Details

sample109.0ms

Algorithm: halfpoints

simplify4.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
7	4047
6	1485
5	622
4	223
3	106
2	51
1	21
0	11

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize247.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

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`
4×	`associate--l+` `associate--r+`
3×	`associate-*l/` `p16-flip--`
2×	`associate--l-` `insert-quire-sub` `sub-neg` `*-commutative` `insert-quire-fdp-sub` `associate--r-` `difference-of-squares`

Counts

4 → 65

Calls

4 calls:

2.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.im)
3.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.re)
3.0ms	(-.p16 (.p16 x.re x.re) (.p16 x.im x.im))
3.0ms	(-.p16 (.p16 (-.p16 (.p16 x.re x.re) (.p16 x.im x.im)) x.re) (.p16 (+.p16 (.p16 x.re x.im) (.p16 x.im x.re)) 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.im)
0.0ms	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) x.re)
0.0ms	(-.p16 (.p16 x.re x.re) (.p16 x.im x.im))
0.0ms	(-.p16 (.p16 (-.p16 (.p16 x.re x.re) (.p16 x.im x.im)) x.re) (.p16 (+.p16 (.p16 x.re x.im) (.p16 x.im x.re)) x.im))

simplify2.5s

Counts

69 → 69

Iterations

Iter	Nodes
done	5021
3	2193
2	359
1	95
0	46

prune919.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize317.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.p16 (+.p16 x.re x.re) x.im)
0.2b	(*.p16 x.re (-.p16 x.re x.im))
0.2b	(.p16 (.p16 x.re (-.p16 x.re x.im)) (+.p16 x.im x.re))
7.9b	(quire16-mul-sub (posit16->quire16 (.p16 (.p16 x.re (-.p16 x.re x.im)) (+.p16 x.im x.re))) (*.p16 (+.p16 x.re x.re) x.im) x.im)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

7.0ms	(*.p16 (+.p16 x.re x.re) x.im)
7.0ms	(*.p16 x.re (-.p16 x.re x.im))
22.0ms	(.p16 (.p16 x.re (-.p16 x.re x.im)) (+.p16 x.im x.re))
1.0ms	(quire16-mul-sub (posit16->quire16 (.p16 (.p16 x.re (-.p16 x.re x.im)) (+.p16 x.im x.re))) (*.p16 (+.p16 x.re x.re) x.im) x.im)

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.0s

Counts

56 → 56

Iterations

Iter	Nodes
done	5111
3	1275
2	265
1	85
0	36

prune776.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize315.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.p16 (+.p16 x.re x.re) x.im)
0.1b	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
0.2b	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
7.9b	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 (+.p16 x.re x.re) x.im) x.im)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

6.0ms	(*.p16 (+.p16 x.re x.re) x.im)
7.0ms	(*.p16 (-.p16 x.re x.im) (+.p16 x.im x.re))
8.0ms	(.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))
1.0ms	(quire16-mul-sub (posit16->quire16 (.p16 x.re (.p16 (-.p16 x.re x.im) (+.p16 x.im x.re)))) (*.p16 (+.p16 x.re x.re) x.im) x.im)

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.7s

Counts

59 → 59

Iterations

Iter	Nodes
done	5034
3	2528
2	318
1	79
0	38

prune815.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize346.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.p16 (-.p16 x.re x.im) x.re)
0.2b	(.p16 (.p16 (-.p16 x.re x.im) x.im) x.re)
0.4b	(+.p16 (.p16 (.p16 (-.p16 x.re x.im) x.im) x.re) (.p16 (.p16 (-.p16 x.re x.im) x.re) x.re))
7.9b	(quire16-mul-sub (posit16->quire16 (+.p16 (.p16 (.p16 (-.p16 x.re x.im) x.im) x.re) (.p16 (.p16 (-.p16 x.re x.im) x.re) x.re))) (*.p16 (+.p16 x.re x.re) x.im) x.im)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 45

Calls

4 calls:

6.0ms	(*.p16 (-.p16 x.re x.im) x.re)
8.0ms	(.p16 (.p16 (-.p16 x.re x.im) x.im) x.re)
11.0ms	(+.p16 (.p16 (.p16 (-.p16 x.re x.im) x.im) x.re) (.p16 (.p16 (-.p16 x.re x.im) x.re) x.re))
1.0ms	(quire16-mul-sub (posit16->quire16 (+.p16 (.p16 (.p16 (-.p16 x.re x.im) x.im) x.re) (.p16 (.p16 (-.p16 x.re x.im) x.re) x.re))) (*.p16 (+.p16 x.re x.re) x.im) x.im)

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify2.3s

Counts

49 → 49

Iterations

Iter	Nodes
done	5001
4	1485
3	367
2	116
1	56
0	29

prune723.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes269.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
0	13

end0.0ms

sample3.0s

Algorithm: halfpoints