Details

sample114.0ms

Algorithm: halfpoints

simplify5.0s

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize210.0ms

Local error

Found 4 expressions with local error:

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

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

simplify2.7s

Counts

69 → 69

Iterations

Iter	Nodes
done	5042
3	2329
2	368
1	96
0	46

prune836.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize351.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (+.p16 x.re x.re) x.im)
0.1b	(*.p16 x.re (-.p16 x.re x.im))
0.2b	(.p16 (.p16 x.re (-.p16 x.re x.im)) (+.p16 x.im x.re))
7.6b	(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)

rewrite19.0ms

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:

3.0ms	(*.p16 (+.p16 x.re x.re) x.im)
10.0ms	(*.p16 x.re (-.p16 x.re x.im))
5.0ms	(.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)

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)

simplify1.3s

Counts

56 → 56

Iterations

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

prune820.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize457.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (+.p16 x.re x.re) x.im)
0.2b	(.p16 (+.p16 (.p16 x.re x.re) (*.p16 (neg.p16 x.im) x.re)) (+.p16 x.im x.re))
0.4b	(+.p16 (.p16 x.re x.re) (.p16 (neg.p16 x.im) x.re))
7.6b	(quire16-mul-sub (posit16->quire16 (.p16 (+.p16 (.p16 x.re x.re) (.p16 (neg.p16 x.im) x.re)) (+.p16 x.im x.re))) (.p16 (+.p16 x.re x.re) x.im) x.im)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

6.0ms	(*.p16 (+.p16 x.re x.re) x.im)
8.0ms	(.p16 (+.p16 (.p16 x.re x.re) (*.p16 (neg.p16 x.im) x.re)) (+.p16 x.im x.re))
8.0ms	(+.p16 (.p16 x.re x.re) (.p16 (neg.p16 x.im) x.re))
1.0ms	(quire16-mul-sub (posit16->quire16 (.p16 (+.p16 (.p16 x.re x.re) (.p16 (neg.p16 x.im) x.re)) (+.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 (.p16 x.re x.re) (*.p16 (neg.p16 x.im) x.re)) (+.p16 x.im x.re))
0.0ms	(+.p16 (.p16 x.re x.re) (.p16 (neg.p16 x.im) x.re))
0.0ms	(quire16-mul-sub (posit16->quire16 (.p16 (+.p16 (.p16 x.re x.re) (.p16 (neg.p16 x.im) x.re)) (+.p16 x.im x.re))) (.p16 (+.p16 x.re x.re) x.im) x.im)

simplify1.9s

Counts

55 → 55

Iterations

Iter	Nodes
done	5001
3	1320
2	265
1	72
0	32

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize198.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.p16 (+.p16 x.im x.im) x.im)
0.1b	(*.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im)
0.2b	(.p16 x.re (-.p16 (.p16 x.re x.re) (*.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im)))
0.4b	(-.p16 (.p16 x.re x.re) (.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

17.0ms	(+.p16 (+.p16 x.im x.im) x.im)
9.0ms	(*.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im)
4.0ms	(.p16 x.re (-.p16 (.p16 x.re x.re) (*.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im)))
4.0ms	(-.p16 (.p16 x.re x.re) (.p16 (+.p16 (+.p16 x.im x.im) x.im) x.im))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.2s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
3	1222
2	235
1	74
0	42

prune551.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes273.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
0	9

end0.0ms

sample3.0s

Algorithm: halfpoints