Details

sample82.0ms

Algorithm: halfpoints

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
7	3127
6	1308
5	586
4	220
3	107
2	49
1	20
0	11

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize213.0ms

Local error

Found 4 expressions with local error:

0.1b	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
0.2b	(-.p16 (.p16 x.re x.re) (.p16 x.im x.im))
0.3b	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
0.3b	(+.p16 (.p16 (-.p16 (.p16 x.re x.re) (.p16 x.im x.im)) x.im) (.p16 (+.p16 (.p16 x.re x.im) (.p16 x.im x.re)) x.re))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

8×	`+p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `+p16-rgt-identity-expand`
7×	`associate-l`
6×	`p16-lft-identity-expand` `/p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
3×	`associate-*l/`
2×	`associate-+l+` `associate-+r+` `associate--l+` `p16-flip--` `*-commutative` `associate--r+` `difference-of-squares`
1×	`associate--l-` `+-commutative` `insert-quire-sub` `associate-+r-` `sub-neg` `insert-quire-add` `insert-quire-fdp-add` `associate-+l-` `insert-quire-fdp-sub` `associate--r-`

Counts

4 → 64

Calls

4 calls:

4.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
6.0ms	(-.p16 (.p16 x.re x.re) (.p16 x.im x.im))
18.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
7.0ms	(+.p16 (.p16 (-.p16 (.p16 x.re x.re) (.p16 x.im x.im)) x.im) (.p16 (+.p16 (.p16 x.re x.im) (.p16 x.im x.re)) x.re))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
0.0ms	(-.p16 (.p16 x.re x.re) (.p16 x.im x.im))
0.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
0.0ms	(+.p16 (.p16 (-.p16 (.p16 x.re x.re) (.p16 x.im x.im)) x.im) (.p16 (+.p16 (.p16 x.re x.im) (.p16 x.im x.re)) x.re))

simplify15.5s

Counts

68 → 68

Iterations

Iter	Nodes
4	12015
3	1045
2	222
1	74
0	41

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize267.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))
0.1b	(*.p16 x.re (+.p16 x.im x.im))
0.3b	(.p16 x.im (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))
9.4b	(quire16-mul-add (posit16->quire16 (.p16 x.im (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

18×	`distribute-rgt-in` `distribute-lft-in`
11×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
9×	`associate-*r/` `/p16-rgt-identity-expand`
7×	`associate-r`
6×	`sub-neg` `p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
3×	`introduce-quire` `associate-l` `-p16-rgt-identity-expand` `*-commutative`
2×	`associate-*l/` `p16-flip--`

Counts

4 → 69

Calls

4 calls:

8.0ms	(*.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))
5.0ms	(*.p16 x.re (+.p16 x.im x.im))
24.0ms	(.p16 x.im (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 x.im (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(*.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))
0.0ms	(*.p16 x.re (+.p16 x.im x.im))
0.0ms	(.p16 x.im (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 x.im (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

simplify3.7s

Counts

73 → 73

Iterations

Iter	Nodes
3	2327
2	350
1	124
0	53

prune2.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize240.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))
0.1b	(+.p16 (.p16 x.re x.im) (.p16 x.re x.im))
0.3b	(.p16 x.im (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))
9.4b	(quire16-mul-add (posit16->quire16 (.p16 x.im (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))) (+.p16 (.p16 x.re x.im) (.p16 x.re x.im)) x.re)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

17×	`distribute-rgt-in` `distribute-lft-in`
13×	`+p16-lft-identity-expand` `+p16-rgt-identity-expand`
8×	`associate-*r/` `/p16-rgt-identity-expand`
6×	`sub-neg`
5×	`p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
4×	`associate-r`
3×	`associate-l`
2×	`associate-+l+` `associate-+r+` `associate-l/` `p16-flip--` `-commutative`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `p16-distribute-lft-out` `distribute-rgt-out` `insert-quire-fdp-add` `associate-+l-` `distribute-lft-out`

Counts

4 → 74

Calls

4 calls:

9.0ms	(*.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))
6.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.re x.im))
12.0ms	(.p16 x.im (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))
1.0ms	(quire16-mul-add (posit16->quire16 (.p16 x.im (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))) (+.p16 (.p16 x.re x.im) (.p16 x.re x.im)) x.re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(*.p16 (+.p16 x.im x.re) (-.p16 x.re x.im))
0.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.re x.im))
0.0ms	(.p16 x.im (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 x.im (.p16 (+.p16 x.im x.re) (-.p16 x.re x.im)))) (+.p16 (.p16 x.re x.im) (.p16 x.re x.im)) x.re)

simplify7.0s

Counts

78 → 78

Iterations

Iter	Nodes
3	2726
2	400
1	131
0	56

prune3.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize289.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 x.re (+.p16 x.im x.im))
0.1b	(*.p16 x.im (+.p16 x.im x.re))
0.2b	(.p16 (.p16 x.im (+.p16 x.im x.re)) (-.p16 x.re x.im))
9.4b	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (+.p16 x.im x.re)) (-.p16 x.re x.im))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

9×	`associate-r`
8×	`/p16-rgt-identity-expand`
6×	`p16-lft-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
5×	`distribute-rgt-in` `distribute-lft-in` `+p16-lft-identity-expand` `associate-*r/` `+p16-rgt-identity-expand`
3×	`introduce-quire` `-p16-rgt-identity-expand` `*-commutative`
2×	`sub-neg` `associate-*l/`
1×	`associate-l` `p16-flip--`

Counts

4 → 53

Calls

4 calls:

3.0ms	(*.p16 x.re (+.p16 x.im x.im))
3.0ms	(*.p16 x.im (+.p16 x.im x.re))
5.0ms	(.p16 (.p16 x.im (+.p16 x.im x.re)) (-.p16 x.re x.im))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (+.p16 x.im x.re)) (-.p16 x.re x.im))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(*.p16 x.re (+.p16 x.im x.im))
0.0ms	(*.p16 x.im (+.p16 x.im x.re))
0.0ms	(.p16 (.p16 x.im (+.p16 x.im x.re)) (-.p16 x.re x.im))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (+.p16 x.im x.re)) (-.p16 x.re x.im))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

simplify1.3m

Counts

57 → 57

Iterations

Iter	Nodes
4	12997
3	1200
2	248
1	73
0	33

prune2.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes328.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
1	11
0	11

end0.0ms

sample3.5s

Algorithm: halfpoints