0ms

Algorithm: halfpoints

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5025
4	2074
3	418
2	93
1	35
0	19

prune51.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize398.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))
0.2b	(+.p16 (/.p16 (.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 alpha (+.p16 (.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))) (real->posit16 1.0))
0.2b	(+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))
1.3b	(/.p16 (.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 alpha (+.p16 (.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

24×	`/p16-rgt-identity-expand`
21×	`p16-lft-identity-expand` `p16--un-lft-identity`
19×	`*p16-rgt-identity-expand`
15×	`associate-/r/`
12×	`distribute-rgt-out`
10×	`-p16-rgt-identity-expand`
8×	`introduce-quire` `associate-*l/`
7×	`associate-+r-` `associate-*r/`
6×	`p16-distribute-lft-out` `+p16-lft-identity-expand` `+p16-rgt-identity-expand` `distribute-lft-out`
4×	`distribute-lft1-in` `associate-/l/`
3×	`associate-+r+` `associate-r` `associate-l` `insert-quire-fdp-add` `associate-+l-`
2×	`+-commutative` `associate-+l+`
1×	`distribute-rgt-in` `associate-/r` `insert-quire-add` `distribute-lft-in` `p16-times-frac` `p16-flip--` `-commutative` `associate-/l*`

Counts

4 → 98

Calls

4 calls:

24.0ms	(.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))
13.0ms	(+.p16 (/.p16 (.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 alpha (+.p16 (.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))) (real->posit16 1.0))
12.0ms	(+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))
7.0ms	(/.p16 (.p16 (-.p16 beta alpha) (+.p16 beta alpha)) (.p16 (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha)) (+.p16 alpha (+.p16 (.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify3.9s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
3	3976
2	511
1	118
0	46

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize418.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

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×	`+p16-lft-identity-expand` `introduce-quire` `/p16-rgt-identity-expand` `+p16-rgt-identity-expand`
7×	`associate-+r-`
6×	`associate-+l+` `associate-/r` `associate-/l`
3×	`associate-+r+` `insert-quire-fdp-add` `associate-+l-` `associate-/l/`
2×	`distribute-rgt-in` `+-commutative` `distribute-lft-in` `associate-/r/`
1×	`insert-quire-add` `p16-flip--`

Counts

4 → 88

Calls

4 calls:

4.0ms	(+.p16 (.p16 (/.p16 (-.p16 beta alpha) (+.p16 (.p16 (real->posit16 2) i) (+.p16 beta alpha))) (/.p16 (+.p16 beta alpha) (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))) (real->posit16 1.0))
11.0ms	(+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))
20.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))
32.0ms	(/.p16 (+.p16 beta alpha) (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify4.4s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
3	1484
2	320
1	96
0	52

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.4b

localize393.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))
0.3b	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))) (+.p16 beta alpha)))
0.6b	(/.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))) (+.p16 beta alpha))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

93×	`p16-times-frac`
62×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
19×	`associate-/r*`
13×	`/p16-rgt-identity-expand`
9×	`associate-/l*`
8×	`-p16-rgt-identity-expand`
7×	`associate-/r/`
6×	`associate-+r-`
4×	`+p16-lft-identity-expand` `introduce-quire` `+p16-rgt-identity-expand` `associate-/l/`
2×	`associate-+l-`
1×	`+-commutative` `associate-+r+` `p16-flip--`

Counts

4 → 130

Calls

4 calls:

23.0ms	(+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))
45.0ms	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))) (+.p16 beta alpha)))
28.0ms	(/.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))) (+.p16 beta alpha))
19.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (*.p16 (real->posit16 2) i) (+.p16 beta alpha)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify4.1s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
4	4776
3	931
2	219
1	82
0	46

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize495.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))
0.3b	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))) (+.p16 beta alpha)))
0.6b	(/.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))) (+.p16 beta alpha))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 (*.p16 i (real->posit16 2)) beta)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

93×	`p16-times-frac`
62×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
19×	`associate-/r*`
13×	`/p16-rgt-identity-expand`
9×	`associate-/l*`
8×	`-p16-rgt-identity-expand`
7×	`associate-/r/`
6×	`associate-+r-`
4×	`+p16-lft-identity-expand` `introduce-quire` `+p16-rgt-identity-expand` `associate-/l/`
2×	`associate-+l-`
1×	`+-commutative` `associate-+r+` `p16-flip--`

Counts

4 → 130

Calls

4 calls:

22.0ms	(+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta)))
53.0ms	(/.p16 (real->posit16 1.0) (/.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))) (+.p16 beta alpha)))
28.0ms	(/.p16 (+.p16 alpha (+.p16 (*.p16 (real->posit16 2) i) (+.p16 (real->posit16 2.0) beta))) (+.p16 beta alpha))
7.0ms	(/.p16 (-.p16 beta alpha) (+.p16 alpha (+.p16 (*.p16 i (real->posit16 2)) beta)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.7s

Counts

134 → 134

Iterations

Iter	Nodes
done	5033
3	1457
2	252
1	93
0	51

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

regimes1.2s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	23
0	23

end0.0ms

sample14.4s

Algorithm: halfpoints