Details

sample104.0ms

Algorithm: halfpoints

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	17
2	17
1	16
0	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize191.0ms

Local error

Found 3 expressions with local error:

0.2b	(+.p16 (.p16 y.re y.re) (.p16 y.im y.im))
0.3b	(-.p16 (.p16 x.im y.re) (.p16 x.re y.im))
1.0b	(/.p16 (-.p16 (.p16 x.im y.re) (.p16 x.re y.im)) (+.p16 (.p16 y.re y.re) (.p16 y.im y.im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

163×	`p16-lft-identity-expand` `p16--un-lft-identity`
96×	`p16-times-frac`
75×	`*p16-rgt-identity-expand`
56×	`distribute-lft-out--`
40×	`p16-distribute-lft-out` `distribute-lft-out`
15×	`introduce-quire`
14×	`distribute-rgt-out--`
12×	`associate-/r*`
10×	`distribute-rgt-out`
8×	`associate-/l*`
7×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
5×	`/p16-rgt-identity-expand` `insert-quire-fdp-add` `insert-quire-fdp-sub`
2×	`associate-+l+` `associate-+r+` `associate--l+` `p16-flip--` `*-commutative` `associate--r+` `associate-/l/`
1×	`associate--l-` `+-commutative` `insert-quire-sub` `associate-+r-` `sub-neg` `insert-quire-add` `associate-/r/` `associate-+l-` `associate--r-`

Counts

3 → 184

Calls

3 calls:

11.0ms	(+.p16 (.p16 y.re y.re) (.p16 y.im y.im))
7.0ms	(-.p16 (.p16 x.im y.re) (.p16 x.re y.im))
34.0ms	(/.p16 (-.p16 (.p16 x.im y.re) (.p16 x.re y.im)) (+.p16 (.p16 y.re y.re) (.p16 y.im y.im)))

series0.0ms

Counts

3 → 3

Calls

3 calls:

0.0ms	(+.p16 (.p16 y.re y.re) (.p16 y.im y.im))
0.0ms	(-.p16 (.p16 x.im y.re) (.p16 x.re y.im))
0.0ms	(/.p16 (-.p16 (.p16 x.im y.re) (.p16 x.re y.im)) (+.p16 (.p16 y.re y.re) (.p16 y.im y.im)))

simplify1.9s

Counts

187 → 187

Iterations

Iter	Nodes
done	5014
3	2254
2	354
1	79
0	45

prune707.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.8b

localize239.0ms

Local error

Found 3 expressions with local error:

0.2b

(+.p16 (*.p16 y.re y.re) (*.p16 y.im y.im))

1.0b

(/.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)) (+.p16 (*.p16 y.re y.re) (*.p16 y.im y.im)))

6.3b

(quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

60×	`p16-lft-identity-expand` `p16--un-lft-identity`
36×	`p16-times-frac`
30×	`*p16-rgt-identity-expand`
20×	`p16-distribute-lft-out` `distribute-lft-out`
12×	`associate-/r*`
8×	`introduce-quire`
5×	`distribute-rgt-out` `insert-quire-fdp-add`
4×	`+p16-lft-identity-expand` `-p16-rgt-identity-expand` `/p16-rgt-identity-expand` `+p16-rgt-identity-expand`
3×	`associate-/l*`
2×	`associate-+l+` `associate-+r+`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `associate-/r/` `*-commutative` `associate-+l-` `associate-/l/`

Counts

3 → 91

Calls

3 calls:

17.0ms

(+.p16 (*.p16 y.re y.re) (*.p16 y.im y.im))

34.0ms

(/.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)) (+.p16 (*.p16 y.re y.re) (*.p16 y.im y.im)))

0.0ms

(quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)

series0.0ms

Counts

3 → 3

Calls

3 calls:

0.0ms

(+.p16 (*.p16 y.re y.re) (*.p16 y.im y.im))

0.0ms

(/.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)) (+.p16 (*.p16 y.re y.re) (*.p16 y.im y.im)))

0.0ms

(quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)

simplify6.0s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
4	1113
3	252
2	87
1	38
0	31

prune692.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.8b

localize280.0ms

Local error

Found 3 expressions with local error:

1.0b

(/.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)) (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)))

5.4b

(quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)

6.3b

(quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`p16-lft-identity-expand` `p16-times-frac` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
3×	`associate-/r` `/p16-rgt-identity-expand` `associate-/l`
1×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `associate-/r/` `+p16-rgt-identity-expand` `associate-/l/`

Counts

3 → 25

Calls

3 calls:

2.0ms

(/.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)) (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)))

0.0ms

(quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)

0.0ms

(quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)

series0.0ms

Counts

3 → 3

Calls

3 calls:

0.0ms

(/.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)) (quire16->posit16 (quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)))

0.0ms

(quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)

0.0ms

(quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)

simplify83.0ms

Counts

28 → 28

Iterations

Iter	Nodes
done	102
7	102
6	101
5	94
4	85
3	75
2	58
1	26
0	24

prune462.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.8b

localize371.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.p16 (real->posit16 1.0) (/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.im y.re)) x.re y.im))))
1.1b	(/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.im y.re)) x.re y.im)))
5.4b	(quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)
6.3b	(quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

84×	`p16-times-frac`
55×	`p16-lft-identity-expand` `p16--un-lft-identity`
54×	`*p16-rgt-identity-expand`
19×	`associate-/r*`
14×	`associate-/r/`
11×	`/p16-rgt-identity-expand` `associate-/l*`
3×	`associate-/l/`
2×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand` `remove-double-div.p16`

Counts

4 → 100

Calls

4 calls:

7.0ms	(/.p16 (real->posit16 1.0) (/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.im y.re)) x.re y.im))))
2.0ms	(/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.im y.re)) x.re y.im)))
0.0ms	(quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)
0.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/.p16 (real->posit16 1.0) (/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.im y.re)) x.re y.im))))
0.0ms	(/.p16 (quire16->posit16 (quire16-mul-add (posit16->quire16 (.p16 y.re y.re)) y.im y.im)) (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.im y.re)) x.re y.im)))
0.0ms	(quire16-mul-add (posit16->quire16 (*.p16 y.re y.re)) y.im y.im)
0.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 x.im y.re)) x.re y.im)

simplify936.0ms

Counts

104 → 104

Iterations

Iter	Nodes
done	1053
6	1053
5	1045
4	997
3	587
2	99
1	45
0	32

prune675.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.7b

regimes1.2s

Accuracy

0% (0.4b remaining)

Error of 1.0b against oracle of 0.6b and baseline of 1.0b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
0	13

end0.0ms

sample3.7s

Algorithm: halfpoints