Details

sample120.0ms

Algorithm: halfpoints

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
7	2002
6	1308
5	586
4	220
3	107
2	49
1	20
0	11

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize175.0ms

Local error

Found 4 expressions with local error:

0.1b	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
0.3b	(.p16 (-.p16 (.p16 x.re x.re) (*.p16 x.im x.im)) 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.im) (.p16 (+.p16 (.p16 x.re x.im) (.p16 x.im x.re)) x.re))

rewrite13.0ms

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

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 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.im) (.p16 (+.p16 (.p16 x.re x.im) (.p16 x.im x.re)) x.re))

simplify1.2s

Counts

68 → 68

Iterations

Iter	Nodes
done	2023
4	2023
3	1200
2	258
1	79
0	41

prune654.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize199.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.p16 (+.p16 x.im x.re) x.im)
0.1b	(+.p16 (.p16 x.re x.im) (.p16 x.re x.im))
0.2b	(.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.im))
8.1b	(quire16-mul-add (posit16->quire16 (.p16 (-.p16 x.re x.im) (.p16 (+.p16 x.im x.re) x.im))) (+.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-l`
5×	`p16-lft-identity-expand` `introduce-quire` `-p16-rgt-identity-expand` `p16-rgt-identity-expand` `p16-*-un-lft-identity`
4×	`associate-*l/`
2×	`distribute-rgt-in` `associate-+l+` `associate-+r+` `distribute-lft-in` `associate-r/` `-commutative`
1×	`+-commutative` `associate-+r-` `insert-quire-add` `p16-distribute-lft-out` `distribute-rgt-out` `associate-r` `p16-flip--` `insert-quire-fdp-add` `associate-+l-` `distribute-lft-out`

Counts

4 → 54

Calls

4 calls:

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

simplify1.3s

Counts

58 → 58

Iterations

Iter	Nodes
done	2203
4	2203
3	1279
2	215
1	72
0	35

prune796.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize267.0ms

Local error

Found 4 expressions with local error:

0.1b	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
0.2b	(*.p16 (-.p16 x.re x.im) x.im)
0.2b	(.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re x.im) x.im))
0.3b	(+.p16 (.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re x.im) x.im)) (.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

5.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
5.0ms	(*.p16 (-.p16 x.re x.im) x.im)
11.0ms	(.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re x.im) x.im))
11.0ms	(+.p16 (.p16 (+.p16 x.re x.im) (.p16 (-.p16 x.re x.im) x.im)) (.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re))

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

simplify4.7s

Counts

73 → 73

Iterations

Iter	Nodes
done	2015
3	2015
2	274
1	85
0	39

prune777.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize238.0ms

Local error

Found 4 expressions with local error:

0.1b	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
0.3b	(.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.re x.re)) x.im x.im)) x.im)
0.3b	(+.p16 (.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.re x.re)) x.im x.im)) x.im) (.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re))
6.7b	(quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

2.0ms	(.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re)
2.0ms	(.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.re x.re)) x.im x.im)) x.im)
4.0ms	(+.p16 (.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.re x.re)) x.im x.im)) x.im) (.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re))
0.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) 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 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.re x.re)) x.im x.im)) x.im)
0.0ms	(+.p16 (.p16 (quire16->posit16 (quire16-mul-sub (posit16->quire16 (.p16 x.re x.re)) x.im x.im)) x.im) (.p16 (+.p16 (.p16 x.re x.im) (*.p16 x.im x.re)) x.re))
0.0ms	(quire16-mul-sub (posit16->quire16 (*.p16 x.re x.re)) x.im x.im)

simplify1.1s

Counts

47 → 47

Iterations

Iter	Nodes
done	2010
7	2010
6	1761
5	873
4	363
3	187
2	73
1	39
0	26

prune502.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes339.0ms

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	11
0	11

end0.0ms

sample3.0s

Algorithm: halfpoints