Details

sample664.0ms

Algorithm: halfpoints

simplify1.8s

Counts

1 → 1

Iterations

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

prune59.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize288.0ms

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)))

rewrite381.0ms

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))
265.0ms	(+.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))
79.0ms	(/.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)))

simplify3.8s

Counts

192 → 192

Iterations

Iter	Nodes
done	5000
3	3357
2	461
1	118
0	60

prune2.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.4b

localize346.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0)))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2)))))
0.2b	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0)))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2))))) (real->posit16 1.0))
0.5b	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

35.0ms	(.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0)))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2)))))
5.0ms	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0)))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2))))) (real->posit16 1.0))
51.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))))
19.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha 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 (+.p16 beta alpha) (real->posit16 2.0)))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2)))))
0.0ms	(+.p16 (.p16 (/.p16 (+.p16 beta alpha) (+.p16 (.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0)))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2))))) (real->posit16 1.0))
0.0ms	(/.p16 (+.p16 beta alpha) (+.p16 (*.p16 i (real->posit16 2)) (+.p16 (+.p16 beta alpha) (real->posit16 2.0))))
0.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2))))

simplify2.8s

Counts

119 → 119

Iterations

Iter	Nodes
done	5035
3	2931
2	840
1	134
0	59

prune2.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize493.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.p16 (.p16 (/.p16 (+.p16 alpha beta) (+.p16 (real->posit16 2.0) (+.p16 (+.p16 beta (.p16 (real->posit16 2) i)) alpha))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2))))) (real->posit16 1.0))
0.2b	(+.p16 (+.p16 beta (*.p16 (real->posit16 2) i)) alpha)
0.5b	(/.p16 (+.p16 alpha beta) (+.p16 (real->posit16 2.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 2) i)) alpha)))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2))))

rewrite144.0ms

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*`
9×	`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×	`distribute-rgt-out`
3×	`insert-quire-fdp-add` `associate-+l-` `associate-/l/`
2×	`distribute-rgt-in` `+-commutative` `associate-+r+` `associate-+r-` `insert-quire-add` `distribute-lft-in` `associate-/r/`
1×	`p16-flip--`

Counts

4 → 123

Calls

4 calls:

7.0ms	(+.p16 (.p16 (/.p16 (+.p16 alpha beta) (+.p16 (real->posit16 2.0) (+.p16 (+.p16 beta (.p16 (real->posit16 2) i)) alpha))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2))))) (real->posit16 1.0))
13.0ms	(+.p16 (+.p16 beta (*.p16 (real->posit16 2) i)) alpha)
96.0ms	(/.p16 (+.p16 alpha beta) (+.p16 (real->posit16 2.0) (+.p16 (+.p16 beta (*.p16 (real->posit16 2) i)) alpha)))
24.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.5s

Counts

127 → 127

Iterations

Iter	Nodes
done	5022
3	1664
2	371
1	97
0	56

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize343.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (/.p16 (+.p16 alpha beta) (+.p16 (real->posit16 2.0) (+.p16 beta (+.p16 (.p16 (real->posit16 2) i) alpha)))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2)))))
0.2b	(+.p16 (.p16 (/.p16 (+.p16 alpha beta) (+.p16 (real->posit16 2.0) (+.p16 beta (+.p16 (.p16 (real->posit16 2) i) alpha)))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2))))) (real->posit16 1.0))
0.5b	(/.p16 (+.p16 alpha beta) (+.p16 (real->posit16 2.0) (+.p16 beta (+.p16 (*.p16 (real->posit16 2) i) alpha))))
0.6b	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

109×	`p16-lft-identity-expand` `p16--un-lft-identity`
90×	`p16-times-frac`
67×	`*p16-rgt-identity-expand`
40×	`associate-l`
28×	`p16-distribute-lft-out` `distribute-lft-out`
15×	`associate-/r*`
13×	`associate-r`
10×	`+p16-lft-identity-expand` `/p16-rgt-identity-expand` `+p16-rgt-identity-expand`
8×	`introduce-quire`
7×	`distribute-rgt-out`
6×	`associate-+l+` `-p16-rgt-identity-expand` `associate-/l*`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/`
3×	`insert-quire-fdp-add` `associate-/l/`
2×	`associate-+r+`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `associate-l/` `associate-r/` `p16-flip--` `*-commutative` `associate-+l-`

Counts

4 → 178

Calls

4 calls:

19.0ms	(.p16 (/.p16 (+.p16 alpha beta) (+.p16 (real->posit16 2.0) (+.p16 beta (+.p16 (.p16 (real->posit16 2) i) alpha)))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2)))))
5.0ms	(+.p16 (.p16 (/.p16 (+.p16 alpha beta) (+.p16 (real->posit16 2.0) (+.p16 beta (+.p16 (.p16 (real->posit16 2) i) alpha)))) (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2))))) (real->posit16 1.0))
25.0ms	(/.p16 (+.p16 alpha beta) (+.p16 (real->posit16 2.0) (+.p16 beta (+.p16 (*.p16 (real->posit16 2) i) alpha))))
26.0ms	(/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (*.p16 i (real->posit16 2))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify3.8s

Counts

182 → 182

Iterations

Iter	Nodes
done	5003
3	4114
2	823
1	135
0	60

prune2.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

regimes1.3s

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
done	22
0	22

end0.0ms

sample14.1s

Algorithm: halfpoints