Details

sample95.0ms

Algorithm: halfpoints

simplify1.9s

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize254.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
0.2b	(.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))
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:

4.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
5.0ms	(.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))
6.0ms	(-.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.im) (*.p16 x.im x.re)) x.re)
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))
0.0ms	(-.p16 (.p16 x.re x.re) (.p16 x.im x.im))

simplify14.6s

Counts

68 → 68

Iterations

Iter	Nodes
4	11473
3	923
2	204
1	74
0	41

prune814.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize308.0ms

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.re x.im))
0.1b	(.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))
7.3b	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))) (*.p16 x.re (+.p16 x.im x.im)) x.re)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

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

simplify3.5s

Counts

58 → 58

Iterations

Iter	Nodes
4	6228
3	981
2	251
1	77
0	38

prune776.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize285.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 x.im (-.p16 x.re x.im))
0.1b	(.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))
0.2b	(+.p16 (.p16 x.re x.im) (.p16 x.re x.im))
7.3b	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))) (+.p16 (.p16 x.re x.im) (.p16 x.re x.im)) x.re)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

3.0ms	(*.p16 x.im (-.p16 x.re x.im))
5.0ms	(.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))
4.0ms	(+.p16 (.p16 x.re x.im) (.p16 x.re x.im))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (-.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 x.im (-.p16 x.re x.im))
0.0ms	(.p16 (.p16 x.im (-.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	(quire16-mul-add (posit16->quire16 (.p16 (.p16 x.im (-.p16 x.re x.im)) (+.p16 x.im x.re))) (+.p16 (.p16 x.re x.im) (.p16 x.re x.im)) x.re)

simplify10.9s

Counts

63 → 63

Iterations

Iter	Nodes
4	9325
3	1254
2	275
1	85
0	42

prune988.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize314.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 x.re (+.p16 x.im x.im))
0.1b	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 (neg.p16 x.im) x.im)) (+.p16 x.im x.re))
0.3b	(+.p16 (.p16 x.re x.im) (.p16 (neg.p16 x.im) x.im))
7.3b	(quire16-mul-add (posit16->quire16 (.p16 (+.p16 (.p16 x.re x.im) (.p16 (neg.p16 x.im) x.im)) (+.p16 x.im x.re))) (.p16 x.re (+.p16 x.im x.im)) x.re)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

17.0ms	(*.p16 x.re (+.p16 x.im x.im))
6.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 (neg.p16 x.im) x.im)) (+.p16 x.im x.re))
7.0ms	(+.p16 (.p16 x.re x.im) (.p16 (neg.p16 x.im) x.im))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (+.p16 (.p16 x.re x.im) (.p16 (neg.p16 x.im) 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 x.re (+.p16 x.im x.im))
0.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 (neg.p16 x.im) x.im)) (+.p16 x.im x.re))
0.0ms	(+.p16 (.p16 x.re x.im) (.p16 (neg.p16 x.im) x.im))
0.0ms	(quire16-mul-add (posit16->quire16 (.p16 (+.p16 (.p16 x.re x.im) (.p16 (neg.p16 x.im) x.im)) (+.p16 x.im x.re))) (.p16 x.re (+.p16 x.im x.im)) x.re)

simplify2.1s

Counts

57 → 57

Iterations

Iter	Nodes
4	4190
3	928
2	243
1	73
0	33

prune919.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes376.0ms

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

sample3.0s

Algorithm: halfpoints