Details

sample72.0ms

Algorithm: halfpoints

simplify4.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
8	4615
7	3127
6	1308
5	586
4	220
3	107
2	49
1	20
0	11

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize276.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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:

3.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.im)
3.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
12.0ms	(+.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))
4.0ms	(-.p16 (.p16 x.re x.re) (.p16 x.im x.im))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.5s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
3	1073
2	219
1	79
0	41

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize308.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.1b	(*.p16 x.re (+.p16 x.im x.im))
0.2b	(.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
6.8b	(quire16-mul-add (posit16->quire16 (.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

8.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
6.0ms	(*.p16 x.re (+.p16 x.im x.im))
10.0ms	(.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
1.0ms	(quire16-mul-add (posit16->quire16 (.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.5s

Counts

61 → 61

Iterations

Iter	Nodes
done	5008
3	1925
2	310
1	85
0	42

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize350.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.1b	(+.p16 (.p16 x.re x.im) (.p16 x.re x.im))
0.2b	(.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
6.8b	(quire16-mul-add (posit16->quire16 (.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (+.p16 (.p16 x.re x.im) (.p16 x.re x.im)) x.re)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

8×	`/p16-rgt-identity-expand`
7×	`distribute-rgt-in` `distribute-lft-in` `+p16-lft-identity-expand` `+p16-rgt-identity-expand`
6×	`associate-*r/`
5×	`p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
4×	`associate-r` `associate-*l/`
3×	`associate-l`
2×	`associate-+l+` `associate-+r+` `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 → 62

Calls

4 calls:

8.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
7.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.re x.im))
10.0ms	(.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
1.0ms	(quire16-mul-add (posit16->quire16 (.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (+.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.re x.im) (+.p16 x.im x.re))
0.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.re x.im))
0.0ms	(.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 x.im (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (+.p16 (.p16 x.re x.im) (.p16 x.re x.im)) x.re)

simplify1.9s

Counts

66 → 66

Iterations

Iter	Nodes
done	5002
3	1656
2	300
1	90
0	45

prune966.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize269.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.p16 (-.p16 x.re x.im) x.re)
0.2b	(.p16 x.im (+.p16 (.p16 (-.p16 x.re x.im) x.im) (*.p16 (-.p16 x.re x.im) x.re)))
0.4b	(+.p16 (.p16 (-.p16 x.re x.im) x.im) (.p16 (-.p16 x.re x.im) x.re))
6.8b	(quire16-mul-add (posit16->quire16 (.p16 x.im (+.p16 (.p16 (-.p16 x.re x.im) x.im) (.p16 (-.p16 x.re x.im) x.re)))) (.p16 x.re (+.p16 x.im x.im)) x.re)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

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

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.5s

Counts

54 → 54

Iterations

Iter	Nodes
done	5039
4	2127
3	467
2	148
1	62
0	32

prune838.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes204.0ms

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
done	11
0	11

end0.0ms

sample3.2s

Algorithm: halfpoints