Details

sample114.0ms

Algorithm: halfpoints

simplify6.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5015
7	4760
6	1736
5	675
4	237
3	106
2	51
1	21
0	11

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize190.0ms

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))

rewrite22.0ms

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:

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

simplify1.5s

Counts

69 → 69

Iterations

Iter	Nodes
done	5007
3	2370
2	380
1	96
0	46

prune689.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize288.0ms

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)

rewrite21.0ms

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)
3.0ms	(*.p16 x.re (-.p16 x.re x.im))
14.0ms	(.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)

simplify1.1s

Counts

56 → 56

Iterations

Iter	Nodes
done	5127
3	1449
2	280
1	85
0	36

prune650.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize266.0ms

Local error

Found 4 expressions with local error:

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))
0.4b	(.p16 (.p16 x.im x.im) (+.p16 x.re x.re))
10.3b	(quire16-mul-sub (posit16->quire16 (.p16 (.p16 x.re (-.p16 x.re x.im)) (+.p16 x.im x.re))) (.p16 (.p16 x.im x.im) (+.p16 x.re x.re)) (real->posit16 1.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`associate-r` `/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`
4×	`associate-*l/`
3×	`introduce-quire` `-p16-rgt-identity-expand` `*-commutative`
2×	`sub-neg` `associate-l` `p16-flip--`

Counts

4 → 56

Calls

4 calls:

3.0ms	(*.p16 x.re (-.p16 x.re x.im))
4.0ms	(.p16 (.p16 x.re (-.p16 x.re x.im)) (+.p16 x.im x.re))
5.0ms	(.p16 (.p16 x.im x.im) (+.p16 x.re 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.im x.im) (+.p16 x.re x.re)) (real->posit16 1.0))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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	(.p16 (.p16 x.im x.im) (+.p16 x.re 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.im x.im) (+.p16 x.re x.re)) (real->posit16 1.0))

simplify1.3s

Counts

60 → 60

Iterations

Iter	Nodes
done	5001
3	1460
2	305
1	98
0	39

prune917.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize421.0ms

Local error

Found 4 expressions with local error:

0.2b	(.p16 (+.p16 (.p16 x.re x.re) (*.p16 x.re (neg.p16 x.im))) (+.p16 x.im x.re))
0.4b	(.p16 (.p16 x.im x.im) (+.p16 x.re x.re))
0.4b	(+.p16 (.p16 x.re x.re) (.p16 x.re (neg.p16 x.im)))
10.3b	(quire16-mul-sub (posit16->quire16 (.p16 (+.p16 (.p16 x.re x.re) (.p16 x.re (neg.p16 x.im))) (+.p16 x.im x.re))) (.p16 (*.p16 x.im x.im) (+.p16 x.re x.re)) (real->posit16 1.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

8.0ms	(.p16 (+.p16 (.p16 x.re x.re) (*.p16 x.re (neg.p16 x.im))) (+.p16 x.im x.re))
21.0ms	(.p16 (.p16 x.im x.im) (+.p16 x.re x.re))
8.0ms	(+.p16 (.p16 x.re x.re) (.p16 x.re (neg.p16 x.im)))
1.0ms	(quire16-mul-sub (posit16->quire16 (.p16 (+.p16 (.p16 x.re x.re) (.p16 x.re (neg.p16 x.im))) (+.p16 x.im x.re))) (.p16 (*.p16 x.im x.im) (+.p16 x.re x.re)) (real->posit16 1.0))

series0.0ms

Counts

4 → 4

Calls

4 calls:

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

simplify1.3s

Counts

65 → 65

Iterations

Iter	Nodes
done	5009
3	1720
2	338
1	103
0	42

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes341.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	14
0	14

end0.0ms

sample3.0s

Algorithm: halfpoints